) -> ((A -> B) -> (A -> C))), axiom
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-66530.        ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E)))), M:tm-42, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66531
in-theory        66531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-32 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       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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-66531.        ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E)))), M:tm-32, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66532
in-theory        66532
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (B -> (B and C))))
theorem-size     25
proof            (modus-ponens tm-24 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       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-4.            ((A and B) -> B), axiom
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-66532.        (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (B -> (B and C)))), M:tm-24, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66533
in-theory        66533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-23 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       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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-66533.        ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E)))), M:tm-23, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66534
in-theory        66534
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-22 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       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-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-66534.        (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E)))), M:tm-22, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66535
in-theory        66535
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-21 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       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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-66535.        (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E)))), M:tm-21, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66536
in-theory        66536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-20 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       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-4.            ((A and B) -> B), axiom
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-66536.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-20, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66537
in-theory        66537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-19 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       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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-66537.        ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E)))), M:tm-19, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66538
in-theory        66538
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (not (B -> (B and C)))) -> (not ((A and (B -> C)) or (B -> C))))
theorem-size     27
proof            (modus-ponens tm-9 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-66538.        ((((A and (B -> C)) or (B -> C)) -> (not (B -> (B and C)))) -> (not ((A and (B -> C)) or (B -> C)))), M:tm-9, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66539
in-theory        66539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> ((((D and (A -> B)) or (A -> B)) or (A -> (A and B))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 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       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-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-66539.        (((A -> (A and B)) -> C) -> ((((D and (A -> B)) or (A -> B)) or (A -> (A and B))) -> C)), M:tm-8, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66540
in-theory        66540
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C -> D)) or (C -> D)) -> (C -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-66540.        (A or (((B and (C -> D)) or (C -> D)) -> (C -> (C and D)))), M:tm-7, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66541
in-theory        66541
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-66541.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) or D), M:tm-6, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66542
in-theory        66542
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) or (C -> D)) -> (C -> (C and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 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       99
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-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-66542.        (A -> ((((B and (C -> D)) or (C -> D)) -> (C -> (C and D))) and A)), M:tm-5, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66543
in-theory        66543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> B) -> (((A and (B -> C)) or (B -> C)) -> (B and C)))
theorem-size     25
proof            (modus-ponens tm-2 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Bm) (C (and Bm Cm))))
axioms-used      (tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66543.        ((((A and (B -> C)) or (B -> C)) -> B) -> (((A and (B -> C)) or (B -> C)) -> (B and C))), M:tm-2, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Bm) (C (and Bm Cm)))
================================================================
tm-name          tm-66544
in-theory        66544
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C -> D)) or (C -> D)) -> (C -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-66544.        (A -> (((B and (C -> D)) or (C -> D)) -> (C -> (C and D)))), M:tm-1, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66545
in-theory        66545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66545.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-757, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66546
in-theory        66546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((((A and B) or B) and E) or ((A and B) or B)) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-747 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
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-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-66546.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((((A and B) or B) and E) or ((A and B) or B)) -> (C -> (D -> (C and D))))), M:tm-747, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66547
in-theory        66547
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)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66547.        (((((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))))), M:tm-708, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66548
in-theory        66548
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66548.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-665, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66549
in-theory        66549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66549.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-622, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66550
in-theory        66550
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D or ((A and B) or B)) and C)))
theorem-size     17
proof            (modus-ponens tm-617 tm-784 ((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (-> Dm (and (or B (or (and Am Bm) Bm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66550.        (((A and B) or B) -> (C -> ((D or ((A and B) or B)) and C))), M:tm-617, m:tm-784, u:((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (-> Dm (and (or B (or (and Am Bm) Bm)) Dm))))
================================================================
tm-name          tm-66551
in-theory        66551
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66551.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66552
in-theory        66552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66552.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-605, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66553
in-theory        66553
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and (((A and B) or B) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66553.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and (((A and B) or B) -> (C -> (D -> (C and D)))))), M:tm-595, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66554
in-theory        66554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66554.        (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-550, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66555
in-theory        66555
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-66555.        ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-540, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66556
in-theory        66556
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66556.        ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-530, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66557
in-theory        66557
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66557.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-520, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66558
in-theory        66558
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66558.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-510, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66559
in-theory        66559
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66559.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-500, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66560
in-theory        66560
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66560.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H -> (G and H))))), M:tm-490, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66561
in-theory        66561
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66561.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-480, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66562
in-theory        66562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66562.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-469, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66563
in-theory        66563
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((((A and B) or B) or D) and C)))
theorem-size     17
proof            (modus-ponens tm-464 tm-784 ((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (-> Dm (and (or (or (and Am Bm) Bm) B) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66563.        (((A and B) or B) -> (C -> ((((A and B) or B) or D) and C))), M:tm-464, m:tm-784, u:((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (-> Dm (and (or (or (and Am Bm) Bm) B) Dm))))
================================================================
tm-name          tm-66564
in-theory        66564
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66564.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66565
in-theory        66565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66565.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-453, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66566
in-theory        66566
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and (((A and B) or B) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66566.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and (((A and B) or B) -> (C -> (D -> (C and D)))))), M:tm-443, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66567
in-theory        66567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-66567.        (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-409, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66568
in-theory        66568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66568.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-400, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66569
in-theory        66569
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66569.        ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-391, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66570
in-theory        66570
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66570.        ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-382, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66571
in-theory        66571
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66571.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (H -> (G and H))))), M:tm-373, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66572
in-theory        66572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66572.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-364, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66573
in-theory        66573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66573.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-354, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66574
in-theory        66574
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (((A and B) or B) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-349 tm-784 ((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (-> Dm (and (-> B (and (or (and Am Bm) Bm) B)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-66574.        (((A and B) or B) -> (C -> ((D -> (((A and B) or B) and D)) and C))), M:tm-349, m:tm-784, u:((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (-> Dm (and (-> B (and (or (and Am Bm) Bm) B)) Dm))))
================================================================
tm-name          tm-66575
in-theory        66575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-66575.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66576
in-theory        66576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66576.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (F -> (E and F))))), M:tm-338, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66577
in-theory        66577
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((A and B) or B) -> (((A and B) or B) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-328 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
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-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-66577.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((A and B) or B) -> (((A and B) or B) and (C -> (D -> (C and D)))))), M:tm-328, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66578
in-theory        66578
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66578.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (C -> (D -> (C and D)))))), M:tm-327, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66579
in-theory        66579
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and (((A and B) or B) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66579.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and (((A and B) or B) -> (C -> (D -> (C and D)))))), M:tm-326, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66580
in-theory        66580
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and (((A and B) or B) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66580.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and (((A and B) or B) -> (C -> (D -> (C and D)))))), M:tm-325, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66581
in-theory        66581
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66581.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (C -> (D -> (C and D)))))), M:tm-324, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66582
in-theory        66582
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and (((A and B) or B) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66582.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and (((A and B) or B) -> (C -> (D -> (C and D)))))), M:tm-323, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66583
in-theory        66583
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66583.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66584
in-theory        66584
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66584.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66585
in-theory        66585
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66585.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66586
in-theory        66586
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     25
proof            (modus-ponens tm-316 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
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-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-66586.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66587
in-theory        66587
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-66587.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66588
in-theory        66588
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((((A and B) or B) -> (not (C -> (D -> (C and D))))) -> (not ((A and B) or B))))
theorem-size     35
proof            (modus-ponens tm-313 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
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-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-66588.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((((A and B) or B) -> (not (C -> (D -> (C and D))))) -> (not ((A and B) or B)))), M:tm-313, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66589
in-theory        66589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> ((((A and B) or B) or (C -> (D -> (C and D)))) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
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-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-66589.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> ((((A and B) or B) or (C -> (D -> (C and D)))) -> E))), M:tm-312, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66590
in-theory        66590
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E or (((A and B) or B) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66590.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E or (((A and B) or B) -> (C -> (D -> (C and D)))))), M:tm-311, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66591
in-theory        66591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((((A and B) or B) -> (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66591.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((((A and B) or B) -> (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66592
in-theory        66592
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> ((((A and B) or B) -> (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66592.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> ((((A and B) or B) -> (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66593
in-theory        66593
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-306 tm-784 ((A (or (and Am Bm) Bm)) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-66593.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (D -> (C and D))))), M:tm-306, m:tm-784, u:((A (or (and Am Bm) Bm)) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-66594
in-theory        66594
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (((A and B) or B) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66594.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (E -> (((A and B) or B) -> (C -> (D -> (C and D)))))), M:tm-305, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66595
in-theory        66595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66595.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-303, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66596
in-theory        66596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66596.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-270, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66597
in-theory        66597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66597.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-239, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66598
in-theory        66598
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)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66598.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> (H -> (G and H))))), M:tm-210, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66599
in-theory        66599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66599.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-183, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66600
in-theory        66600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66600.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-157, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66601
in-theory        66601
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)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66601.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-147, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66602
in-theory        66602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66602.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-134, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66603
in-theory        66603
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)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66603.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-125, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66604
in-theory        66604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66604.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H -> (G and H))))), M:tm-113, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66605
in-theory        66605
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)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66605.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-105, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66606
in-theory        66606
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((A and B) or B) and C)))
theorem-size     15
proof            (modus-ponens tm-99 tm-784 ((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (-> Dm (and (or (and Am Bm) Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 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-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-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-66606.        (((A and B) or B) -> (C -> (((A and B) or B) and C))), M:tm-99, m:tm-784, u:((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (-> Dm (and (or (and Am Bm) Bm) Dm))))
================================================================
tm-name          tm-66607
in-theory        66607
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> ((A and B) or B)) and C)))
theorem-size     17
proof            (modus-ponens tm-98 tm-784 ((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (-> Dm (and (-> B (or (and Am Bm) Bm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66607.        (((A and B) or B) -> (C -> ((D -> ((A and B) or B)) and C))), M:tm-98, m:tm-784, u:((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (-> Dm (and (-> B (or (and Am Bm) Bm)) Dm))))
================================================================
tm-name          tm-66608
in-theory        66608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66608.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (F -> (E and F))))), M:tm-95, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66609
in-theory        66609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-66609.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-83, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66610
in-theory        66610
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66610.        (((not (not A)) -> A) and (((B and C) or C) -> (D -> (E -> (D and E))))), M:tm-76, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66611
in-theory        66611
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-73 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-10 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66611.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (D -> (C and D)))), M:tm-73, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66612
in-theory        66612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66612.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (F -> (E and F))))), M:tm-69, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66613
in-theory        66613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66613.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-54, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66614
in-theory        66614
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-50 tm-784 ((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66614.        ((A or ((B and A) or A)) -> (C -> (D -> (C and D)))), M:tm-50, m:tm-784, u:((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66615
in-theory        66615
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-49 tm-784 ((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66615.        (((A and B) or ((A and B) or B)) -> (C -> (D -> (C and D)))), M:tm-49, m:tm-784, u:((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66616
in-theory        66616
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-47 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-66616.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (E -> (D and E)))), M:tm-47, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66617
in-theory        66617
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-46 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66617.        (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (E -> (D and E)))), M:tm-46, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66618
in-theory        66618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66618.        ((A -> (B or A)) and (((C and D) or D) -> (E -> (F -> (E and F))))), M:tm-42, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66619
in-theory        66619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66619.        ((A -> (A or B)) and (((C and D) or D) -> (E -> (F -> (E and F))))), M:tm-32, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66620
in-theory        66620
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (C -> (D -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-24 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
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-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-66620.        (((A and B) or B) -> (((A and B) or B) and (C -> (D -> (C and D))))), M:tm-24, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66621
in-theory        66621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66621.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (F -> (E and F))))), M:tm-23, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66622
in-theory        66622
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66622.        (((A and B) -> B) and (((C and D) or D) -> (E -> (F -> (E and F))))), M:tm-22, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66623
in-theory        66623
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66623.        (((A and B) -> A) and (((C and D) or D) -> (E -> (F -> (E and F))))), M:tm-21, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66624
in-theory        66624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66624.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-20, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66625
in-theory        66625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66625.        ((A -> (B -> A)) and (((C and D) or D) -> (E -> (F -> (E and F))))), M:tm-19, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66626
in-theory        66626
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (C -> (D -> (C and D))))) -> (not ((A and B) or B)))
theorem-size     21
proof            (modus-ponens tm-9 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66626.        ((((A and B) or B) -> (not (C -> (D -> (C and D))))) -> (not ((A and B) or B))), M:tm-9, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66627
in-theory        66627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> ((((D and E) or E) or (A -> (B -> (A and B)))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
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-5.            (A -> (B -> (A and 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-66627.        (((A -> (B -> (A and B))) -> C) -> ((((D and E) or E) or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-66628
in-theory        66628
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66628.        (A or (((B and C) or C) -> (D -> (E -> (D and E))))), M:tm-7, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66629
in-theory        66629
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66629.        ((((A and B) or B) -> (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66630
in-theory        66630
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66630.        (A -> ((((B and C) or C) -> (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66631
in-theory        66631
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> C) -> (((A and B) or B) -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-2 tm-784 ((A (or (and Am Bm) Bm)) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66631.        ((((A and B) or B) -> C) -> (((A and B) or B) -> (D -> (C and D)))), M:tm-2, m:tm-784, u:((A (or (and Am Bm) Bm)) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-66632
in-theory        66632
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-66632.        (A -> (((B and C) or C) -> (D -> (E -> (D and E))))), M:tm-1, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-66633
in-theory        66633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     25
proof            (modus-ponens tm-757 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66633.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-757, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66634
in-theory        66634
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C -> (C or D)) and B)))
theorem-size     35
proof            (modus-ponens tm-747 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66634.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C -> (C or D)) and B))), M:tm-747, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66635
in-theory        66635
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 -> (G or H)) and F)))
theorem-size     39
proof            (modus-ponens tm-708 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66635.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G -> (G or H)) and F))), M:tm-708, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66636
in-theory        66636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     27
proof            (modus-ponens tm-665 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66636.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-665, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66637
in-theory        66637
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or ((D -> (D or E)) and B)))
theorem-size     15
proof            (modus-ponens tm-623 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66637.        (((A and B) or B) -> (C or ((D -> (D or E)) and B))), M:tm-623, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66638
in-theory        66638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-622 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66638.        ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-622, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66639
in-theory        66639
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66639.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (F or E))), M:tm-609, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66640
in-theory        66640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     23
proof            (modus-ponens tm-605 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66640.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-605, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66641
in-theory        66641
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (F or E)) and (((A and B) or B) -> ((C -> (C or D)) and B))))
theorem-size     33
proof            (modus-ponens tm-595 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-66641.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (F or E)) and (((A and B) or B) -> ((C -> (C or D)) and B)))), M:tm-595, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66642
in-theory        66642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-550 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66642.        (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-550, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66643
in-theory        66643
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-540 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66643.        ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-540, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66644
in-theory        66644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-530 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66644.        ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-530, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66645
in-theory        66645
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     23
proof            (modus-ponens tm-520 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66645.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-520, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66646
in-theory        66646
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-510 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-66646.        ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-510, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66647
in-theory        66647
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-500 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66647.        ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-500, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66648
in-theory        66648
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (G or H)) and F)))
theorem-size     29
proof            (modus-ponens tm-490 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66648.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (G or H)) and F))), M:tm-490, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66649
in-theory        66649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-480 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66649.        ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-480, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66650
in-theory        66650
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (C or D)) and B) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm 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-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-66650.        (((A and B) or B) -> (((C -> (C or D)) and B) or E)), M:tm-470, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66651
in-theory        66651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-469 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66651.        ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-469, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66652
in-theory        66652
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66652.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (E or F))), M:tm-456, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66653
in-theory        66653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     23
proof            (modus-ponens tm-453 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-66653.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-453, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66654
in-theory        66654
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (E or F)) and (((A and B) or B) -> ((C -> (C or D)) and B))))
theorem-size     33
proof            (modus-ponens tm-443 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66654.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (E or F)) and (((A and B) or B) -> ((C -> (C or D)) and B)))), M:tm-443, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66655
in-theory        66655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-409 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66655.        (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-409, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66656
in-theory        66656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     23
proof            (modus-ponens tm-400 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-66656.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-400, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66657
in-theory        66657
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-391 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66657.        ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-391, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66658
in-theory        66658
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-382 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66658.        ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-382, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66659
in-theory        66659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (G or H)) and F)))
theorem-size     29
proof            (modus-ponens tm-373 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66659.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (G or H)) and F))), M:tm-373, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66660
in-theory        66660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-364 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66660.        (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-364, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66661
in-theory        66661
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D -> (D or E)) and B) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-66661.        (((A and B) or B) -> (C -> (((D -> (D or E)) and B) and C))), M:tm-355, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66662
in-theory        66662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     23
proof            (modus-ponens tm-354 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66662.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-354, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66663
in-theory        66663
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-66663.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66664
in-theory        66664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-338 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66664.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (E or F)) and D))), M:tm-338, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66665
in-theory        66665
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((A and B) or B) -> (((A and B) or B) and ((C -> (C or D)) and B))))
theorem-size     33
proof            (modus-ponens tm-328 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66665.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((A and B) or B) -> (((A and B) or B) and ((C -> (C or D)) and B)))), M:tm-328, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66666
in-theory        66666
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C -> (C or D)) and B))))
theorem-size     35
proof            (modus-ponens tm-327 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-66666.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C -> (C or D)) and B)))), M:tm-327, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66667
in-theory        66667
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((E and F) -> F) and (((A and B) or B) -> ((C -> (C or D)) and B))))
theorem-size     33
proof            (modus-ponens tm-326 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-66667.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((E and F) -> F) and (((A and B) or B) -> ((C -> (C or D)) and B)))), M:tm-326, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66668
in-theory        66668
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((E and F) -> E) and (((A and B) or B) -> ((C -> (C or D)) and B))))
theorem-size     33
proof            (modus-ponens tm-325 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-66668.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((E and F) -> E) and (((A and B) or B) -> ((C -> (C or D)) and B)))), M:tm-325, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66669
in-theory        66669
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C -> (C or D)) and B))))
theorem-size     41
proof            (modus-ponens tm-324 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-66669.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C -> (C or D)) and B)))), M:tm-324, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66670
in-theory        66670
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C -> (C or D)) and B))))
theorem-size     33
proof            (modus-ponens tm-323 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-66670.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C -> (C or D)) and B)))), M:tm-323, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66671
in-theory        66671
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-66671.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E and F) -> F)), M:tm-322, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66672
in-theory        66672
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66672.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E and F) -> E)), M:tm-320, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66673
in-theory        66673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66673.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66674
in-theory        66674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     25
proof            (modus-ponens tm-316 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-66674.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66675
in-theory        66675
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66675.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (F -> E))), M:tm-315, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66676
in-theory        66676
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((((A and B) or B) -> (not ((C -> (C or D)) and B))) -> (not ((A and B) or B))))
theorem-size     35
proof            (modus-ponens tm-313 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-66676.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((((A and B) or B) -> (not ((C -> (C or D)) and B))) -> (not ((A and B) or B)))), M:tm-313, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66677
in-theory        66677
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((((C -> (C or D)) and B) -> E) -> ((((A and B) or B) or ((C -> (C or D)) and B)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-66677.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((((C -> (C or D)) and B) -> E) -> ((((A and B) or B) or ((C -> (C or D)) and B)) -> E))), M:tm-312, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66678
in-theory        66678
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E or (((A and B) or B) -> ((C -> (C or D)) and B))))
theorem-size     29
proof            (modus-ponens tm-311 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-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-66678.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E or (((A and B) or B) -> ((C -> (C or D)) and B)))), M:tm-311, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66679
in-theory        66679
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((((A and B) or B) -> ((C -> (C or D)) and B)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66679.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((((A and B) or B) -> ((C -> (C or D)) and B)) or E)), M:tm-310, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66680
in-theory        66680
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> ((((A and B) or B) -> ((C -> (C or D)) and B)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
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-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-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-66680.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> ((((A and B) or B) -> ((C -> (C or D)) and B)) and E))), M:tm-309, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66681
in-theory        66681
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (((A and B) or B) -> ((C -> (C or D)) and B))))
theorem-size     29
proof            (modus-ponens tm-305 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-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-66681.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (E -> (((A and B) or B) -> ((C -> (C or D)) and B)))), M:tm-305, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66682
in-theory        66682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     25
proof            (modus-ponens tm-303 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66682.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-303, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66683
in-theory        66683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     23
proof            (modus-ponens tm-270 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 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-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-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-66683.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-270, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66684
in-theory        66684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     23
proof            (modus-ponens tm-239 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66684.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-239, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66685
in-theory        66685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (G or H)) and F)))
theorem-size     31
proof            (modus-ponens tm-210 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-66685.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (G or H)) and F))), M:tm-210, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66686
in-theory        66686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     23
proof            (modus-ponens tm-183 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66686.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-183, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66687
in-theory        66687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-157 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-66687.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-157, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66688
in-theory        66688
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     29
proof            (modus-ponens tm-147 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-66688.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-147, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66689
in-theory        66689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-134 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66689.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-134, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66690
in-theory        66690
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     29
proof            (modus-ponens tm-125 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66690.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-125, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66691
in-theory        66691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (G or H)) and F)))
theorem-size     29
proof            (modus-ponens tm-113 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66691.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (G or H)) and F))), M:tm-113, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66692
in-theory        66692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     33
proof            (modus-ponens tm-105 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-66692.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-105, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66693
in-theory        66693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (E or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-95 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66693.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (E or F)) and D))), M:tm-95, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66694
in-theory        66694
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (D or E)) and B)))
theorem-size     15
proof            (modus-ponens tm-84 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66694.        (((A and B) or B) -> (C -> ((D -> (D or E)) and B))), M:tm-84, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66695
in-theory        66695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     21
proof            (modus-ponens tm-83 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66695.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-83, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66696
in-theory        66696
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (D or E)) and C)))
theorem-size     19
proof            (modus-ponens tm-76 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66696.        (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (D or E)) and C))), M:tm-76, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66697
in-theory        66697
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (C or D)) and B))
theorem-size     21
proof            (modus-ponens tm-73 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-8 tm-10 tm-4 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-4.            ((A and B) -> B), axiom
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-66697.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (C or D)) and B)), M:tm-73, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66698
in-theory        66698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (E or F)) and D)))
theorem-size     25
proof            (modus-ponens tm-69 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66698.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (E or F)) and D))), M:tm-69, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66699
in-theory        66699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     27
proof            (modus-ponens tm-54 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66699.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-54, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66700
in-theory        66700
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> ((C -> (C or D)) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-785 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-8 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
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-66700.        ((A or ((B and A) or A)) -> ((C -> (C or D)) and A)), M:tm-50, m:tm-785, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66701
in-theory        66701
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> ((C -> (C or D)) and B))
theorem-size     17
proof            (modus-ponens tm-49 tm-785 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Cm 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-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-66701.        (((A and B) or ((A and B) or B)) -> ((C -> (C or D)) and B)), M:tm-49, m:tm-785, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66702
in-theory        66702
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (D or E)) and C))
theorem-size     21
proof            (modus-ponens tm-47 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-8 tm-4 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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-66702.        (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (D or E)) and C)), M:tm-47, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66703
in-theory        66703
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (D or E)) and B))
theorem-size     21
proof            (modus-ponens tm-46 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
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-66703.        (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (D or E)) and B)), M:tm-46, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66704
in-theory        66704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-42 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-66704.        ((A -> (B or A)) and (((C and D) or D) -> ((E -> (E or F)) and D))), M:tm-42, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66705
in-theory        66705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-32 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66705.        ((A -> (A or B)) and (((C and D) or D) -> ((E -> (E or F)) and D))), M:tm-32, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66706
in-theory        66706
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and ((C -> (C or D)) and B)))
theorem-size     19
proof            (modus-ponens tm-24 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-66706.        (((A and B) or B) -> (((A and B) or B) and ((C -> (C or D)) and B))), M:tm-24, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66707
in-theory        66707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (E or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-23 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66707.        ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (E or F)) and D))), M:tm-23, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66708
in-theory        66708
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-22 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
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-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-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-66708.        (((A and B) -> B) and (((C and D) or D) -> ((E -> (E or F)) and D))), M:tm-22, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66709
in-theory        66709
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-21 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-66709.        (((A and B) -> A) and (((C and D) or D) -> ((E -> (E or F)) and D))), M:tm-21, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66710
in-theory        66710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     27
proof            (modus-ponens tm-20 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-66710.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-20, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66711
in-theory        66711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-19 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-66711.        ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (E or F)) and D))), M:tm-19, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66712
in-theory        66712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not ((C -> (C or D)) and B))) -> (not ((A and B) or B)))
theorem-size     21
proof            (modus-ponens tm-9 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66712.        ((((A and B) or B) -> (not ((C -> (C or D)) and B))) -> (not ((A and B) or B))), M:tm-9, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66713
in-theory        66713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> D) -> ((((E and C) or C) or ((A -> (A or B)) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-6.            (A -> (A or 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-66713.        ((((A -> (A or B)) and C) -> D) -> ((((E and C) or C) or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-66714
in-theory        66714
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-7 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66714.        (A or (((B and C) or C) -> ((D -> (D or E)) and C))), M:tm-7, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66715
in-theory        66715
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm 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-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-66715.        ((((A and B) or B) -> ((C -> (C or D)) and B)) or E), M:tm-6, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66716
in-theory        66716
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> ((D -> (D or E)) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66716.        (A -> ((((B and C) or C) -> ((D -> (D or E)) and C)) and A)), M:tm-5, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66717
in-theory        66717
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-1 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66717.        (A -> (((B and C) or C) -> ((D -> (D or E)) and C))), M:tm-1, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-66718
in-theory        66718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66718.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-757, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66719
in-theory        66719
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (((((A and B) or B) and E) or ((A and B) or B)) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-747 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66719.        ((((A and B) or B) -> (C -> (C or D))) and (((((A and B) or B) and E) or ((A and B) or B)) -> (C -> (C or D)))), M:tm-747, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66720
in-theory        66720
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 -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66720.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G -> (G or H)))), M:tm-708, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66721
in-theory        66721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66721.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-665, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66722
in-theory        66722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66722.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-622, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66723
in-theory        66723
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or ((A and B) or B)) or D))
theorem-size     15
proof            (modus-ponens tm-617 tm-786 ((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (or (or B (or (and Am Bm) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66723.        (((A and B) or B) -> ((C or ((A and B) or B)) or D)), M:tm-617, m:tm-786, u:((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (or (or B (or (and Am Bm) Bm)) Dm)))
================================================================
tm-name          tm-66724
in-theory        66724
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66724.        ((((A and B) or B) -> (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66725
in-theory        66725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66725.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-605, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66726
in-theory        66726
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((E -> (F or E)) and (((A and B) or B) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66726.        ((((A and B) or B) -> (C -> (C or D))) and ((E -> (F or E)) and (((A and B) or B) -> (C -> (C or D))))), M:tm-595, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66727
in-theory        66727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66727.        (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (F or G)))), M:tm-550, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66728
in-theory        66728
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66728.        ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-540, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66729
in-theory        66729
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66729.        ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-530, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66730
in-theory        66730
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66730.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-520, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66731
in-theory        66731
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-6.            (A -> (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-66731.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-510, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66732
in-theory        66732
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66732.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-500, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66733
in-theory        66733
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66733.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (G or H)))), M:tm-490, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66734
in-theory        66734
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66734.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-480, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66735
in-theory        66735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66735.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-469, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66736
in-theory        66736
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((A and B) or B) or C) or D))
theorem-size     15
proof            (modus-ponens tm-464 tm-786 ((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (or (or (or (and Am Bm) Bm) B) Dm))))
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-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-66736.        (((A and B) or B) -> ((((A and B) or B) or C) or D)), M:tm-464, m:tm-786, u:((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (or (or (or (and Am Bm) Bm) B) Dm)))
================================================================
tm-name          tm-66737
in-theory        66737
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66737.        ((((A and B) or B) -> (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66738
in-theory        66738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66738.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-453, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66739
in-theory        66739
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((E -> (E or F)) and (((A and B) or B) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66739.        ((((A and B) or B) -> (C -> (C or D))) and ((E -> (E or F)) and (((A and B) or B) -> (C -> (C or D))))), M:tm-443, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66740
in-theory        66740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66740.        (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (F or G)))), M:tm-409, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66741
in-theory        66741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66741.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (F or G)))), M:tm-400, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66742
in-theory        66742
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66742.        ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (F or G)))), M:tm-391, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66743
in-theory        66743
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66743.        ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (F or G)))), M:tm-382, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66744
in-theory        66744
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66744.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (G or H)))), M:tm-373, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66745
in-theory        66745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66745.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (F or G)))), M:tm-364, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66746
in-theory        66746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66746.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-354, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66747
in-theory        66747
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (((A and B) or B) and C)) or D))
theorem-size     17
proof            (modus-ponens tm-349 tm-786 ((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (or (-> B (and (or (and Am Bm) Bm) B)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66747.        (((A and B) or B) -> ((C -> (((A and B) or B) and C)) or D)), M:tm-349, m:tm-786, u:((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (or (-> B (and (or (and Am Bm) Bm) B)) Dm)))
================================================================
tm-name          tm-66748
in-theory        66748
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66748.        ((((A and B) or B) -> (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66749
in-theory        66749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66749.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (E or F)))), M:tm-338, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66750
in-theory        66750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (((A and B) or B) -> (((A and B) or B) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66750.        ((((A and B) or B) -> (C -> (C or D))) and (((A and B) or B) -> (((A and B) or B) and (C -> (C or D))))), M:tm-328, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66751
in-theory        66751
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (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-66751.        ((((A and B) or B) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (C -> (C or D))))), M:tm-327, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66752
in-theory        66752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (((E and F) -> F) and (((A and B) or B) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (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-66752.        ((((A and B) or B) -> (C -> (C or D))) and (((E and F) -> F) and (((A and B) or B) -> (C -> (C or D))))), M:tm-326, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66753
in-theory        66753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (((E and F) -> E) and (((A and B) or B) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66753.        ((((A and B) or B) -> (C -> (C or D))) and (((E and F) -> E) and (((A and B) or B) -> (C -> (C or D))))), M:tm-325, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66754
in-theory        66754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66754.        ((((A and B) or B) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (C -> (C or D))))), M:tm-324, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66755
in-theory        66755
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((E -> (F -> E)) and (((A and B) or B) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66755.        ((((A and B) or B) -> (C -> (C or D))) and ((E -> (F -> E)) and (((A and B) or B) -> (C -> (C or D))))), M:tm-323, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66756
in-theory        66756
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-66756.        ((((A and B) or B) -> (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66757
in-theory        66757
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66757.        ((((A and B) or B) -> (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66758
in-theory        66758
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66758.        ((((A and B) or B) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66759
in-theory        66759
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     23
proof            (modus-ponens tm-316 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-66759.        ((((A and B) or B) -> (C -> (C or D))) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66760
in-theory        66760
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66760.        ((((A and B) or B) -> (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66761
in-theory        66761
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((((A and B) or B) -> (not (C -> (C or D)))) -> (not ((A and B) or B))))
theorem-size     31
proof            (modus-ponens tm-313 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66761.        ((((A and B) or B) -> (C -> (C or D))) and ((((A and B) or B) -> (not (C -> (C or D)))) -> (not ((A and B) or B)))), M:tm-313, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66762
in-theory        66762
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> ((((A and B) or B) or (C -> (C or D))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm 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-47.           ((A -> B) -> (((C and 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-66762.        ((((A and B) or B) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> ((((A and B) or B) or (C -> (C or D))) -> E))), M:tm-312, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66763
in-theory        66763
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (E or (((A and B) or B) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-6.            (A -> (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-66763.        ((((A and B) or B) -> (C -> (C or D))) and (E or (((A and B) or B) -> (C -> (C or D))))), M:tm-311, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66764
in-theory        66764
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((((A and B) or B) -> (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66764.        ((((A and B) or B) -> (C -> (C or D))) and ((((A and B) or B) -> (C -> (C or D))) or E)), M:tm-310, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66765
in-theory        66765
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (E -> ((((A and B) or B) -> (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66765.        ((((A and B) or B) -> (C -> (C or D))) and (E -> ((((A and B) or B) -> (C -> (C or D))) and E))), M:tm-309, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66766
in-theory        66766
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (C or D))))
theorem-size     29
proof            (modus-ponens tm-306 tm-786 ((A (or (and Am Bm) Bm)) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-6.            (A -> (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-66766.        ((((A and B) or B) -> (C -> (C or D))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (C or D)))), M:tm-306, m:tm-786, u:((A (or (and Am Bm) Bm)) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-66767
in-theory        66767
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (E -> (((A and B) or B) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-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-66767.        ((((A and B) or B) -> (C -> (C or D))) and (E -> (((A and B) or B) -> (C -> (C or D))))), M:tm-305, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66768
in-theory        66768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66768.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-303, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66769
in-theory        66769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-47.           ((A -> B) -> (((C and 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-66769.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-270, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66770
in-theory        66770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66770.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-239, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66771
in-theory        66771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66771.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> (G or H)))), M:tm-210, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66772
in-theory        66772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66772.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-183, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66773
in-theory        66773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-66773.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-157, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66774
in-theory        66774
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (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-66774.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-147, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66775
in-theory        66775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66775.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-134, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66776
in-theory        66776
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66776.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-125, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66777
in-theory        66777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66777.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (G or H)))), M:tm-113, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66778
in-theory        66778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66778.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-105, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66779
in-theory        66779
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) or C))
theorem-size     13
proof            (modus-ponens tm-99 tm-786 ((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (or (or (and Am Bm) Bm) Dm))))
axioms-used      (tm-2 tm-1 tm-8 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-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-6.            (A -> (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-66779.        (((A and B) or B) -> (((A and B) or B) or C)), M:tm-99, m:tm-786, u:((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (or (or (and Am Bm) Bm) Dm)))
================================================================
tm-name          tm-66780
in-theory        66780
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> ((A and B) or B)) or D))
theorem-size     15
proof            (modus-ponens tm-98 tm-786 ((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (or (-> B (or (and Am Bm) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66780.        (((A and B) or B) -> ((C -> ((A and B) or B)) or D)), M:tm-98, m:tm-786, u:((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (or (-> B (or (and Am Bm) Bm)) Dm)))
================================================================
tm-name          tm-66781
in-theory        66781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66781.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (E or F)))), M:tm-95, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66782
in-theory        66782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66782.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-83, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66783
in-theory        66783
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66783.        (((not (not A)) -> A) and (((B and C) or C) -> (D -> (D or E)))), M:tm-76, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66784
in-theory        66784
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-73 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-10 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66784.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (C or D))), M:tm-73, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66785
in-theory        66785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66785.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (E or F)))), M:tm-69, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66786
in-theory        66786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66786.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-54, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66787
in-theory        66787
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-50 tm-786 ((A (and Am Bm)) (B Bm) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66787.        ((A or ((B and A) or A)) -> (C -> (C or D))), M:tm-50, m:tm-786, u:((A (and Am Bm)) (B Bm) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66788
in-theory        66788
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-49 tm-786 ((A (and Am Bm)) (B Bm) (C (-> Cm (or Cm 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-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-66788.        (((A and B) or ((A and B) or B)) -> (C -> (C or D))), M:tm-49, m:tm-786, u:((A (and Am Bm)) (B Bm) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66789
in-theory        66789
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-47 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-66789.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (D or E))), M:tm-47, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66790
in-theory        66790
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-46 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66790.        (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (D or E))), M:tm-46, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66791
in-theory        66791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66791.        ((A -> (B or A)) and (((C and D) or D) -> (E -> (E or F)))), M:tm-42, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66792
in-theory        66792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66792.        ((A -> (A or B)) and (((C and D) or D) -> (E -> (E or F)))), M:tm-32, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66793
in-theory        66793
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (C -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-24 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66793.        (((A and B) or B) -> (((A and B) or B) and (C -> (C or D)))), M:tm-24, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66794
in-theory        66794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66794.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (E or F)))), M:tm-23, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66795
in-theory        66795
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-47.           ((A -> B) -> (((C and 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-66795.        (((A and B) -> B) and (((C and D) or D) -> (E -> (E or F)))), M:tm-22, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66796
in-theory        66796
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66796.        (((A and B) -> A) and (((C and D) or D) -> (E -> (E or F)))), M:tm-21, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66797
in-theory        66797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66797.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (F or G)))), M:tm-20, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66798
in-theory        66798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-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-66798.        ((A -> (B -> A)) and (((C and D) or D) -> (E -> (E or F)))), M:tm-19, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66799
in-theory        66799
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (C -> (C or D)))) -> (not ((A and B) or B)))
theorem-size     19
proof            (modus-ponens tm-9 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66799.        ((((A and B) or B) -> (not (C -> (C or D)))) -> (not ((A and B) or B))), M:tm-9, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66800
in-theory        66800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> ((((D and E) or E) or (A -> (A or B))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
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-6.            (A -> (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-66800.        (((A -> (A or B)) -> C) -> ((((D and E) or E) or (A -> (A or B))) -> C)), M:tm-8, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-66801
in-theory        66801
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66801.        (A or (((B and C) or C) -> (D -> (D or E)))), M:tm-7, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66802
in-theory        66802
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm 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-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-66802.        ((((A and B) or B) -> (C -> (C or D))) or E), M:tm-6, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66803
in-theory        66803
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66803.        (A -> ((((B and C) or C) -> (D -> (D or E))) and A)), M:tm-5, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66804
in-theory        66804
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> C) -> (((A and B) or B) -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-2 tm-786 ((A (or (and Am Bm) Bm)) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66804.        ((((A and B) or B) -> C) -> (((A and B) or B) -> (C or D))), M:tm-2, m:tm-786, u:((A (or (and Am Bm) Bm)) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-66805
in-theory        66805
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66805.        (A -> (((B and C) or C) -> (D -> (D or E)))), M:tm-1, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-66806
in-theory        66806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     25
proof            (modus-ponens tm-757 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66806.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-757, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66807
in-theory        66807
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C -> (D or C)) and B)))
theorem-size     35
proof            (modus-ponens tm-747 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66807.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C -> (D or C)) and B))), M:tm-747, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66808
in-theory        66808
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 or G)) and F)))
theorem-size     39
proof            (modus-ponens tm-708 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66808.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G -> (H or G)) and F))), M:tm-708, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66809
in-theory        66809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     27
proof            (modus-ponens tm-665 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66809.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-665, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66810
in-theory        66810
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or ((D -> (E or D)) and B)))
theorem-size     15
proof            (modus-ponens tm-623 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or 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-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-66810.        (((A and B) or B) -> (C or ((D -> (E or D)) and B))), M:tm-623, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66811
in-theory        66811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-622 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or 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-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-66811.        ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-622, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66812
in-theory        66812
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or 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-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-66812.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (F or E))), M:tm-609, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66813
in-theory        66813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     23
proof            (modus-ponens tm-605 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66813.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-605, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66814
in-theory        66814
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (F or E)) and (((A and B) or B) -> ((C -> (D or C)) and B))))
theorem-size     33
proof            (modus-ponens tm-595 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66814.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (F or E)) and (((A and B) or B) -> ((C -> (D or C)) and B)))), M:tm-595, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66815
in-theory        66815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-550 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66815.        (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-550, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66816
in-theory        66816
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-540 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66816.        ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-540, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66817
in-theory        66817
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-530 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66817.        ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-530, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66818
in-theory        66818
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     23
proof            (modus-ponens tm-520 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66818.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-520, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66819
in-theory        66819
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-510 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66819.        ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-510, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66820
in-theory        66820
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-500 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or 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-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-66820.        ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-500, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66821
in-theory        66821
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H or G)) and F)))
theorem-size     29
proof            (modus-ponens tm-490 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66821.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H or G)) and F))), M:tm-490, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66822
in-theory        66822
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-480 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or 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-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-66822.        ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-480, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66823
in-theory        66823
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D or C)) and B) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66823.        (((A and B) or B) -> (((C -> (D or C)) and B) or E)), M:tm-470, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66824
in-theory        66824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-469 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66824.        ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-469, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66825
in-theory        66825
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66825.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (E or F))), M:tm-456, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66826
in-theory        66826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     23
proof            (modus-ponens tm-453 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66826.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-453, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66827
in-theory        66827
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (E or F)) and (((A and B) or B) -> ((C -> (D or C)) and B))))
theorem-size     33
proof            (modus-ponens tm-443 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-66827.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (E or F)) and (((A and B) or B) -> ((C -> (D or C)) and B)))), M:tm-443, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66828
in-theory        66828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-409 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66828.        (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-409, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66829
in-theory        66829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     23
proof            (modus-ponens tm-400 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66829.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-400, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66830
in-theory        66830
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-391 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-66830.        ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-391, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66831
in-theory        66831
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-382 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66831.        ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-382, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66832
in-theory        66832
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (H or G)) and F)))
theorem-size     29
proof            (modus-ponens tm-373 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66832.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (H or G)) and F))), M:tm-373, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66833
in-theory        66833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-364 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66833.        (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-364, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66834
in-theory        66834
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D -> (E or D)) and B) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-66834.        (((A and B) or B) -> (C -> (((D -> (E or D)) and B) and C))), M:tm-355, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66835
in-theory        66835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     23
proof            (modus-ponens tm-354 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66835.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-354, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66836
in-theory        66836
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-66836.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66837
in-theory        66837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-338 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66837.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (F or E)) and D))), M:tm-338, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66838
in-theory        66838
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((A and B) or B) -> (((A and B) or B) and ((C -> (D or C)) and B))))
theorem-size     33
proof            (modus-ponens tm-328 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66838.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((A and B) or B) -> (((A and B) or B) and ((C -> (D or C)) and B)))), M:tm-328, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66839
in-theory        66839
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C -> (D or C)) and B))))
theorem-size     35
proof            (modus-ponens tm-327 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-66839.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C -> (D or C)) and B)))), M:tm-327, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66840
in-theory        66840
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((E and F) -> F) and (((A and B) or B) -> ((C -> (D or C)) and B))))
theorem-size     33
proof            (modus-ponens tm-326 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-66840.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((E and F) -> F) and (((A and B) or B) -> ((C -> (D or C)) and B)))), M:tm-326, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66841
in-theory        66841
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((E and F) -> E) and (((A and B) or B) -> ((C -> (D or C)) and B))))
theorem-size     33
proof            (modus-ponens tm-325 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-66841.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((E and F) -> E) and (((A and B) or B) -> ((C -> (D or C)) and B)))), M:tm-325, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66842
in-theory        66842
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C -> (D or C)) and B))))
theorem-size     41
proof            (modus-ponens tm-324 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-66842.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C -> (D or C)) and B)))), M:tm-324, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66843
in-theory        66843
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C -> (D or C)) and B))))
theorem-size     33
proof            (modus-ponens tm-323 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-66843.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C -> (D or C)) and B)))), M:tm-323, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66844
in-theory        66844
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-66844.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E and F) -> F)), M:tm-322, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66845
in-theory        66845
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66845.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E and F) -> E)), M:tm-320, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66846
in-theory        66846
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66846.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66847
in-theory        66847
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     25
proof            (modus-ponens tm-316 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-66847.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66848
in-theory        66848
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66848.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (F -> E))), M:tm-315, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66849
in-theory        66849
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((((A and B) or B) -> (not ((C -> (D or C)) and B))) -> (not ((A and B) or B))))
theorem-size     35
proof            (modus-ponens tm-313 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-66849.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((((A and B) or B) -> (not ((C -> (D or C)) and B))) -> (not ((A and B) or B)))), M:tm-313, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66850
in-theory        66850
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((((C -> (D or C)) and B) -> E) -> ((((A and B) or B) or ((C -> (D or C)) and B)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-66850.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((((C -> (D or C)) and B) -> E) -> ((((A and B) or B) or ((C -> (D or C)) and B)) -> E))), M:tm-312, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66851
in-theory        66851
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E or (((A and B) or B) -> ((C -> (D or C)) and B))))
theorem-size     29
proof            (modus-ponens tm-311 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66851.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E or (((A and B) or B) -> ((C -> (D or C)) and B)))), M:tm-311, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66852
in-theory        66852
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((((A and B) or B) -> ((C -> (D or C)) and B)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-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-66852.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((((A and B) or B) -> ((C -> (D or C)) and B)) or E)), M:tm-310, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66853
in-theory        66853
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> ((((A and B) or B) -> ((C -> (D or C)) and B)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm 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-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-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-66853.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> ((((A and B) or B) -> ((C -> (D or C)) and B)) and E))), M:tm-309, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66854
in-theory        66854
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (((A and B) or B) -> ((C -> (D or C)) and B))))
theorem-size     29
proof            (modus-ponens tm-305 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-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-66854.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (E -> (((A and B) or B) -> ((C -> (D or C)) and B)))), M:tm-305, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66855
in-theory        66855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     25
proof            (modus-ponens tm-303 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66855.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-303, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66856
in-theory        66856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     23
proof            (modus-ponens tm-270 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 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-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-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-66856.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-270, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66857
in-theory        66857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     23
proof            (modus-ponens tm-239 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66857.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-239, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66858
in-theory        66858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (H or G)) and F)))
theorem-size     31
proof            (modus-ponens tm-210 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-66858.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (H or G)) and F))), M:tm-210, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66859
in-theory        66859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     23
proof            (modus-ponens tm-183 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66859.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-183, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66860
in-theory        66860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-157 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-66860.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-157, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66861
in-theory        66861
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     29
proof            (modus-ponens tm-147 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-66861.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-147, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66862
in-theory        66862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-134 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66862.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-134, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66863
in-theory        66863
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     29
proof            (modus-ponens tm-125 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66863.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-125, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66864
in-theory        66864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H or G)) and F)))
theorem-size     29
proof            (modus-ponens tm-113 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66864.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H or G)) and F))), M:tm-113, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66865
in-theory        66865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     33
proof            (modus-ponens tm-105 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-66865.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-105, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66866
in-theory        66866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (F or E)) and D)))
theorem-size     21
proof            (modus-ponens tm-95 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66866.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (F or E)) and D))), M:tm-95, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66867
in-theory        66867
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (E or D)) and B)))
theorem-size     15
proof            (modus-ponens tm-84 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66867.        (((A and B) or B) -> (C -> ((D -> (E or D)) and B))), M:tm-84, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66868
in-theory        66868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     21
proof            (modus-ponens tm-83 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66868.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-83, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66869
in-theory        66869
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (E or D)) and C)))
theorem-size     19
proof            (modus-ponens tm-76 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66869.        (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (E or D)) and C))), M:tm-76, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66870
in-theory        66870
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (D or C)) and B))
theorem-size     21
proof            (modus-ponens tm-73 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-8 tm-10 tm-4 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-4.            ((A and B) -> B), axiom
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-66870.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (D or C)) and B)), M:tm-73, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66871
in-theory        66871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (F or E)) and D)))
theorem-size     25
proof            (modus-ponens tm-69 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66871.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (F or E)) and D))), M:tm-69, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66872
in-theory        66872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     27
proof            (modus-ponens tm-54 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66872.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-54, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66873
in-theory        66873
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> ((C -> (D or C)) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-787 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) 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-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-66873.        ((A or ((B and A) or A)) -> ((C -> (D or C)) and A)), M:tm-50, m:tm-787, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66874
in-theory        66874
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> ((C -> (D or C)) and B))
theorem-size     17
proof            (modus-ponens tm-49 tm-787 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-8 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
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-66874.        (((A and B) or ((A and B) or B)) -> ((C -> (D or C)) and B)), M:tm-49, m:tm-787, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66875
in-theory        66875
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (E or D)) and C))
theorem-size     21
proof            (modus-ponens tm-47 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-8 tm-4 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-66875.        (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (E or D)) and C)), M:tm-47, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66876
in-theory        66876
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (E or D)) and B))
theorem-size     21
proof            (modus-ponens tm-46 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
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-66876.        (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (E or D)) and B)), M:tm-46, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66877
in-theory        66877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-42 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-66877.        ((A -> (B or A)) and (((C and D) or D) -> ((E -> (F or E)) and D))), M:tm-42, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66878
in-theory        66878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-32 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-66878.        ((A -> (A or B)) and (((C and D) or D) -> ((E -> (F or E)) and D))), M:tm-32, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66879
in-theory        66879
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and ((C -> (D or C)) and B)))
theorem-size     19
proof            (modus-ponens tm-24 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-66879.        (((A and B) or B) -> (((A and B) or B) and ((C -> (D or C)) and B))), M:tm-24, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66880
in-theory        66880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (F or E)) and D)))
theorem-size     21
proof            (modus-ponens tm-23 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66880.        ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (F or E)) and D))), M:tm-23, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66881
in-theory        66881
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-22 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm 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-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-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-66881.        (((A and B) -> B) and (((C and D) or D) -> ((E -> (F or E)) and D))), M:tm-22, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66882
in-theory        66882
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-21 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-66882.        (((A and B) -> A) and (((C and D) or D) -> ((E -> (F or E)) and D))), M:tm-21, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66883
in-theory        66883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     27
proof            (modus-ponens tm-20 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-66883.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-20, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66884
in-theory        66884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-19 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-66884.        ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (F or E)) and D))), M:tm-19, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66885
in-theory        66885
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not ((C -> (D or C)) and B))) -> (not ((A and B) or B)))
theorem-size     21
proof            (modus-ponens tm-9 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66885.        ((((A and B) or B) -> (not ((C -> (D or C)) and B))) -> (not ((A and B) or B))), M:tm-9, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66886
in-theory        66886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> D) -> ((((E and C) or C) or ((A -> (B or A)) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-7.            (A -> (B or 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-66886.        ((((A -> (B or A)) and C) -> D) -> ((((E and C) or C) or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-66887
in-theory        66887
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-7 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) 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-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-66887.        (A or (((B and C) or C) -> ((D -> (E or D)) and C))), M:tm-7, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66888
in-theory        66888
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66888.        ((((A and B) or B) -> ((C -> (D or C)) and B)) or E), M:tm-6, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66889
in-theory        66889
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> ((D -> (E or D)) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66889.        (A -> ((((B and C) or C) -> ((D -> (E or D)) and C)) and A)), M:tm-5, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66890
in-theory        66890
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-1 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-66890.        (A -> (((B and C) or C) -> ((D -> (E or D)) and C))), M:tm-1, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-66891
in-theory        66891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66891.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-757, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66892
in-theory        66892
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (((((A and B) or B) and E) or ((A and B) or B)) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66892.        ((((A and B) or B) -> (C -> (D or C))) and (((((A and B) or B) and E) or ((A and B) or B)) -> (C -> (D or C)))), M:tm-747, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66893
in-theory        66893
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 or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66893.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G -> (H or G)))), M:tm-708, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66894
in-theory        66894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66894.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-665, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66895
in-theory        66895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66895.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-622, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66896
in-theory        66896
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D or ((A and B) or B))))
theorem-size     15
proof            (modus-ponens tm-617 tm-788 ((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (or 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-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-66896.        (((A and B) or B) -> (C or (D or ((A and B) or B)))), M:tm-617, m:tm-788, u:((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (or Dm (or B (or (and Am Bm) Bm)))))
================================================================
tm-name          tm-66897
in-theory        66897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66897.        ((((A and B) or B) -> (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66898
in-theory        66898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66898.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-605, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66899
in-theory        66899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((E -> (F or E)) and (((A and B) or B) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66899.        ((((A and B) or B) -> (C -> (D or C))) and ((E -> (F or E)) and (((A and B) or B) -> (C -> (D or C))))), M:tm-595, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66900
in-theory        66900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66900.        (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (G or F)))), M:tm-550, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66901
in-theory        66901
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66901.        ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-540, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66902
in-theory        66902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66902.        ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-530, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66903
in-theory        66903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66903.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-520, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66904
in-theory        66904
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66904.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-510, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66905
in-theory        66905
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66905.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-500, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66906
in-theory        66906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66906.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H or G)))), M:tm-490, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66907
in-theory        66907
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66907.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-480, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66908
in-theory        66908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66908.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-469, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66909
in-theory        66909
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (((A and B) or B) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-788 ((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (or Dm (or (or (and Am Bm) Bm) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66909.        (((A and B) or B) -> (C or (((A and B) or B) or D))), M:tm-464, m:tm-788, u:((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (or Dm (or (or (and Am Bm) Bm) B))))
================================================================
tm-name          tm-66910
in-theory        66910
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66910.        ((((A and B) or B) -> (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66911
in-theory        66911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66911.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-453, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66912
in-theory        66912
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((E -> (E or F)) and (((A and B) or B) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66912.        ((((A and B) or B) -> (C -> (D or C))) and ((E -> (E or F)) and (((A and B) or B) -> (C -> (D or C))))), M:tm-443, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66913
in-theory        66913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66913.        (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (G or F)))), M:tm-409, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66914
in-theory        66914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66914.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (G or F)))), M:tm-400, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66915
in-theory        66915
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-7.            (A -> (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-66915.        ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (G or F)))), M:tm-391, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66916
in-theory        66916
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66916.        ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (G or F)))), M:tm-382, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66917
in-theory        66917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66917.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (H or G)))), M:tm-373, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66918
in-theory        66918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66918.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (G or F)))), M:tm-364, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66919
in-theory        66919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66919.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-354, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66920
in-theory        66920
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D -> (((A and B) or B) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-788 ((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (or Dm (-> B (and (or (and Am Bm) Bm) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66920.        (((A and B) or B) -> (C or (D -> (((A and B) or B) and D)))), M:tm-349, m:tm-788, u:((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (or Dm (-> B (and (or (and Am Bm) Bm) B)))))
================================================================
tm-name          tm-66921
in-theory        66921
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66921.        ((((A and B) or B) -> (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66922
in-theory        66922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66922.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (F or E)))), M:tm-338, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66923
in-theory        66923
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (((A and B) or B) -> (((A and B) or B) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66923.        ((((A and B) or B) -> (C -> (D or C))) and (((A and B) or B) -> (((A and B) or B) and (C -> (D or C))))), M:tm-328, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66924
in-theory        66924
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (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-66924.        ((((A and B) or B) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (C -> (D or C))))), M:tm-327, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66925
in-theory        66925
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (((E and F) -> F) and (((A and B) or B) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (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-66925.        ((((A and B) or B) -> (C -> (D or C))) and (((E and F) -> F) and (((A and B) or B) -> (C -> (D or C))))), M:tm-326, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66926
in-theory        66926
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (((E and F) -> E) and (((A and B) or B) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66926.        ((((A and B) or B) -> (C -> (D or C))) and (((E and F) -> E) and (((A and B) or B) -> (C -> (D or C))))), M:tm-325, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66927
in-theory        66927
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66927.        ((((A and B) or B) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (C -> (D or C))))), M:tm-324, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66928
in-theory        66928
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((E -> (F -> E)) and (((A and B) or B) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66928.        ((((A and B) or B) -> (C -> (D or C))) and ((E -> (F -> E)) and (((A and B) or B) -> (C -> (D or C))))), M:tm-323, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66929
in-theory        66929
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-66929.        ((((A and B) or B) -> (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66930
in-theory        66930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66930.        ((((A and B) or B) -> (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66931
in-theory        66931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66931.        ((((A and B) or B) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66932
in-theory        66932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     23
proof            (modus-ponens tm-316 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-66932.        ((((A and B) or B) -> (C -> (D or C))) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66933
in-theory        66933
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66933.        ((((A and B) or B) -> (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66934
in-theory        66934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((((A and B) or B) -> (not (C -> (D or C)))) -> (not ((A and B) or B))))
theorem-size     31
proof            (modus-ponens tm-313 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66934.        ((((A and B) or B) -> (C -> (D or C))) and ((((A and B) or B) -> (not (C -> (D or C)))) -> (not ((A and B) or B)))), M:tm-313, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66935
in-theory        66935
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> ((((A and B) or B) or (C -> (D or C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
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-47.           ((A -> B) -> (((C and 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-66935.        ((((A and B) or B) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> ((((A and B) or B) or (C -> (D or C))) -> E))), M:tm-312, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66936
in-theory        66936
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (E or (((A and B) or B) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66936.        ((((A and B) or B) -> (C -> (D or C))) and (E or (((A and B) or B) -> (C -> (D or C))))), M:tm-311, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66937
in-theory        66937
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((((A and B) or B) -> (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-7.            (A -> (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-66937.        ((((A and B) or B) -> (C -> (D or C))) and ((((A and B) or B) -> (C -> (D or C))) or E)), M:tm-310, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66938
in-theory        66938
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (E -> ((((A and B) or B) -> (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66938.        ((((A and B) or B) -> (C -> (D or C))) and (E -> ((((A and B) or B) -> (C -> (D or C))) and E))), M:tm-309, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66939
in-theory        66939
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (D or C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-788 ((A (or (and Am Bm) Bm)) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-7.            (A -> (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-66939.        ((((A and B) or B) -> (C -> (D or C))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (D or C)))), M:tm-306, m:tm-788, u:((A (or (and Am Bm) Bm)) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-66940
in-theory        66940
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (E -> (((A and B) or B) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-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-66940.        ((((A and B) or B) -> (C -> (D or C))) and (E -> (((A and B) or B) -> (C -> (D or C))))), M:tm-305, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66941
in-theory        66941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66941.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-303, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66942
in-theory        66942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-47.           ((A -> B) -> (((C and 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-66942.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-270, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66943
in-theory        66943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66943.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-239, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66944
in-theory        66944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66944.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> (H or G)))), M:tm-210, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66945
in-theory        66945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66945.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-183, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66946
in-theory        66946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-66946.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-157, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66947
in-theory        66947
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-7.            (A -> (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-66947.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-147, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66948
in-theory        66948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66948.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-134, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66949
in-theory        66949
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66949.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-125, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66950
in-theory        66950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66950.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H or G)))), M:tm-113, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66951
in-theory        66951
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66951.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-105, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66952
in-theory        66952
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or ((A and B) or B)))
theorem-size     13
proof            (modus-ponens tm-99 tm-788 ((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (or Dm (or (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-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-7.            (A -> (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-66952.        (((A and B) or B) -> (C or ((A and B) or B))), M:tm-99, m:tm-788, u:((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (or Dm (or (and Am Bm) Bm))))
================================================================
tm-name          tm-66953
in-theory        66953
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D -> ((A and B) or B))))
theorem-size     15
proof            (modus-ponens tm-98 tm-788 ((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (or Dm (-> B (or (and Am Bm) Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66953.        (((A and B) or B) -> (C or (D -> ((A and B) or B)))), M:tm-98, m:tm-788, u:((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (or Dm (-> B (or (and Am Bm) Bm)))))
================================================================
tm-name          tm-66954
in-theory        66954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66954.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (F or E)))), M:tm-95, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66955
in-theory        66955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66955.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-83, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66956
in-theory        66956
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66956.        (((not (not A)) -> A) and (((B and C) or C) -> (D -> (E or D)))), M:tm-76, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66957
in-theory        66957
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66957.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (D or C))), M:tm-73, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66958
in-theory        66958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66958.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (F or E)))), M:tm-69, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66959
in-theory        66959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66959.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-54, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66960
in-theory        66960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-50 tm-788 ((A (and Am Bm)) (B Bm) (C (-> Cm (or 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-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-66960.        ((A or ((B and A) or A)) -> (C -> (D or C))), M:tm-50, m:tm-788, u:((A (and Am Bm)) (B Bm) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66961
in-theory        66961
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-788 ((A (and Am Bm)) (B Bm) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66961.        (((A and B) or ((A and B) or B)) -> (C -> (D or C))), M:tm-49, m:tm-788, u:((A (and Am Bm)) (B Bm) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66962
in-theory        66962
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-66962.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (E or D))), M:tm-47, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66963
in-theory        66963
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66963.        (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (E or D))), M:tm-46, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66964
in-theory        66964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66964.        ((A -> (B or A)) and (((C and D) or D) -> (E -> (F or E)))), M:tm-42, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66965
in-theory        66965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66965.        ((A -> (A or B)) and (((C and D) or D) -> (E -> (F or E)))), M:tm-32, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66966
in-theory        66966
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (C -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66966.        (((A and B) or B) -> (((A and B) or B) and (C -> (D or C)))), M:tm-24, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66967
in-theory        66967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66967.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (F or E)))), M:tm-23, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66968
in-theory        66968
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-47.           ((A -> B) -> (((C and 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-66968.        (((A and B) -> B) and (((C and D) or D) -> (E -> (F or E)))), M:tm-22, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66969
in-theory        66969
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66969.        (((A and B) -> A) and (((C and D) or D) -> (E -> (F or E)))), M:tm-21, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66970
in-theory        66970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66970.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (G or F)))), M:tm-20, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66971
in-theory        66971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-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-66971.        ((A -> (B -> A)) and (((C and D) or D) -> (E -> (F or E)))), M:tm-19, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66972
in-theory        66972
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (C -> (D or C)))) -> (not ((A and B) or B)))
theorem-size     19
proof            (modus-ponens tm-9 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66972.        ((((A and B) or B) -> (not (C -> (D or C)))) -> (not ((A and B) or B))), M:tm-9, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66973
in-theory        66973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> ((((D and E) or E) or (A -> (B or A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
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-7.            (A -> (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-66973.        (((A -> (B or A)) -> C) -> ((((D and E) or E) or (A -> (B or A))) -> C)), M:tm-8, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-66974
in-theory        66974
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or 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-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-66974.        (A or (((B and C) or C) -> (D -> (E or D)))), M:tm-7, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66975
in-theory        66975
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66975.        ((((A and B) or B) -> (C -> (D or C))) or E), M:tm-6, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66976
in-theory        66976
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66976.        (A -> ((((B and C) or C) -> (D -> (E or D))) and A)), M:tm-5, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66977
in-theory        66977
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> C) -> (((A and B) or B) -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-788 ((A (or (and Am Bm) Bm)) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66977.        ((((A and B) or B) -> C) -> (((A and B) or B) -> (D or C))), M:tm-2, m:tm-788, u:((A (or (and Am Bm) Bm)) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-66978
in-theory        66978
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-66978.        (A -> (((B and C) or C) -> (D -> (E or D)))), M:tm-1, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-66979
in-theory        66979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-757 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66979.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-757, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66980
in-theory        66980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((((A and ((B -> C) -> D)) or ((B -> C) -> D)) and E) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D)))
theorem-size     59
proof            (modus-ponens tm-747 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-66980.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((((A and ((B -> C) -> D)) or ((B -> C) -> D)) and E) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D))), M:tm-747, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-66981
in-theory        66981
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)) -> ((G or (F -> G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-708 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66981.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H))), M:tm-708, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66982
in-theory        66982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-665 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-66982.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-665, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66983
in-theory        66983
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (E or ((C or (B -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-623 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-66983.        (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (E or ((C or (B -> C)) -> D))), M:tm-623, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-66984
in-theory        66984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-622 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-66984.        ((A -> (B -> (C or B))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-622, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66985
in-theory        66985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-66985.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66986
in-theory        66986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-605 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66986.        ((A -> ((B -> (C or B)) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-605, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66987
in-theory        66987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (F or E)) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-595 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66987.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (F or E)) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))), M:tm-595, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66988
in-theory        66988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-550 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66988.        (((A -> (B or A)) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-550, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66989
in-theory        66989
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-540 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66989.        ((A or (B -> (C or B))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-540, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66990
in-theory        66990
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-530 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66990.        ((A or (B -> (B or C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-530, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66991
in-theory        66991
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-520 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66991.        ((A or (B -> (C -> (B and C)))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-520, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66992
in-theory        66992
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-510 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-66992.        ((A or ((B and C) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-510, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66993
in-theory        66993
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-500 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66993.        ((A or ((B and C) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-500, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66994
in-theory        66994
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-490 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66994.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H))), M:tm-490, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66995
in-theory        66995
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-480 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-66995.        ((A or (B -> (C -> B))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-480, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66996
in-theory        66996
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((C or (B -> C)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-66996.        (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((C or (B -> C)) -> D) or E)), M:tm-470, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-66997
in-theory        66997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-469 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-66997.        ((A -> (B -> (B or C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-469, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66998
in-theory        66998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-66998.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-66999
in-theory        66999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-453 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-66999.        ((A -> ((B -> (B or C)) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-453, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67000
in-theory        67000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (E or F)) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-443 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67000.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (E or F)) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))), M:tm-443, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67001
in-theory        67001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-409 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67001.        (((A -> (A or B)) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-409, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67002
in-theory        67002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-400 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67002.        (((A -> (B -> (A and B))) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-400, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67003
in-theory        67003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-391 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-67003.        ((((A and B) -> B) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-391, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67004
in-theory        67004
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-382 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67004.        ((((A and B) -> A) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-382, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67005
in-theory        67005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-373 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67005.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H))), M:tm-373, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67006
in-theory        67006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-364 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67006.        (((A -> (B -> A)) or C) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-364, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67007
in-theory        67007
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (E -> (((C or (B -> C)) -> D) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67007.        (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (E -> (((C or (B -> C)) -> D) and E))), M:tm-355, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67008
in-theory        67008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-354 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67008.        ((A -> (B -> (C -> (B and C)))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-354, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67009
in-theory        67009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-67009.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67010
in-theory        67010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-338 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67010.        (((A -> B) -> (A -> (A and B))) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-338, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67011
in-theory        67011
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) and ((C or (B -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-328 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-67011.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) and ((C or (B -> C)) -> D)))), M:tm-328, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67012
in-theory        67012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))))
theorem-size     51
proof            (modus-ponens tm-327 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67012.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))), M:tm-327, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67013
in-theory        67013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((E and F) -> F) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-326 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-67013.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((E and F) -> F) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))), M:tm-326, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67014
in-theory        67014
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((E and F) -> E) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-325 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67014.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((E and F) -> E) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))), M:tm-325, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67015
in-theory        67015
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-324 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67015.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))), M:tm-324, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67016
in-theory        67016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (F -> E)) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-323 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-67016.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (F -> E)) and (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))), M:tm-323, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67017
in-theory        67017
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
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-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67017.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67018
in-theory        67018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67018.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67019
in-theory        67019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-67019.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67020
in-theory        67020
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> 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-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-67020.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> 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-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67021
in-theory        67021
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67021.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67022
in-theory        67022
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (not ((C or (B -> C)) -> D))) -> (not ((A and ((B -> C) -> D)) or ((B -> C) -> D)))))
theorem-size     59
proof            (modus-ponens tm-313 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67022.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (not ((C or (B -> C)) -> D))) -> (not ((A and ((B -> C) -> D)) or ((B -> C) -> D))))), M:tm-313, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67023
in-theory        67023
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((C or (B -> C)) -> D) -> E) -> ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) or ((C or (B -> C)) -> D)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67023.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((C or (B -> C)) -> D) -> E) -> ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) or ((C or (B -> C)) -> D)) -> E))), M:tm-312, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67024
in-theory        67024
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E or (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-311 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67024.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E or (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))), M:tm-311, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67025
in-theory        67025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67025.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) or E)), M:tm-310, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67026
in-theory        67026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67026.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and E))), M:tm-309, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67027
in-theory        67027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (C or (B -> C))) -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> D)))
theorem-size     57
proof            (modus-ponens tm-306 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (or Cm (-> Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-67027.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (C or (B -> C))) -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> D))), M:tm-306, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (or Cm (-> Bm Cm))) (C Dm))
================================================================
tm-name          tm-67028
in-theory        67028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-305 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> 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-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-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-67028.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (E -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))), M:tm-305, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67029
in-theory        67029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-303 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67029.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-303, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67030
in-theory        67030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-270 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 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-47.           ((A -> B) -> (((C and 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-67030.        ((A -> (((B and C) -> C) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-270, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67031
in-theory        67031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-239 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67031.        ((A -> (((B and C) -> B) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-239, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67032
in-theory        67032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-210 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67032.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H))), M:tm-210, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67033
in-theory        67033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-183 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67033.        ((A -> ((B -> (C -> B)) and A)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-183, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67034
in-theory        67034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-157 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67034.        ((A -> ((B and C) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-157, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67035
in-theory        67035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-147 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
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-47.           ((A -> B) -> (((C and 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-67035.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-147, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67036
in-theory        67036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-134 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67036.        ((A -> ((B and C) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-134, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67037
in-theory        67037
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-125 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67037.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-125, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67038
in-theory        67038
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> (D -> E))) or ((B -> C) -> (D -> E))) -> (((C or (B -> C)) -> D) -> ((C or (B -> C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-114 tm-789 ((A (or (and Am (-> (-> Bm Cm) (-> C D))) (-> (-> Bm Cm) (-> C D)))) (B (or Cm (-> Bm Cm))) (Dm (-> C D))))
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-14.           (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-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-67038.        (((A and ((B -> C) -> (D -> E))) or ((B -> C) -> (D -> E))) -> (((C or (B -> C)) -> D) -> ((C or (B -> C)) -> E))), M:tm-114, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) (-> C D))) (-> (-> Bm Cm) (-> C D)))) (B (or Cm (-> Bm Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-67039
in-theory        67039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-113 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67039.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H))), M:tm-113, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67040
in-theory        67040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-105 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67040.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-105, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67041
in-theory        67041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-95 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-67041.        (((A -> B) -> (A -> A)) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-95, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67042
in-theory        67042
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (E -> ((C or (B -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-84 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67042.        (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (E -> ((C or (B -> C)) -> D))), M:tm-84, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67043
in-theory        67043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-83 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67043.        ((A -> (B -> (C -> B))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-83, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67044
in-theory        67044
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and ((C -> D) -> E)) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-76 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67044.        (((not (not A)) -> A) and (((B and ((C -> D) -> E)) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-76, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67045
in-theory        67045
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))) -> ((C or (B -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-73 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67045.        (((not (not ((A and ((B -> C) -> D)) or ((B -> C) -> D)))) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D)), M:tm-73, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67046
in-theory        67046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-69 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67046.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-69, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67047
in-theory        67047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-54 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67047.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-54, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67048
in-theory        67048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((D and ((A -> B) -> C)) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C))
theorem-size     27
proof            (modus-ponens tm-50 tm-789 ((A (and Am (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67048.        ((((A -> B) -> C) or ((D and ((A -> B) -> C)) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C)), M:tm-50, m:tm-789, u:((A (and Am (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67049
in-theory        67049
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D))
theorem-size     29
proof            (modus-ponens tm-49 tm-789 ((A (and Am (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67049.        (((A and ((B -> C) -> D)) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D)), M:tm-49, m:tm-789, u:((A (and Am (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67050
in-theory        67050
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))) -> ((D or (C -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-47 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-4 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-1.            (A -> (B -> A)), 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-67050.        (((A and ((B and ((C -> D) -> E)) or ((C -> D) -> E))) or ((B and ((C -> D) -> E)) or ((C -> D) -> E))) -> ((D or (C -> D)) -> E)), M:tm-47, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67051
in-theory        67051
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))) -> ((C or (B -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-46 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67051.        (((((A and ((B -> C) -> D)) or ((B -> C) -> D)) and E) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D)), M:tm-46, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67052
in-theory        67052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-42 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67052.        ((A -> (B or A)) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-42, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67053
in-theory        67053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-32 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67053.        ((A -> (A or B)) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-32, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67054
in-theory        67054
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) and ((C or (B -> C)) -> D)))
theorem-size     35
proof            (modus-ponens tm-24 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67054.        (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) and ((C or (B -> C)) -> D))), M:tm-24, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67055
in-theory        67055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-23 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67055.        ((A -> (B -> (A and B))) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-23, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67056
in-theory        67056
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-22 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 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-47.           ((A -> B) -> (((C and 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-67056.        (((A and B) -> B) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-22, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67057
in-theory        67057
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-21 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67057.        (((A and B) -> A) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-21, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67058
in-theory        67058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-20 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-67058.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-20, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67059
in-theory        67059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-19 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67059.        ((A -> (B -> A)) and (((C and ((D -> E) -> F)) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-19, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67060
in-theory        67060
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-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
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-12.           ((A -> B) -> (A -> A)), M: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-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-67060.        (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((A and ((B -> C) -> D)) or ((B -> C) -> D))), M:tm-12, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67061
in-theory        67061
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (not ((C or (B -> C)) -> D))) -> (not ((A and ((B -> C) -> D)) or ((B -> C) -> D))))
theorem-size     37
proof            (modus-ponens tm-9 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67061.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (not ((C or (B -> C)) -> D))) -> (not ((A and ((B -> C) -> D)) or ((B -> C) -> D)))), M:tm-9, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67062
in-theory        67062
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> ((((E and ((B -> A) -> C)) or ((B -> A) -> C)) or ((A or (B -> A)) -> C)) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       127
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-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-67062.        ((((A or (B -> A)) -> C) -> D) -> ((((E and ((B -> A) -> C)) or ((B -> A) -> C)) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67063
in-theory        67063
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and ((C -> D) -> E)) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-7 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67063.        (A or (((B and ((C -> D) -> E)) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-7, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67064
in-theory        67064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67064.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) or E), M:tm-6, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67065
in-theory        67065
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and ((C -> D) -> E)) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67065.        (A -> ((((B and ((C -> D) -> E)) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)) and A)), M:tm-5, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67066
in-theory        67066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (C or (B -> C))) -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> D))
theorem-size     35
proof            (modus-ponens tm-2 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (or Cm (-> Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-67066.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (C or (B -> C))) -> (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> D)), M:tm-2, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (or Cm (-> Bm Cm))) (C Dm))
================================================================
tm-name          tm-67067
in-theory        67067
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C -> D) -> E)) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-1 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       109
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-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-67067.        (A -> (((B and ((C -> D) -> E)) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-1, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-67068
in-theory        67068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     49
proof            (modus-ponens tm-757 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67068.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-757, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67069
in-theory        67069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) and F) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     99
proof            (modus-ponens tm-747 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67069.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) and F) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-747, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67070
in-theory        67070
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)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))
theorem-size     63
proof            (modus-ponens tm-708 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67070.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))), M:tm-708, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67071
in-theory        67071
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     51
proof            (modus-ponens tm-665 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67071.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-665, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67072
in-theory        67072
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (F or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     39
proof            (modus-ponens tm-623 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67072.        (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (F or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-623, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67073
in-theory        67073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-622 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67073.        ((A -> (B -> (C or B))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-622, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67074
in-theory        67074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F -> (G or F)))
theorem-size     43
proof            (modus-ponens tm-609 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67074.        ((((A and (((B -> C) -> (B -> D)) -> E)) 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-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67075
in-theory        67075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     47
proof            (modus-ponens tm-605 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67075.        ((A -> ((B -> (C or B)) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-605, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67076
in-theory        67076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F -> (G or F)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     81
proof            (modus-ponens tm-595 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67076.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F -> (G or F)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-595, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67077
in-theory        67077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-550 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67077.        (((A -> (B or A)) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-550, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67078
in-theory        67078
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-540 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67078.        ((A or (B -> (C or B))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-540, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67079
in-theory        67079
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-530 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67079.        ((A or (B -> (B or C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-530, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67080
in-theory        67080
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     47
proof            (modus-ponens tm-520 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67080.        ((A or (B -> (C -> (B and C)))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-520, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67081
in-theory        67081
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-510 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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       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-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67081.        ((A or ((B and C) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-510, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67082
in-theory        67082
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-500 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67082.        ((A or ((B and C) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-500, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67083
in-theory        67083
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))
theorem-size     53
proof            (modus-ponens tm-490 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67083.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))), M:tm-490, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67084
in-theory        67084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-480 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67084.        ((A or (B -> (C -> B))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-480, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67085
in-theory        67085
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) or F))
theorem-size     39
proof            (modus-ponens tm-470 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67085.        (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) or F)), M:tm-470, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67086
in-theory        67086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-469 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67086.        ((A -> (B -> (B or C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-469, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67087
in-theory        67087
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F -> (F or G)))
theorem-size     43
proof            (modus-ponens tm-456 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67087.        ((((A and (((B -> C) -> (B -> D)) -> E)) 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-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67088
in-theory        67088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     47
proof            (modus-ponens tm-453 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67088.        ((A -> ((B -> (B or C)) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-453, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67089
in-theory        67089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F -> (F or G)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     81
proof            (modus-ponens tm-443 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67089.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F -> (F or G)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-443, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67090
in-theory        67090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-409 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67090.        (((A -> (A or B)) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-409, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67091
in-theory        67091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     47
proof            (modus-ponens tm-400 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67091.        (((A -> (B -> (A and B))) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-400, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67092
in-theory        67092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-391 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67092.        ((((A and B) -> B) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-391, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67093
in-theory        67093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-382 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67093.        ((((A and B) -> A) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-382, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67094
in-theory        67094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))
theorem-size     53
proof            (modus-ponens tm-373 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67094.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))), M:tm-373, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67095
in-theory        67095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-364 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67095.        (((A -> (B -> A)) or C) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-364, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67096
in-theory        67096
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (F -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) and F)))
theorem-size     41
proof            (modus-ponens tm-355 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67096.        (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (F -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) and F))), M:tm-355, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67097
in-theory        67097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     47
proof            (modus-ponens tm-354 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67097.        ((A -> (B -> (C -> (B and C)))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-354, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67098
in-theory        67098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F -> (G -> (F and G))))
theorem-size     45
proof            (modus-ponens tm-341 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67098.        ((((A and (((B -> C) -> (B -> D)) -> E)) 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-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67099
in-theory        67099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-338 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67099.        (((A -> B) -> (A -> (A and B))) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-338, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67100
in-theory        67100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     97
proof            (modus-ponens tm-328 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67100.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-328, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67101
in-theory        67101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F -> (G -> (F and G))) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     83
proof            (modus-ponens tm-327 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67101.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F -> (G -> (F and G))) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-327, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67102
in-theory        67102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((F and G) -> G) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     81
proof            (modus-ponens tm-326 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67102.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((F and G) -> G) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-326, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67103
in-theory        67103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((F and G) -> F) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     81
proof            (modus-ponens tm-325 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67103.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((F and G) -> F) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-325, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67104
in-theory        67104
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) 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 and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     89
proof            (modus-ponens tm-324 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67104.        ((((A and (((B -> C) -> (B -> D)) -> E)) 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 and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-324, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67105
in-theory        67105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F -> (G -> F)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     81
proof            (modus-ponens tm-323 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67105.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F -> (G -> F)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-323, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67106
in-theory        67106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F and G) -> G))
theorem-size     43
proof            (modus-ponens tm-322 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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       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-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67106.        ((((A and (((B -> C) -> (B -> D)) -> E)) 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-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67107
in-theory        67107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((F and G) -> F))
theorem-size     43
proof            (modus-ponens tm-320 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67107.        ((((A and (((B -> C) -> (B -> D)) -> E)) 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-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67108
in-theory        67108
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) 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     51
proof            (modus-ponens tm-318 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67108.        ((((A and (((B -> C) -> (B -> D)) -> E)) 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-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67109
in-theory        67109
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))))
theorem-size     81
proof            (modus-ponens tm-316 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67109.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)))), M:tm-316, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67110
in-theory        67110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F -> (G -> F)))
theorem-size     43
proof            (modus-ponens tm-315 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67110.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F -> (G -> F))), M:tm-315, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67111
in-theory        67111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)))))
theorem-size     99
proof            (modus-ponens tm-313 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67111.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))))), M:tm-313, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67112
in-theory        67112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)))
theorem-size     95
proof            (modus-ponens tm-312 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67112.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F))), M:tm-312, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67113
in-theory        67113
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F or (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     77
proof            (modus-ponens tm-311 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67113.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F or (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-311, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67114
in-theory        67114
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F))
theorem-size     77
proof            (modus-ponens tm-310 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67114.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F)), M:tm-310, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67115
in-theory        67115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F -> ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and F)))
theorem-size     79
proof            (modus-ponens tm-309 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67115.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F -> ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and F))), M:tm-309, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67116
in-theory        67116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> E)))
theorem-size     97
proof            (modus-ponens tm-306 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Em)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67116.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> E))), M:tm-306, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Em))
================================================================
tm-name          tm-67117
in-theory        67117
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     77
proof            (modus-ponens tm-305 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67117.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (F -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-305, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67118
in-theory        67118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     49
proof            (modus-ponens tm-303 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67118.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-303, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67119
in-theory        67119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     47
proof            (modus-ponens tm-270 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-8 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-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67119.        ((A -> (((B and C) -> C) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-270, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67120
in-theory        67120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     47
proof            (modus-ponens tm-239 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67120.        ((A -> (((B and C) -> B) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-239, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67121
in-theory        67121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))
theorem-size     55
proof            (modus-ponens tm-210 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67121.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))), M:tm-210, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67122
in-theory        67122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     47
proof            (modus-ponens tm-183 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67122.        ((A -> ((B -> (C -> B)) and A)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-183, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67123
in-theory        67123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-157 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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       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-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67123.        ((A -> ((B and C) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-157, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67124
in-theory        67124
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     53
proof            (modus-ponens tm-147 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67124.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-147, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67125
in-theory        67125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-134 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> 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-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67125.        ((A -> ((B and C) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-134, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67126
in-theory        67126
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     53
proof            (modus-ponens tm-125 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67126.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-125, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67127
in-theory        67127
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> (E -> F))) 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     57
proof            (modus-ponens tm-114 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> C D))) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> C D)))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67127.        (((A and (((B -> C) -> (B -> D)) -> (E -> F))) 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-114, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> C D))) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> C D)))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (-> C D)))
================================================================
tm-name          tm-67128
in-theory        67128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))
theorem-size     53
proof            (modus-ponens tm-113 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67128.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))), M:tm-113, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67129
in-theory        67129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     57
proof            (modus-ponens tm-105 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67129.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-105, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67130
in-theory        67130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-95 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67130.        (((A -> B) -> (A -> A)) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-95, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67131
in-theory        67131
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (F -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     39
proof            (modus-ponens tm-84 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67131.        (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (F -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-84, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67132
in-theory        67132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     45
proof            (modus-ponens tm-83 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67132.        ((A -> (B -> (C -> B))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-83, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67133
in-theory        67133
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     43
proof            (modus-ponens tm-76 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67133.        (((not (not A)) -> A) and (((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-76, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67134
in-theory        67134
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)))) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))
theorem-size     61
proof            (modus-ponens tm-73 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-10 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67134.        (((not (not ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)))) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)), M:tm-73, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67135
in-theory        67135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     49
proof            (modus-ponens tm-69 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67135.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-69, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67136
in-theory        67136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     51
proof            (modus-ponens tm-54 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67136.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-54, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67137
in-theory        67137
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or ((E and (((A -> B) -> (A -> C)) -> D)) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     47
proof            (modus-ponens tm-50 tm-790 ((A (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67137.        (((((A -> B) -> (A -> C)) -> D) or ((E and (((A -> B) -> (A -> C)) -> D)) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-50, m:tm-790, u:((A (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67138
in-theory        67138
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))
theorem-size     49
proof            (modus-ponens tm-49 tm-790 ((A (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67138.        (((A and (((B -> C) -> (B -> D)) -> E)) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)), M:tm-49, m:tm-790, u:((A (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67139
in-theory        67139
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F))) or ((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))
theorem-size     61
proof            (modus-ponens tm-47 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-4 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67139.        (((A and ((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F))) or ((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)), M:tm-47, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67140
in-theory        67140
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) and F) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))
theorem-size     61
proof            (modus-ponens tm-46 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67140.        (((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) and F) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)), M:tm-46, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67141
in-theory        67141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-42 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67141.        ((A -> (B or A)) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-42, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67142
in-theory        67142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-32 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67142.        ((A -> (A or B)) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-32, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67143
in-theory        67143
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     59
proof            (modus-ponens tm-24 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67143.        (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-24, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67144
in-theory        67144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-23 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67144.        ((A -> (B -> (A and B))) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-23, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67145
in-theory        67145
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-22 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-8 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-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67145.        (((A and B) -> B) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-22, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67146
in-theory        67146
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-21 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67146.        (((A and B) -> A) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-21, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67147
in-theory        67147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     51
proof            (modus-ponens tm-20 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67147.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-20, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67148
in-theory        67148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-19 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67148.        ((A -> (B -> A)) and (((C and (((D -> E) -> (D -> F)) -> G)) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-19, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67149
in-theory        67149
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)))
theorem-size     43
proof            (modus-ponens tm-12 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67149.        (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))), M:tm-12, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67150
in-theory        67150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))))
theorem-size     61
proof            (modus-ponens tm-9 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67150.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)))), M:tm-9, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67151
in-theory        67151
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((F and (((A -> B) -> (A -> C)) -> D)) 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-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       187
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-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-67151.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((F and (((A -> B) -> (A -> C)) -> D)) or (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67152
in-theory        67152
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     39
proof            (modus-ponens tm-7 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67152.        (A or (((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-7, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67153
in-theory        67153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F)
theorem-size     39
proof            (modus-ponens tm-6 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67153.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F), M:tm-6, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67154
in-theory        67154
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A))
theorem-size     41
proof            (modus-ponens tm-5 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67154.        (A -> ((((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A)), M:tm-5, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67155
in-theory        67155
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> E))
theorem-size     59
proof            (modus-ponens tm-2 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Em)))
axioms-used      (tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67155.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> E)), M:tm-2, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Em))
================================================================
tm-name          tm-67156
in-theory        67156
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     39
proof            (modus-ponens tm-1 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-67156.        (A -> (((B and (((C -> D) -> (C -> E)) -> F)) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-1, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-67157
in-theory        67157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-757 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67157.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-757, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67158
in-theory        67158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((((A and (B -> C)) or (B -> C)) and E) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C)))
theorem-size     47
proof            (modus-ponens tm-747 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-67158.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((((A and (B -> C)) or (B -> C)) and E) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C))), M:tm-747, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67159
in-theory        67159
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 and H) or F) -> G)))
theorem-size     43
proof            (modus-ponens tm-708 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
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-67159.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G))), M:tm-708, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67160
in-theory        67160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-665 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
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-67160.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-665, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67161
in-theory        67161
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D or (((B and E) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-623 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67161.        (((A and (B -> C)) or (B -> C)) -> (D or (((B and E) or B) -> C))), M:tm-623, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67162
in-theory        67162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-622 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67162.        ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-622, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67163
in-theory        67163
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67163.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (F or E))), M:tm-609, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67164
in-theory        67164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-605 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67164.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-605, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67165
in-theory        67165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (F or E)) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-595 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-67165.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (F or E)) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)))), M:tm-595, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67166
in-theory        67166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-550 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67166.        (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-550, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67167
in-theory        67167
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-540 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67167.        ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-540, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67168
in-theory        67168
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-530 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67168.        ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-530, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67169
in-theory        67169
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-520 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67169.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-520, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67170
in-theory        67170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-510 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
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-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-67170.        ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-510, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67171
in-theory        67171
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-500 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-67171.        ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-500, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67172
in-theory        67172
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-490 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67172.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G))), M:tm-490, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67173
in-theory        67173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-480 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67173.        ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-480, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67174
in-theory        67174
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((((B and D) or B) -> C) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67174.        (((A and (B -> C)) or (B -> C)) -> ((((B and D) or B) -> C) or E)), M:tm-470, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67175
in-theory        67175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-469 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67175.        ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-469, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67176
in-theory        67176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67176.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (E or F))), M:tm-456, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67177
in-theory        67177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-453 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67177.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-453, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67178
in-theory        67178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (E or F)) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-443 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-67178.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (E or F)) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)))), M:tm-443, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67179
in-theory        67179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-409 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67179.        (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-409, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67180
in-theory        67180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-400 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67180.        (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-400, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67181
in-theory        67181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-391 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
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-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-67181.        ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-391, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67182
in-theory        67182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-382 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-67182.        ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-382, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67183
in-theory        67183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-373 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67183.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G))), M:tm-373, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67184
in-theory        67184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-364 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67184.        (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-364, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67185
in-theory        67185
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> ((((B and E) or B) -> C) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67185.        (((A and (B -> C)) or (B -> C)) -> (D -> ((((B and E) or B) -> C) and D))), M:tm-355, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67186
in-theory        67186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-354 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-67186.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-354, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67187
in-theory        67187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-67187.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67188
in-theory        67188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-338 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67188.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E))), M:tm-338, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67189
in-theory        67189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (((B and D) or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-328 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67189.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (((B and D) or B) -> C)))), M:tm-328, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67190
in-theory        67190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (F -> (E and F))) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-327 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-67190.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (F -> (E and F))) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)))), M:tm-327, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67191
in-theory        67191
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((E and F) -> F) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-326 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
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-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-67191.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((E and F) -> F) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)))), M:tm-326, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67192
in-theory        67192
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((E and F) -> E) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-325 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-67192.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((E and F) -> E) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)))), M:tm-325, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67193
in-theory        67193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))))
theorem-size     49
proof            (modus-ponens tm-324 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-67193.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)))), M:tm-324, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67194
in-theory        67194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (F -> E)) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-323 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-67194.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (F -> E)) and (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)))), M:tm-323, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67195
in-theory        67195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
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-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-67195.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67196
in-theory        67196
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67196.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67197
in-theory        67197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-67197.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67198
in-theory        67198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C))))
theorem-size     37
proof            (modus-ponens tm-316 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-67198.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C)))), M:tm-316, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67199
in-theory        67199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67199.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67200
in-theory        67200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> (not (((B and D) or B) -> C))) -> (not ((A and (B -> C)) or (B -> C)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67200.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> (not (((B and D) or B) -> C))) -> (not ((A and (B -> C)) or (B -> C))))), M:tm-313, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67201
in-theory        67201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((((B and D) or B) -> C) -> E) -> ((((A and (B -> C)) or (B -> C)) or (((B and D) or B) -> C)) -> E)))
theorem-size     47
proof            (modus-ponens tm-312 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-67201.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((((B and D) or B) -> C) -> E) -> ((((A and (B -> C)) or (B -> C)) or (((B and D) or B) -> C)) -> E))), M:tm-312, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67202
in-theory        67202
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E or (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-311 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or 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-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-67202.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E or (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)))), M:tm-311, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67203
in-theory        67203
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or 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-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-67203.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) or E)), M:tm-310, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67204
in-theory        67204
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-67204.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and E))), M:tm-309, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67205
in-theory        67205
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> ((B and D) or B)) -> (((A and (B -> C)) or (B -> C)) -> C)))
theorem-size     45
proof            (modus-ponens tm-306 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (or (and Bm Dm) Bm)) (C Cm)))
axioms-used      (tm-2 tm-5 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-67205.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> ((B and D) or B)) -> (((A and (B -> C)) or (B -> C)) -> C))), M:tm-306, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (or (and Bm Dm) Bm)) (C Cm))
================================================================
tm-name          tm-67206
in-theory        67206
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-305 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-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-67206.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (E -> (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)))), M:tm-305, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67207
in-theory        67207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-303 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67207.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-303, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67208
in-theory        67208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-270 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
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-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-67208.        ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-270, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67209
in-theory        67209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-239 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67209.        ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-239, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67210
in-theory        67210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G)))
theorem-size     35
proof            (modus-ponens tm-210 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67210.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G))), M:tm-210, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67211
in-theory        67211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-183 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-67211.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-183, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67212
in-theory        67212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-157 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
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-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-67212.        ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-157, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67213
in-theory        67213
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-147 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
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-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-67213.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-147, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67214
in-theory        67214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-134 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67214.        ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-134, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67215
in-theory        67215
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-125 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-67215.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-125, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67216
in-theory        67216
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((((B and E) or B) -> C) -> (((B and E) or B) -> D)))
theorem-size     29
proof            (modus-ponens tm-114 tm-791 ((A (or (and Am (-> Bm (-> C D))) (-> Bm (-> C D)))) (B (or (and Bm Dm) Bm)) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67216.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((((B and E) or B) -> C) -> (((B and E) or B) -> D))), M:tm-114, m:tm-791, u:((A (or (and Am (-> Bm (-> C D))) (-> Bm (-> C D)))) (B (or (and Bm Dm) Bm)) (Cm (-> C D)))
================================================================
tm-name          tm-67217
in-theory        67217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-113 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67217.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G))), M:tm-113, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67218
in-theory        67218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     37
proof            (modus-ponens tm-105 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67218.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-105, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67219
in-theory        67219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-95 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67219.        (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E))), M:tm-95, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67220
in-theory        67220
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> (((B and E) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-84 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67220.        (((A and (B -> C)) or (B -> C)) -> (D -> (((B and E) or B) -> C))), M:tm-84, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67221
in-theory        67221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-83 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67221.        ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-83, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67222
in-theory        67222
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> (((C and E) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-76 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67222.        (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> (((C and E) or C) -> D))), M:tm-76, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67223
in-theory        67223
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C))
theorem-size     29
proof            (modus-ponens tm-73 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-8 tm-10 tm-4 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-4.            ((A and B) -> B), axiom
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-67223.        (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C)), M:tm-73, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67224
in-theory        67224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-69 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67224.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E))), M:tm-69, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67225
in-theory        67225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-54 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67225.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-54, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67226
in-theory        67226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C and (A -> B)) or (A -> B))) -> (((A and D) or A) -> B))
theorem-size     21
proof            (modus-ponens tm-50 tm-791 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-8 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
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-67226.        (((A -> B) or ((C and (A -> B)) or (A -> B))) -> (((A and D) or A) -> B)), M:tm-50, m:tm-791, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67227
in-theory        67227
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C))
theorem-size     23
proof            (modus-ponens tm-49 tm-791 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-8 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
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-67227.        (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C)), M:tm-49, m:tm-791, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67228
in-theory        67228
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> (((C and E) or C) -> D))
theorem-size     29
proof            (modus-ponens tm-47 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
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-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-67228.        (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> (((C and E) or C) -> D)), M:tm-47, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67229
in-theory        67229
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (((B and E) or B) -> C))
theorem-size     29
proof            (modus-ponens tm-46 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-67229.        (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (((B and E) or B) -> C)), M:tm-46, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67230
in-theory        67230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-42 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67230.        ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E))), M:tm-42, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67231
in-theory        67231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-32 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67231.        ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E))), M:tm-32, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67232
in-theory        67232
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (((B and D) or B) -> C)))
theorem-size     27
proof            (modus-ponens tm-24 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-67232.        (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (((B and D) or B) -> C))), M:tm-24, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67233
in-theory        67233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-23 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67233.        ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E))), M:tm-23, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67234
in-theory        67234
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-22 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
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-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-67234.        (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E))), M:tm-22, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67235
in-theory        67235
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-21 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-67235.        (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E))), M:tm-21, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67236
in-theory        67236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-20 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-67236.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-20, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67237
in-theory        67237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-19 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67237.        ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> (((D and F) or D) -> E))), M:tm-19, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67238
in-theory        67238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (not (((B and D) or B) -> C))) -> (not ((A and (B -> C)) or (B -> C))))
theorem-size     29
proof            (modus-ponens tm-9 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-9 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67238.        ((((A and (B -> C)) or (B -> C)) -> (not (((B and D) or B) -> C))) -> (not ((A and (B -> C)) or (B -> C)))), M:tm-9, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67239
in-theory        67239
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> ((((E and (A -> C)) or (A -> C)) or (((A and B) or A) -> C)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-8 tm-4 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-3.            ((A and B) -> A), axiom
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-67239.        (((((A and B) or A) -> C) -> D) -> ((((E and (A -> C)) or (A -> C)) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-67240
in-theory        67240
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C -> D)) or (C -> D)) -> (((C and E) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-7 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-7 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67240.        (A or (((B and (C -> D)) or (C -> D)) -> (((C and E) or C) -> D))), M:tm-7, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67241
in-theory        67241
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-6 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67241.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) or E), M:tm-6, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67242
in-theory        67242
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) or (C -> D)) -> (((C and E) or C) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-67242.        (A -> ((((B and (C -> D)) or (C -> D)) -> (((C and E) or C) -> D)) and A)), M:tm-5, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67243
in-theory        67243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B and D) or B)) -> (((A and (B -> C)) or (B -> C)) -> C))
theorem-size     27
proof            (modus-ponens tm-2 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (or (and Bm Dm) Bm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67243.        ((((A and (B -> C)) or (B -> C)) -> ((B and D) or B)) -> (((A and (B -> C)) or (B -> C)) -> C)), M:tm-2, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (or (and Bm Dm) Bm)) (C Cm))
================================================================
tm-name          tm-67244
in-theory        67244
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C -> D)) or (C -> D)) -> (((C and E) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-1 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-67244.        (A -> (((B and (C -> D)) or (C -> D)) -> (((C and E) or C) -> D))), M:tm-1, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-67245
in-theory        67245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-757 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67245.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-757, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67246
in-theory        67246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((((A and (B -> C)) or (B -> C)) and E) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C)))
theorem-size     47
proof            (modus-ponens tm-747 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-67246.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((((A and (B -> C)) or (B -> C)) and E) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C))), M:tm-747, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67247
in-theory        67247
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)) -> (((H and F) or F) -> G)))
theorem-size     43
proof            (modus-ponens tm-708 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67247.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G))), M:tm-708, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67248
in-theory        67248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-665 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-67248.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-665, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67249
in-theory        67249
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D or (((E and B) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-623 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67249.        (((A and (B -> C)) or (B -> C)) -> (D or (((E and B) or B) -> C))), M:tm-623, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67250
in-theory        67250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-622 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67250.        ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-622, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67251
in-theory        67251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67251.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (F or E))), M:tm-609, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67252
in-theory        67252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-605 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67252.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-605, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67253
in-theory        67253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (F or E)) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-595 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-67253.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (F or E)) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)))), M:tm-595, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67254
in-theory        67254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-550 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-67254.        (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-550, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67255
in-theory        67255
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-540 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-67255.        ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-540, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67256
in-theory        67256
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-530 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-67256.        ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-530, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67257
in-theory        67257
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-520 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67257.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-520, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67258
in-theory        67258
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-510 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-67258.        ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-510, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67259
in-theory        67259
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-500 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-67259.        ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-500, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67260
in-theory        67260
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-490 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67260.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G))), M:tm-490, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67261
in-theory        67261
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-480 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-67261.        ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-480, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67262
in-theory        67262
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((((D and B) or B) -> C) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67262.        (((A and (B -> C)) or (B -> C)) -> ((((D and B) or B) -> C) or E)), M:tm-470, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67263
in-theory        67263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-469 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67263.        ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-469, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67264
in-theory        67264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67264.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (E or F))), M:tm-456, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67265
in-theory        67265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-453 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67265.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-453, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67266
in-theory        67266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (E or F)) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-443 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-67266.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (E or F)) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)))), M:tm-443, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67267
in-theory        67267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-409 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-67267.        (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-409, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67268
in-theory        67268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-400 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67268.        (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-400, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67269
in-theory        67269
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-391 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-67269.        ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-391, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67270
in-theory        67270
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-382 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-67270.        ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-382, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67271
in-theory        67271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-373 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67271.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G))), M:tm-373, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67272
in-theory        67272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-364 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-67272.        (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-364, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67273
in-theory        67273
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> ((((E and B) or B) -> C) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-67273.        (((A and (B -> C)) or (B -> C)) -> (D -> ((((E and B) or B) -> C) and D))), M:tm-355, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67274
in-theory        67274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-354 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-67274.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-354, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67275
in-theory        67275
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-67275.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67276
in-theory        67276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-338 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-67276.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E))), M:tm-338, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67277
in-theory        67277
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (((D and B) or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-328 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-67277.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (((D and B) or B) -> C)))), M:tm-328, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67278
in-theory        67278
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (F -> (E and F))) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-327 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-67278.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (F -> (E and F))) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)))), M:tm-327, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67279
in-theory        67279
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((E and F) -> F) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-326 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-67279.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((E and F) -> F) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)))), M:tm-326, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67280
in-theory        67280
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((E and F) -> E) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-325 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-67280.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((E and F) -> E) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)))), M:tm-325, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67281
in-theory        67281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))))
theorem-size     49
proof            (modus-ponens tm-324 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-67281.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)))), M:tm-324, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67282
in-theory        67282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (F -> E)) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-323 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-67282.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (F -> E)) and (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)))), M:tm-323, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67283
in-theory        67283
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-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-67283.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67284
in-theory        67284
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67284.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67285
in-theory        67285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-67285.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67286
in-theory        67286
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C))))
theorem-size     37
proof            (modus-ponens tm-316 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
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-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-67286.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C)))), M:tm-316, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67287
in-theory        67287
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67287.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67288
in-theory        67288
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> (not (((D and B) or B) -> C))) -> (not ((A and (B -> C)) or (B -> C)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-67288.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> (not (((D and B) or B) -> C))) -> (not ((A and (B -> C)) or (B -> C))))), M:tm-313, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67289
in-theory        67289
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((((D and B) or B) -> C) -> E) -> ((((A and (B -> C)) or (B -> C)) or (((D and B) or B) -> C)) -> E)))
theorem-size     47
proof            (modus-ponens tm-312 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-67289.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((((D and B) or B) -> C) -> E) -> ((((A and (B -> C)) or (B -> C)) or (((D and B) or B) -> C)) -> E))), M:tm-312, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67290
in-theory        67290
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E or (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-311 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-67290.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E or (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)))), M:tm-311, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67291
in-theory        67291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-67291.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) or E)), M:tm-310, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67292
in-theory        67292
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-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-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-67292.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and E))), M:tm-309, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67293
in-theory        67293
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> ((D and B) or B)) -> (((A and (B -> C)) or (B -> C)) -> C)))
theorem-size     45
proof            (modus-ponens tm-306 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (or (and Dm Bm) Bm)) (C Cm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-67293.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and ((((A and (B -> C)) or (B -> C)) -> ((D and B) or B)) -> (((A and (B -> C)) or (B -> C)) -> C))), M:tm-306, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (or (and Dm Bm) Bm)) (C Cm))
================================================================
tm-name          tm-67294
in-theory        67294
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-305 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-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-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-67294.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (E -> (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)))), M:tm-305, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67295
in-theory        67295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-303 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67295.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-303, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67296
in-theory        67296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-270 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-67296.        ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-270, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67297
in-theory        67297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-239 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67297.        ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-239, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67298
in-theory        67298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G)))
theorem-size     35
proof            (modus-ponens tm-210 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-67298.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G))), M:tm-210, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67299
in-theory        67299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-183 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-67299.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-183, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67300
in-theory        67300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-157 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-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-67300.        ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-157, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67301
in-theory        67301
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-147 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-67301.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-147, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67302
in-theory        67302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-134 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67302.        ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-134, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67303
in-theory        67303
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-125 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-67303.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-125, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67304
in-theory        67304
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((((E and B) or B) -> C) -> (((E and B) or B) -> D)))
theorem-size     29
proof            (modus-ponens tm-114 tm-792 ((A (or (and Am (-> Bm (-> C D))) (-> Bm (-> C D)))) (B (or (and Dm Bm) Bm)) (Cm (-> C D))))
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-14.           (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-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-67304.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((((E and B) or B) -> C) -> (((E and B) or B) -> D))), M:tm-114, m:tm-792, u:((A (or (and Am (-> Bm (-> C D))) (-> Bm (-> C D)))) (B (or (and Dm Bm) Bm)) (Cm (-> C D)))
================================================================
tm-name          tm-67305
in-theory        67305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-113 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67305.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G))), M:tm-113, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67306
in-theory        67306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     37
proof            (modus-ponens tm-105 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-67306.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-105, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67307
in-theory        67307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-95 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-67307.        (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E))), M:tm-95, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67308
in-theory        67308
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> (((E and B) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-84 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67308.        (((A and (B -> C)) or (B -> C)) -> (D -> (((E and B) or B) -> C))), M:tm-84, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67309
in-theory        67309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-83 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67309.        ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-83, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67310
in-theory        67310
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> (((E and C) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-76 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67310.        (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> (((E and C) or C) -> D))), M:tm-76, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67311
in-theory        67311
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C))
theorem-size     29
proof            (modus-ponens tm-73 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-8 tm-10 tm-4)
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-4.            ((A and B) -> B), axiom
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-67311.        (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C)), M:tm-73, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67312
in-theory        67312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-69 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67312.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E))), M:tm-69, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67313
in-theory        67313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-54 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-67313.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-54, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67314
in-theory        67314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C and (A -> B)) or (A -> B))) -> (((D and A) or A) -> B))
theorem-size     21
proof            (modus-ponens tm-50 tm-792 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-8 tm-7 tm-4)
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-4.            ((A and B) -> B), axiom
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-67314.        (((A -> B) or ((C and (A -> B)) or (A -> B))) -> (((D and A) or A) -> B)), M:tm-50, m:tm-792, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67315
in-theory        67315
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C))
theorem-size     23
proof            (modus-ponens tm-49 tm-792 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-8 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-67315.        (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C)), M:tm-49, m:tm-792, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67316
in-theory        67316
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> (((E and C) or C) -> D))
theorem-size     29
proof            (modus-ponens tm-47 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-8 tm-4)
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-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-67316.        (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> (((E and C) or C) -> D)), M:tm-47, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67317
in-theory        67317
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (((E and B) or B) -> C))
theorem-size     29
proof            (modus-ponens tm-46 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67317.        (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (((E and B) or B) -> C)), M:tm-46, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67318
in-theory        67318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-42 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-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-67318.        ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E))), M:tm-42, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67319
in-theory        67319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-32 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-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-67319.        ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E))), M:tm-32, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67320
in-theory        67320
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (((D and B) or B) -> C)))
theorem-size     27
proof            (modus-ponens tm-24 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
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-4.            ((A and B) -> B), axiom
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-67320.        (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (((D and B) or B) -> C))), M:tm-24, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67321
in-theory        67321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-23 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67321.        ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E))), M:tm-23, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67322
in-theory        67322
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-22 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-67322.        (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E))), M:tm-22, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67323
in-theory        67323
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-21 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67323.        (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E))), M:tm-21, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67324
in-theory        67324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-20 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-67324.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-20, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67325
in-theory        67325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-19 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
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-19.           (A -> ((B -> (C -> B)) and 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-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-67325.        ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> (((F and D) or D) -> E))), M:tm-19, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67326
in-theory        67326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (not (((D and B) or B) -> C))) -> (not ((A and (B -> C)) or (B -> C))))
theorem-size     29
proof            (modus-ponens tm-9 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67326.        ((((A and (B -> C)) or (B -> C)) -> (not (((D and B) or B) -> C))) -> (not ((A and (B -> C)) or (B -> C)))), M:tm-9, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67327
in-theory        67327
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> ((((E and (B -> C)) or (B -> C)) or (((A and B) or B) -> C)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-8 tm-4)
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-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-67327.        (((((A and B) or B) -> C) -> D) -> ((((E and (B -> C)) or (B -> C)) or (((A and B) or B) -> C)) -> D)), M:tm-8, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-67328
in-theory        67328
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C -> D)) or (C -> D)) -> (((E and C) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-7 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67328.        (A or (((B and (C -> D)) or (C -> D)) -> (((E and C) or C) -> D))), M:tm-7, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67329
in-theory        67329
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67329.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) or E), M:tm-6, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67330
in-theory        67330
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) or (C -> D)) -> (((E and C) or C) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-67330.        (A -> ((((B and (C -> D)) or (C -> D)) -> (((E and C) or C) -> D)) and A)), M:tm-5, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67331
in-theory        67331
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((D and B) or B)) -> (((A and (B -> C)) or (B -> C)) -> C))
theorem-size     27
proof            (modus-ponens tm-2 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (or (and Dm Bm) Bm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67331.        ((((A and (B -> C)) or (B -> C)) -> ((D and B) or B)) -> (((A and (B -> C)) or (B -> C)) -> C)), M:tm-2, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (or (and Dm Bm) Bm)) (C Cm))
================================================================
tm-name          tm-67332
in-theory        67332
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C -> D)) or (C -> D)) -> (((E and C) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-1 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       99
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-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-67332.        (A -> (((B and (C -> D)) or (C -> D)) -> (((E and C) or C) -> D))), M:tm-1, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-67333
in-theory        67333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-757 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67333.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-757, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67334
in-theory        67334
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((((((A -> B) and C) or (A -> B)) and E) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B)))
theorem-size     47
proof            (modus-ponens tm-747 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-67334.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((((((A -> B) and C) or (A -> B)) and E) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B))), M:tm-747, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67335
in-theory        67335
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)) -> (((H and E) or E) -> F)))
theorem-size     43
proof            (modus-ponens tm-708 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67335.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F))), M:tm-708, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67336
in-theory        67336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-665 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-67336.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-665, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67337
in-theory        67337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D or (((E and A) or A) -> B)))
theorem-size     19
proof            (modus-ponens tm-623 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67337.        ((((A -> B) and C) or (A -> B)) -> (D or (((E and A) or A) -> B))), M:tm-623, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67338
in-theory        67338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-622 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67338.        ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-622, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67339
in-theory        67339
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67339.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (F or E))), M:tm-609, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67340
in-theory        67340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-605 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67340.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-605, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67341
in-theory        67341
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (F or E)) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-595 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-67341.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (F or E)) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)))), M:tm-595, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67342
in-theory        67342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-550 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67342.        (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-550, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67343
in-theory        67343
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-540 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67343.        ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-540, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67344
in-theory        67344
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-530 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67344.        ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-530, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67345
in-theory        67345
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-520 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67345.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-520, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67346
in-theory        67346
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-510 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) 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-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-67346.        ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-510, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67347
in-theory        67347
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-500 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-67347.        ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-500, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67348
in-theory        67348
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-490 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67348.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F))), M:tm-490, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67349
in-theory        67349
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-480 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67349.        ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-480, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67350
in-theory        67350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((((D and A) or A) -> B) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67350.        ((((A -> B) and C) or (A -> B)) -> ((((D and A) or A) -> B) or E)), M:tm-470, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67351
in-theory        67351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-469 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67351.        ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-469, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67352
in-theory        67352
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67352.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (E or F))), M:tm-456, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67353
in-theory        67353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-453 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67353.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-453, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67354
in-theory        67354
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (E or F)) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-443 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-67354.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (E or F)) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)))), M:tm-443, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67355
in-theory        67355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-409 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67355.        (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-409, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67356
in-theory        67356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-400 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67356.        (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-400, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67357
in-theory        67357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-391 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) 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-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-67357.        ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-391, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67358
in-theory        67358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-382 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-67358.        ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-382, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67359
in-theory        67359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-373 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67359.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F))), M:tm-373, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67360
in-theory        67360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-364 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67360.        (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-364, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67361
in-theory        67361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> ((((E and A) or A) -> B) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-67361.        ((((A -> B) and C) or (A -> B)) -> (D -> ((((E and A) or A) -> B) and D))), M:tm-355, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67362
in-theory        67362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-354 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-67362.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-354, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67363
in-theory        67363
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-67363.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67364
in-theory        67364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D)))
theorem-size     27
proof            (modus-ponens tm-338 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-67364.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D))), M:tm-338, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67365
in-theory        67365
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (((D and A) or A) -> B))))
theorem-size     45
proof            (modus-ponens tm-328 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-328.          ((A -> 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-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-67365.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (((D and A) or A) -> B)))), M:tm-328, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67366
in-theory        67366
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (F -> (E and F))) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))))
theorem-size     43
proof            (modus-ponens tm-327 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-67366.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (F -> (E and F))) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)))), M:tm-327, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67367
in-theory        67367
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((E and F) -> F) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-326 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) 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-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-67367.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((E and F) -> F) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)))), M:tm-326, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67368
in-theory        67368
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((E and F) -> E) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-325 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-67368.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((E and F) -> E) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)))), M:tm-325, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67369
in-theory        67369
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))))
theorem-size     49
proof            (modus-ponens tm-324 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-67369.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)))), M:tm-324, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67370
in-theory        67370
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (F -> E)) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-323 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-67370.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (F -> E)) and ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)))), M:tm-323, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67371
in-theory        67371
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) 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-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-67371.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E and F) -> F)), M:tm-322, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67372
in-theory        67372
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67372.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E and F) -> E)), M:tm-320, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67373
in-theory        67373
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-67373.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67374
in-theory        67374
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) 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-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-67374.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B)))), M:tm-316, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67375
in-theory        67375
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67375.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (F -> E))), M:tm-315, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67376
in-theory        67376
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> (not (((D and A) or A) -> B))) -> (not (((A -> B) and C) or (A -> B)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-67376.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> (not (((D and A) or A) -> B))) -> (not (((A -> B) and C) or (A -> B))))), M:tm-313, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67377
in-theory        67377
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((((D and A) or A) -> B) -> E) -> (((((A -> B) and C) or (A -> B)) or (((D and A) or A) -> B)) -> E)))
theorem-size     47
proof            (modus-ponens tm-312 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-67377.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((((D and A) or A) -> B) -> E) -> (((((A -> B) and C) or (A -> B)) or (((D and A) or A) -> B)) -> E))), M:tm-312, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67378
in-theory        67378
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E or ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-311 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or 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-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-67378.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E or ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)))), M:tm-311, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67379
in-theory        67379
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or 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-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-67379.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) or E)), M:tm-310, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67380
in-theory        67380
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-67380.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and E))), M:tm-309, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67381
in-theory        67381
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> ((D and A) or A)) -> ((((A -> B) and C) or (A -> B)) -> B)))
theorem-size     45
proof            (modus-ponens tm-306 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (or (and Dm Am) Am)) (C Bm)))
axioms-used      (tm-2 tm-5 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-67381.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> ((D and A) or A)) -> ((((A -> B) and C) or (A -> B)) -> B))), M:tm-306, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (or (and Dm Am) Am)) (C Bm))
================================================================
tm-name          tm-67382
in-theory        67382
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-305 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-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-67382.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (E -> ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)))), M:tm-305, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67383
in-theory        67383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-303 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67383.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-303, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67384
in-theory        67384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-270 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) 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-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-67384.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-270, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67385
in-theory        67385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-239 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67385.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-239, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67386
in-theory        67386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F)))
theorem-size     35
proof            (modus-ponens tm-210 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-67386.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F))), M:tm-210, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67387
in-theory        67387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-183 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-67387.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-183, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67388
in-theory        67388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-157 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) 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-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-67388.        ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-157, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67389
in-theory        67389
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     33
proof            (modus-ponens tm-147 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) 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-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-67389.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-147, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67390
in-theory        67390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-134 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67390.        ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-134, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67391
in-theory        67391
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     33
proof            (modus-ponens tm-125 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-67391.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-125, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67392
in-theory        67392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((((E and A) or A) -> B) -> (((E and A) or A) -> C)))
theorem-size     29
proof            (modus-ponens tm-114 tm-793 ((A (or (and (-> Am (-> C D)) Cm) (-> Am (-> C D)))) (B (or (and Dm Am) Am)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-67392.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((((E and A) or A) -> B) -> (((E and A) or A) -> C))), M:tm-114, m:tm-793, u:((A (or (and (-> Am (-> C D)) Cm) (-> Am (-> C D)))) (B (or (and Dm Am) Am)) (Bm (-> C D)))
================================================================
tm-name          tm-67393
in-theory        67393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-113 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67393.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F))), M:tm-113, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67394
in-theory        67394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     37
proof            (modus-ponens tm-105 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-67394.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-105, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67395
in-theory        67395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D)))
theorem-size     25
proof            (modus-ponens tm-95 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-67395.        (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D))), M:tm-95, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67396
in-theory        67396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> (((E and A) or A) -> B)))
theorem-size     19
proof            (modus-ponens tm-84 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67396.        ((((A -> B) and C) or (A -> B)) -> (D -> (((E and A) or A) -> B))), M:tm-84, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67397
in-theory        67397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-83 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67397.        ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-83, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67398
in-theory        67398
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> (((E and B) or B) -> C)))
theorem-size     23
proof            (modus-ponens tm-76 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67398.        (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> (((E and B) or B) -> C))), M:tm-76, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67399
in-theory        67399
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B))
theorem-size     29
proof            (modus-ponens tm-73 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-8 tm-10 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67399.        (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B)), M:tm-73, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67400
in-theory        67400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-69 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67400.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D))), M:tm-69, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67401
in-theory        67401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-54 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-67401.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-54, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67402
in-theory        67402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B))
theorem-size     21
proof            (modus-ponens tm-50 tm-793 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-8 tm-7 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67402.        (((A -> B) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B)), M:tm-50, m:tm-793, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67403
in-theory        67403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B))
theorem-size     23
proof            (modus-ponens tm-49 tm-793 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-8 tm-6 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67403.        ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B)), M:tm-49, m:tm-793, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67404
in-theory        67404
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> (((E and B) or B) -> C))
theorem-size     29
proof            (modus-ponens tm-47 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) 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-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-67404.        (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> (((E and B) or B) -> C)), M:tm-47, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67405
in-theory        67405
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (((E and A) or A) -> B))
theorem-size     29
proof            (modus-ponens tm-46 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67405.        ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (((E and A) or A) -> B)), M:tm-46, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67406
in-theory        67406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-42 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67406.        ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D))), M:tm-42, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67407
in-theory        67407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-32 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67407.        ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D))), M:tm-32, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67408
in-theory        67408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (((D and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-24 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm 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-4.            ((A and B) -> B), axiom
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-67408.        ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (((D and A) or A) -> B))), M:tm-24, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67409
in-theory        67409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D)))
theorem-size     25
proof            (modus-ponens tm-23 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67409.        ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D))), M:tm-23, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67410
in-theory        67410
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-22 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) 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-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-67410.        (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D))), M:tm-22, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67411
in-theory        67411
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-21 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67411.        (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D))), M:tm-21, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67412
in-theory        67412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-20 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-67412.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-20, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67413
in-theory        67413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-19 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67413.        ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> (((F and C) or C) -> D))), M:tm-19, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67414
in-theory        67414
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (not (((D and A) or A) -> B))) -> (not (((A -> B) and C) or (A -> B))))
theorem-size     29
proof            (modus-ponens tm-9 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-9 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67414.        (((((A -> B) and C) or (A -> B)) -> (not (((D and A) or A) -> B))) -> (not (((A -> B) and C) or (A -> B)))), M:tm-9, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67415
in-theory        67415
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> (((((B -> C) and E) or (B -> C)) or (((A and B) or B) -> C)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-8 tm-3 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-4.            ((A and B) -> B), axiom
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-67415.        (((((A and B) or B) -> C) -> D) -> (((((B -> C) and E) or (B -> C)) or (((A and B) or B) -> C)) -> D)), M:tm-8, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-67416
in-theory        67416
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) and D) or (B -> C)) -> (((E and B) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-7 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67416.        (A or ((((B -> C) and D) or (B -> C)) -> (((E and B) or B) -> C))), M:tm-7, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67417
in-theory        67417
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-6 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67417.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) or E), M:tm-6, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67418
in-theory        67418
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) or (B -> C)) -> (((E and B) or B) -> C)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm 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-4.            ((A and B) -> B), axiom
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-67418.        (A -> (((((B -> C) and D) or (B -> C)) -> (((E and B) or B) -> C)) and A)), M:tm-5, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67419
in-theory        67419
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((D and A) or A)) -> ((((A -> B) and C) or (A -> B)) -> B))
theorem-size     27
proof            (modus-ponens tm-2 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (or (and Dm Am) Am)) (C Bm)))
axioms-used      (tm-2 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67419.        (((((A -> B) and C) or (A -> B)) -> ((D and A) or A)) -> ((((A -> B) and C) or (A -> B)) -> B)), M:tm-2, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (or (and Dm Am) Am)) (C Bm))
================================================================
tm-name          tm-67420
in-theory        67420
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and D) or (B -> C)) -> (((E and B) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-1 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-1 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67420.        (A -> ((((B -> C) and D) or (B -> C)) -> (((E and B) or B) -> C))), M:tm-1, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-67421
in-theory        67421
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (B -> C)))
theorem-size     15
proof            (modus-ponens tm-794 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-67421.        (((A and (B -> C)) or (B -> C)) -> (B -> (B -> C))), M:tm-794, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-67422
in-theory        67422
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> ((B -> C) and B)))
theorem-size     17
proof            (modus-ponens tm-794 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-4 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-4.            ((A and B) -> B), axiom
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-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-67422.        (((A and (B -> C)) or (B -> C)) -> (B -> ((B -> C) and B))), M:tm-794, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-67423
in-theory        67423
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) or ((B -> C) -> B)) -> ((B -> C) -> (((B -> C) or B) -> C)))
theorem-size     25
proof            (modus-ponens tm-794 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-4 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-4.            ((A and B) -> B), axiom
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-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-67423.        (((A and ((B -> C) -> B)) or ((B -> C) -> B)) -> ((B -> C) -> (((B -> C) or B) -> C))), M:tm-794, 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-67424
in-theory        67424
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (D -> B)))
theorem-size     15
proof            (modus-ponens tm-794 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 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-4.            ((A and B) -> B), axiom
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-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-67424.        (((A and (B -> C)) or (B -> C)) -> (B -> (D -> B))), M:tm-794, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-67425
in-theory        67425
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> E)) or ((B -> (C -> D)) -> E)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     31
proof            (modus-ponens tm-794 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-4 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-4.            ((A and B) -> B), axiom
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-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-67425.        (((A and ((B -> (C -> D)) -> E)) or ((B -> (C -> D)) -> E)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-794, 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-67426
in-theory        67426
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) -> D)) or ((B and C) -> D)) -> ((B and C) -> B))
theorem-size     19
proof            (modus-ponens tm-794 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-4 tm-7 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-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-67426.        (((A and ((B and C) -> D)) or ((B and C) -> D)) -> ((B and C) -> B)), M:tm-794, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-67427
in-theory        67427
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) -> D)) or ((B and C) -> D)) -> ((B and C) -> C))
theorem-size     19
proof            (modus-ponens tm-794 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-4 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-4.            ((A and B) -> B), axiom
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-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-67427.        (((A and ((B and C) -> D)) or ((B and C) -> D)) -> ((B and C) -> C)), M:tm-794, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-67428
in-theory        67428
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (D -> (B and D))))
theorem-size     17
proof            (modus-ponens tm-794 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-4 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-4.            ((A and B) -> B), axiom
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-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-67428.        (((A and (B -> C)) or (B -> C)) -> (B -> (D -> (B and D)))), M:tm-794, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-67429
in-theory        67429
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (B or D)))
theorem-size     15
proof            (modus-ponens tm-794 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67429.        (((A and (B -> C)) or (B -> C)) -> (B -> (B or D))), M:tm-794, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-67430
in-theory        67430
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (D or B)))
theorem-size     15
proof            (modus-ponens tm-794 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 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-4.            ((A and B) -> B), axiom
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-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-67430.        (((A and (B -> C)) or (B -> C)) -> (B -> (D or B))), M:tm-794, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-67431
in-theory        67431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-757 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-67431.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-757, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67432
in-theory        67432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) 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 and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     71
proof            (modus-ponens tm-747 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-67432.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) 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 and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-747, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67433
in-theory        67433
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 (E -> F)) or (E -> F)) -> (E -> G))))
theorem-size     53
proof            (modus-ponens tm-708 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
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-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-67433.        (((((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 (E -> F)) or (E -> F)) -> (E -> G)))), M:tm-708, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67434
in-theory        67434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-665 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67434.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-665, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67435
in-theory        67435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((E and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-623 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-67435.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((E and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-623, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67436
in-theory        67436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-622 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67436.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-622, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67437
in-theory        67437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-609 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67437.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (F or E))), M:tm-609, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67438
in-theory        67438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-605 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67438.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-605, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67439
in-theory        67439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-67439.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-595, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67440
in-theory        67440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-550 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-67440.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-550, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67441
in-theory        67441
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-540 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-67441.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-540, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67442
in-theory        67442
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-530 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-67442.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-530, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67443
in-theory        67443
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-520 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67443.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-520, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67444
in-theory        67444
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-510 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-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-67444.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-510, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67445
in-theory        67445
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-500 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-67445.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-500, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67446
in-theory        67446
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-490 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67446.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G)))), M:tm-490, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67447
in-theory        67447
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-480 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-67447.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-480, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67448
in-theory        67448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and (A -> B)) or (A -> B)) -> (A -> C)) or E))
theorem-size     29
proof            (modus-ponens tm-470 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-67448.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and (A -> B)) or (A -> B)) -> (A -> C)) or E)), M:tm-470, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67449
in-theory        67449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-469 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67449.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-469, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67450
in-theory        67450
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-456 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67450.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (E or F))), M:tm-456, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67451
in-theory        67451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-453 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67451.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-453, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67452
in-theory        67452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-67452.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-443, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67453
in-theory        67453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-409 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-67453.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-409, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67454
in-theory        67454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-400 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67454.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-400, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67455
in-theory        67455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-391 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-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-67455.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-391, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67456
in-theory        67456
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-382 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-67456.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-382, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67457
in-theory        67457
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-373 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67457.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G)))), M:tm-373, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67458
in-theory        67458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-364 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-67458.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-364, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67459
in-theory        67459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((E and (A -> B)) or (A -> B)) -> (A -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67459.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((E and (A -> B)) or (A -> B)) -> (A -> C)) and D))), M:tm-355, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67460
in-theory        67460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-354 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67460.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-354, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67461
in-theory        67461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-341 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-67461.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67462
in-theory        67462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-338 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-67462.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E)))), M:tm-338, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67463
in-theory        67463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-328 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67463.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-328, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67464
in-theory        67464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-67464.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-327, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67465
in-theory        67465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-67465.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-326, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67466
in-theory        67466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-67466.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-325, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67467
in-theory        67467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-67467.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-324, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67468
in-theory        67468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-67468.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-323, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67469
in-theory        67469
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-322 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-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-67469.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E and F) -> F)), M:tm-322, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67470
in-theory        67470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-320 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67470.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E and F) -> E)), M:tm-320, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67471
in-theory        67471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-318 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-67471.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67472
in-theory        67472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> 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     55
proof            (modus-ponens tm-316 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-67472.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> 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-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67473
in-theory        67473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-315 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67473.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (F -> E))), M:tm-315, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67474
in-theory        67474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and (A -> B)) or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67474.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and (A -> B)) or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67475
in-theory        67475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((((D and (A -> B)) or (A -> B)) -> (A -> C)) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((D and (A -> B)) or (A -> B)) -> (A -> C))) -> E)))
theorem-size     73
proof            (modus-ponens tm-312 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67475.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((((D and (A -> B)) or (A -> B)) -> (A -> C)) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((D and (A -> B)) or (A -> B)) -> (A -> C))) -> E))), M:tm-312, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67476
in-theory        67476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-67476.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-311, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67477
in-theory        67477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((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))) or E))
theorem-size     57
proof            (modus-ponens tm-310 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-67477.        ((((A -> (B -> C)) or ((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))) or E)), M:tm-310, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67478
in-theory        67478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and E)))
theorem-size     59
proof            (modus-ponens tm-309 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am 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-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-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-67478.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and E))), M:tm-309, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67479
in-theory        67479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((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 -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C))))
theorem-size     69
proof            (modus-ponens tm-306 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and Dm (-> Am Bm)) (-> Am Bm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67479.        ((((A -> (B -> C)) or ((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 -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C)))), M:tm-306, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and Dm (-> Am Bm)) (-> Am Bm))) (C (-> Am Cm)))
================================================================
tm-name          tm-67480
in-theory        67480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-67480.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-305, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67481
in-theory        67481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-303 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-67481.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-303, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67482
in-theory        67482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-270 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-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-67482.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-270, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67483
in-theory        67483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-239 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67483.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-239, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67484
in-theory        67484
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 (E -> F)) or (E -> F)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-210 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67484.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G)))), M:tm-210, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67485
in-theory        67485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-183 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67485.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-183, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67486
in-theory        67486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-157 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-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-67486.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-157, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67487
in-theory        67487
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 (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-147 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-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-67487.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-147, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67488
in-theory        67488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-134 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67488.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-134, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67489
in-theory        67489
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 (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-125 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-67489.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-125, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67490
in-theory        67490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and (A -> B)) or (A -> B)) -> A) -> (((D and (A -> B)) or (A -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-114 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and Dm (-> Am Bm)) (-> Am Bm))) (C Am) (D Cm)))
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-14.           (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-4.            ((A and B) -> B), axiom
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-67490.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and (A -> B)) or (A -> B)) -> A) -> (((D and (A -> B)) or (A -> B)) -> C))), M:tm-114, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and Dm (-> Am Bm)) (-> Am Bm))) (C Am) (D Cm))
================================================================
tm-name          tm-67491
in-theory        67491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-113 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67491.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G)))), M:tm-113, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67492
in-theory        67492
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 (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     47
proof            (modus-ponens tm-105 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67492.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-105, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67493
in-theory        67493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-95 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-67493.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E)))), M:tm-95, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67494
in-theory        67494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-84 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-67494.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-84, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67495
in-theory        67495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-83 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67495.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-83, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67496
in-theory        67496
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and (B -> C)) or (B -> C)) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-76 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67496.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and (B -> C)) or (B -> C)) -> (B -> D)))), M:tm-76, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67497
in-theory        67497
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 (A -> B)) or (A -> B)) -> (A -> C)))
theorem-size     43
proof            (modus-ponens tm-73 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67497.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))), M:tm-73, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67498
in-theory        67498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E))))
theorem-size     39
proof            (modus-ponens tm-69 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67498.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E)))), M:tm-69, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67499
in-theory        67499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-54 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-67499.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-54, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67500
in-theory        67500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))
theorem-size     35
proof            (modus-ponens tm-50 tm-794 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67500.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))), M:tm-50, m:tm-794, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67501
in-theory        67501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-49 tm-794 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67501.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))), M:tm-49, m:tm-794, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67502
in-theory        67502
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 (B -> C)) or (B -> C)) -> (B -> D)))
theorem-size     43
proof            (modus-ponens tm-47 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
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-67502.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((E and (B -> C)) or (B -> C)) -> (B -> D))), M:tm-47, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67503
in-theory        67503
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 (A -> B)) or (A -> B)) -> (A -> C)))
theorem-size     43
proof            (modus-ponens tm-46 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67503.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((E and (A -> B)) or (A -> B)) -> (A -> C))), M:tm-46, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67504
in-theory        67504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-42 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67504.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E)))), M:tm-42, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67505
in-theory        67505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-32 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67505.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E)))), M:tm-32, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67506
in-theory        67506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-24 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67506.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-24, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67507
in-theory        67507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-23 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-67507.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E)))), M:tm-23, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67508
in-theory        67508
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-22 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> 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-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-67508.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E)))), M:tm-22, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67509
in-theory        67509
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-21 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67509.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E)))), M:tm-21, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67510
in-theory        67510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-20 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67510.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-20, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67511
in-theory        67511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-19 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67511.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and (C -> D)) or (C -> D)) -> (C -> E)))), M:tm-19, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67512
in-theory        67512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and (A -> B)) or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-9 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67512.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and (A -> B)) or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67513
in-theory        67513
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) or (B -> C)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) or (((A and (B -> C)) or (B -> C)) -> (B -> D))) -> E))
theorem-size     45
proof            (modus-ponens tm-8 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67513.        (((((A and (B -> C)) or (B -> C)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) or (((A and (B -> C)) or (B -> C)) -> (B -> D))) -> E)), M:tm-8, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67514
in-theory        67514
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and (B -> C)) or (B -> C)) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-7 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-7 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67514.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and (B -> C)) or (B -> C)) -> (B -> D)))), M:tm-7, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67515
in-theory        67515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) or E)
theorem-size     29
proof            (modus-ponens tm-6 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-6 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67515.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) or E), M:tm-6, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67516
in-theory        67516
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and (B -> C)) or (B -> C)) -> (B -> D))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-67516.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and (B -> C)) or (B -> C)) -> (B -> D))) and A)), M:tm-5, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67517
in-theory        67517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and (A -> B)) or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C)))
theorem-size     41
proof            (modus-ponens tm-2 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and Dm (-> Am Bm)) (-> Am Bm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67517.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and (A -> B)) or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C))), M:tm-2, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and Dm (-> Am Bm)) (-> Am Bm))) (C (-> Am Cm)))
================================================================
tm-name          tm-67518
in-theory        67518
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and (B -> C)) or (B -> C)) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-1 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-1 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-67518.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and (B -> C)) or (B -> C)) -> (B -> D)))), M:tm-1, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-67519
in-theory        67519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-67519.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-757, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67520
in-theory        67520
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (((C and B) or B) -> A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-67520.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (((C and B) or B) -> A))), M:tm-747, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67521
in-theory        67521
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 F) or F) -> E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67521.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (((G and F) or F) -> E))), M:tm-708, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67522
in-theory        67522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67522.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-665, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67523
in-theory        67523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (((D and B) or B) -> A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67523.        ((A or (B -> A)) -> (C or (((D and B) or B) -> A))), M:tm-623, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67524
in-theory        67524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67524.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-622, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67525
in-theory        67525
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-67525.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (E or D))), M:tm-609, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67526
in-theory        67526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67526.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-605, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67527
in-theory        67527
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (E or D)) and ((A or (B -> A)) -> (((C and B) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 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-1.            (A -> (B -> A)), 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-67527.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (E or D)) and ((A or (B -> A)) -> (((C and B) or B) -> A)))), M:tm-595, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67528
in-theory        67528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67528.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-550, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67529
in-theory        67529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67529.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-540, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67530
in-theory        67530
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67530.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-530, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67531
in-theory        67531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67531.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-520, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67532
in-theory        67532
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-67532.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-510, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67533
in-theory        67533
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67533.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-500, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67534
in-theory        67534
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and F) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67534.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and F) or F) -> E))), M:tm-490, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67535
in-theory        67535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67535.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-480, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67536
in-theory        67536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C and B) or B) -> A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67536.        ((A or (B -> A)) -> ((((C and B) or B) -> A) or D)), M:tm-470, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67537
in-theory        67537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67537.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-469, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67538
in-theory        67538
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-67538.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (D or E))), M:tm-456, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67539
in-theory        67539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67539.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-453, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67540
in-theory        67540
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (D or E)) and ((A or (B -> A)) -> (((C and B) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 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-1.            (A -> (B -> A)), 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-67540.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (D or E)) and ((A or (B -> A)) -> (((C and B) or B) -> A)))), M:tm-443, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67541
in-theory        67541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67541.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-409, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67542
in-theory        67542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67542.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-400, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67543
in-theory        67543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-67543.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-391, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67544
in-theory        67544
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67544.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-382, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67545
in-theory        67545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((G and F) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67545.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((G and F) or F) -> E))), M:tm-373, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67546
in-theory        67546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67546.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-364, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67547
in-theory        67547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((((D and B) or B) -> A) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67547.        ((A or (B -> A)) -> (C -> ((((D and B) or B) -> A) and C))), M:tm-355, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67548
in-theory        67548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67548.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-354, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67549
in-theory        67549
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-67549.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67550
in-theory        67550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((E and D) or D) -> C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-67550.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((E and D) or D) -> C))), M:tm-338, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67551
in-theory        67551
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((A or (B -> A)) -> ((A or (B -> A)) and (((C and B) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
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-328.          ((A -> 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-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-67551.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((A or (B -> A)) -> ((A or (B -> A)) and (((C and B) or B) -> A)))), M:tm-328, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67552
in-theory        67552
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (((C and B) or B) -> A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-67552.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (((C and B) or B) -> A)))), M:tm-327, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67553
in-theory        67553
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((D and E) -> E) and ((A or (B -> A)) -> (((C and B) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-67553.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((D and E) -> E) and ((A or (B -> A)) -> (((C and B) or B) -> A)))), M:tm-326, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67554
in-theory        67554
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((D and E) -> D) and ((A or (B -> A)) -> (((C and B) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 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-1.            (A -> (B -> A)), 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-67554.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((D and E) -> D) and ((A or (B -> A)) -> (((C and B) or B) -> A)))), M:tm-325, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67555
in-theory        67555
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (((C and B) or B) -> A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-67555.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (((C and B) or B) -> A)))), M:tm-324, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67556
in-theory        67556
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (E -> D)) and ((A or (B -> A)) -> (((C and B) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
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-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-67556.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (E -> D)) and ((A or (B -> A)) -> (((C and B) or B) -> A)))), M:tm-323, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67557
in-theory        67557
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-67557.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D and E) -> E)), M:tm-322, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67558
in-theory        67558
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-67558.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D and E) -> D)), M:tm-320, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67559
in-theory        67559
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-67559.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67560
in-theory        67560
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     25
proof            (modus-ponens tm-316 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-67560.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67561
in-theory        67561
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-67561.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (E -> D))), M:tm-315, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67562
in-theory        67562
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((A or (B -> A)) -> (not (((C and B) or B) -> A))) -> (not (A or (B -> A)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-67562.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((A or (B -> A)) -> (not (((C and B) or B) -> A))) -> (not (A or (B -> A))))), M:tm-313, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67563
in-theory        67563
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((((C and B) or B) -> A) -> D) -> (((A or (B -> A)) or (((C and B) or B) -> A)) -> D)))
theorem-size     39
proof            (modus-ponens tm-312 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) 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-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-67563.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((((C and B) or B) -> A) -> D) -> (((A or (B -> A)) or (((C and B) or B) -> A)) -> D))), M:tm-312, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67564
in-theory        67564
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D or ((A or (B -> A)) -> (((C and B) or B) -> A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-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-67564.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D or ((A or (B -> A)) -> (((C and B) or B) -> A)))), M:tm-311, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67565
in-theory        67565
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((A or (B -> A)) -> (((C and B) or B) -> A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-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-67565.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((A or (B -> A)) -> (((C and B) or B) -> A)) or D)), M:tm-310, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67566
in-theory        67566
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (((A or (B -> A)) -> (((C and B) or B) -> A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
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-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-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-67566.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> (((A or (B -> A)) -> (((C and B) or B) -> A)) and D))), M:tm-309, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67567
in-theory        67567
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((A or (B -> A)) -> ((C and B) or B)) -> ((A or (B -> A)) -> A)))
theorem-size     33
proof            (modus-ponens tm-306 tm-795 ((A (or Am (-> Bm Am))) (B (or (and Cm Bm) Bm)) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-67567.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((A or (B -> A)) -> ((C and B) or B)) -> ((A or (B -> A)) -> A))), M:tm-306, m:tm-795, u:((A (or Am (-> Bm Am))) (B (or (and Cm Bm) Bm)) (C Am))
================================================================
tm-name          tm-67568
in-theory        67568
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> ((A or (B -> A)) -> (((C and B) or B) -> A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
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-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-67568.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (D -> ((A or (B -> A)) -> (((C and B) or B) -> A)))), M:tm-305, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67569
in-theory        67569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-67569.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-303, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67570
in-theory        67570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-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-67570.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-270, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67571
in-theory        67571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67571.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-239, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67572
in-theory        67572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((G and F) or F) -> E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67572.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((G and F) or F) -> E))), M:tm-210, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67573
in-theory        67573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67573.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-183, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67574
in-theory        67574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-67574.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-157, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67575
in-theory        67575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-67575.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-147, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67576
in-theory        67576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67576.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-134, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67577
in-theory        67577
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67577.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-125, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67578
in-theory        67578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> ((((D and C) or C) -> A) -> (((D and C) or C) -> B)))
theorem-size     25
proof            (modus-ponens tm-114 tm-795 ((A (or (-> C D) (-> Bm (-> C D)))) (B (or (and Cm Bm) Bm)) (Am (-> C D))))
axioms-used      (tm-2 tm-1 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-14.           (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-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-67578.        (((A -> B) or (C -> (A -> B))) -> ((((D and C) or C) -> A) -> (((D and C) or C) -> B))), M:tm-114, m:tm-795, u:((A (or (-> C D) (-> Bm (-> C D)))) (B (or (and Cm Bm) Bm)) (Am (-> C D)))
================================================================
tm-name          tm-67579
in-theory        67579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and F) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67579.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and F) or F) -> E))), M:tm-113, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67580
in-theory        67580
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-67580.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-105, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67581
in-theory        67581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((E and D) or D) -> C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67581.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((E and D) or D) -> C))), M:tm-95, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67582
in-theory        67582
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D and B) or B) -> A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67582.        ((A or (B -> A)) -> (C -> (((D and B) or B) -> A))), M:tm-84, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67583
in-theory        67583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67583.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-83, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67584
in-theory        67584
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (((D and C) or C) -> B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67584.        (((not (not A)) -> A) and ((B or (C -> B)) -> (((D and C) or C) -> B))), M:tm-76, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67585
in-theory        67585
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((C and B) or B) -> A))
theorem-size     21
proof            (modus-ponens tm-73 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-8 tm-10 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67585.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((C and B) or B) -> A)), M:tm-73, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67586
in-theory        67586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((E and D) or D) -> C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67586.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((E and D) or D) -> C))), M:tm-69, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67587
in-theory        67587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67587.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-54, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67588
in-theory        67588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (((C and A) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-50 tm-795 ((A Am) (B (-> Bm Am)) (C (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67588.        (((A -> B) or (B or (A -> B))) -> (((C and A) or A) -> B)), M:tm-50, m:tm-795, u:((A Am) (B (-> Bm Am)) (C (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67589
in-theory        67589
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (((C and B) or B) -> A))
theorem-size     15
proof            (modus-ponens tm-49 tm-795 ((A Am) (B (-> Bm Am)) (C (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67589.        ((A or (A or (B -> A))) -> (((C and B) or B) -> A)), M:tm-49, m:tm-795, u:((A Am) (B (-> Bm Am)) (C (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67590
in-theory        67590
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (((D and C) or C) -> B))
theorem-size     21
proof            (modus-ponens tm-47 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
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-67590.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (((D and C) or C) -> B)), M:tm-47, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67591
in-theory        67591
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((D and B) or B) -> A))
theorem-size     21
proof            (modus-ponens tm-46 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-8 tm-3 tm-1 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-1.            (A -> (B -> A)), 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-67591.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((D and B) or B) -> A)), M:tm-46, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67592
in-theory        67592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (((E and D) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67592.        ((A -> (B or A)) and ((C or (D -> C)) -> (((E and D) or D) -> C))), M:tm-42, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67593
in-theory        67593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (((E and D) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67593.        ((A -> (A or B)) and ((C or (D -> C)) -> (((E and D) or D) -> C))), M:tm-32, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67594
in-theory        67594
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (((C and B) or B) -> A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
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-1.            (A -> (B -> A)), 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-67594.        ((A or (B -> A)) -> ((A or (B -> A)) and (((C and B) or B) -> A))), M:tm-24, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67595
in-theory        67595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((E and D) or D) -> C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67595.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((E and D) or D) -> C))), M:tm-23, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67596
in-theory        67596
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (((E and D) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
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-67596.        (((A and B) -> B) and ((C or (D -> C)) -> (((E and D) or D) -> C))), M:tm-22, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67597
in-theory        67597
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (((E and D) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67597.        (((A and B) -> A) and ((C or (D -> C)) -> (((E and D) or D) -> C))), M:tm-21, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67598
in-theory        67598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-67598.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-20, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67599
in-theory        67599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (((E and D) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67599.        ((A -> (B -> A)) and ((C or (D -> C)) -> (((E and D) or D) -> C))), M:tm-19, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67600
in-theory        67600
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (((C and B) or B) -> A))) -> (not (A or (B -> A))))
theorem-size     21
proof            (modus-ponens tm-9 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-9 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67600.        (((A or (B -> A)) -> (not (((C and B) or B) -> A))) -> (not (A or (B -> A)))), M:tm-9, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67601
in-theory        67601
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> (((C or (B -> C)) or (((A and B) or B) -> C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67601.        (((((A and B) or B) -> C) -> D) -> (((C or (B -> C)) or (((A and B) or B) -> C)) -> D)), M:tm-8, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-67602
in-theory        67602
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (((D and C) or C) -> B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-7 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67602.        (A or ((B or (C -> B)) -> (((D and C) or C) -> B))), M:tm-7, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67603
in-theory        67603
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-6 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67603.        (((A or (B -> A)) -> (((C and B) or B) -> A)) or D), M:tm-6, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67604
in-theory        67604
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (((D and C) or C) -> B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) 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-1.            (A -> (B -> A)), 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-67604.        (A -> (((B or (C -> B)) -> (((D and C) or C) -> B)) and A)), M:tm-5, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67605
in-theory        67605
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and B) or B)) -> ((A or (B -> A)) -> A))
theorem-size     19
proof            (modus-ponens tm-2 tm-795 ((A (or Am (-> Bm Am))) (B (or (and Cm Bm) Bm)) (C Am)))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-67605.        (((A or (B -> A)) -> ((C and B) or B)) -> ((A or (B -> A)) -> A)), M:tm-2, m:tm-795, u:((A (or Am (-> Bm Am))) (B (or (and Cm Bm) Bm)) (C Am))
================================================================
tm-name          tm-67606
in-theory        67606
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (((D and C) or C) -> B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67606.        (A -> ((B or (C -> B)) -> (((D and C) or C) -> B))), M:tm-1, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-67607
in-theory        67607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or 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-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-67607.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-757, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67608
in-theory        67608
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 and G) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or 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-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-67608.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-708, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67609
in-theory        67609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or 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-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-67609.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-665, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67610
in-theory        67610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-67610.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-622, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67611
in-theory        67611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-67611.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67612
in-theory        67612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-67612.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-605, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67613
in-theory        67613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-67613.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-595, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67614
in-theory        67614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-67614.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-550, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67615
in-theory        67615
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-67615.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-540, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67616
in-theory        67616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-67616.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-530, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67617
in-theory        67617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-67617.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-520, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67618
in-theory        67618
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm 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-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-67618.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-510, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67619
in-theory        67619
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-67619.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-500, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67620
in-theory        67620
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-67620.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-490, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67621
in-theory        67621
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-67621.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-480, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67622
in-theory        67622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-67622.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-469, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67623
in-theory        67623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-67623.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67624
in-theory        67624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67624.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-453, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67625
in-theory        67625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-67625.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-443, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67626
in-theory        67626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> B), axiom
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-67626.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-409, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67627
in-theory        67627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67627.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-400, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67628
in-theory        67628
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-67628.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-391, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67629
in-theory        67629
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-4.            ((A and B) -> B), axiom
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-67629.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-382, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67630
in-theory        67630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67630.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-373, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67631
in-theory        67631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-67631.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-364, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67632
in-theory        67632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67632.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-354, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67633
in-theory        67633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67633.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67634
in-theory        67634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67634.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-338, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67635
in-theory        67635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-67635.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-327, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67636
in-theory        67636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-67636.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-326, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67637
in-theory        67637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-67637.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-325, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67638
in-theory        67638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-67638.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-324, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67639
in-theory        67639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> B), axiom
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-67639.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-323, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67640
in-theory        67640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-67640.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67641
in-theory        67641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-67641.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67642
in-theory        67642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67642.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67643
in-theory        67643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-67643.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67644
in-theory        67644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F or ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-67644.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F or ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-311, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67645
in-theory        67645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-67645.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) or F)), M:tm-310, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67646
in-theory        67646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-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-4.            ((A and B) -> B), axiom
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-67646.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and F))), M:tm-309, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67647
in-theory        67647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-796 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67647.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-308, m:tm-796, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-67648
in-theory        67648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (A -> (B or A)))
theorem-size     23
proof            (modus-ponens tm-307 tm-796 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-4.            ((A and B) -> B), axiom
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-67648.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (A -> (B or A))), M:tm-307, m:tm-796, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-67649
in-theory        67649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) 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-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-4.            ((A and B) -> B), axiom
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-67649.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-305, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67650
in-theory        67650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67650.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-303, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67651
in-theory        67651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm 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-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-67651.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-270, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67652
in-theory        67652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67652.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-239, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67653
in-theory        67653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67653.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-210, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67654
in-theory        67654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67654.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-183, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67655
in-theory        67655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-67655.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-157, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67656
in-theory        67656
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-67656.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-147, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67657
in-theory        67657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-67657.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-134, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67658
in-theory        67658
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67658.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-125, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67659
in-theory        67659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67659.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-113, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67660
in-theory        67660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67660.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-105, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67661
in-theory        67661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67661.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-95, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67662
in-theory        67662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-67662.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-83, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67663
in-theory        67663
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67663.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-76, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67664
in-theory        67664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67664.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-69, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67665
in-theory        67665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or 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-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-67665.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-54, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67666
in-theory        67666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-67666.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-42, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67667
in-theory        67667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67667.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-32, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67668
in-theory        67668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67668.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-23, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67669
in-theory        67669
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm 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-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-67669.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-22, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67670
in-theory        67670
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67670.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-21, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67671
in-theory        67671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67671.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-20, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67672
in-theory        67672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-67672.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-19, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67673
in-theory        67673
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-7 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67673.        (A or ((B -> (C or B)) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-7, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67674
in-theory        67674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67674.        (((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))) or F), M:tm-6, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67675
in-theory        67675
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> E) -> (((F and D) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67675.        (A -> (((B -> (C or B)) and ((D -> E) -> (((F and D) or D) -> E))) and A)), M:tm-5, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67676
in-theory        67676
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-1 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67676.        (A -> ((B -> (C or B)) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-1, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67677
in-theory        67677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or 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-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-67677.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-757, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67678
in-theory        67678
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 and G) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or 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-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-67678.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-708, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67679
in-theory        67679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or 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-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-67679.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-665, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67680
in-theory        67680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-67680.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-622, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67681
in-theory        67681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-67681.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67682
in-theory        67682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67682.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-605, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67683
in-theory        67683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-67683.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-595, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67684
in-theory        67684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-67684.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-550, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67685
in-theory        67685
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> B), axiom
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-67685.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-540, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67686
in-theory        67686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-67686.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-530, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67687
in-theory        67687
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67687.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-520, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67688
in-theory        67688
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-67688.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-510, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67689
in-theory        67689
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-4.            ((A and B) -> B), axiom
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-67689.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-500, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67690
in-theory        67690
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67690.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-490, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67691
in-theory        67691
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-67691.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-480, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67692
in-theory        67692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-67692.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-469, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67693
in-theory        67693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-67693.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67694
in-theory        67694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-67694.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-453, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67695
in-theory        67695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-67695.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-443, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67696
in-theory        67696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-67696.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-409, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67697
in-theory        67697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-67697.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-400, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67698
in-theory        67698
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-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-67698.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-391, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67699
in-theory        67699
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-67699.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-382, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67700
in-theory        67700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-67700.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-373, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67701
in-theory        67701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-67701.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-364, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67702
in-theory        67702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67702.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-354, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67703
in-theory        67703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67703.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67704
in-theory        67704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67704.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-338, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67705
in-theory        67705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-67705.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-327, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67706
in-theory        67706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-67706.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-326, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67707
in-theory        67707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-67707.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-325, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67708
in-theory        67708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-67708.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-324, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67709
in-theory        67709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> B), axiom
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-67709.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-323, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67710
in-theory        67710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-67710.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67711
in-theory        67711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-67711.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67712
in-theory        67712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67712.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67713
in-theory        67713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-67713.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67714
in-theory        67714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F or ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-67714.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F or ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-311, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67715
in-theory        67715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-67715.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) or F)), M:tm-310, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67716
in-theory        67716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
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-67716.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and F))), M:tm-309, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67717
in-theory        67717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-797 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67717.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-308, m:tm-797, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-67718
in-theory        67718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (A -> (A or B)))
theorem-size     23
proof            (modus-ponens tm-307 tm-797 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-4.            ((A and B) -> B), axiom
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-67718.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (A -> (A or B))), M:tm-307, m:tm-797, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-67719
in-theory        67719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) 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-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-4.            ((A and B) -> B), axiom
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-67719.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-305, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67720
in-theory        67720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67720.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-303, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67721
in-theory        67721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-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-67721.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-270, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67722
in-theory        67722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67722.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-239, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67723
in-theory        67723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67723.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-210, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67724
in-theory        67724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67724.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-183, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67725
in-theory        67725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-67725.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-157, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67726
in-theory        67726
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-67726.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-147, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67727
in-theory        67727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-67727.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-134, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67728
in-theory        67728
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67728.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-125, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67729
in-theory        67729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67729.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-113, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67730
in-theory        67730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67730.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-105, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67731
in-theory        67731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67731.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-95, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67732
in-theory        67732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-67732.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-83, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67733
in-theory        67733
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67733.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-76, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67734
in-theory        67734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67734.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-69, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67735
in-theory        67735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or 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-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-67735.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-54, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67736
in-theory        67736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67736.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-42, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67737
in-theory        67737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-67737.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-32, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67738
in-theory        67738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67738.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-23, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67739
in-theory        67739
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-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-67739.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-22, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67740
in-theory        67740
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67740.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-21, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67741
in-theory        67741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67741.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-20, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67742
in-theory        67742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-67742.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-19, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67743
in-theory        67743
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-7 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67743.        (A or ((B -> (B or C)) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-7, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67744
in-theory        67744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67744.        (((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))) or F), M:tm-6, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67745
in-theory        67745
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> E) -> (((F and D) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67745.        (A -> (((B -> (B or C)) and ((D -> E) -> (((F and D) or D) -> E))) and A)), M:tm-5, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67746
in-theory        67746
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-1 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67746.        (A -> ((B -> (B or C)) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-1, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-67747
in-theory        67747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and A) or A) -> (B -> A)))
theorem-size     15
proof            (modus-ponens tm-798 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-67747.        ((A -> (B -> A)) and (((C and A) or A) -> (B -> A))), M:tm-798, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-67748
in-theory        67748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (A -> (B -> C))) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-798 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-67748.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (A -> (B -> C))) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))), M:tm-798, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-67749
in-theory        67749
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (A and B)) or (A and B)) -> A))
theorem-size     17
proof            (modus-ponens tm-798 tm-3 ((A (and Am Bm)) (B Am)))
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-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-3.            ((A and B) -> A), axiom
tm-67749.        (((A and B) -> A) and (((C and (A and B)) or (A and B)) -> A)), M:tm-798, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-67750
in-theory        67750
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (A and B)) or (A and B)) -> B))
theorem-size     17
proof            (modus-ponens tm-798 tm-4 ((A (and Am Bm)) (B Bm)))
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-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-67750.        (((A and B) -> B) and (((C and (A and B)) or (A and B)) -> B)), M:tm-798, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-67751
in-theory        67751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and A) or A) -> (B -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-798 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-67751.        ((A -> (B -> (A and B))) and (((C and A) or A) -> (B -> (A and B)))), M:tm-798, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-67752
in-theory        67752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and A) or A) -> (A or B)))
theorem-size     15
proof            (modus-ponens tm-798 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-67752.        ((A -> (A or B)) and (((C and A) or A) -> (A or B))), M:tm-798, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-67753
in-theory        67753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and A) or A) -> (B or A)))
theorem-size     15
proof            (modus-ponens tm-798 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-67753.        ((A -> (B or A)) and (((C and A) or A) -> (B or A))), M:tm-798, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-67754
in-theory        67754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (A -> B)) or (A -> B)) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-798 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-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-67754.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (A -> B)) or (A -> B)) -> ((B -> C) -> ((A or B) -> C)))), M:tm-798, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-67755
in-theory        67755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (A -> B)) or (A -> B)) -> ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-798 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67755.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (A -> B)) or (A -> B)) -> ((A -> (not B)) -> (not A)))), M:tm-798, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-67756
in-theory        67756
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (not (not A))) or (not (not A))) -> A))
theorem-size     17
proof            (modus-ponens tm-798 tm-10 ((A (not (not Am))) (B Am)))
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-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-10.           ((not (not A)) -> A), axiom
tm-67756.        (((not (not A)) -> A) and (((B and (not (not A))) or (not (not A))) -> A)), M:tm-798, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-67757
in-theory        67757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and A) or A) -> (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-798 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-67757.        ((A -> (B -> (C -> B))) and (((D and A) or A) -> (B -> (C -> B)))), M:tm-798, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-67758
in-theory        67758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (A -> B)) or (A -> B)) -> (A -> A)))
theorem-size     21
proof            (modus-ponens tm-798 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
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-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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-67758.        (((A -> B) -> (A -> A)) and (((C and (A -> B)) or (A -> B)) -> (A -> A))), M:tm-798, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-67759
in-theory        67759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-798 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> 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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-67759.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-798, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-67760
in-theory        67760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and A) or A) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-798 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-67760.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and A) or A) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-798, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-67761
in-theory        67761
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))
theorem-size     41
proof            (modus-ponens tm-798 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-67761.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))), M:tm-798, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-67762
in-theory        67762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and A) or A) -> ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-798 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-67762.        ((A -> ((B and C) -> B)) and (((D and A) or A) -> ((B and C) -> B))), M:tm-798, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-67763
in-theory        67763
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))
theorem-size     41
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-67763.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))), M:tm-798, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-67764
in-theory        67764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and A) or A) -> ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-798 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-67764.        ((A -> ((B and C) -> C)) and (((D and A) or A) -> ((B and C) -> C))), M:tm-798, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-67765
in-theory        67765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and A) or A) -> ((B -> (C -> B)) and A)))
theorem-size     23
proof            (modus-ponens tm-798 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-67765.        ((A -> ((B -> (C -> B)) and A)) and (((D and A) or A) -> ((B -> (C -> B)) and A))), M:tm-798, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-67766
in-theory        67766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and A) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-798 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-67766.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and A) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-798, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-67767
in-theory        67767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and A) or A) -> (((B and C) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-798 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-67767.        ((A -> (((B and C) -> B) and A)) and (((D and A) or A) -> (((B and C) -> B) and A))), M:tm-798, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-67768
in-theory        67768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and A) or A) -> (((B and C) -> C) and A)))
theorem-size     23
proof            (modus-ponens tm-798 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-67768.        ((A -> (((B and C) -> C) and A)) and (((D and A) or A) -> (((B and C) -> C) and A))), M:tm-798, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-67769
in-theory        67769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and A) or A) -> ((B -> (C -> (B and C))) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-67769.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and A) or A) -> ((B -> (C -> (B and C))) and A))), M:tm-798, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-67770
in-theory        67770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (A -> B)) or (A -> B)) -> (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-798 tm-24 ((A (-> Am Bm)) (B (-> Am (and 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-67770.        (((A -> B) -> (A -> (A and B))) and (((C and (A -> B)) or (A -> B)) -> (A -> (A and B)))), M:tm-798, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-67771
in-theory        67771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and A) or A) -> (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-67771.        ((A -> (B -> (C -> (B and C)))) and (((D and A) or A) -> (B -> (C -> (B and C))))), M:tm-798, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-67772
in-theory        67772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and A) or A) -> ((B -> (B or C)) and A)))
theorem-size     23
proof            (modus-ponens tm-798 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-67772.        ((A -> ((B -> (B or C)) and A)) and (((D and A) or A) -> ((B -> (B or C)) and A))), M:tm-798, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-67773
in-theory        67773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and A) or A) -> (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-798 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-67773.        ((A -> (B -> (B or C))) and (((D and A) or A) -> (B -> (B or C)))), M:tm-798, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-67774
in-theory        67774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and A) or A) -> ((B -> (C or B)) and A)))
theorem-size     23
proof            (modus-ponens tm-798 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-67774.        ((A -> ((B -> (C or B)) and A)) and (((D and A) or A) -> ((B -> (C or B)) and A))), M:tm-798, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-67775
in-theory        67775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and A) or A) -> (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-798 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-67775.        ((A -> (B -> (C or B))) and (((D and A) or A) -> (B -> (C or B)))), M:tm-798, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-67776
in-theory        67776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((A -> B) -> C)) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-798 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-67776.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((A -> B) -> C)) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))), M:tm-798, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-67777
in-theory        67777
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (((A -> B) -> (A -> C)) -> D)) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     63
proof            (modus-ponens tm-798 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-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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-67777.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (((A -> B) -> (A -> C)) -> D)) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-798, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-67778
in-theory        67778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-798 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-67778.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> (((A and C) or A) -> B))), M:tm-798, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-67779
in-theory        67779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-798 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) 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-4.            ((A and B) -> B), axiom
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-67779.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> (((C and A) or A) -> B))), M:tm-798, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-67780
in-theory        67780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((A -> (B and A)) -> C)) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))
theorem-size     45
proof            (modus-ponens tm-798 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-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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-67780.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((A -> (B and A)) -> C)) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))), M:tm-798, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-67781
in-theory        67781
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-798 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-67781.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> ((A or (A or B)) -> C))), M:tm-798, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-67782
in-theory        67782
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-798 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-67782.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> ((B or (A or B)) -> C))), M:tm-798, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-67783
in-theory        67783
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (((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     69
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-67783.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (((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-798, 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-67784
in-theory        67784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((E and A) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-798 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-67784.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((E and A) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))), M:tm-798, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-67785
in-theory        67785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((D and ((A -> B) -> (B -> C))) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-798 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67785.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((D and ((A -> B) -> (B -> C))) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C)))), M:tm-798, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-67786
in-theory        67786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and A) or A) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     35
proof            (modus-ponens tm-798 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67786.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and A) or A) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))), M:tm-798, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-67787
in-theory        67787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (((C and (A -> (not (B -> A)))) or (A -> (not (B -> A)))) -> (not A)))
theorem-size     28
proof            (modus-ponens tm-798 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67787.        (((A -> (not (B -> A))) -> (not A)) and (((C and (A -> (not (B -> A)))) or (A -> (not (B -> A)))) -> (not A))), M:tm-798, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-67788
in-theory        67788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((D and ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C)))))
theorem-size     60
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-67788.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((D and ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C))))), M:tm-798, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-67789
in-theory        67789
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (((C and ((A and B) -> (not A))) or ((A and B) -> (not A))) -> (not (A and B))))
theorem-size     32
proof            (modus-ponens tm-798 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67789.        ((((A and B) -> (not A)) -> (not (A and B))) and (((C and ((A and B) -> (not A))) or ((A and B) -> (not A))) -> (not (A and B)))), M:tm-798, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-67790
in-theory        67790
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (((C and ((A and B) -> (not B))) or ((A and B) -> (not B))) -> (not (A and B))))
theorem-size     32
proof            (modus-ponens tm-798 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67790.        ((((A and B) -> (not B)) -> (not (A and B))) and (((C and ((A and B) -> (not B))) or ((A and B) -> (not B))) -> (not (A and B)))), M:tm-798, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-67791
in-theory        67791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (((C and (A -> (not (B -> (A and B))))) or (A -> (not (B -> (A and B))))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-798 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67791.        (((A -> (not (B -> (A and B)))) -> (not A)) and (((C and (A -> (not (B -> (A and B))))) or (A -> (not (B -> (A and B))))) -> (not A))), M:tm-798, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-67792
in-theory        67792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (((C and (A -> (not (A or B)))) or (A -> (not (A or B)))) -> (not A)))
theorem-size     28
proof            (modus-ponens tm-798 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67792.        (((A -> (not (A or B))) -> (not A)) and (((C and (A -> (not (A or B)))) or (A -> (not (A or B)))) -> (not A))), M:tm-798, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-67793
in-theory        67793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (((C and (A -> (not (B or A)))) or (A -> (not (B or A)))) -> (not A)))
theorem-size     28
proof            (modus-ponens tm-798 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67793.        (((A -> (not (B or A))) -> (not A)) and (((C and (A -> (not (B or A)))) or (A -> (not (B or A)))) -> (not A))), M:tm-798, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-67794
in-theory        67794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((D and ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B))))
theorem-size     56
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-67794.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((D and ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B)))), M:tm-798, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-67795
in-theory        67795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((C and ((A -> B) -> (not ((A -> (not B)) -> (not A))))) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B))))
theorem-size     50
proof            (modus-ponens tm-798 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67795.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((C and ((A -> B) -> (not ((A -> (not B)) -> (not A))))) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B)))), M:tm-798, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-67796
in-theory        67796
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((D and (((A -> (not B)) -> (not A)) -> C)) or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))
theorem-size     59
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-67796.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((D and (((A -> (not B)) -> (not A)) -> C)) or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))), M:tm-798, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-67797
in-theory        67797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((D and A) or A) -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-67797.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((D and A) or A) -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))), M:tm-798, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-67798
in-theory        67798
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((C and ((A -> B) -> (A -> (not B)))) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A))))
theorem-size     42
proof            (modus-ponens tm-798 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67798.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((C and ((A -> B) -> (A -> (not B)))) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A)))), M:tm-798, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-67799
in-theory        67799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and A) or A) -> ((B -> C) -> ((B -> (not C)) -> (not B)))))
theorem-size     31
proof            (modus-ponens tm-798 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67799.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and A) or A) -> ((B -> C) -> ((B -> (not C)) -> (not B))))), M:tm-798, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-67800
in-theory        67800
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((B and ((not (not A)) -> (not A))) or ((not (not A)) -> (not A))) -> (not (not (not A)))))
theorem-size     32
proof            (modus-ponens tm-798 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67800.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((B and ((not (not A)) -> (not A))) or ((not (not A)) -> (not A))) -> (not (not (not A))))), M:tm-798, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-67801
in-theory        67801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (((C and (A -> B)) or (A -> B)) -> (((not (not A)) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-798 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-67801.        (((A -> B) -> (((not (not A)) or A) -> B)) and (((C and (A -> B)) or (A -> B)) -> (((not (not A)) or A) -> B))), M:tm-798, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-67802
in-theory        67802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (((C and A) or A) -> (((not (not B)) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-798 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-67802.        ((A -> (((not (not B)) -> B) and A)) and (((C and A) or A) -> (((not (not B)) -> B) and A))), M:tm-798, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-67803
in-theory        67803
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((C and ((not (not (A -> B))) -> A)) or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B)))
theorem-size     41
proof            (modus-ponens tm-798 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67803.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((C and ((not (not (A -> B))) -> A)) or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B))), M:tm-798, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-67804
in-theory        67804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (((C and A) or A) -> ((not (not B)) -> B)))
theorem-size     19
proof            (modus-ponens tm-798 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67804.        ((A -> ((not (not B)) -> B)) and (((C and A) or A) -> ((not (not B)) -> B))), M:tm-798, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-67805
in-theory        67805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (((D and (A -> (not (B -> (C -> B))))) or (A -> (not (B -> (C -> B))))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-798 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67805.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (((D and (A -> (not (B -> (C -> B))))) or (A -> (not (B -> (C -> B))))) -> (not A))), M:tm-798, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-67806
in-theory        67806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((E and ((A -> (B -> A)) -> C)) or ((A -> (B -> A)) -> C)) -> ((D or (A -> (B -> A))) -> C)))
theorem-size     45
proof            (modus-ponens tm-798 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67806.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((E and ((A -> (B -> A)) -> C)) or ((A -> (B -> A)) -> C)) -> ((D or (A -> (B -> A))) -> C))), M:tm-798, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-67807
in-theory        67807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (((E and A) or A) -> ((B -> (C -> (D -> C))) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-67807.        ((A -> ((B -> (C -> (D -> C))) and A)) and (((E and A) or A) -> ((B -> (C -> (D -> C))) and A))), M:tm-798, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-67808
in-theory        67808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (((D and (A -> B)) or (A -> B)) -> (A -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-798 tm-84 ((A (-> Am Bm)) (B (-> Am (-> 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-67808.        (((A -> B) -> (A -> (C -> B))) and (((D and (A -> B)) or (A -> B)) -> (A -> (C -> B)))), M:tm-798, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-67809
in-theory        67809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (((E and A) or A) -> (B -> (C -> (D -> C)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67809.        ((A -> (B -> (C -> (D -> C)))) and (((E and A) or A) -> (B -> (C -> (D -> C))))), M:tm-798, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-67810
in-theory        67810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (((B and A) or A) -> A))
theorem-size     11
proof            (modus-ponens tm-798 tm-86 ((A Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67810.        ((A -> A) and (((B and A) or A) -> A)), M:tm-798, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-67811
in-theory        67811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (((D and (A -> (B -> C))) or (A -> (B -> C))) -> (A -> (B -> C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67811.        (((A -> (B -> C)) -> (A -> (B -> C))) and (((D and (A -> (B -> C))) or (A -> (B -> C))) -> (A -> (B -> C)))), M:tm-798, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-67812
in-theory        67812
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (((C and (A and B)) or (A and B)) -> (A and B)))
theorem-size     21
proof            (modus-ponens tm-798 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67812.        (((A and B) -> (A and B)) and (((C and (A and B)) or (A and B)) -> (A and B))), M:tm-798, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-67813
in-theory        67813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (((C and (A -> B)) or (A -> B)) -> (A -> B)))
theorem-size     21
proof            (modus-ponens tm-798 tm-89 ((A (-> Am Bm)) (B (-> Am 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67813.        (((A -> B) -> (A -> B)) and (((C and (A -> B)) or (A -> B)) -> (A -> B))), M:tm-798, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-67814
in-theory        67814
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (((B and (not (not A))) or (not (not A))) -> (not (not A))))
theorem-size     21
proof            (modus-ponens tm-798 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (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-67814.        (((not (not A)) -> (not (not A))) and (((B and (not (not A))) or (not (not A))) -> (not (not A)))), M:tm-798, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-67815
in-theory        67815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((C and ((A -> B) -> (not (A -> A)))) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B))))
theorem-size     38
proof            (modus-ponens tm-798 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67815.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((C and ((A -> B) -> (not (A -> A)))) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B)))), M:tm-798, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-67816
in-theory        67816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((D and ((A -> A) -> B)) or ((A -> A) -> B)) -> (((A -> C) or (A -> A)) -> B)))
theorem-size     39
proof            (modus-ponens tm-798 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67816.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((D and ((A -> A) -> B)) or ((A -> A) -> B)) -> (((A -> C) or (A -> A)) -> B))), M:tm-798, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-67817
in-theory        67817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (((D and A) or A) -> (((B -> C) -> (B -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-67817.        ((A -> (((B -> C) -> (B -> B)) and A)) and (((D and A) or A) -> (((B -> C) -> (B -> B)) and A))), M:tm-798, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-67818
in-theory        67818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (((C and ((A -> B) -> A)) or ((A -> B) -> A)) -> ((A -> B) -> A)))
theorem-size     31
proof            (modus-ponens tm-798 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67818.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (((C and ((A -> B) -> A)) or ((A -> B) -> A)) -> ((A -> B) -> A))), M:tm-798, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-67819
in-theory        67819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (((D and A) or A) -> ((B -> C) -> (B -> B))))
theorem-size     23
proof            (modus-ponens tm-798 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67819.        ((A -> ((B -> C) -> (B -> B))) and (((D and A) or A) -> ((B -> C) -> (B -> B)))), M:tm-798, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-67820
in-theory        67820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (((D and (A -> ((B -> A) -> C))) or (A -> ((B -> A) -> C))) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-798 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-67820.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (((D and (A -> ((B -> A) -> C))) or (A -> ((B -> A) -> C))) -> (A -> C))), M:tm-798, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-67821
in-theory        67821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (((C and (A -> (A -> B))) or (A -> (A -> B))) -> (A -> B)))
theorem-size     27
proof            (modus-ponens tm-798 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-67821.        (((A -> (A -> B)) -> (A -> B)) and (((C and (A -> (A -> B))) or (A -> (A -> B))) -> (A -> B))), M:tm-798, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-67822
in-theory        67822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((D and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B))))
theorem-size     51
proof            (modus-ponens tm-798 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67822.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((D and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B)))), M:tm-798, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-67823
in-theory        67823
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((D and (((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     86
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-67823.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((D and (((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-798, 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-67824
in-theory        67824
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 (((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     81
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-67824.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((E and (((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-798, 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-67825
in-theory        67825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((E and A) or A) -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))
theorem-size     51
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-67825.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((E and A) or A) -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))), M:tm-798, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-67826
in-theory        67826
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((D and (((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     77
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> 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-67826.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((D and (((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-798, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-67827
in-theory        67827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and A) or A) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     47
proof            (modus-ponens tm-798 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67827.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and A) or A) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-798, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-67828
in-theory        67828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((E and ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D)))
theorem-size     65
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-67828.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((E and ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D))), M:tm-798, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-67829
in-theory        67829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((E and (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A)))
theorem-size     58
proof            (modus-ponens tm-798 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67829.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((E and (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A))), M:tm-798, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-67830
in-theory        67830
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 (((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     85
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-14.           (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-67830.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((F and (((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-798, 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-67831
in-theory        67831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and A) or A) -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))
theorem-size     43
proof            (modus-ponens tm-798 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-67831.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and A) or A) -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))), M:tm-798, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-67832
in-theory        67832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((E and (A -> (B -> (C -> D)))) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-798 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-14.           (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-67832.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((E and (A -> (B -> (C -> D)))) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D))))), M:tm-798, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-67833
in-theory        67833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and A) or A) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     39
proof            (modus-ponens tm-798 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-14.           (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-67833.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and A) or A) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-798, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-67834
in-theory        67834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (((C and ((A -> B) and A)) or ((A -> B) and A)) -> B))
theorem-size     23
proof            (modus-ponens tm-798 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-67834.        ((((A -> B) and A) -> B) and (((C and ((A -> B) and A)) or ((A -> B) and A)) -> B)), M:tm-798, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-67835
in-theory        67835
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (((E and (((A -> (B -> A)) -> C) and D)) or (((A -> (B -> A)) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-798 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-67835.        (((((A -> (B -> A)) -> C) and D) -> C) and (((E and (((A -> (B -> A)) -> C) and D)) or (((A -> (B -> A)) -> C) and D)) -> C)), M:tm-798, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-67836
in-theory        67836
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((F and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) -> D))
theorem-size     59
proof            (modus-ponens tm-798 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-67836.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((F and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) -> D)), M:tm-798, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-67837
in-theory        67837
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((D and ((((A -> B) -> A) and C) -> (A -> B))) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B)))
theorem-size     57
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> 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-67837.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((D and ((((A -> B) -> A) and C) -> (A -> B))) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B))), M:tm-798, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-67838
in-theory        67838
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((D and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A)))
theorem-size     41
proof            (modus-ponens tm-798 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67838.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((D and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A))), M:tm-798, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-67839
in-theory        67839
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((D and ((((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     70
proof            (modus-ponens tm-798 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-4 tm-9 tm-3)
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-4.            ((A and B) -> B), axiom
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-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-67839.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((D and ((((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-798, 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-67840
in-theory        67840
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 ((((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     67
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-67840.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((E and ((((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-798, 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-67841
in-theory        67841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((E and A) or A) -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))
theorem-size     43
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-67841.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((E and A) or A) -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))), M:tm-798, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-67842
in-theory        67842
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((D and ((((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     63
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-67842.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((D and ((((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-798, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-67843
in-theory        67843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and A) or A) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))
theorem-size     39
proof            (modus-ponens tm-798 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67843.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and A) or A) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))), M:tm-798, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-67844
in-theory        67844
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (((E and ((((A and B) -> A) -> C) and D)) or ((((A and B) -> A) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-798 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-67844.        ((((((A and B) -> A) -> C) and D) -> C) and (((E and ((((A and B) -> A) -> C) and D)) or ((((A and B) -> A) -> C) and D)) -> C)), M:tm-798, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-67845
in-theory        67845
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((D and ((A and B) -> (A -> C))) or ((A and B) -> (A -> C))) -> ((A and B) -> C)))
theorem-size     37
proof            (modus-ponens tm-798 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-67845.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((D and ((A and B) -> (A -> C))) or ((A and B) -> (A -> C))) -> ((A and B) -> C))), M:tm-798, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-67846
in-theory        67846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (((D and (A -> (not ((B and C) -> B)))) or (A -> (not ((B and C) -> B)))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-798 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9 tm-1 tm-3)
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-4.            ((A and B) -> B), axiom
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-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-67846.        (((A -> (not ((B and C) -> B))) -> (not A)) and (((D and (A -> (not ((B and C) -> B)))) or (A -> (not ((B and C) -> B)))) -> (not A))), M:tm-798, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-67847
in-theory        67847
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((E and (((A and B) -> A) -> C)) or (((A and B) -> A) -> C)) -> ((D or ((A and B) -> A)) -> C)))
theorem-size     45
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-67847.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((E and (((A and B) -> A) -> C)) or (((A and B) -> A) -> C)) -> ((D or ((A and B) -> A)) -> C))), M:tm-798, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-67848
in-theory        67848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (((E and A) or A) -> ((B -> ((C and D) -> C)) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-67848.        ((A -> ((B -> ((C and D) -> C)) and A)) and (((E and A) or A) -> ((B -> ((C and D) -> C)) and A))), M:tm-798, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-67849
in-theory        67849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (((D and (A -> (B and C))) or (A -> (B and C))) -> (A -> B)))
theorem-size     27
proof            (modus-ponens tm-798 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-67849.        (((A -> (B and C)) -> (A -> B)) and (((D and (A -> (B and C))) or (A -> (B and C))) -> (A -> B))), M:tm-798, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-67850
in-theory        67850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (((E and A) or A) -> (B -> ((C and D) -> C))))
theorem-size     23
proof            (modus-ponens tm-798 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-67850.        ((A -> (B -> ((C and D) -> C))) and (((E and A) or A) -> (B -> ((C and D) -> C)))), M:tm-798, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-67851
in-theory        67851
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (((C and (A and (A -> B))) or (A and (A -> B))) -> B))
theorem-size     23
proof            (modus-ponens tm-798 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-17.           (((A and (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-67851.        (((A and (A -> B)) -> B) and (((C and (A and (A -> B))) or (A and (A -> B))) -> B)), M:tm-798, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-67852
in-theory        67852
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (((E and (A and ((B -> (C -> B)) -> D))) or (A and ((B -> (C -> B)) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-67852.        (((A and ((B -> (C -> B)) -> D)) -> D) and (((E and (A and ((B -> (C -> B)) -> D))) or (A and ((B -> (C -> B)) -> D))) -> D)), M:tm-798, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-67853
in-theory        67853
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((F and (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) -> E))
theorem-size     59
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-67853.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((F and (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) -> E)), M:tm-798, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-67854
in-theory        67854
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (((E and (A and (((B and C) -> B) -> D))) or (A and (((B and C) -> B) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-67854.        (((A and (((B and C) -> B) -> D)) -> D) and (((E and (A and (((B and C) -> B) -> D))) or (A and (((B and C) -> B) -> D))) -> D)), M:tm-798, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-67855
in-theory        67855
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((D and ((A and ((B -> C) -> B)) -> (B -> C))) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C)))
theorem-size     57
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> 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-67855.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((D and ((A and ((B -> C) -> B)) -> (B -> C))) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C))), M:tm-798, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-67856
in-theory        67856
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((D and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B)))
theorem-size     41
proof            (modus-ponens tm-798 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67856.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((D and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B))), M:tm-798, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-67857
in-theory        67857
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((D and (((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     70
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-67857.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((D and (((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-798, 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-67858
in-theory        67858
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 (((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     67
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-67858.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((E and (((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-798, 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-67859
in-theory        67859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((E and A) or A) -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))
theorem-size     43
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-67859.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((E and A) or A) -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))), M:tm-798, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-67860
in-theory        67860
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((D and (((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     63
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (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-67860.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((D and (((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-798, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-67861
in-theory        67861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and A) or A) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))
theorem-size     39
proof            (modus-ponens tm-798 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67861.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and A) or A) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))), M:tm-798, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-67862
in-theory        67862
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (((E and (A and (((B and C) -> C) -> D))) or (A and (((B and C) -> C) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-67862.        (((A and (((B and C) -> C) -> D)) -> D) and (((E and (A and (((B and C) -> C) -> D))) or (A and (((B and C) -> C) -> D))) -> D)), M:tm-798, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-67863
in-theory        67863
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (((E and ((((A and B) -> B) -> C) and D)) or ((((A and B) -> B) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-798 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-67863.        ((((((A and B) -> B) -> C) and D) -> C) and (((E and ((((A and B) -> B) -> C) and D)) or ((((A and B) -> B) -> C) and D)) -> C)), M:tm-798, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-67864
in-theory        67864
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((D and ((A and B) -> (B -> C))) or ((A and B) -> (B -> C))) -> ((A and B) -> C)))
theorem-size     37
proof            (modus-ponens tm-798 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-67864.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((D and ((A and B) -> (B -> C))) or ((A and B) -> (B -> C))) -> ((A and B) -> C))), M:tm-798, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-67865
in-theory        67865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (((D and (A -> (not ((B and C) -> C)))) or (A -> (not ((B and C) -> C)))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-798 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67865.        (((A -> (not ((B and C) -> C))) -> (not A)) and (((D and (A -> (not ((B and C) -> C)))) or (A -> (not ((B and C) -> C)))) -> (not A))), M:tm-798, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-67866
in-theory        67866
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((E and (((A and B) -> B) -> C)) or (((A and B) -> B) -> C)) -> ((D or ((A and B) -> B)) -> C)))
theorem-size     45
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67866.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((E and (((A and B) -> B) -> C)) or (((A and B) -> B) -> C)) -> ((D or ((A and B) -> B)) -> C))), M:tm-798, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-67867
in-theory        67867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (((E and A) or A) -> ((B -> ((C and D) -> D)) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67867.        ((A -> ((B -> ((C and D) -> D)) and A)) and (((E and A) or A) -> ((B -> ((C and D) -> D)) and A))), M:tm-798, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-67868
in-theory        67868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (((D and (A -> (B and C))) or (A -> (B and C))) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-798 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67868.        (((A -> (B and C)) -> (A -> C)) and (((D and (A -> (B and C))) or (A -> (B and C))) -> (A -> C))), M:tm-798, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-67869
in-theory        67869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (((E and A) or A) -> (B -> ((C and D) -> D))))
theorem-size     23
proof            (modus-ponens tm-798 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67869.        ((A -> (B -> ((C and D) -> D))) and (((E and A) or A) -> (B -> ((C and D) -> D)))), M:tm-798, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-67870
in-theory        67870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((D and (A -> (not ((B -> (C -> B)) and A)))) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-798 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67870.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((D and (A -> (not ((B -> (C -> B)) and A)))) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A))), M:tm-798, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-67871
in-theory        67871
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((E and (((A -> (B -> A)) and C) -> D)) or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D)))
theorem-size     55
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67871.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((E and (((A -> (B -> A)) and C) -> D)) or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D))), M:tm-798, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-67872
in-theory        67872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((E and A) or A) -> ((B -> ((C -> (D -> C)) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-798 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-67872.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((E and A) or A) -> ((B -> ((C -> (D -> C)) and B)) and A))), M:tm-798, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-67873
in-theory        67873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (((E and A) or A) -> (B -> ((C -> (D -> C)) and B))))
theorem-size     27
proof            (modus-ponens tm-798 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67873.        ((A -> (B -> ((C -> (D -> C)) and B))) and (((E and A) or A) -> (B -> ((C -> (D -> C)) and B)))), M:tm-798, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-67874
in-theory        67874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((E and (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     64
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-67874.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((E and (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-798, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-67875
in-theory        67875
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 ((((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     95
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-20.           (A -> (((B -> (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-67875.        ((((((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 ((((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-798, 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-67876
in-theory        67876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((F and A) or A) -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))
theorem-size     47
proof            (modus-ponens tm-798 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-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-4.            ((A and B) -> B), axiom
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-67876.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((F and A) or A) -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))), M:tm-798, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-67877
in-theory        67877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and A) or A) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     43
proof            (modus-ponens tm-798 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67877.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and A) or A) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-798, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-67878
in-theory        67878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((D and (A -> (not (((B and C) -> B) and A)))) or (A -> (not (((B and C) -> B) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-798 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9 tm-3)
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-4.            ((A and B) -> B), axiom
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-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-67878.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((D and (A -> (not (((B and C) -> B) and A)))) or (A -> (not (((B and C) -> B) and A)))) -> (not A))), M:tm-798, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-67879
in-theory        67879
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((E and ((((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     55
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-67879.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((E and ((((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-798, 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-67880
in-theory        67880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((E and A) or A) -> ((B -> (((C and D) -> C) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-798 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-67880.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((E and A) or A) -> ((B -> (((C and D) -> C) and B)) and A))), M:tm-798, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-67881
in-theory        67881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (((E and A) or A) -> (B -> (((C and D) -> C) and B))))
theorem-size     27
proof            (modus-ponens tm-798 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67881.        ((A -> (B -> (((C and D) -> C) and B))) and (((E and A) or A) -> (B -> (((C and D) -> C) and B)))), M:tm-798, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-67882
in-theory        67882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((D and (A -> (not (((B and C) -> C) and A)))) or (A -> (not (((B and C) -> C) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-798 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67882.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((D and (A -> (not (((B and C) -> C) and A)))) or (A -> (not (((B and C) -> C) and A)))) -> (not A))), M:tm-798, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-67883
in-theory        67883
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((E and ((((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     55
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-67883.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((E and ((((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-798, 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-67884
in-theory        67884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((E and A) or A) -> ((B -> (((C and D) -> D) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-67884.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((E and A) or A) -> ((B -> (((C and D) -> D) and B)) and A))), M:tm-798, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-67885
in-theory        67885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (((E and A) or A) -> (B -> (((C and D) -> D) and B))))
theorem-size     27
proof            (modus-ponens tm-798 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67885.        ((A -> (B -> (((C and D) -> D) and B))) and (((E and A) or A) -> (B -> (((C and D) -> D) and B)))), M:tm-798, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-67886
in-theory        67886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((D and (A -> (not ((B -> (C -> (B and C))) and A)))) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A)))
theorem-size     46
proof            (modus-ponens tm-798 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67886.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((D and (A -> (not ((B -> (C -> (B and C))) and A)))) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A))), M:tm-798, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-67887
in-theory        67887
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 (((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     65
proof            (modus-ponens tm-798 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-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-4.            ((A and B) -> B), axiom
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-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-67887.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((E and (((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-798, 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-67888
in-theory        67888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((E and A) or A) -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-67888.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((E and A) or A) -> ((B -> ((C -> (D -> (C and D))) and B)) and A))), M:tm-798, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-67889
in-theory        67889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((E and A) or A) -> (B -> ((C -> (D -> (C and D))) and B))))
theorem-size     31
proof            (modus-ponens tm-798 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67889.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((E and A) or A) -> (B -> ((C -> (D -> (C and D))) and B)))), M:tm-798, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-67890
in-theory        67890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (((C and A) or A) -> (A and (B -> A))))
theorem-size     19
proof            (modus-ponens tm-798 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-67890.        ((A -> (A and (B -> A))) and (((C and A) or A) -> (A and (B -> A)))), M:tm-798, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-67891
in-theory        67891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((D and (A -> (B -> C))) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-798 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-67891.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((D and (A -> (B -> C))) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))), M:tm-798, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-67892
in-theory        67892
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (((C and (A and B)) or (A and B)) -> ((A and B) and A)))
theorem-size     25
proof            (modus-ponens tm-798 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-67892.        (((A and B) -> ((A and B) and A)) and (((C and (A and B)) or (A and B)) -> ((A and B) and A))), M:tm-798, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-67893
in-theory        67893
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (((C and (A and B)) or (A and B)) -> ((A and B) and B)))
theorem-size     25
proof            (modus-ponens tm-798 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-67893.        (((A and B) -> ((A and B) and B)) and (((C and (A and B)) or (A and B)) -> ((A and B) and B))), M:tm-798, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-67894
in-theory        67894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (((C and A) or A) -> (A and (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-67894.        ((A -> (A and (B -> (A and B)))) and (((C and A) or A) -> (A and (B -> (A and B))))), M:tm-798, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-67895
in-theory        67895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (((C and A) or A) -> (A and (A or B))))
theorem-size     19
proof            (modus-ponens tm-798 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-67895.        ((A -> (A and (A or B))) and (((C and A) or A) -> (A and (A or B)))), M:tm-798, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-67896
in-theory        67896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (((C and A) or A) -> (A and (B or A))))
theorem-size     19
proof            (modus-ponens tm-798 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-67896.        ((A -> (A and (B or A))) and (((C and A) or A) -> (A and (B or A)))), M:tm-798, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-67897
in-theory        67897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((D and (A -> B)) or (A -> B)) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-798 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-4.            ((A and B) -> B), axiom
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-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-67897.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((D and (A -> B)) or (A -> B)) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))), M:tm-798, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-67898
in-theory        67898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((C and (A -> B)) or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-798 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-67898.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((C and (A -> B)) or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A))))), M:tm-798, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-67899
in-theory        67899
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (((B and (not (not A))) or (not (not A))) -> ((not (not A)) and A)))
theorem-size     25
proof            (modus-ponens tm-798 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67899.        (((not (not A)) -> ((not (not A)) and A)) and (((B and (not (not A))) or (not (not A))) -> ((not (not A)) and A))), M:tm-798, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-67900
in-theory        67900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (((D and A) or A) -> (A and (B -> (C -> B)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-67900.        ((A -> (A and (B -> (C -> B)))) and (((D and A) or A) -> (A and (B -> (C -> B))))), M:tm-798, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-67901
in-theory        67901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (((C and (A -> B)) or (A -> B)) -> ((A -> B) and (A -> A))))
theorem-size     29
proof            (modus-ponens tm-798 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-67901.        (((A -> B) -> ((A -> B) and (A -> A))) and (((C and (A -> B)) or (A -> B)) -> ((A -> B) and (A -> A)))), M:tm-798, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-67902
in-theory        67902
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((D and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> 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-67902.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((D and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-798, 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-67903
in-theory        67903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((E and A) or A) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     39
proof            (modus-ponens tm-798 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-67903.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((E and A) or A) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-798, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-67904
in-theory        67904
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((D and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))
theorem-size     57
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-67904.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((D and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))), M:tm-798, 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-67905
in-theory        67905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (((D and A) or A) -> (A and ((B and C) -> B))))
theorem-size     23
proof            (modus-ponens tm-798 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-67905.        ((A -> (A and ((B and C) -> B))) and (((D and A) or A) -> (A and ((B and C) -> B)))), M:tm-798, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-67906
in-theory        67906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((D and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))
theorem-size     57
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (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-67906.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((D and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))), M:tm-798, 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-67907
in-theory        67907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (((D and A) or A) -> (A and ((B and C) -> C))))
theorem-size     23
proof            (modus-ponens tm-798 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-67907.        ((A -> (A and ((B and C) -> C))) and (((D and A) or A) -> (A and ((B and C) -> C)))), M:tm-798, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-67908
in-theory        67908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (((D and A) or A) -> (A and ((B -> (C -> B)) and A))))
theorem-size     27
proof            (modus-ponens tm-798 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-67908.        ((A -> (A and ((B -> (C -> B)) and A))) and (((D and A) or A) -> (A and ((B -> (C -> B)) and A)))), M:tm-798, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-67909
in-theory        67909
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((E and A) or A) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     43
proof            (modus-ponens tm-798 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-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-4.            ((A and B) -> B), axiom
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-67909.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((E and A) or A) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-798, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-67910
in-theory        67910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (((D and A) or A) -> (A and (((B and C) -> B) and A))))
theorem-size     27
proof            (modus-ponens tm-798 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-67910.        ((A -> (A and (((B and C) -> B) and A))) and (((D and A) or A) -> (A and (((B and C) -> B) and A)))), M:tm-798, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-67911
in-theory        67911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (((D and A) or A) -> (A and (((B and C) -> C) and A))))
theorem-size     27
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-67911.        ((A -> (A and (((B and C) -> C) and A))) and (((D and A) or A) -> (A and (((B and C) -> C) and A)))), M:tm-798, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-67912
in-theory        67912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((D and A) or A) -> (A and ((B -> (C -> (B and C))) and A))))
theorem-size     31
proof            (modus-ponens tm-798 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-67912.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((D and A) or A) -> (A and ((B -> (C -> (B and C))) and A)))), M:tm-798, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-67913
in-theory        67913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((C and (A -> B)) or (A -> B)) -> ((A -> B) and (A -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-798 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-67913.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((C and (A -> B)) or (A -> B)) -> ((A -> B) and (A -> (A and B))))), M:tm-798, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-67914
in-theory        67914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((C and ((A -> B) -> (not (A -> (A and B))))) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B))))
theorem-size     44
proof            (modus-ponens tm-798 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67914.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((C and ((A -> B) -> (not (A -> (A and B))))) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B)))), M:tm-798, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-67915
in-theory        67915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((D and ((A -> (A and B)) -> C)) or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C)))
theorem-size     49
proof            (modus-ponens tm-798 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-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-4.            ((A and B) -> B), axiom
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-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-67915.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((D and ((A -> (A and B)) -> C)) or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C))), M:tm-798, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-67916
in-theory        67916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((D and A) or A) -> (((B -> C) -> (B -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-798 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-67916.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((D and A) or A) -> (((B -> C) -> (B -> (B and C))) and A))), M:tm-798, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-67917
in-theory        67917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((C and ((A -> B) -> A)) or ((A -> B) -> A)) -> ((A -> B) -> (A and B))))
theorem-size     35
proof            (modus-ponens tm-798 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67917.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((C and ((A -> B) -> A)) or ((A -> B) -> A)) -> ((A -> B) -> (A and B)))), M:tm-798, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-67918
in-theory        67918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (((D and A) or A) -> ((B -> C) -> (B -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-798 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67918.        ((A -> ((B -> C) -> (B -> (B and C)))) and (((D and A) or A) -> ((B -> C) -> (B -> (B and C))))), M:tm-798, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-67919
in-theory        67919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (((D and A) or A) -> (A and (B -> (C -> (B and C))))))
theorem-size     27
proof            (modus-ponens tm-798 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-67919.        ((A -> (A and (B -> (C -> (B and C))))) and (((D and A) or A) -> (A and (B -> (C -> (B and C)))))), M:tm-798, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-67920
in-theory        67920
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((E and (A and ((B -> (C -> (B and C))) -> D))) or (A and ((B -> (C -> (B and C))) -> D))) -> D))
theorem-size     41
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-67920.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((E and (A and ((B -> (C -> (B and C))) -> D))) or (A and ((B -> (C -> (B and C))) -> D))) -> D)), M:tm-798, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-67921
in-theory        67921
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((E and (((A -> (B -> (A and B))) -> C) and D)) or (((A -> (B -> (A and B))) -> C) and D)) -> C))
theorem-size     41
proof            (modus-ponens tm-798 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-67921.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((E and (((A -> (B -> (A and B))) -> C) and D)) or (((A -> (B -> (A and B))) -> C) and D)) -> C)), M:tm-798, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-67922
in-theory        67922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((D and (A -> ((B -> (A and B)) -> C))) or (A -> ((B -> (A and B)) -> C))) -> (A -> C)))
theorem-size     39
proof            (modus-ponens tm-798 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-67922.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((D and (A -> ((B -> (A and B)) -> C))) or (A -> ((B -> (A and B)) -> C))) -> (A -> C))), M:tm-798, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-67923
in-theory        67923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((D and (A -> (not (B -> (C -> (B and C)))))) or (A -> (not (B -> (C -> (B and C)))))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-798 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67923.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((D and (A -> (not (B -> (C -> (B and C)))))) or (A -> (not (B -> (C -> (B and C)))))) -> (not A))), M:tm-798, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-67924
in-theory        67924
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((E and ((A -> (B -> (A and B))) -> C)) or ((A -> (B -> (A and B))) -> C)) -> ((D or (A -> (B -> (A and B)))) -> C)))
theorem-size     55
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> 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-67924.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((E and ((A -> (B -> (A and B))) -> C)) or ((A -> (B -> (A and B))) -> C)) -> ((D or (A -> (B -> (A and B)))) -> C))), M:tm-798, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-67925
in-theory        67925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((E and A) or A) -> ((B -> (C -> (D -> (C and D)))) and A)))
theorem-size     31
proof            (modus-ponens tm-798 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-67925.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((E and A) or A) -> ((B -> (C -> (D -> (C and D)))) and A))), M:tm-798, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-67926
in-theory        67926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (((D and (A -> B)) or (A -> B)) -> (A -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-798 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> 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-67926.        (((A -> B) -> (A -> (C -> (B and C)))) and (((D and (A -> B)) or (A -> B)) -> (A -> (C -> (B and C))))), M:tm-798, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-67927
in-theory        67927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (((E and A) or A) -> (B -> (C -> (D -> (C and D))))))
theorem-size     27
proof            (modus-ponens tm-798 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> 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-67927.        ((A -> (B -> (C -> (D -> (C and D))))) and (((E and A) or A) -> (B -> (C -> (D -> (C and D)))))), M:tm-798, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-67928
in-theory        67928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (((E and A) or A) -> (((B -> (C -> B)) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-67928.        ((A -> (((B -> (C -> B)) or D) and A)) and (((E and A) or A) -> (((B -> (C -> B)) or D) and A))), M:tm-798, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-67929
in-theory        67929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (((E and A) or A) -> ((B -> (C -> B)) or D)))
theorem-size     23
proof            (modus-ponens tm-798 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67929.        ((A -> ((B -> (C -> B)) or D)) and (((E and A) or A) -> ((B -> (C -> B)) or D))), M:tm-798, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-67930
in-theory        67930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((F and A) or A) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))
theorem-size     43
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-67930.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((F and A) or A) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))), M:tm-798, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-67931
in-theory        67931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and A) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))
theorem-size     39
proof            (modus-ponens tm-798 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67931.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and A) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))), M:tm-798, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-67932
in-theory        67932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (((E and A) or A) -> ((((B and C) -> B) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-67932.        ((A -> ((((B and C) -> B) or D) and A)) and (((E and A) or A) -> ((((B and C) -> B) or D) and A))), M:tm-798, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-67933
in-theory        67933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (((E and A) or A) -> (((B and C) -> B) or D)))
theorem-size     23
proof            (modus-ponens tm-798 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67933.        ((A -> (((B and C) -> B) or D)) and (((E and A) or A) -> (((B and C) -> B) or D))), M:tm-798, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-67934
in-theory        67934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (((E and A) or A) -> ((((B and C) -> C) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67934.        ((A -> ((((B and C) -> C) or D) and A)) and (((E and A) or A) -> ((((B and C) -> C) or D) and A))), M:tm-798, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-67935
in-theory        67935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (((E and A) or A) -> (((B and C) -> C) or D)))
theorem-size     23
proof            (modus-ponens tm-798 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67935.        ((A -> (((B and C) -> C) or D)) and (((E and A) or A) -> (((B and C) -> C) or D))), M:tm-798, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-67936
in-theory        67936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((E and A) or A) -> (((B -> (C -> (B and C))) or D) and A)))
theorem-size     31
proof            (modus-ponens tm-798 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-67936.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((E and A) or A) -> (((B -> (C -> (B and C))) or D) and A))), M:tm-798, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-67937
in-theory        67937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (((E and A) or A) -> ((B -> (C -> (B and C))) or D)))
theorem-size     27
proof            (modus-ponens tm-798 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67937.        ((A -> ((B -> (C -> (B and C))) or D)) and (((E and A) or A) -> ((B -> (C -> (B and C))) or D))), M:tm-798, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-67938
in-theory        67938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (((E and A) or A) -> (((B -> (B or C)) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-67938.        ((A -> (((B -> (B or C)) or D) and A)) and (((E and A) or A) -> (((B -> (B or C)) or D) and A))), M:tm-798, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-67939
in-theory        67939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (((E and A) or A) -> ((B -> (B or C)) or D)))
theorem-size     23
proof            (modus-ponens tm-798 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67939.        ((A -> ((B -> (B or C)) or D)) and (((E and A) or A) -> ((B -> (B or C)) or D))), M:tm-798, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-67940
in-theory        67940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (((D and A) or A) -> (A and ((B -> (B or C)) and A))))
theorem-size     27
proof            (modus-ponens tm-798 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-67940.        ((A -> (A and ((B -> (B or C)) and A))) and (((D and A) or A) -> (A and ((B -> (B or C)) and A)))), M:tm-798, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-67941
in-theory        67941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((D and (A -> (not ((B -> (B or C)) and A)))) or (A -> (not ((B -> (B or C)) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-798 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67941.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((D and (A -> (not ((B -> (B or C)) and A)))) or (A -> (not ((B -> (B or C)) and A)))) -> (not A))), M:tm-798, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-67942
in-theory        67942
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((E and (((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     55
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-67942.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((E and (((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-798, 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-67943
in-theory        67943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((E and A) or A) -> ((B -> ((C -> (C or D)) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-798 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-67943.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((E and A) or A) -> ((B -> ((C -> (C or D)) and B)) and A))), M:tm-798, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-67944
in-theory        67944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (((E and A) or A) -> (B -> ((C -> (C or D)) and B))))
theorem-size     27
proof            (modus-ponens tm-798 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67944.        ((A -> (B -> ((C -> (C or D)) and B))) and (((E and A) or A) -> (B -> ((C -> (C or D)) and B)))), M:tm-798, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-67945
in-theory        67945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (((D and A) or A) -> (A and (B -> (B or C)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-67945.        ((A -> (A and (B -> (B or C)))) and (((D and A) or A) -> (A and (B -> (B or C))))), M:tm-798, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-67946
in-theory        67946
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (((E and (A and ((B -> (B or C)) -> D))) or (A and ((B -> (B or C)) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-67946.        (((A and ((B -> (B or C)) -> D)) -> D) and (((E and (A and ((B -> (B or C)) -> D))) or (A and ((B -> (B or C)) -> D))) -> D)), M:tm-798, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-67947
in-theory        67947
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (((E and (((A -> (A or B)) -> C) and D)) or (((A -> (A or B)) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-798 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-67947.        (((((A -> (A or B)) -> C) and D) -> C) and (((E and (((A -> (A or B)) -> C) and D)) or (((A -> (A or B)) -> C) and D)) -> C)), M:tm-798, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-67948
in-theory        67948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (((D and (A -> ((A or B) -> C))) or (A -> ((A or B) -> C))) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-798 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-67948.        (((A -> ((A or B) -> C)) -> (A -> C)) and (((D and (A -> ((A or B) -> C))) or (A -> ((A or B) -> C))) -> (A -> C))), M:tm-798, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-67949
in-theory        67949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (((D and (A -> (not (B -> (B or C))))) or (A -> (not (B -> (B or C))))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-798 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67949.        (((A -> (not (B -> (B or C)))) -> (not A)) and (((D and (A -> (not (B -> (B or C))))) or (A -> (not (B -> (B or C))))) -> (not A))), M:tm-798, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-67950
in-theory        67950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((E and ((A -> (A or B)) -> C)) or ((A -> (A or B)) -> C)) -> ((D or (A -> (A or B))) -> C)))
theorem-size     45
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-67950.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((E and ((A -> (A or B)) -> C)) or ((A -> (A or B)) -> C)) -> ((D or (A -> (A or B))) -> C))), M:tm-798, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-67951
in-theory        67951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (((E and A) or A) -> ((B -> (C -> (C or D))) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-67951.        ((A -> ((B -> (C -> (C or D))) and A)) and (((E and A) or A) -> ((B -> (C -> (C or D))) and A))), M:tm-798, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-67952
in-theory        67952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (((D and (A -> B)) or (A -> B)) -> (A -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-798 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-67952.        (((A -> B) -> (A -> (B or C))) and (((D and (A -> B)) or (A -> B)) -> (A -> (B or C)))), M:tm-798, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-67953
in-theory        67953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (((E and A) or A) -> (B -> (C -> (C or D)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-67953.        ((A -> (B -> (C -> (C or D)))) and (((E and A) or A) -> (B -> (C -> (C or D))))), M:tm-798, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-67954
in-theory        67954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (((E and A) or A) -> ((B or (C -> (D -> C))) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-67954.        ((A -> ((B or (C -> (D -> C))) and A)) and (((E and A) or A) -> ((B or (C -> (D -> C))) and A))), M:tm-798, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-67955
in-theory        67955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (((E and A) or A) -> (B or (C -> (D -> C)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67955.        ((A -> (B or (C -> (D -> C)))) and (((E and A) or A) -> (B or (C -> (D -> C))))), M:tm-798, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-67956
in-theory        67956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and A) or A) -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))
theorem-size     43
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-67956.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and A) or A) -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))), M:tm-798, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-67957
in-theory        67957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and A) or A) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     39
proof            (modus-ponens tm-798 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67957.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and A) or A) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-798, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-67958
in-theory        67958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (((E and A) or A) -> ((B or ((C and D) -> C)) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-67958.        ((A -> ((B or ((C and D) -> C)) and A)) and (((E and A) or A) -> ((B or ((C and D) -> C)) and A))), M:tm-798, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-67959
in-theory        67959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (((E and A) or A) -> (B or ((C and D) -> C))))
theorem-size     23
proof            (modus-ponens tm-798 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67959.        ((A -> (B or ((C and D) -> C))) and (((E and A) or A) -> (B or ((C and D) -> C)))), M:tm-798, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-67960
in-theory        67960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (((E and A) or A) -> ((B or ((C and D) -> D)) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67960.        ((A -> ((B or ((C and D) -> D)) and A)) and (((E and A) or A) -> ((B or ((C and D) -> D)) and A))), M:tm-798, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-67961
in-theory        67961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (((E and A) or A) -> (B or ((C and D) -> D))))
theorem-size     23
proof            (modus-ponens tm-798 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67961.        ((A -> (B or ((C and D) -> D))) and (((E and A) or A) -> (B or ((C and D) -> D)))), M:tm-798, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-67962
in-theory        67962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((E and A) or A) -> ((B or (C -> (D -> (C and D)))) and A)))
theorem-size     31
proof            (modus-ponens tm-798 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-67962.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((E and A) or A) -> ((B or (C -> (D -> (C and D)))) and A))), M:tm-798, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-67963
in-theory        67963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (((E and A) or A) -> (B or (C -> (D -> (C and D))))))
theorem-size     27
proof            (modus-ponens tm-798 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67963.        ((A -> (B or (C -> (D -> (C and D))))) and (((E and A) or A) -> (B or (C -> (D -> (C and D)))))), M:tm-798, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-67964
in-theory        67964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (((E and A) or A) -> ((B or (C -> (C or D))) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-67964.        ((A -> ((B or (C -> (C or D))) and A)) and (((E and A) or A) -> ((B or (C -> (C or D))) and A))), M:tm-798, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-67965
in-theory        67965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (((E and A) or A) -> (B or (C -> (C or D)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67965.        ((A -> (B or (C -> (C or D)))) and (((E and A) or A) -> (B or (C -> (C or D))))), M:tm-798, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-67966
in-theory        67966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (((E and A) or A) -> ((B or (C -> (D or C))) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-67966.        ((A -> ((B or (C -> (D or C))) and A)) and (((E and A) or A) -> ((B or (C -> (D or C))) and A))), M:tm-798, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-67967
in-theory        67967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (((E and A) or A) -> (B or (C -> (D or C)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-67967.        ((A -> (B or (C -> (D or C)))) and (((E and A) or A) -> (B or (C -> (D or C))))), M:tm-798, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-67968
in-theory        67968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (((E and A) or A) -> (((B -> (C or B)) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-67968.        ((A -> (((B -> (C or B)) or D) and A)) and (((E and A) or A) -> (((B -> (C or B)) or D) and A))), M:tm-798, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-67969
in-theory        67969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (((E and A) or A) -> ((B -> (C or B)) or D)))
theorem-size     23
proof            (modus-ponens tm-798 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67969.        ((A -> ((B -> (C or B)) or D)) and (((E and A) or A) -> ((B -> (C or B)) or D))), M:tm-798, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-67970
in-theory        67970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (((D and A) or A) -> (A and ((B -> (C or B)) and A))))
theorem-size     27
proof            (modus-ponens tm-798 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-67970.        ((A -> (A and ((B -> (C or B)) and A))) and (((D and A) or A) -> (A and ((B -> (C or B)) and A)))), M:tm-798, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-67971
in-theory        67971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((D and (A -> (not ((B -> (C or B)) and A)))) or (A -> (not ((B -> (C or B)) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-798 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67971.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((D and (A -> (not ((B -> (C or B)) and A)))) or (A -> (not ((B -> (C or B)) and A)))) -> (not A))), M:tm-798, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-67972
in-theory        67972
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((E and (((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     55
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-67972.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((E and (((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-798, 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-67973
in-theory        67973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((E and A) or A) -> ((B -> ((C -> (D or C)) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-798 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-67973.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((E and A) or A) -> ((B -> ((C -> (D or C)) and B)) and A))), M:tm-798, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-67974
in-theory        67974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (((E and A) or A) -> (B -> ((C -> (D or C)) and B))))
theorem-size     27
proof            (modus-ponens tm-798 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67974.        ((A -> (B -> ((C -> (D or C)) and B))) and (((E and A) or A) -> (B -> ((C -> (D or C)) and B)))), M:tm-798, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-67975
in-theory        67975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (((D and A) or A) -> (A and (B -> (C or B)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-67975.        ((A -> (A and (B -> (C or B)))) and (((D and A) or A) -> (A and (B -> (C or B))))), M:tm-798, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-67976
in-theory        67976
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (((E and (A and ((B -> (C or B)) -> D))) or (A and ((B -> (C or B)) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-67976.        (((A and ((B -> (C or B)) -> D)) -> D) and (((E and (A and ((B -> (C or B)) -> D))) or (A and ((B -> (C or B)) -> D))) -> D)), M:tm-798, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-67977
in-theory        67977
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (((E and (((A -> (B or A)) -> C) and D)) or (((A -> (B or A)) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-798 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-67977.        (((((A -> (B or A)) -> C) and D) -> C) and (((E and (((A -> (B or A)) -> C) and D)) or (((A -> (B or A)) -> C) and D)) -> C)), M:tm-798, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-67978
in-theory        67978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (((D and (A -> ((B or A) -> C))) or (A -> ((B or A) -> C))) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-798 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-67978.        (((A -> ((B or A) -> C)) -> (A -> C)) and (((D and (A -> ((B or A) -> C))) or (A -> ((B or A) -> C))) -> (A -> C))), M:tm-798, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-67979
in-theory        67979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (((D and (A -> (not (B -> (C or B))))) or (A -> (not (B -> (C or B))))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-798 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-67979.        (((A -> (not (B -> (C or B)))) -> (not A)) and (((D and (A -> (not (B -> (C or B))))) or (A -> (not (B -> (C or B))))) -> (not A))), M:tm-798, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-67980
in-theory        67980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((E and ((A -> (B or A)) -> C)) or ((A -> (B or A)) -> C)) -> ((D or (A -> (B or A))) -> C)))
theorem-size     45
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-67980.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((E and ((A -> (B or A)) -> C)) or ((A -> (B or A)) -> C)) -> ((D or (A -> (B or A))) -> C))), M:tm-798, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-67981
in-theory        67981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (((E and A) or A) -> ((B -> (C -> (D or C))) and A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-67981.        ((A -> ((B -> (C -> (D or C))) and A)) and (((E and A) or A) -> ((B -> (C -> (D or C))) and A))), M:tm-798, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-67982
in-theory        67982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (((D and (A -> B)) or (A -> B)) -> (A -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-798 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-67982.        (((A -> B) -> (A -> (C or B))) and (((D and (A -> B)) or (A -> B)) -> (A -> (C or B)))), M:tm-798, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-67983
in-theory        67983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (((E and A) or A) -> (B -> (C -> (D or C)))))
theorem-size     23
proof            (modus-ponens tm-798 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-67983.        ((A -> (B -> (C -> (D or C)))) and (((E and A) or A) -> (B -> (C -> (D or C))))), M:tm-798, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-67984
in-theory        67984
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (C -> (B -> A))))
theorem-size     31
proof            (modus-ponens tm-798 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67984.        (((A or (B -> A)) -> (C -> (B -> A))) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (C -> (B -> A)))), M:tm-798, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-67985
in-theory        67985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((D and ((A -> B) or (C -> (A -> B)))) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B))))
theorem-size     47
proof            (modus-ponens tm-798 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67985.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((D and ((A -> B) or (C -> (A -> B)))) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B)))), M:tm-798, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-67986
in-theory        67986
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (C -> ((B -> A) and C))))
theorem-size     35
proof            (modus-ponens tm-798 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67986.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (C -> ((B -> A) and C)))), M:tm-798, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-67987
in-theory        67987
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (((D and (A or (B -> A))) or (A or (B -> A))) -> ((B -> A) or C)))
theorem-size     31
proof            (modus-ponens tm-798 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67987.        (((A or (B -> A)) -> ((B -> A) or C)) and (((D and (A or (B -> A))) or (A or (B -> A))) -> ((B -> A) or C))), M:tm-798, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-67988
in-theory        67988
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (C or (B -> A))))
theorem-size     31
proof            (modus-ponens tm-798 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67988.        (((A or (B -> A)) -> (C or (B -> A))) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (C or (B -> A)))), M:tm-798, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-67989
in-theory        67989
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((D and (A or (B -> A))) or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C))))
theorem-size     39
proof            (modus-ponens tm-798 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67989.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((D and (A or (B -> A))) or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C)))), M:tm-798, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-67990
in-theory        67990
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((C and (A or (B -> A))) or (A or (B -> A))) -> ((B -> (not A)) -> (not B))))
theorem-size     35
proof            (modus-ponens tm-798 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67990.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((C and (A or (B -> A))) or (A or (B -> A))) -> ((B -> (not A)) -> (not B)))), M:tm-798, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-67991
in-theory        67991
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67991.        (((A or (B -> A)) -> (C -> (D -> C))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (C -> (D -> C)))), M:tm-798, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-67992
in-theory        67992
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (((C and (A or (B -> A))) or (A or (B -> A))) -> (B -> B)))
theorem-size     27
proof            (modus-ponens tm-798 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67992.        (((A or (B -> A)) -> (B -> B)) and (((C and (A or (B -> A))) or (A or (B -> A))) -> (B -> B))), M:tm-798, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-67993
in-theory        67993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     63
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67993.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-798, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-67994
in-theory        67994
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-798 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67994.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-798, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-67995
in-theory        67995
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((D and (A or (((A -> B) and C) -> A))) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)))
theorem-size     47
proof            (modus-ponens tm-798 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-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67995.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((D and (A or (((A -> B) and C) -> A))) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))), M:tm-798, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-67996
in-theory        67996
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-798 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67996.        (((A or (B -> A)) -> ((C and D) -> C)) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C and D) -> C))), M:tm-798, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-67997
in-theory        67997
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((D and (A or ((B and (A -> C)) -> A))) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C)))
theorem-size     47
proof            (modus-ponens tm-798 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-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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67997.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((D and (A or ((B and (A -> C)) -> A))) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C))), M:tm-798, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-67998
in-theory        67998
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-798 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67998.        (((A or (B -> A)) -> ((C and D) -> D)) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C and D) -> D))), M:tm-798, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-67999
in-theory        67999
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-67999.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A)))), M:tm-798, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-68000
in-theory        68000
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((F and (A or (B -> A))) or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))
theorem-size     55
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68000.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((F and (A or (B -> A))) or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))), M:tm-798, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-68001
in-theory        68001
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (((C and D) -> C) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68001.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (((C and D) -> C) and (B -> A)))), M:tm-798, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-68002
in-theory        68002
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (((C and D) -> D) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68002.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (((C and D) -> D) and (B -> A)))), M:tm-798, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-68003
in-theory        68003
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A))))
theorem-size     43
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68003.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A)))), M:tm-798, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-68004
in-theory        68004
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (((C and (A or (B -> A))) or (A or (B -> A))) -> (B -> (B and A))))
theorem-size     31
proof            (modus-ponens tm-798 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68004.        (((A or (B -> A)) -> (B -> (B and A))) and (((C and (A or (B -> A))) or (A or (B -> A))) -> (B -> (B and A)))), M:tm-798, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-68005
in-theory        68005
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-798 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68005.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (C -> (D -> (C and D))))), M:tm-798, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-68006
in-theory        68006
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68006.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A)))), M:tm-798, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-68007
in-theory        68007
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-798 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68007.        (((A or (B -> A)) -> (C -> (C or D))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (C -> (C or D)))), M:tm-798, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-68008
in-theory        68008
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68008.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A)))), M:tm-798, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-68009
in-theory        68009
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68009.        (((A or (B -> A)) -> (C -> (D or C))) and (((E and (A or (B -> A))) or (A or (B -> A))) -> (C -> (D or C)))), M:tm-798, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-68010
in-theory        68010
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((D and (A or ((B -> C) -> A))) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A)))
theorem-size     41
proof            (modus-ponens tm-798 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68010.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((D and (A or ((B -> C) -> A))) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A))), M:tm-798, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-68011
in-theory        68011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((D and ((A -> B) -> C)) or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))
theorem-size     47
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-68011.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((D and ((A -> B) -> C)) or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))), M:tm-798, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-68012
in-theory        68012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (((D and ((A -> B) -> C)) or ((A -> B) -> C)) -> ((A -> B) -> C)))
theorem-size     31
proof            (modus-ponens tm-798 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (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-68012.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (((D and ((A -> B) -> C)) or ((A -> B) -> C)) -> ((A -> B) -> C))), M:tm-798, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-68013
in-theory        68013
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((D and (((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     60
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-68013.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((D and (((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-798, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-68014
in-theory        68014
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((E and (((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     63
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-68014.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((E and (((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-798, 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-68015
in-theory        68015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((E and A) or A) -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))
theorem-size     39
proof            (modus-ponens tm-798 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-68015.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((E and A) or A) -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))), M:tm-798, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-68016
in-theory        68016
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((D and (((A -> B) -> C) -> (B or (A -> B)))) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C)))
theorem-size     53
proof            (modus-ponens tm-798 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68016.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((D and (((A -> B) -> C) -> (B or (A -> B)))) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C))), M:tm-798, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-68017
in-theory        68017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and A) or A) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))
theorem-size     35
proof            (modus-ponens tm-798 tm-667 ((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68017.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and A) or A) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))), M:tm-798, m:tm-667, u:((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-68018
in-theory        68018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((E and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68018.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((E and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C))))), M:tm-798, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-68019
in-theory        68019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((D and ((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     67
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68019.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((D and ((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-798, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-68020
in-theory        68020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((E and ((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     67
proof            (modus-ponens tm-798 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-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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68020.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((E and ((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-798, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-68021
in-theory        68021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((E and ((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     63
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68021.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((E and ((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-798, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-68022
in-theory        68022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((E and ((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     63
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68022.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((E and ((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-798, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-68023
in-theory        68023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((E and ((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     75
proof            (modus-ponens tm-798 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-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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68023.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((E and ((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-798, 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-68024
in-theory        68024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((D and ((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     71
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68024.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((D and ((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-798, 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-68025
in-theory        68025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D))))
theorem-size     55
proof            (modus-ponens tm-798 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68025.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D)))), M:tm-798, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-68026
in-theory        68026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((D and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B))))
theorem-size     59
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68026.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((D and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B)))), M:tm-798, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-68027
in-theory        68027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((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     75
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68027.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((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-798, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-68028
in-theory        68028
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and ((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     71
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68028.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and ((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-798, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-68029
in-theory        68029
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D)))
theorem-size     55
proof            (modus-ponens tm-798 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-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68029.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D))), M:tm-798, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-68030
in-theory        68030
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E)))
theorem-size     55
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68030.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E))), M:tm-798, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-68031
in-theory        68031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((F and ((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     71
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68031.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((F and ((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-798, 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-68032
in-theory        68032
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 ((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     87
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68032.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((G and ((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-798, 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-68033
in-theory        68033
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((F and ((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     71
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68033.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((F and ((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-798, 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-68034
in-theory        68034
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((F and ((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     71
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68034.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((F and ((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-798, 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-68035
in-theory        68035
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 ((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     75
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68035.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((F and ((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-798, 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-68036
in-theory        68036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((D and ((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     67
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68036.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((D and ((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-798, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-68037
in-theory        68037
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E)))))
theorem-size     59
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68037.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E))))), M:tm-798, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-68038
in-theory        68038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((F and ((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     71
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68038.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((F and ((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-798, 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-68039
in-theory        68039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E))))
theorem-size     55
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68039.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E)))), M:tm-798, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-68040
in-theory        68040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((F and ((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     71
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68040.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((F and ((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-798, 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-68041
in-theory        68041
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D))))
theorem-size     55
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68041.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((F and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D)))), M:tm-798, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-68042
in-theory        68042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((D and ((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     63
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-68042.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((D and ((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-798, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-68043
in-theory        68043
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 (((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     113
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68043.        (((((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 (((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-798, 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-68044
in-theory        68044
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((E and (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     69
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68044.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((E and (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-798, 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-68045
in-theory        68045
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 (((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     83
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-68045.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((E and (((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-798, 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-68046
in-theory        68046
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((E and (((A -> B) -> (A -> C)) -> D)) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D)))
theorem-size     51
proof            (modus-ponens tm-798 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-68046.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((E and (((A -> B) -> (A -> C)) -> D)) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D))), M:tm-798, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-68047
in-theory        68047
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 ((((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     104
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-68047.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((E and ((((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-798, 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-68048
in-theory        68048
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 ((((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     111
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-68048.        ((((((A -> (B -> 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 ((((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-798, 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-68049
in-theory        68049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((F and A) 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-798 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-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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-68049.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((F and A) or A) -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))), M:tm-798, 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-68050
in-theory        68050
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 ((((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     97
proof            (modus-ponens tm-798 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-4)
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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68050.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((E and ((((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-798, 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-68051
in-theory        68051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and A) or A) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     59
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-68051.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and A) or A) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-798, m:tm-710, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-68052
in-theory        68052
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (((D and ((A and B) or A)) or ((A and B) or A)) -> (C -> A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68052.        ((((A and B) or A) -> (C -> A)) and (((D and ((A and B) or A)) or ((A and B) or A)) -> (C -> A))), M:tm-798, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-68053
in-theory        68053
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((E and (((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     59
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68053.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((E and (((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-798, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-68054
in-theory        68054
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (((D and (((A and B) and C) or (A and B))) or (((A and B) and C) or (A and B))) -> A))
theorem-size     35
proof            (modus-ponens tm-798 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68054.        (((((A and B) and C) or (A and B)) -> A) and (((D and (((A and B) and C) or (A and B))) or (((A and B) and C) or (A and B))) -> A)), M:tm-798, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-68055
in-theory        68055
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (((D and (((A and B) and C) or (A and B))) or (((A and B) and C) or (A and B))) -> B))
theorem-size     35
proof            (modus-ponens tm-798 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68055.        (((((A and B) and C) or (A and B)) -> B) and (((D and (((A and B) and C) or (A and B))) or (((A and B) and C) or (A and B))) -> B)), M:tm-798, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-68056
in-theory        68056
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (((D and ((A and B) or A)) or ((A and B) or A)) -> (C -> (A and C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68056.        ((((A and B) or A) -> (C -> (A and C))) and (((D and ((A and B) or A)) or ((A and B) or A)) -> (C -> (A and C)))), M:tm-798, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-68057
in-theory        68057
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (((D and ((A and B) or A)) or ((A and B) or A)) -> (A or C)))
theorem-size     27
proof            (modus-ponens tm-798 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68057.        ((((A and B) or A) -> (A or C)) and (((D and ((A and B) or A)) or ((A and B) or A)) -> (A or C))), M:tm-798, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-68058
in-theory        68058
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (((D and ((A and B) or A)) or ((A and B) or A)) -> (C or A)))
theorem-size     27
proof            (modus-ponens tm-798 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68058.        ((((A and B) or A) -> (C or A)) and (((D and ((A and B) or A)) or ((A and B) or A)) -> (C or A))), M:tm-798, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-68059
in-theory        68059
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((E and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D))))
theorem-size     51
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68059.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((E and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D)))), M:tm-798, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-68060
in-theory        68060
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((D and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A))))
theorem-size     47
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68060.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((D and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A)))), M:tm-798, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-68061
in-theory        68061
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (((C and (((not (not A)) and B) or (not (not A)))) or (((not (not A)) and B) or (not (not A)))) -> A))
theorem-size     35
proof            (modus-ponens tm-798 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68061.        (((((not (not A)) and B) or (not (not A))) -> A) and (((C and (((not (not A)) and B) or (not (not A)))) or (((not (not A)) and B) or (not (not A)))) -> A)), M:tm-798, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-68062
in-theory        68062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68062.        ((((A and B) or A) -> (C -> (D -> C))) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (C -> (D -> C)))), M:tm-798, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-68063
in-theory        68063
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((D and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> (A -> A)))
theorem-size     39
proof            (modus-ponens tm-798 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68063.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((D and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> (A -> A))), M:tm-798, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-68064
in-theory        68064
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 ((((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     87
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68064.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((E and ((((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-798, 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-68065
in-theory        68065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68065.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-798, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-68066
in-theory        68066
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 (((((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     71
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68066.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((E and (((((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-798, 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-68067
in-theory        68067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-798 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68067.        ((((A and B) or A) -> ((C and D) -> C)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C and D) -> C))), M:tm-798, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-68068
in-theory        68068
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 ((((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     71
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68068.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((E and ((((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-798, 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-68069
in-theory        68069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-798 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68069.        ((((A and B) or A) -> ((C and D) -> D)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C and D) -> D))), M:tm-798, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-68070
in-theory        68070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (D -> C)) and A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68070.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (D -> C)) and A))), M:tm-798, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-68071
in-theory        68071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((F and ((A and B) or A)) or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))
theorem-size     51
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68071.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((F and ((A and B) or A)) or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))), M:tm-798, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-68072
in-theory        68072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (((C and D) -> C) and A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68072.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (((C and D) -> C) and A))), M:tm-798, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-68073
in-theory        68073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (((C and D) -> D) and A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68073.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (((C and D) -> D) and A))), M:tm-798, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-68074
in-theory        68074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A)))
theorem-size     39
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68074.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A))), M:tm-798, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-68075
in-theory        68075
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((D and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B))))
theorem-size     43
proof            (modus-ponens tm-798 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68075.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((D and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B)))), M:tm-798, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-68076
in-theory        68076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-798 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68076.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (C -> (D -> (C and D))))), M:tm-798, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-68077
in-theory        68077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (C or D)) and A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68077.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (C or D)) and A))), M:tm-798, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-68078
in-theory        68078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-798 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68078.        ((((A and B) or A) -> (C -> (C or D))) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (C -> (C or D)))), M:tm-798, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-68079
in-theory        68079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (D or C)) and A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68079.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((E and ((A and B) or A)) or ((A and B) or A)) -> ((C -> (D or C)) and A))), M:tm-798, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-68080
in-theory        68080
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68080.        ((((A and B) or A) -> (C -> (D or C))) and (((E and ((A and B) or A)) or ((A and B) or A)) -> (C -> (D or C)))), M:tm-798, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-68081
in-theory        68081
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((E and ((((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     59
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-68081.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((E and ((((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-798, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-68082
in-theory        68082
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 (((((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     99
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68082.        (((((((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 (((((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-798, 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-68083
in-theory        68083
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((E and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B)))
theorem-size     47
proof            (modus-ponens tm-798 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-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68083.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((E and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B))), M:tm-798, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-68084
in-theory        68084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((E and ((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     71
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68084.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((E and ((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-798, 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-68085
in-theory        68085
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (((B and C) or B) -> A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68085.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (((B and C) or B) -> A))), M:tm-798, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-68086
in-theory        68086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((D and (A -> B)) or (A -> B)) -> ((A -> B) and (((A and C) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-798 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-68086.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((D and (A -> B)) or (A -> B)) -> ((A -> B) and (((A and C) or A) -> B)))), M:tm-798, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-68087
in-theory        68087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((D and ((A -> B) -> (not (((A and C) or A) -> B)))) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B))))
theorem-size     50
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-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-68087.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((D and ((A -> B) -> (not (((A and C) or A) -> B)))) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B)))), M:tm-798, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68088
in-theory        68088
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((E and ((((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     59
proof            (modus-ponens tm-798 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-68088.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((E and ((((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-798, 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-68089
in-theory        68089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((E and A) or A) -> (((B -> C) -> (((B and D) or B) -> C)) and A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-68089.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((E and A) or A) -> (((B -> C) -> (((B and D) or B) -> C)) and A))), M:tm-798, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-68090
in-theory        68090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((D and ((A -> B) -> ((A and C) or A))) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B)))
theorem-size     43
proof            (modus-ponens tm-798 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68090.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((D and ((A -> B) -> ((A and C) or A))) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B))), M:tm-798, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-68091
in-theory        68091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((E and A) or A) -> ((B -> C) -> (((B and D) or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-759 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-68091.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((E and A) or A) -> ((B -> C) -> (((B and D) or B) -> C)))), M:tm-798, m:tm-759, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-68092
in-theory        68092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (((D and ((A and B) or B)) or ((A and B) or B)) -> (C -> B)))
theorem-size     27
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68092.        ((((A and B) or B) -> (C -> B)) and (((D and ((A and B) or B)) or ((A and B) or B)) -> (C -> B))), M:tm-798, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-68093
in-theory        68093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((E and ((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     59
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68093.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((E and ((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-798, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-68094
in-theory        68094
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (((D and ((A and (B and C)) or (B and C))) or ((A and (B and C)) or (B and C))) -> B))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68094.        ((((A and (B and C)) or (B and C)) -> B) and (((D and ((A and (B and C)) or (B and C))) or ((A and (B and C)) or (B and C))) -> B)), M:tm-798, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-68095
in-theory        68095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (((D and ((A and (B and C)) or (B and C))) or ((A and (B and C)) or (B and C))) -> C))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68095.        ((((A and (B and C)) or (B and C)) -> C) and (((D and ((A and (B and C)) or (B and C))) or ((A and (B and C)) or (B and C))) -> C)), M:tm-798, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-68096
in-theory        68096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (((D and ((A and B) or B)) or ((A and B) or B)) -> (C -> (B and C))))
theorem-size     31
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68096.        ((((A and B) or B) -> (C -> (B and C))) and (((D and ((A and B) or B)) or ((A and B) or B)) -> (C -> (B and C)))), M:tm-798, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-68097
in-theory        68097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (((D and ((A and B) or B)) or ((A and B) or B)) -> (B or C)))
theorem-size     27
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68097.        ((((A and B) or B) -> (B or C)) and (((D and ((A and B) or B)) or ((A and B) or B)) -> (B or C))), M:tm-798, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-68098
in-theory        68098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (((D and ((A and B) or B)) or ((A and B) or B)) -> (C or B)))
theorem-size     27
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68098.        ((((A and B) or B) -> (C or B)) and (((D and ((A and B) or B)) or ((A and B) or B)) -> (C or B))), M:tm-798, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-68099
in-theory        68099
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((E and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     51
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68099.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((E and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D)))), M:tm-798, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-68100
in-theory        68100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((D and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B))))
theorem-size     47
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68100.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((D and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B)))), M:tm-798, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-68101
in-theory        68101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (((C and ((A and (not (not B))) or (not (not B)))) or ((A and (not (not B))) or (not (not B)))) -> B))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68101.        ((((A and (not (not B))) or (not (not B))) -> B) and (((C and ((A and (not (not B))) or (not (not B)))) or ((A and (not (not B))) or (not (not B)))) -> B)), M:tm-798, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-68102
in-theory        68102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68102.        ((((A and B) or B) -> (C -> (D -> C))) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (C -> (D -> C)))), M:tm-798, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-68103
in-theory        68103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((D and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> (B -> B)))
theorem-size     39
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-1.            (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-68103.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((D and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> (B -> B))), M:tm-798, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-68104
in-theory        68104
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 ((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     87
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-13.           (((A -> (B -> C)) -> (A -> 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-68104.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((E and ((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-798, 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-68105
in-theory        68105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-14.           (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-68105.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-798, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-68106
in-theory        68106
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 ((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     71
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-68106.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((E and ((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-798, 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-68107
in-theory        68107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-68107.        ((((A and B) or B) -> ((C and D) -> C)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C and D) -> C))), M:tm-798, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-68108
in-theory        68108
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 ((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     71
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-17.           (((A and (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-68108.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((E and ((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-798, 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-68109
in-theory        68109
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-1.            (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-68109.        ((((A and B) or B) -> ((C and D) -> D)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C and D) -> D))), M:tm-798, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-68110
in-theory        68110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (D -> C)) and B)))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-1.            (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-68110.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (D -> C)) and B))), M:tm-798, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-68111
in-theory        68111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((F and ((A and B) or B)) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     51
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-20.           (A -> (((B -> (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-68111.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((F and ((A and B) or B)) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-798, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-68112
in-theory        68112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (((C and D) -> C) and B)))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-68112.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (((C and D) -> C) and B))), M:tm-798, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-68113
in-theory        68113
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (((C and D) -> D) and B)))
theorem-size     35
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68113.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (((C and D) -> D) and B))), M:tm-798, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-68114
in-theory        68114
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B)))
theorem-size     39
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68114.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B))), M:tm-798, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-68115
in-theory        68115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((D and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C))))
theorem-size     43
proof            (modus-ponens tm-798 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       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-4.            ((A and B) -> B), axiom
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-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-68115.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((D and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C)))), M:tm-798, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-68116
in-theory        68116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-798 tm-784 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68116.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (C -> (D -> (C and D))))), M:tm-798, m:tm-784, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-68117
in-theory        68117
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (C or D)) and B)))
theorem-size     35
proof            (modus-ponens tm-798 tm-785 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-68117.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (C or D)) and B))), M:tm-798, m:tm-785, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-68118
in-theory        68118
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-798 tm-786 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-68118.        ((((A and B) or B) -> (C -> (C or D))) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (C -> (C or D)))), M:tm-798, m:tm-786, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-68119
in-theory        68119
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (D or C)) and B)))
theorem-size     35
proof            (modus-ponens tm-798 tm-787 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-68119.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((E and ((A and B) or B)) or ((A and B) or B)) -> ((C -> (D or C)) and B))), M:tm-798, m:tm-787, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-68120
in-theory        68120
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-788 ((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-68120.        ((((A and B) or B) -> (C -> (D or C))) and (((E and ((A and B) or B)) or ((A and B) or B)) -> (C -> (D or C)))), M:tm-798, m:tm-788, u:((A (or (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-68121
in-theory        68121
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((E and ((A and ((B -> C) -> D)) or ((B -> C) -> D))) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D)))
theorem-size     59
proof            (modus-ponens tm-798 tm-789 ((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-68121.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((E and ((A and ((B -> C) -> D)) or ((B -> C) -> D))) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D))), M:tm-798, m:tm-789, u:((A (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm))) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-68122
in-theory        68122
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((F and ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     99
proof            (modus-ponens tm-798 tm-790 ((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-68122.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((F and ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-798, m:tm-790, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-68123
in-theory        68123
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((E and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C)))
theorem-size     47
proof            (modus-ponens tm-798 tm-791 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-68123.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((E and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C))), M:tm-798, m:tm-791, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-68124
in-theory        68124
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((E and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C)))
theorem-size     47
proof            (modus-ponens tm-798 tm-792 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-68124.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((E and ((A and (B -> C)) or (B -> C))) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C))), M:tm-798, m:tm-792, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-68125
in-theory        68125
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((E and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B)))
theorem-size     47
proof            (modus-ponens tm-798 tm-793 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
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-68125.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((E and (((A -> B) and C) or (A -> B))) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B))), M:tm-798, m:tm-793, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-68126
in-theory        68126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((E and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     71
proof            (modus-ponens tm-798 tm-794 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
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-68126.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((E and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-798, m:tm-794, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-68127
in-theory        68127
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (((C and B) or B) -> A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-795 ((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
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-68127.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((D and (A or (B -> A))) or (A or (B -> A))) -> (((C and B) or B) -> A))), M:tm-798, m:tm-795, u:((A (or Am (-> Bm Am))) (B (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-68128
in-theory        68128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((D and (A -> B)) or (A -> B)) -> ((A -> B) and (((C and A) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-798 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-68128.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((D and (A -> B)) or (A -> B)) -> ((A -> B) and (((C and A) or A) -> B)))), M:tm-798, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68129
in-theory        68129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-757 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-68129.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-757, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68130
in-theory        68130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((D and ((A and C) or A)) or ((A and C) or A)) -> B)))
theorem-size     35
proof            (modus-ponens tm-754 tm-798 ((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (or (and Cm (or (and A B) A)) (or (and A B) A)) Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68130.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((D and ((A and C) or A)) or ((A and C) or A)) -> B))), M:tm-754, m:tm-798, u:((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (or (and Cm (or (and A B) A)) (or (and A B) A)) Bm))))
================================================================
tm-name          tm-68131
in-theory        68131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((((A -> B) and D) or (A -> B)) -> ((A -> B) and (((C and A) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-747 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-68131.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((((A -> B) and D) or (A -> B)) -> ((A -> B) and (((C and A) or A) -> B)))), M:tm-747, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68132
in-theory        68132
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-708 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-68132.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F)))), M:tm-708, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68133
in-theory        68133
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 ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)))
theorem-size     73
proof            (modus-ponens tm-705 tm-798 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (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-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68133.        (((((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 ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))), M:tm-705, m:tm-798, 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 Cm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Bm))))
================================================================
tm-name          tm-68134
in-theory        68134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-703 tm-798 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and Cm (-> A B)) (-> A B)) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68134.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-703, m:tm-798, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and Cm (-> A B)) (-> A B)) (-> A C)))))
================================================================
tm-name          tm-68135
in-theory        68135
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and (A -> B)) or (A -> B)) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and (A -> B)) or (A -> B)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-697 tm-798 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and Cm (-> A B)) (-> A B)) (-> A C))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-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-68135.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and (A -> B)) or (A -> B)) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and (A -> B)) or (A -> B)) -> (A -> C))))), M:tm-697, m:tm-798, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and Cm (-> A B)) (-> A B)) (-> A C)))))
================================================================
tm-name          tm-68136
in-theory        68136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-665 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-68136.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-665, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68137
in-theory        68137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((D and (B or (A -> B))) or (B or (A -> B))) -> C)))
theorem-size     37
proof            (modus-ponens tm-662 tm-798 ((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (or (and Cm (or A (-> B A))) (or A (-> B A))) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68137.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((D and (B or (A -> B))) or (B or (A -> B))) -> C))), M:tm-662, m:tm-798, u:((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (or (and Cm (or A (-> B A))) (or A (-> B A))) Bm))))
================================================================
tm-name          tm-68138
in-theory        68138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((B or (A -> B)) -> ((A -> B) and (((C and A) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-798 ((A Am) (B Bm) (C (and (-> Am Bm) (-> (or (and Cm Am) Am) 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-4.            ((A and B) -> B), axiom
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-68138.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((B or (A -> B)) -> ((A -> B) and (((C and A) or A) -> B)))), M:tm-654, m:tm-798, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68139
in-theory        68139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((A -> B) and (((D and A) or A) -> B))))
theorem-size     17
proof            (modus-ponens tm-623 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68139.        ((A -> B) -> (C or ((A -> B) and (((D and A) or A) -> B)))), M:tm-623, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68140
in-theory        68140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-622 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68140.        ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-622, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68141
in-theory        68141
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((D and B) or B) -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-798 ((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> (or (and Cm Am) Am) (or B Am))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68141.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((D and B) or B) -> (C or B)))), M:tm-619, m:tm-798, u:((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> (or (and Cm Am) Am) (or B Am)))))
================================================================
tm-name          tm-68142
in-theory        68142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68142.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (E or D))), M:tm-609, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68143
in-theory        68143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-605 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68143.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-605, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68144
in-theory        68144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (E or D)) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68144.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (E or D)) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))), M:tm-595, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68145
in-theory        68145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-550 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68145.        (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-550, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68146
in-theory        68146
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-540 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68146.        ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-540, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68147
in-theory        68147
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-530 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68147.        ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-530, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68148
in-theory        68148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-520 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68148.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-520, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68149
in-theory        68149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-510 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-68149.        ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-510, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68150
in-theory        68150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-500 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68150.        ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-500, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68151
in-theory        68151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-490 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68151.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F)))), M:tm-490, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68152
in-theory        68152
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-480 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68152.        ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-480, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68153
in-theory        68153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((A -> B) and (((C and A) or A) -> B)) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68153.        ((A -> B) -> (((A -> B) and (((C and A) or A) -> B)) or D)), M:tm-470, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68154
in-theory        68154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-469 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68154.        ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-469, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68155
in-theory        68155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((D and B) or B) -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-798 ((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> (or (and Cm Am) Am) (or Am B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68155.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((D and B) or B) -> (B or C)))), M:tm-466, m:tm-798, u:((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> (or (and Cm Am) Am) (or Am B)))))
================================================================
tm-name          tm-68156
in-theory        68156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68156.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (D or E))), M:tm-456, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68157
in-theory        68157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-453 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68157.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-453, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68158
in-theory        68158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (D or E)) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68158.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (D or E)) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))), M:tm-443, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68159
in-theory        68159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-409 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68159.        (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-409, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68160
in-theory        68160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-400 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68160.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-400, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68161
in-theory        68161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-391 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-68161.        ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-391, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68162
in-theory        68162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-382 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68162.        ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-382, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68163
in-theory        68163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-373 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68163.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F)))), M:tm-373, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68164
in-theory        68164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-364 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68164.        (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-364, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68165
in-theory        68165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((A -> B) and (((D and A) or A) -> B)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68165.        ((A -> B) -> (C -> (((A -> B) and (((D and A) or A) -> B)) and C))), M:tm-355, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68166
in-theory        68166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-354 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68166.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-354, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68167
in-theory        68167
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((D and B) or B) -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-351 tm-798 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> (or (and Cm Am) Am) (-> B (and Am B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 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-5.            (A -> (B -> (A and 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-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-68167.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((D and B) or B) -> (C -> (B and C))))), M:tm-351, m:tm-798, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> (or (and Cm Am) Am) (-> B (and Am B))))))
================================================================
tm-name          tm-68168
in-theory        68168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-68168.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68169
in-theory        68169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D))))
theorem-size     25
proof            (modus-ponens tm-338 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68169.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D)))), M:tm-338, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68170
in-theory        68170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((C and A) or A) -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-798 ((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> (or (and Cm Am) Am) (and Am B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68170.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((C and A) or A) -> (A and B)))), M:tm-335, m:tm-798, u:((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> (or (and Cm Am) Am) (and Am B)))))
================================================================
tm-name          tm-68171
in-theory        68171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((A -> B) -> ((A -> B) and ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     35
proof            (modus-ponens tm-328 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
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-328.          ((A -> 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-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-68171.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((A -> B) -> ((A -> B) and ((A -> B) and (((C and A) or A) -> B))))), M:tm-328, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68172
in-theory        68172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (E -> (D and E))) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68172.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (E -> (D and E))) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))), M:tm-327, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68173
in-theory        68173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((D and E) -> E) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68173.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((D and E) -> E) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))), M:tm-326, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68174
in-theory        68174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((D and E) -> D) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68174.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((D and E) -> D) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))), M:tm-325, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68175
in-theory        68175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68175.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))), M:tm-324, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68176
in-theory        68176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (E -> D)) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68176.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (E -> D)) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))), M:tm-323, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68177
in-theory        68177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68177.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D and E) -> E)), M:tm-322, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68178
in-theory        68178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68178.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D and E) -> D)), M:tm-320, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68179
in-theory        68179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68179.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68180
in-theory        68180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((A -> B) -> (A -> B)))
theorem-size     23
proof            (modus-ponens tm-316 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) 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-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-68180.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68181
in-theory        68181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-68181.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (E -> D))), M:tm-315, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68182
in-theory        68182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((A -> B) -> (not ((A -> B) and (((C and A) or A) -> B)))) -> (not (A -> B))))
theorem-size     37
proof            (modus-ponens tm-313 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-68182.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((A -> B) -> (not ((A -> B) and (((C and A) or A) -> B)))) -> (not (A -> B)))), M:tm-313, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68183
in-theory        68183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((((A -> B) and (((C and A) or A) -> B)) -> D) -> (((A -> B) or ((A -> B) and (((C and A) or A) -> B))) -> D)))
theorem-size     47
proof            (modus-ponens tm-312 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-68183.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and ((((A -> B) and (((C and A) or A) -> B)) -> D) -> (((A -> B) or ((A -> B) and (((C and A) or A) -> B))) -> D))), M:tm-312, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68184
in-theory        68184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D or ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68184.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D or ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))), M:tm-311, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68185
in-theory        68185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68185.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) or D)), M:tm-310, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68186
in-theory        68186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68186.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and D))), M:tm-309, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68187
in-theory        68187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-68187.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) and (D -> ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))), M:tm-305, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68188
in-theory        68188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-303 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-4.            ((A and B) -> B), axiom
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-68188.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-303, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68189
in-theory        68189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-270 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-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-68189.        ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-270, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68190
in-theory        68190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-239 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68190.        ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-239, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68191
in-theory        68191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-210 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> B), axiom
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-68191.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F)))), M:tm-210, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68192
in-theory        68192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-183 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68192.        ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-183, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68193
in-theory        68193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-157 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-68193.        ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-157, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68194
in-theory        68194
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((D and (B and C)) or (B and C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-154 tm-798 ((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (or (and Cm (and A Bm)) (and A Bm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 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-4.            ((A 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-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-68194.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((D and (B and C)) or (B and C)) -> C))), M:tm-154, m:tm-798, u:((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (or (and Cm (and A Bm)) (and A Bm)) Bm))))
================================================================
tm-name          tm-68195
in-theory        68195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-147 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am 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-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-68195.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-147, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68196
in-theory        68196
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((D and (A and (B -> C))) or (A and (B -> C))) -> C)))
theorem-size     39
proof            (modus-ponens tm-144 tm-798 ((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (or (and Cm (and A (-> B Bm))) (and A (-> B Bm))) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (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-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-68196.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((D and (A and (B -> C))) or (A and (B -> C))) -> C))), M:tm-144, m:tm-798, u:((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (or (and Cm (and A (-> B Bm))) (and A (-> B Bm))) Bm))))
================================================================
tm-name          tm-68197
in-theory        68197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-134 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68197.        ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-134, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68198
in-theory        68198
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((D and (B and C)) or (B and C)) -> B)))
theorem-size     25
proof            (modus-ponens tm-131 tm-798 ((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (or (and Cm (and Bm B)) (and Bm B)) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68198.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((D and (B and C)) or (B and C)) -> B))), M:tm-131, m:tm-798, u:((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (or (and Cm (and Bm B)) (and Bm B)) Bm))))
================================================================
tm-name          tm-68199
in-theory        68199
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-125 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68199.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-125, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68200
in-theory        68200
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((D and ((A -> B) and C)) or ((A -> B) and C)) -> B)))
theorem-size     39
proof            (modus-ponens tm-122 tm-798 ((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (or (and Cm (and (-> A Bm) C)) (and (-> A Bm) C)) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68200.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((D and ((A -> B) and C)) or ((A -> B) and C)) -> B))), M:tm-122, m:tm-798, u:((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (or (and Cm (and (-> A Bm) C)) (and (-> A Bm) C)) Bm))))
================================================================
tm-name          tm-68201
in-theory        68201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-113 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68201.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F)))), M:tm-113, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68202
in-theory        68202
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     51
proof            (modus-ponens tm-110 tm-798 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (or (and Cm (-> A (-> B C))) (-> A (-> B C))) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68202.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-798, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (or (and Cm (-> A (-> B C))) (-> A (-> B C))) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-68203
in-theory        68203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-105 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68203.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-105, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68204
in-theory        68204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((D and (A -> (B -> C))) or (A -> (B -> C))) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-102 tm-798 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (or (and Cm (-> A (-> B C))) (-> A (-> B C))) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> 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-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-68204.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((D and (A -> (B -> C))) or (A -> (B -> C))) -> (A -> C)))), M:tm-102, m:tm-798, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (or (and Cm (-> A (-> B C))) (-> A (-> B C))) (-> A C)))))
================================================================
tm-name          tm-68205
in-theory        68205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-95 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68205.        (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D)))), M:tm-95, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68206
in-theory        68206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (((C and A) or A) -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-798 ((Bm Am) (A Am) (B (and (-> Am Am) (-> (or (and Cm Am) Am) Am)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68206.        (((A -> B) or (A -> A)) -> ((A -> A) and (((C and A) or A) -> A))), M:tm-92, m:tm-798, u:((Bm Am) (A Am) (B (and (-> Am Am) (-> (or (and Cm Am) Am) Am))))
================================================================
tm-name          tm-68207
in-theory        68207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> B) and (((D and A) or A) -> B))))
theorem-size     17
proof            (modus-ponens tm-84 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68207.        ((A -> B) -> (C -> ((A -> B) and (((D and A) or A) -> B)))), M:tm-84, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68208
in-theory        68208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-83 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68208.        ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-83, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68209
in-theory        68209
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((D and B) or B) -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-798 ((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> (or (and Cm Am) Am) (-> B Am))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68209.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((D and B) or B) -> (C -> B)))), M:tm-80, m:tm-798, u:((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> (or (and Cm Am) Am) (-> B Am)))))
================================================================
tm-name          tm-68210
in-theory        68210
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and (((D and B) or B) -> C))))
theorem-size     21
proof            (modus-ponens tm-76 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68210.        (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and (((D and B) or B) -> C)))), M:tm-76, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68211
in-theory        68211
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and (((C and A) or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-73 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68211.        (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and (((C and A) or A) -> B))), M:tm-73, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68212
in-theory        68212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D))))
theorem-size     27
proof            (modus-ponens tm-69 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68212.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D)))), M:tm-69, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68213
in-theory        68213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((C and (A -> (not B))) or (A -> (not B))) -> (not A))))
theorem-size     34
proof            (modus-ponens tm-66 tm-798 ((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (or (and Cm (-> A (not B))) (-> A (not B))) (not A))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68213.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((C and (A -> (not B))) or (A -> (not B))) -> (not A)))), M:tm-66, m:tm-798, u:((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (or (and Cm (-> A (not B))) (-> A (not B))) (not A)))))
================================================================
tm-name          tm-68214
in-theory        68214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-54 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-68214.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-54, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68215
in-theory        68215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-51 tm-798 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (or (and Cm (-> A B)) (-> A B)) (-> (or C A) B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68215.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))), M:tm-51, m:tm-798, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (or (and Cm (-> A B)) (-> A B)) (-> (or C A) B)))))
================================================================
tm-name          tm-68216
in-theory        68216
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((C and B) or B) -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-798 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (or (and Cm Am) Am) (and B Am))))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-68216.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((C and B) or B) -> (A and B)))), M:tm-48, m:tm-798, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (or (and Cm Am) Am) (and B Am)))))
================================================================
tm-name          tm-68217
in-theory        68217
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B -> C) and (((D and B) or B) -> C)))
theorem-size     21
proof            (modus-ponens tm-47 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-8 tm-4 tm-2 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am 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-68217.        (((A and (B -> C)) or (B -> C)) -> ((B -> C) and (((D and B) or B) -> C))), M:tm-47, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68218
in-theory        68218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (((D and A) or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-46 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-8 tm-3 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-68218.        ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (((D and A) or A) -> B))), M:tm-46, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68219
in-theory        68219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-45 tm-798 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and Cm (-> A B)) (-> A B)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-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-68219.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-45, m:tm-798, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and Cm (-> A B)) (-> A B)) (-> A C)))))
================================================================
tm-name          tm-68220
in-theory        68220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (((C and B) or B) -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-798 ((A Am) (B Bm) (C (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-68220.        ((A or (B -> A)) -> ((B -> A) and (((C and B) or B) -> A))), M:tm-44, m:tm-798, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68221
in-theory        68221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-42 tm-798 ((A (-> (-> Am Bm) (and (-> 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      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-4.            ((A and B) -> B), axiom
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-68221.        ((A -> (B or A)) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D)))), M:tm-42, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68222
in-theory        68222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-32 tm-798 ((A (-> (-> Am Bm) (and (-> 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      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-4.            ((A and B) -> B), axiom
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-68222.        ((A -> (A or B)) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D)))), M:tm-32, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68223
in-theory        68223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((A -> B) and (((C and A) or A) -> B))))
theorem-size     19
proof            (modus-ponens tm-24 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-68223.        ((A -> B) -> ((A -> B) and ((A -> B) and (((C and A) or A) -> B)))), M:tm-24, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68224
in-theory        68224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-23 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68224.        ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D)))), M:tm-23, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68225
in-theory        68225
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-22 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-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-68225.        (((A and B) -> B) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D)))), M:tm-22, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68226
in-theory        68226
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-21 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68226.        (((A and B) -> A) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D)))), M:tm-21, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68227
in-theory        68227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-20 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68227.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-20, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68228
in-theory        68228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-19 tm-798 ((A (-> (-> Am Bm) (and (-> 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      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-4.            ((A and B) -> B), axiom
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-68228.        ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and (((E and C) or C) -> D)))), M:tm-19, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68229
in-theory        68229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> B) and (((C and A) or A) -> B)))) -> (not (A -> B)))
theorem-size     21
proof            (modus-ponens tm-9 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68229.        (((A -> B) -> (not ((A -> B) and (((C and A) or A) -> B)))) -> (not (A -> B))), M:tm-9, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68230
in-theory        68230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and (((C and A) or A) -> B)) -> D) -> (((A -> B) or ((A -> B) and (((C and A) or A) -> B))) -> D))
theorem-size     31
proof            (modus-ponens tm-8 tm-798 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68230.        ((((A -> B) and (((C and A) or A) -> B)) -> D) -> (((A -> B) or ((A -> B) and (((C and A) or A) -> B))) -> D)), M:tm-8, m:tm-798, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-68231
in-theory        68231
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> ((B -> C) and (((D and B) or B) -> C))))
theorem-size     17
proof            (modus-ponens tm-7 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68231.        (A or ((B -> C) -> ((B -> C) and (((D and B) or B) -> C)))), M:tm-7, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68232
in-theory        68232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68232.        (((A -> B) -> ((A -> B) and (((C and A) or A) -> B))) or D), M:tm-6, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68233
in-theory        68233
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((B -> C) and (((D and B) or B) -> C))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-798 ((A (-> (-> Am Bm) (and (-> 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-68233.        (A -> (((B -> C) -> ((B -> C) and (((D and B) or B) -> C))) and A)), M:tm-5, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68234
in-theory        68234
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> ((B -> C) and (((D and B) or B) -> C))))
theorem-size     17
proof            (modus-ponens tm-1 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-68234.        (A -> ((B -> C) -> ((B -> C) and (((D and B) or B) -> C)))), M:tm-1, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-68235
in-theory        68235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-68235.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-757, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68236
in-theory        68236
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 and G) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-68236.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-708, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68237
in-theory        68237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-68237.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-665, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68238
in-theory        68238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68238.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-622, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68239
in-theory        68239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68239.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68240
in-theory        68240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68240.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-605, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68241
in-theory        68241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68241.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-595, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68242
in-theory        68242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-4.            ((A and B) -> B), axiom
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-68242.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-550, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68243
in-theory        68243
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> B), axiom
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-68243.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-540, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68244
in-theory        68244
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-4.            ((A and B) -> B), axiom
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-68244.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-530, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68245
in-theory        68245
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68245.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-520, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68246
in-theory        68246
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-68246.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-510, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68247
in-theory        68247
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-4.            ((A and B) -> B), axiom
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-68247.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-500, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68248
in-theory        68248
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68248.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-490, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68249
in-theory        68249
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68249.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-480, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68250
in-theory        68250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68250.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-469, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68251
in-theory        68251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68251.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68252
in-theory        68252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68252.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-453, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68253
in-theory        68253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68253.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-443, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68254
in-theory        68254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> B), axiom
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-68254.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-409, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68255
in-theory        68255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68255.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-400, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68256
in-theory        68256
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-68256.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-391, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68257
in-theory        68257
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-4.            ((A and B) -> B), axiom
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-68257.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-382, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68258
in-theory        68258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68258.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-373, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68259
in-theory        68259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68259.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-364, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68260
in-theory        68260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-4.            ((A and B) -> B), axiom
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-68260.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-354, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68261
in-theory        68261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> B), axiom
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-68261.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68262
in-theory        68262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> B), axiom
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-68262.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-338, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68263
in-theory        68263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-68263.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-327, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68264
in-theory        68264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-68264.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-326, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68265
in-theory        68265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68265.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-325, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68266
in-theory        68266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-68266.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-324, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68267
in-theory        68267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> B), axiom
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-68267.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-323, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68268
in-theory        68268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am 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-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-68268.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68269
in-theory        68269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-68269.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68270
in-theory        68270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-68270.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68271
in-theory        68271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68271.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68272
in-theory        68272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F or ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-68272.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F or ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-311, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68273
in-theory        68273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-68273.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) or F)), M:tm-310, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68274
in-theory        68274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-4.            ((A and B) -> B), axiom
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-68274.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and F))), M:tm-309, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68275
in-theory        68275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     31
proof            (modus-ponens tm-308 tm-799 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am 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-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-68275.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-308, m:tm-799, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-68276
in-theory        68276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (A -> (B -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-307 tm-799 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-4.            ((A and B) -> B), axiom
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-68276.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-799, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-68277
in-theory        68277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-4.            ((A and B) -> B), axiom
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-68277.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-305, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68278
in-theory        68278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68278.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-303, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68279
in-theory        68279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-68279.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-270, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68280
in-theory        68280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68280.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-239, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68281
in-theory        68281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> B), axiom
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-68281.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-210, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68282
in-theory        68282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-4.            ((A and B) -> B), axiom
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-68282.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-183, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68283
in-theory        68283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am 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-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-68283.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-157, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68284
in-theory        68284
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-68284.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-147, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68285
in-theory        68285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-68285.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-134, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68286
in-theory        68286
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-68286.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-125, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68287
in-theory        68287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68287.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-113, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68288
in-theory        68288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> B), axiom
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-68288.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-105, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68289
in-theory        68289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> B), axiom
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-68289.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-95, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68290
in-theory        68290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68290.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-83, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68291
in-theory        68291
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68291.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-76, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68292
in-theory        68292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68292.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-69, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68293
in-theory        68293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-68293.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-54, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68294
in-theory        68294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-4.            ((A and B) -> B), axiom
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-68294.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-42, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68295
in-theory        68295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-4.            ((A and B) -> B), axiom
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-68295.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-32, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68296
in-theory        68296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68296.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-23, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68297
in-theory        68297
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-68297.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-22, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68298
in-theory        68298
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68298.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-21, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68299
in-theory        68299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) 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-20.           (A -> (((B -> (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-4.            ((A and B) -> B), axiom
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-68299.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-20, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68300
in-theory        68300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-4.            ((A and B) -> B), axiom
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-68300.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-19, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68301
in-theory        68301
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-7 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68301.        (A or ((B -> (C -> (B and C))) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-7, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68302
in-theory        68302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68302.        (((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))) or F), M:tm-6, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68303
in-theory        68303
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> E) -> (((F and D) or D) -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68303.        (A -> (((B -> (C -> (B and C))) and ((D -> E) -> (((F and D) or D) -> E))) and A)), M:tm-5, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68304
in-theory        68304
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-1 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68304.        (A -> ((B -> (C -> (B and C))) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-1, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68305
in-theory        68305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68305.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-757, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68306
in-theory        68306
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 and G) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-68306.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-708, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68307
in-theory        68307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-68307.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-665, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68308
in-theory        68308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-68308.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-622, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68309
in-theory        68309
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-68309.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68310
in-theory        68310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68310.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-605, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68311
in-theory        68311
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-68311.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-595, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68312
in-theory        68312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-68312.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-550, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68313
in-theory        68313
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-68313.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-540, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68314
in-theory        68314
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-68314.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-530, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68315
in-theory        68315
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68315.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-520, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68316
in-theory        68316
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-22.           (A -> (((B and C) -> C) and A)), 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-68316.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-510, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68317
in-theory        68317
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68317.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-500, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68318
in-theory        68318
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68318.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-490, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68319
in-theory        68319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-68319.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-480, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68320
in-theory        68320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-68320.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-469, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68321
in-theory        68321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-68321.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68322
in-theory        68322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68322.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-453, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68323
in-theory        68323
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-68323.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-443, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68324
in-theory        68324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-68324.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-409, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68325
in-theory        68325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68325.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-400, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68326
in-theory        68326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-22.           (A -> (((B and C) -> C) and A)), 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-68326.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-391, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68327
in-theory        68327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68327.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-382, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68328
in-theory        68328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68328.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-373, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68329
in-theory        68329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-68329.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-364, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68330
in-theory        68330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-68330.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-354, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68331
in-theory        68331
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-68331.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68332
in-theory        68332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68332.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-338, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68333
in-theory        68333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-68333.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-327, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68334
in-theory        68334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-68334.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-326, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68335
in-theory        68335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68335.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-325, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68336
in-theory        68336
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68336.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-324, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68337
in-theory        68337
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-68337.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-323, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68338
in-theory        68338
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-22.           (A -> (((B and C) -> C) and A)), 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-68338.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68339
in-theory        68339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68339.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68340
in-theory        68340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-68340.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68341
in-theory        68341
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-68341.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68342
in-theory        68342
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F or (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-68342.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F or (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-311, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68343
in-theory        68343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-68343.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) or F)), M:tm-310, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68344
in-theory        68344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68344.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and F))), M:tm-309, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68345
in-theory        68345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-800 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
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-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-68345.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-308, m:tm-800, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-68346
in-theory        68346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((A and B) -> B))
theorem-size     23
proof            (modus-ponens tm-307 tm-800 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68346.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and ((A and B) -> B)), M:tm-307, m:tm-800, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-68347
in-theory        68347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) 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-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-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-68347.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-305, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68348
in-theory        68348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68348.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-303, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68349
in-theory        68349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-68349.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-270, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68350
in-theory        68350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68350.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-239, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68351
in-theory        68351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68351.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-210, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68352
in-theory        68352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-68352.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-183, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68353
in-theory        68353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-22.           (A -> (((B and C) -> C) and A)), 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-68353.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-157, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68354
in-theory        68354
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-22.           (A -> (((B and C) -> C) and A)), 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-68354.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-147, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68355
in-theory        68355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68355.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-134, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68356
in-theory        68356
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68356.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-125, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68357
in-theory        68357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68357.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-113, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68358
in-theory        68358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68358.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-105, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68359
in-theory        68359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68359.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-95, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68360
in-theory        68360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-68360.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-83, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68361
in-theory        68361
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68361.        (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-76, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68362
in-theory        68362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68362.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-69, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68363
in-theory        68363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-68363.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-54, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68364
in-theory        68364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68364.        ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-42, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68365
in-theory        68365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68365.        ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-32, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68366
in-theory        68366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68366.        ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-23, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68367
in-theory        68367
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-68367.        (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-22, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68368
in-theory        68368
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68368.        (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-21, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68369
in-theory        68369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68369.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-20, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68370
in-theory        68370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-68370.        ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-19, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68371
in-theory        68371
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-7 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8)
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-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-68371.        (A or (((B and C) -> C) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-7, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68372
in-theory        68372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-8)
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-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-68372.        ((((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))) or F), M:tm-6, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68373
in-theory        68373
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> E) -> (((F and D) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-68373.        (A -> ((((B and C) -> C) and ((D -> E) -> (((F and D) or D) -> E))) and A)), M:tm-5, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68374
in-theory        68374
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-1 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-8)
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-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-68374.        (A -> (((B and C) -> C) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-1, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68375
in-theory        68375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-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-68375.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-757, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68376
in-theory        68376
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 and G) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 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-3.            ((A and B) -> 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-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-68376.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-708, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68377
in-theory        68377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 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-3.            ((A and B) -> 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-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-68377.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-665, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68378
in-theory        68378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68378.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-622, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68379
in-theory        68379
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68379.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68380
in-theory        68380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68380.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-605, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68381
in-theory        68381
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68381.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-595, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68382
in-theory        68382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-4.            ((A and B) -> B), axiom
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-68382.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-550, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68383
in-theory        68383
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> B), axiom
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-68383.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-540, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68384
in-theory        68384
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-4.            ((A and B) -> B), axiom
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-68384.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-530, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68385
in-theory        68385
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68385.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-520, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68386
in-theory        68386
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68386.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-510, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68387
in-theory        68387
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-21.           (A -> (((B and C) -> B) and A)), 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-68387.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-500, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68388
in-theory        68388
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68388.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-490, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68389
in-theory        68389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68389.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-480, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68390
in-theory        68390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68390.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-469, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68391
in-theory        68391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68391.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68392
in-theory        68392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68392.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-453, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68393
in-theory        68393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68393.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-443, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68394
in-theory        68394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> B), axiom
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-68394.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-409, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68395
in-theory        68395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68395.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-400, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68396
in-theory        68396
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68396.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-391, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68397
in-theory        68397
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-21.           (A -> (((B and C) -> B) and A)), 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-68397.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-382, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68398
in-theory        68398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68398.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-373, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68399
in-theory        68399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68399.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-364, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68400
in-theory        68400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68400.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-354, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68401
in-theory        68401
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68401.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68402
in-theory        68402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68402.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-338, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68403
in-theory        68403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-68403.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-327, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68404
in-theory        68404
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68404.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-326, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68405
in-theory        68405
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-68405.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-325, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68406
in-theory        68406
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-68406.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-324, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68407
in-theory        68407
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> B), axiom
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-68407.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-323, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68408
in-theory        68408
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68408.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68409
in-theory        68409
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-21.           (A -> (((B and C) -> B) and A)), 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-68409.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68410
in-theory        68410
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68410.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68411
in-theory        68411
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68411.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68412
in-theory        68412
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F or (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-68412.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F or (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-311, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68413
in-theory        68413
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-68413.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) or F)), M:tm-310, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68414
in-theory        68414
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-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-4.            ((A and B) -> B), axiom
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-68414.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and F))), M:tm-309, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68415
in-theory        68415
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-801 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68415.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-308, m:tm-801, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-68416
in-theory        68416
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((A and B) -> A))
theorem-size     23
proof            (modus-ponens tm-307 tm-801 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-4.            ((A and B) -> B), axiom
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-68416.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and ((A and B) -> A)), M:tm-307, m:tm-801, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-68417
in-theory        68417
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) 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-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-4.            ((A and B) -> B), axiom
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-68417.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-305, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68418
in-theory        68418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68418.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-303, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68419
in-theory        68419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68419.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-270, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68420
in-theory        68420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-68420.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-239, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68421
in-theory        68421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68421.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-210, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68422
in-theory        68422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68422.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-183, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68423
in-theory        68423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68423.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-157, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68424
in-theory        68424
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68424.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-147, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68425
in-theory        68425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-21.           (A -> (((B and C) -> B) and A)), 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-68425.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-134, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68426
in-theory        68426
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-21.           (A -> (((B and C) -> B) and A)), 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-68426.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-125, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68427
in-theory        68427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68427.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-113, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68428
in-theory        68428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68428.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-105, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68429
in-theory        68429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68429.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-95, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68430
in-theory        68430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68430.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-83, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68431
in-theory        68431
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68431.        (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-76, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68432
in-theory        68432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68432.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-69, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68433
in-theory        68433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-68433.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-54, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68434
in-theory        68434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68434.        ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-42, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68435
in-theory        68435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68435.        ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-32, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68436
in-theory        68436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68436.        ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-23, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68437
in-theory        68437
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-68437.        (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-22, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68438
in-theory        68438
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-68438.        (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-21, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68439
in-theory        68439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68439.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-20, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68440
in-theory        68440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-68440.        ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-19, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68441
in-theory        68441
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-7 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68441.        (A or (((B and C) -> B) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-7, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68442
in-theory        68442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68442.        ((((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))) or F), M:tm-6, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68443
in-theory        68443
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> E) -> (((F and D) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68443.        (A -> ((((B and C) -> B) and ((D -> E) -> (((F and D) or D) -> E))) and A)), M:tm-5, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68444
in-theory        68444
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-1 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68444.        (A -> (((B and C) -> B) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-1, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68445
in-theory        68445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-757 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-68445.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-757, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68446
in-theory        68446
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 and H) or H) -> I))))
theorem-size     51
proof            (modus-ponens tm-708 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-68446.        (((((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 and H) or H) -> I)))), M:tm-708, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68447
in-theory        68447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-665 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-68447.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-665, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68448
in-theory        68448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-622 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68448.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-622, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68449
in-theory        68449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H or G)))
theorem-size     31
proof            (modus-ponens tm-609 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68449.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H or G))), M:tm-609, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68450
in-theory        68450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-605 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68450.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-605, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68451
in-theory        68451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68451.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-595, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68452
in-theory        68452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-550 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-4.            ((A and B) -> B), axiom
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-68452.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-550, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68453
in-theory        68453
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-540 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> B), axiom
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-68453.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-540, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68454
in-theory        68454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-530 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-4.            ((A and B) -> B), axiom
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-68454.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-530, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68455
in-theory        68455
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-520 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68455.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-520, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68456
in-theory        68456
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-510 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-68456.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-510, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68457
in-theory        68457
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-500 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-4.            ((A and B) -> B), axiom
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-68457.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-500, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68458
in-theory        68458
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 and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-490 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68458.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-490, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68459
in-theory        68459
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-480 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68459.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-480, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68460
in-theory        68460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-469 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68460.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-469, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68461
in-theory        68461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (G or H)))
theorem-size     31
proof            (modus-ponens tm-456 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68461.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (G or H))), M:tm-456, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68462
in-theory        68462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-453 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68462.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-453, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68463
in-theory        68463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68463.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-443, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68464
in-theory        68464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-409 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> B), axiom
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-68464.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-409, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68465
in-theory        68465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-400 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68465.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-400, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68466
in-theory        68466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-391 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-68466.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-391, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68467
in-theory        68467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-382 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-4.            ((A and B) -> B), axiom
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-68467.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-382, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68468
in-theory        68468
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 and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-373 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68468.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-373, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68469
in-theory        68469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-364 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68469.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-364, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68470
in-theory        68470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-354 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68470.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-354, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68471
in-theory        68471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H -> (G and H))))
theorem-size     33
proof            (modus-ponens tm-341 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> B), axiom
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-68471.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68472
in-theory        68472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-338 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68472.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-338, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68473
in-theory        68473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68473.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-327, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68474
in-theory        68474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-68474.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-326, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68475
in-theory        68475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68475.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-325, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68476
in-theory        68476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-68476.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-324, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68477
in-theory        68477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68477.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-323, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68478
in-theory        68478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G and H) -> H))
theorem-size     31
proof            (modus-ponens tm-322 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-68478.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68479
in-theory        68479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G and H) -> G))
theorem-size     31
proof            (modus-ponens tm-320 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-68479.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68480
in-theory        68480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     39
proof            (modus-ponens tm-318 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68480.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68481
in-theory        68481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H -> G)))
theorem-size     31
proof            (modus-ponens tm-315 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68481.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68482
in-theory        68482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-68482.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-311, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68483
in-theory        68483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) or G))
theorem-size     53
proof            (modus-ponens tm-310 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-68483.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) or G)), M:tm-310, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68484
in-theory        68484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and G)))
theorem-size     55
proof            (modus-ponens tm-309 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-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-4.            ((A and B) -> B), axiom
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-68484.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and G))), M:tm-309, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68485
in-theory        68485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     37
proof            (modus-ponens tm-308 tm-802 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
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-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-68485.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-308, m:tm-802, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))
================================================================
tm-name          tm-68486
in-theory        68486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-307 tm-802 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
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-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-4.            ((A and B) -> B), axiom
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-68486.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-802, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))
================================================================
tm-name          tm-68487
in-theory        68487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-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-4.            ((A and B) -> B), axiom
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-68487.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-305, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68488
in-theory        68488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-303 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68488.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-303, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68489
in-theory        68489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-270 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-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-68489.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-270, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68490
in-theory        68490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-239 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68490.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-239, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68491
in-theory        68491
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 and H) or H) -> I))))
theorem-size     43
proof            (modus-ponens tm-210 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-68491.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-210, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68492
in-theory        68492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-183 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68492.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-183, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68493
in-theory        68493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-157 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-68493.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-157, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68494
in-theory        68494
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 and G) or G) -> H))))
theorem-size     41
proof            (modus-ponens tm-147 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-68494.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-147, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68495
in-theory        68495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-134 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-68495.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-134, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68496
in-theory        68496
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 and G) or G) -> H))))
theorem-size     41
proof            (modus-ponens tm-125 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-68496.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-125, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68497
in-theory        68497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-113 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68497.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-113, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68498
in-theory        68498
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 and G) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-105 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> B), axiom
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-68498.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-105, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68499
in-theory        68499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-95 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> B), axiom
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-68499.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-95, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68500
in-theory        68500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-83 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68500.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-83, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68501
in-theory        68501
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-76 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68501.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-76, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68502
in-theory        68502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-69 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68502.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-69, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68503
in-theory        68503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-54 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-68503.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-54, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68504
in-theory        68504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-42 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68504.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-42, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68505
in-theory        68505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-32 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68505.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-32, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68506
in-theory        68506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-23 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68506.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-23, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68507
in-theory        68507
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-22 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-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-68507.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-22, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68508
in-theory        68508
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-21 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68508.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-21, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68509
in-theory        68509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-20 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-68509.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-20, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68510
in-theory        68510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-19 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-68510.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-19, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68511
in-theory        68511
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-7 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68511.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-7, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68512
in-theory        68512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) or G)
theorem-size     27
proof            (modus-ponens tm-6 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-6 tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68512.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))) or G), M:tm-6, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68513
in-theory        68513
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((G and E) or E) -> F))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-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-68513.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((G and E) or E) -> F))) and A)), M:tm-5, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68514
in-theory        68514
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-1 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-1 tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68514.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-1, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-68515
in-theory        68515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 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-1.            (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-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-68515.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-757, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68516
in-theory        68516
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 and G) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-1.            (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-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-68516.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-708, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68517
in-theory        68517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-68517.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-665, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68518
in-theory        68518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68518.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-622, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68519
in-theory        68519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68519.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68520
in-theory        68520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68520.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-605, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68521
in-theory        68521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68521.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-595, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68522
in-theory        68522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-4.            ((A and B) -> B), axiom
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-68522.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-550, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68523
in-theory        68523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> B), axiom
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-68523.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-540, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68524
in-theory        68524
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-4.            ((A and B) -> B), axiom
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-68524.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-530, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68525
in-theory        68525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68525.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-520, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68526
in-theory        68526
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-68526.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-510, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68527
in-theory        68527
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-4.            ((A and B) -> B), axiom
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-68527.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-500, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68528
in-theory        68528
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68528.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-490, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68529
in-theory        68529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68529.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-480, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68530
in-theory        68530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68530.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-469, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68531
in-theory        68531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68531.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68532
in-theory        68532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68532.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-453, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68533
in-theory        68533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68533.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-443, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68534
in-theory        68534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> B), axiom
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-68534.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-409, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68535
in-theory        68535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68535.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-400, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68536
in-theory        68536
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-68536.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-391, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68537
in-theory        68537
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-4.            ((A and B) -> B), axiom
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-68537.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-382, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68538
in-theory        68538
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68538.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-373, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68539
in-theory        68539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68539.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-364, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68540
in-theory        68540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68540.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-354, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68541
in-theory        68541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68541.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68542
in-theory        68542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68542.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-338, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68543
in-theory        68543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-68543.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-327, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68544
in-theory        68544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-68544.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-326, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68545
in-theory        68545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68545.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-325, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68546
in-theory        68546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-68546.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-324, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68547
in-theory        68547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-68547.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-323, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68548
in-theory        68548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm 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-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-68548.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68549
in-theory        68549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68549.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68550
in-theory        68550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68550.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68551
in-theory        68551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68551.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68552
in-theory        68552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F or ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-68552.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F or ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-311, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68553
in-theory        68553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-68553.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) or F)), M:tm-310, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68554
in-theory        68554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-4.            ((A and B) -> B), axiom
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-68554.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and F))), M:tm-309, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68555
in-theory        68555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-803 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-68555.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-308, m:tm-803, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-68556
in-theory        68556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (A -> (B -> A)))
theorem-size     23
proof            (modus-ponens tm-307 tm-803 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-4.            ((A and B) -> B), axiom
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-68556.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (A -> (B -> A))), M:tm-307, m:tm-803, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))
================================================================
tm-name          tm-68557
in-theory        68557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) 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-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-4.            ((A and B) -> B), axiom
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-68557.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) and (F -> ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))))), M:tm-305, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68558
in-theory        68558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68558.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-303, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68559
in-theory        68559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm 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-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-68559.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-270, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68560
in-theory        68560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68560.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-239, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68561
in-theory        68561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68561.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-210, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68562
in-theory        68562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-68562.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-183, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68563
in-theory        68563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm 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-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-68563.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-157, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68564
in-theory        68564
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-68564.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-147, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68565
in-theory        68565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68565.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-134, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68566
in-theory        68566
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-68566.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-125, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68567
in-theory        68567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68567.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-113, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68568
in-theory        68568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68568.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-105, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68569
in-theory        68569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68569.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-95, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68570
in-theory        68570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-68570.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-83, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68571
in-theory        68571
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68571.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-76, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68572
in-theory        68572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68572.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-69, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68573
in-theory        68573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (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-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-68573.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-54, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68574
in-theory        68574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68574.        ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-42, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68575
in-theory        68575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68575.        ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-32, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68576
in-theory        68576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68576.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-23, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68577
in-theory        68577
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm 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-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-68577.        (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-22, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68578
in-theory        68578
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-68578.        (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-21, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68579
in-theory        68579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-4.            ((A and B) -> B), axiom
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-68579.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-20, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68580
in-theory        68580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
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-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-68580.        ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-19, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68581
in-theory        68581
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-7 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68581.        (A or ((B -> (C -> B)) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-7, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68582
in-theory        68582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68582.        (((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))) or F), M:tm-6, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68583
in-theory        68583
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> E) -> (((F and D) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68583.        (A -> (((B -> (C -> B)) and ((D -> E) -> (((F and D) or D) -> E))) and A)), M:tm-5, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68584
in-theory        68584
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-1 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68584.        (A -> ((B -> (C -> B)) and ((D -> E) -> (((F and D) or D) -> E)))), M:tm-1, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-68585
in-theory        68585
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((D and ((A -> B) -> (not (((C and A) or A) -> B)))) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B))))
theorem-size     50
proof            (modus-ponens tm-798 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
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-68585.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((D and ((A -> B) -> (not (((C and A) or A) -> B)))) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B)))), M:tm-798, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68586
in-theory        68586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-757 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68586.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-757, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68587
in-theory        68587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((((A -> B) -> (not (((C and A) or A) -> B))) and D) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B))))
theorem-size     50
proof            (modus-ponens tm-747 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68587.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((((A -> B) -> (not (((C and A) or A) -> B))) and D) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B)))), M:tm-747, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68588
in-theory        68588
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F))))
theorem-size     43
proof            (modus-ponens tm-708 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68588.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F)))), M:tm-708, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68589
in-theory        68589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-665 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-68589.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-665, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68590
in-theory        68590
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((not (((C and A) or A) -> B)) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B))))
theorem-size     44
proof            (modus-ponens tm-654 tm-804 ((A (-> Am Bm)) (B (not (-> (or (and Cm Am) Am) Bm))) (C (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68590.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((not (((C and A) or A) -> B)) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B)))), M:tm-654, m:tm-804, u:((A (-> Am Bm)) (B (not (-> (or (and Cm Am) Am) Bm))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-68591
in-theory        68591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((C and A) or A) -> B))) -> (D or (not (A -> B))))
theorem-size     19
proof            (modus-ponens tm-623 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68591.        (((A -> B) -> (not (((C and A) or A) -> B))) -> (D or (not (A -> B)))), M:tm-623, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68592
in-theory        68592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-622 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68592.        ((A -> (B -> (C or B))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-622, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68593
in-theory        68593
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (((C and A) or A) -> (B or A)))))
theorem-size     17
proof            (modus-ponens tm-618 tm-804 ((A (-> (-> Am (or C Am)) (not (-> (or (and Cm Am) Am) (or C Am))))) (B Am) (Bm (or C Am))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 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-7.            (A -> (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-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-68593.        (not ((A -> (B or A)) -> (not (((C and A) or A) -> (B or A))))), M:tm-618, m:tm-804, u:((A (-> (-> Am (or C Am)) (not (-> (or (and Cm Am) Am) (or C Am))))) (B Am) (Bm (or C Am)))
================================================================
tm-name          tm-68594
in-theory        68594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68594.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (E or D))), M:tm-609, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68595
in-theory        68595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-605 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 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-605.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-68595.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-605, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68596
in-theory        68596
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (E or D)) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68596.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (E or D)) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))), M:tm-595, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68597
in-theory        68597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-550 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68597.        (((A -> (B or A)) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-550, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68598
in-theory        68598
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-540 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68598.        ((A or (B -> (C or B))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-540, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68599
in-theory        68599
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-530 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68599.        ((A or (B -> (B or C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-530, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68600
in-theory        68600
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-520 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68600.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-520, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68601
in-theory        68601
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-510 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-68601.        ((A or ((B and C) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-510, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68602
in-theory        68602
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-500 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68602.        ((A or ((B and C) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-500, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68603
in-theory        68603
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-490 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68603.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F)))), M:tm-490, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68604
in-theory        68604
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-480 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68604.        ((A or (B -> (C -> B))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-480, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68605
in-theory        68605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((C and A) or A) -> B))) -> ((not (A -> B)) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68605.        (((A -> B) -> (not (((C and A) or A) -> B))) -> ((not (A -> B)) or D)), M:tm-470, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68606
in-theory        68606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-469 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68606.        ((A -> (B -> (B or C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-469, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68607
in-theory        68607
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (((C and A) or A) -> (A or B)))))
theorem-size     17
proof            (modus-ponens tm-465 tm-804 ((A (-> (-> Am (or Am C)) (not (-> (or (and Cm Am) Am) (or Am C))))) (B Am) (Bm (or Am C))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 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-6.            (A -> (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-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-68607.        (not ((A -> (A or B)) -> (not (((C and A) or A) -> (A or B))))), M:tm-465, m:tm-804, u:((A (-> (-> Am (or Am C)) (not (-> (or (and Cm Am) Am) (or Am C))))) (B Am) (Bm (or Am C)))
================================================================
tm-name          tm-68608
in-theory        68608
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68608.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (D or E))), M:tm-456, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68609
in-theory        68609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-453 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 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-453.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-68609.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-453, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68610
in-theory        68610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (D or E)) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68610.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (D or E)) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))), M:tm-443, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68611
in-theory        68611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-409 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68611.        (((A -> (A or B)) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-409, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68612
in-theory        68612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-400 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68612.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-400, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68613
in-theory        68613
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-391 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-68613.        ((((A and B) -> B) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-391, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68614
in-theory        68614
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-382 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68614.        ((((A and B) -> A) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-382, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68615
in-theory        68615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-373 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68615.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F)))), M:tm-373, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68616
in-theory        68616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-364 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68616.        (((A -> (B -> A)) or C) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-364, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68617
in-theory        68617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((C and A) or A) -> B))) -> (D -> ((not (A -> B)) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-4.            ((A and B) -> B), axiom
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-68617.        (((A -> B) -> (not (((C and A) or A) -> B))) -> (D -> ((not (A -> B)) and D))), M:tm-355, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68618
in-theory        68618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-354 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68618.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-354, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68619
in-theory        68619
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (((C and A) or A) -> (B -> (A and B))))))
theorem-size     21
proof            (modus-ponens tm-350 tm-804 ((A (-> (-> Am (-> C (and Am C))) (not (-> (or (and Cm Am) Am) (-> C (and Am C)))))) (B Am) (Bm (-> C (and Am C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and 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-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-68619.        (not ((A -> (B -> (A and B))) -> (not (((C and A) or A) -> (B -> (A and B)))))), M:tm-350, m:tm-804, u:((A (-> (-> Am (-> C (and Am C))) (not (-> (or (and Cm Am) Am) (-> C (and Am C)))))) (B Am) (Bm (-> C (and Am C))))
================================================================
tm-name          tm-68620
in-theory        68620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> B), axiom
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-68620.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68621
in-theory        68621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D))))
theorem-size     27
proof            (modus-ponens tm-338 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> B), axiom
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-68621.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D)))), M:tm-338, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68622
in-theory        68622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (((A -> B) -> (not (((C and A) or A) -> B))) and (not (A -> B)))))
theorem-size     48
proof            (modus-ponens tm-328 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68622.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (((A -> B) -> (not (((C and A) or A) -> B))) and (not (A -> B))))), M:tm-328, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68623
in-theory        68623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> (D and E))) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-68623.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> (D and E))) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))), M:tm-327, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68624
in-theory        68624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((D and E) -> E) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-68624.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((D and E) -> E) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))), M:tm-326, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68625
in-theory        68625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((D and E) -> D) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68625.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((D and E) -> D) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))), M:tm-325, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68626
in-theory        68626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-68626.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))), M:tm-324, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68627
in-theory        68627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> D)) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> B), axiom
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-68627.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> D)) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))), M:tm-323, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68628
in-theory        68628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-68628.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D and E) -> E)), M:tm-322, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68629
in-theory        68629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-68629.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D and E) -> D)), M:tm-320, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68630
in-theory        68630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-68630.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68631
in-theory        68631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((A -> B) -> (not (((C and A) or A) -> B))) -> ((A -> B) -> (not (((C and A) or A) -> B)))))
theorem-size     43
proof            (modus-ponens tm-316 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-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-68631.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((A -> B) -> (not (((C and A) or A) -> B))) -> ((A -> B) -> (not (((C and A) or A) -> B))))), M:tm-316, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68632
in-theory        68632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68632.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (E -> D))), M:tm-315, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68633
in-theory        68633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (((C and A) or A) -> B))))))
theorem-size     50
proof            (modus-ponens tm-313 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68633.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (((C and A) or A) -> B)))))), M:tm-313, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68634
in-theory        68634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((not (A -> B)) -> D) -> ((((A -> B) -> (not (((C and A) or A) -> B))) or (not (A -> B))) -> D)))
theorem-size     44
proof            (modus-ponens tm-312 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68634.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (((not (A -> B)) -> D) -> ((((A -> B) -> (not (((C and A) or A) -> B))) or (not (A -> B))) -> D))), M:tm-312, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68635
in-theory        68635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D or (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-68635.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D or (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))), M:tm-311, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68636
in-theory        68636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-68636.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) or D)), M:tm-310, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68637
in-theory        68637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 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-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-4.            ((A and B) -> B), axiom
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-68637.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and D))), M:tm-309, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68638
in-theory        68638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-4.            ((A and B) -> B), axiom
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-68638.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) and (D -> (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))), M:tm-305, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68639
in-theory        68639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-303 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68639.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-303, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68640
in-theory        68640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-270 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8)
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-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-68640.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-270, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68641
in-theory        68641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-239 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 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-239.          (A -> ((B -> (((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-4.            ((A and B) -> B), axiom
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-68641.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-239, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68642
in-theory        68642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F))))
theorem-size     35
proof            (modus-ponens tm-210 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 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-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> B), axiom
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-68642.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F)))), M:tm-210, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68643
in-theory        68643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-183 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 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-183.          (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-4.            ((A and B) -> B), axiom
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-68643.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-183, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68644
in-theory        68644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-157 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-68644.        ((A -> ((B and C) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-157, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68645
in-theory        68645
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (((C and (A and B)) or (A and B)) -> B))))
theorem-size     19
proof            (modus-ponens tm-153 tm-804 ((A (-> (-> (and B Bm) Bm) (not (-> (or (and Cm (and B Bm)) (and B Bm)) Bm)))) (Am (and B Bm)) (C Bm)))
axioms-used      (tm-9 tm-1 tm-4 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-4.            ((A 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-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-68645.        (not (((A and B) -> B) -> (not (((C and (A and B)) or (A and B)) -> B)))), M:tm-153, m:tm-804, u:((A (-> (-> (and B Bm) Bm) (not (-> (or (and Cm (and B Bm)) (and B Bm)) Bm)))) (Am (and B Bm)) (C Bm))
================================================================
tm-name          tm-68646
in-theory        68646
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-147 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-68646.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-147, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68647
in-theory        68647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-134 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68647.        ((A -> ((B and C) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-134, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68648
in-theory        68648
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (((C and (A and B)) or (A and B)) -> A))))
theorem-size     19
proof            (modus-ponens tm-130 tm-804 ((A (-> (-> (and Bm C) Bm) (not (-> (or (and Cm (and Bm C)) (and Bm C)) Bm)))) (Am (and Bm C)) (B Bm)))
axioms-used      (tm-9 tm-1 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68648.        (not (((A and B) -> A) -> (not (((C and (A and B)) or (A and B)) -> A)))), M:tm-130, m:tm-804, u:((A (-> (-> (and Bm C) Bm) (not (-> (or (and Cm (and Bm C)) (and Bm C)) Bm)))) (Am (and Bm C)) (B Bm))
================================================================
tm-name          tm-68649
in-theory        68649
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-125 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-68649.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-125, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68650
in-theory        68650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-113 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68650.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F)))), M:tm-113, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68651
in-theory        68651
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((D and (A -> (B -> C))) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))))
theorem-size     37
proof            (modus-ponens tm-109 tm-804 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (or (and Cm (-> B (-> C D))) (-> 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-4)
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-4.            ((A and B) -> B), axiom
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-68651.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((D and (A -> (B -> C))) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))), M:tm-109, m:tm-804, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (or (and Cm (-> B (-> C D))) (-> B (-> C D))) (-> (-> B C) (-> B D)))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D))))
================================================================
tm-name          tm-68652
in-theory        68652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     37
proof            (modus-ponens tm-105 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> B), axiom
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-68652.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-105, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68653
in-theory        68653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-95 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> B), axiom
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-68653.        (((A -> B) -> (A -> A)) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D)))), M:tm-95, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68654
in-theory        68654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((C and A) or A) -> B))) -> (D -> (not (A -> B))))
theorem-size     19
proof            (modus-ponens tm-84 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68654.        (((A -> B) -> (not (((C and A) or A) -> B))) -> (D -> (not (A -> B)))), M:tm-84, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68655
in-theory        68655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-83 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68655.        ((A -> (B -> (C -> B))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-83, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68656
in-theory        68656
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (((C and A) or A) -> (B -> A)))))
theorem-size     17
proof            (modus-ponens tm-79 tm-804 ((A (-> (-> Am (-> C Am)) (not (-> (or (and Cm Am) Am) (-> C Am))))) (B Am) (Bm (-> C Am))))
axioms-used      (tm-9 tm-1 tm-8 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-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-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-68656.        (not ((A -> (B -> A)) -> (not (((C and A) or A) -> (B -> A))))), M:tm-79, m:tm-804, u:((A (-> (-> Am (-> C Am)) (not (-> (or (and Cm Am) Am) (-> C Am))))) (B Am) (Bm (-> C Am)))
================================================================
tm-name          tm-68657
in-theory        68657
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (not (((D and B) or B) -> C))) -> (not (B -> C))))
theorem-size     23
proof            (modus-ponens tm-76 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68657.        (((not (not A)) -> A) and (((B -> C) -> (not (((D and B) or B) -> C))) -> (not (B -> C)))), M:tm-76, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68658
in-theory        68658
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> (not (((C and A) or A) -> B))))) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B)))
theorem-size     32
proof            (modus-ponens tm-73 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68658.        (((not (not ((A -> B) -> (not (((C and A) or A) -> B))))) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B))), M:tm-73, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68659
in-theory        68659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D))))
theorem-size     29
proof            (modus-ponens tm-69 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am 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-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-68659.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D)))), M:tm-69, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68660
in-theory        68660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-54 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68660.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-54, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68661
in-theory        68661
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> (not (((D and B) or B) -> C)))) or ((B -> C) -> (not (((D and B) or B) -> C)))) -> (not (B -> C)))
theorem-size     32
proof            (modus-ponens tm-47 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-4 tm-9)
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-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-68661.        (((A and ((B -> C) -> (not (((D and B) or B) -> C)))) or ((B -> C) -> (not (((D and B) or B) -> C)))) -> (not (B -> C))), M:tm-47, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68662
in-theory        68662
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (not (((C and A) or A) -> B))) and D) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B)))
theorem-size     32
proof            (modus-ponens tm-46 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68662.        (((((A -> B) -> (not (((C and A) or A) -> B))) and D) or ((A -> B) -> (not (((C and A) or A) -> B)))) -> (not (A -> B))), M:tm-46, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68663
in-theory        68663
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A and B) or B) -> C)) or ((B -> C) -> (not (((A and B) or B) -> C)))) -> (not (B -> C)))
theorem-size     26
proof            (modus-ponens tm-44 tm-804 ((A (-> Am Bm)) (B (not (-> (or (and Cm Am) Am) Bm))) (C (not (-> Am Bm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68663.        (((not (((A and B) or B) -> C)) or ((B -> C) -> (not (((A and B) or B) -> C)))) -> (not (B -> C))), M:tm-44, m:tm-804, u:((A (-> Am Bm)) (B (not (-> (or (and Cm Am) Am) Bm))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-68664
in-theory        68664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-42 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68664.        ((A -> (B or A)) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D)))), M:tm-42, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68665
in-theory        68665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-32 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68665.        ((A -> (A or B)) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D)))), M:tm-32, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68666
in-theory        68666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((C and A) or A) -> B))) -> (((A -> B) -> (not (((C and A) or A) -> B))) and (not (A -> B))))
theorem-size     30
proof            (modus-ponens tm-24 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68666.        (((A -> B) -> (not (((C and A) or A) -> B))) -> (((A -> B) -> (not (((C and A) or A) -> B))) and (not (A -> B)))), M:tm-24, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68667
in-theory        68667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-23 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 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-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-68667.        ((A -> (B -> (A and B))) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D)))), M:tm-23, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68668
in-theory        68668
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-22 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8)
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-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-68668.        (((A and B) -> B) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D)))), M:tm-22, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68669
in-theory        68669
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-21 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68669.        (((A and B) -> A) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D)))), M:tm-21, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68670
in-theory        68670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-20 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 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-20.           (A -> (((B -> (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-4.            ((A and B) -> B), axiom
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-68670.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-20, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68671
in-theory        68671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-19 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68671.        ((A -> (B -> A)) and (((C -> D) -> (not (((E and C) or C) -> D))) -> (not (C -> D)))), M:tm-19, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68672
in-theory        68672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((C and A) or A) -> B))) -> ((A -> B) -> (not (((C and A) or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-12 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68672.        (((A -> B) -> (not (((C and A) or A) -> B))) -> ((A -> B) -> (not (((C and A) or A) -> B)))), M:tm-12, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68673
in-theory        68673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (((C and A) or A) -> B)))))
theorem-size     32
proof            (modus-ponens tm-9 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68673.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (((C and A) or A) -> B))))), M:tm-9, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68674
in-theory        68674
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> B)) -> C) -> ((((A -> B) -> (not (((D and A) or A) -> B))) or (not (A -> B))) -> C))
theorem-size     26
proof            (modus-ponens tm-8 tm-804 ((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68674.        (((not (A -> B)) -> C) -> ((((A -> B) -> (not (((D and A) or A) -> B))) or (not (A -> B))) -> C)), M:tm-8, m:tm-804, u:((A (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-68675
in-theory        68675
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (not (((D and B) or B) -> C))) -> (not (B -> C))))
theorem-size     19
proof            (modus-ponens tm-7 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-7 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68675.        (A or (((B -> C) -> (not (((D and B) or B) -> C))) -> (not (B -> C)))), M:tm-7, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68676
in-theory        68676
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-6 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68676.        ((((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))) or D), M:tm-6, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68677
in-theory        68677
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (not (((D and B) or B) -> C))) -> (not (B -> C))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-68677.        (A -> ((((B -> C) -> (not (((D and B) or B) -> C))) -> (not (B -> C))) and A)), M:tm-5, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68678
in-theory        68678
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (not (((D and B) or B) -> C))) -> (not (B -> C))))
theorem-size     19
proof            (modus-ponens tm-1 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-1 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68678.        (A -> (((B -> C) -> (not (((D and B) or B) -> C))) -> (not (B -> C)))), M:tm-1, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-68679
in-theory        68679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (((C and A) or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-805 tm-1 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       91
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-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-1.            (A -> (B -> A)), axiom
tm-68679.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (((C and A) or A) -> B))), M:tm-805, m:tm-1, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68680
in-theory        68680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((D and A) or A) -> (B -> C))) -> ((((D and A) or A) -> B) -> (((D and A) or A) -> C)))
theorem-size     31
proof            (modus-ponens tm-805 tm-2 ((Am (or (and A B) B)) (C (-> Bm Cm)) (D (-> (-> (or (and A B) B) Bm) (-> (or (and A B) B) Cm)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-68680.        (((A -> (B -> C)) or (((D and A) or A) -> (B -> C))) -> ((((D and A) or A) -> B) -> (((D and A) or A) -> C))), M:tm-805, m:tm-2, u:((Am (or (and A B) B)) (C (-> Bm Cm)) (D (-> (-> (or (and A B) B) Bm) (-> (or (and A B) B) Cm))))
================================================================
tm-name          tm-68681
in-theory        68681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((((C and A) or A) -> B) and D)))
theorem-size     23
proof            (modus-ponens tm-805 tm-5 ((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> (or (and A B) B) C) Bm)))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       95
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-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-5.            (A -> (B -> (A and B))), axiom
tm-68681.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((((C and A) or A) -> B) and D))), M:tm-805, m:tm-5, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> (or (and A B) B) C) Bm))))
================================================================
tm-name          tm-68682
in-theory        68682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) or D))
theorem-size     21
proof            (modus-ponens tm-805 tm-6 ((Am (-> (or (and A B) B) C)) (D (or (-> (or (and A B) B) C) Bm))))
axioms-used      (tm-8 tm-4 tm-6)
proof-size       91
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-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-6.            (A -> (A or B)), axiom
tm-68682.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) or D)), M:tm-805, m:tm-6, u:((Am (-> (or (and A B) B) C)) (D (or (-> (or (and A B) B) C) Bm)))
================================================================
tm-name          tm-68683
in-theory        68683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D or (((C and A) or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-805 tm-7 ((Am (-> (or (and A B) B) C)) (D (or Bm (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-7)
proof-size       91
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-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-7.            (A -> (B or A)), axiom
tm-68683.        (((A -> B) or (((C and A) or A) -> B)) -> (D or (((C and A) or A) -> B))), M:tm-805, m:tm-7, u:((Am (-> (or (and A B) B) C)) (D (or Bm (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68684
in-theory        68684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((B -> D) -> ((((C and A) or A) or B) -> D)))
theorem-size     25
proof            (modus-ponens tm-805 tm-8 ((Am (or (and A B) B)) (C Bm) (D (-> (-> Bm Cm) (-> (or (or (and A B) B) Bm) Cm)))))
axioms-used      (tm-8 tm-4)
proof-size       103
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-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-68684.        (((A -> B) or (((C and A) or A) -> B)) -> ((B -> D) -> ((((C and A) or A) or B) -> D))), M:tm-805, m:tm-8, u:((Am (or (and A B) B)) (C Bm) (D (-> (-> Bm Cm) (-> (or (or (and A B) B) Bm) Cm))))
================================================================
tm-name          tm-68685
in-theory        68685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> (not B)) -> (not ((C and A) or A))))
theorem-size     27
proof            (modus-ponens tm-805 tm-9 ((Am (or (and A B) B)) (C Bm) (D (-> (-> (or (and A B) B) (not Bm)) (not (or (and A B) B))))))
axioms-used      (tm-8 tm-4 tm-9)
proof-size       103
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68685.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> (not B)) -> (not ((C and A) or A)))), M:tm-805, m:tm-9, u:((Am (or (and A B) B)) (C Bm) (D (-> (-> (or (and A B) B) (not Bm)) (not (or (and A B) B)))))
================================================================
tm-name          tm-68686
in-theory        68686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-805 tm-11 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm Bm)))))
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-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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-68686.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> D))), M:tm-805, m:tm-11, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-68687
in-theory        68687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> ((C and A) or A)))
theorem-size     23
proof            (modus-ponens tm-805 tm-12 ((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-68687.        (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> ((C and A) or A))), M:tm-805, m:tm-12, u:((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (or (and A B) B))))
================================================================
tm-name          tm-68688
in-theory        68688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-805 tm-14 ((Am (-> (or (and A B) B) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       123
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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-68688.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-805, m:tm-14, u:((Am (-> (or (and A B) B) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-68689
in-theory        68689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-805 tm-16 ((Am (-> (or (and A B) B) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-4 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-68689.        (((A -> B) or (((C and A) or A) -> B)) -> ((D and E) -> D)), M:tm-805, m:tm-16, u:((Am (-> (or (and A B) B) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-68690
in-theory        68690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-805 tm-18 ((Am (-> (or (and A B) B) C)) (D (-> (and Bm Cm) Cm))))
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-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-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-68690.        (((A -> B) or (((C and A) or A) -> B)) -> ((D and E) -> E)), M:tm-805, m:tm-18, u:((Am (-> (or (and A B) B) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-68691
in-theory        68691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> D)) and (((C and A) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-805 tm-19 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-68691.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-19, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68692
in-theory        68692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((C and A) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-805 tm-20 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-68692.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((C and A) or A) -> B))), M:tm-805, m:tm-20, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68693
in-theory        68693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D and E) -> D) and (((C and A) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-805 tm-21 ((Am (-> (or (and A B) B) C)) (D (and (-> (and Bm Cm) Bm) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-68693.        (((A -> B) or (((C and A) or A) -> B)) -> (((D and E) -> D) and (((C and A) or A) -> B))), M:tm-805, m:tm-21, u:((Am (-> (or (and A B) B) C)) (D (and (-> (and Bm Cm) Bm) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68694
in-theory        68694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D and E) -> E) and (((C and A) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-805 tm-22 ((Am (-> (or (and A B) B) C)) (D (and (-> (and Bm Cm) Cm) (-> (or (and A B) B) C)))))
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-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-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-68694.        (((A -> B) or (((C and A) or A) -> B)) -> (((D and E) -> E) and (((C and A) or A) -> B))), M:tm-805, m:tm-22, u:((Am (-> (or (and A B) B) C)) (D (and (-> (and Bm Cm) Cm) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68695
in-theory        68695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (D and E))) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-23 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (and A B) B) C)))))
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-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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-68695.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (D and E))) and (((C and A) or A) -> B))), M:tm-805, m:tm-23, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68696
in-theory        68696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (((C and A) or A) and B)))
theorem-size     25
proof            (modus-ponens tm-805 tm-24 ((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (and (or (and A B) B) Bm)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-68696.        (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (((C and A) or A) and B))), M:tm-805, m:tm-24, u:((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (and (or (and A B) B) Bm))))
================================================================
tm-name          tm-68697
in-theory        68697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-805 tm-25 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-68697.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (D and E)))), M:tm-805, m:tm-25, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-68698
in-theory        68698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (D or E)) and (((C and A) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-805 tm-32 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (or Bm Cm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-68698.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (D or E)) and (((C and A) or A) -> B))), M:tm-805, m:tm-32, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (or Bm Cm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68699
in-theory        68699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-805 tm-33 ((Am (-> (or (and A B) B) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-68699.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (D or E))), M:tm-805, m:tm-33, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-68700
in-theory        68700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E or D)) and (((C and A) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-805 tm-42 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (or Cm Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-68700.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E or D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-42, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (or Cm Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68701
in-theory        68701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-805 tm-43 ((Am (-> (or (and A B) B) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-68701.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E or D))), M:tm-805, m:tm-43, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-68702
in-theory        68702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((((C and A) or A) and D) or ((C and A) or A)) -> B))
theorem-size     27
proof            (modus-ponens tm-805 tm-46 ((Am (or (and A B) B)) (C Bm) (D (-> (or (and (or (and A B) B) Cm) (or (and A B) B)) Bm))))
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-68702.        (((A -> B) or (((C and A) or A) -> B)) -> (((((C and A) or A) and D) or ((C and A) or A)) -> B)), M:tm-805, m:tm-46, u:((Am (or (and A B) B)) (C Bm) (D (-> (or (and (or (and A B) B) Cm) (or (and A B) B)) Bm)))
================================================================
tm-name          tm-68703
in-theory        68703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D and ((C and A) or A)) or ((C and A) or A)) -> B))
theorem-size     27
proof            (modus-ponens tm-805 tm-47 ((Am (or (and A B) B)) (C Bm) (D (-> (or (and Cm (or (and A B) B)) (or (and A B) B)) Bm))))
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-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-68703.        (((A -> B) or (((C and A) or A) -> B)) -> (((D and ((C and A) or A)) or ((C and A) or A)) -> B)), M:tm-805, m:tm-47, u:((Am (or (and A B) B)) (C Bm) (D (-> (or (and Cm (or (and A B) B)) (or (and A B) B)) Bm)))
================================================================
tm-name          tm-68704
in-theory        68704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or ((C and A) or A)) -> B))
theorem-size     23
proof            (modus-ponens tm-805 tm-49 ((Am (and A Bm)) (B Bm) (C Cm) (D (-> (or (and A Bm) (or (and A Bm) Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-6)
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-68704.        (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or ((C and A) or A)) -> B)), M:tm-805, m:tm-49, u:((Am (and A Bm)) (B Bm) (C Cm) (D (-> (or (and A Bm) (or (and A Bm) Bm)) Cm)))
================================================================
tm-name          tm-68705
in-theory        68705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((A or ((C and A) or A)) -> B))
theorem-size     21
proof            (modus-ponens tm-805 tm-50 ((Am (and A Bm)) (B Bm) (C Cm) (D (-> (or Bm (or (and A Bm) Bm)) Cm))))
axioms-used      (tm-8 tm-4 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-68705.        (((A -> B) or (((C and A) or A) -> B)) -> ((A or ((C and A) or A)) -> B)), M:tm-805, m:tm-50, u:((Am (and A Bm)) (B Bm) (C Cm) (D (-> (or Bm (or (and A Bm) Bm)) Cm)))
================================================================
tm-name          tm-68706
in-theory        68706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((C and A) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-805 tm-54 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5)
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-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-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-68706.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((C and A) or A) -> B))), M:tm-805, m:tm-54, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68707
in-theory        68707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-805 tm-56 ((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       123
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-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-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-68707.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-805, m:tm-56, u:((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-68708
in-theory        68708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> ((C and A) or A)))) or (((C and A) or A) -> (not (B -> ((C and A) or A))))) -> (not ((C and A) or A)))
theorem-size     32
proof            (modus-ponens tm-805 tm-57 ((Am (or (and A B) B)) (C (not (-> Bm (or (and A B) B)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-1)
proof-size       122
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-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-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-68708.        (((A -> (not (B -> ((C and A) or A)))) or (((C and A) or A) -> (not (B -> ((C and A) or A))))) -> (not ((C and A) or A))), M:tm-805, m:tm-57, u:((Am (or (and A B) B)) (C (not (-> Bm (or (and A B) B)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68709
in-theory        68709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (((C and A) or A) and B)))) or (((C and A) or A) -> (not (B -> (((C and A) or A) and B))))) -> (not ((C and A) or A)))
theorem-size     36
proof            (modus-ponens tm-805 tm-61 ((Am (or (and A B) B)) (C (not (-> Bm (and (or (and A B) B) Bm)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-5)
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-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-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-68709.        (((A -> (not (B -> (((C and A) or A) and B)))) or (((C and A) or A) -> (not (B -> (((C and A) or A) and B))))) -> (not ((C and A) or A))), M:tm-805, m:tm-61, u:((Am (or (and A B) B)) (C (not (-> Bm (and (or (and A B) B) Bm)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68710
in-theory        68710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and A) or A) or C))) or (((B and A) or A) -> (not (((B and A) or A) or C)))) -> (not ((B and A) or A)))
theorem-size     32
proof            (modus-ponens tm-805 tm-62 ((Am (or (and A B) B)) (C (not (or (or (and A B) B) Bm))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-6)
proof-size       122
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-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-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-68710.        (((A -> (not (((B and A) or A) or C))) or (((B and A) or A) -> (not (((B and A) or A) or C)))) -> (not ((B and A) or A))), M:tm-805, m:tm-62, u:((Am (or (and A B) B)) (C (not (or (or (and A B) B) Bm))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68711
in-theory        68711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or ((C and A) or A)))) or (((C and A) or A) -> (not (B or ((C and A) or A))))) -> (not ((C and A) or A)))
theorem-size     32
proof            (modus-ponens tm-805 tm-63 ((Am (or (and A B) B)) (C (not (or Bm (or (and A B) B)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-7)
proof-size       122
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-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-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-68711.        (((A -> (not (B or ((C and A) or A)))) or (((C and A) or A) -> (not (B or ((C and A) or A))))) -> (not ((C and A) or A))), M:tm-805, m:tm-63, u:((Am (or (and A B) B)) (C (not (or Bm (or (and A B) B)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68712
in-theory        68712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((C and A) or A) -> B)))
theorem-size     31
proof            (modus-ponens tm-805 tm-69 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-9)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-68712.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((C and A) or A) -> B))), M:tm-805, m:tm-69, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68713
in-theory        68713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-805 tm-71 ((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-9)
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-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-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-68713.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-805, m:tm-71, u:((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-68714
in-theory        68714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((not (not ((C and A) or A))) or ((C and A) or A)) -> B))
theorem-size     27
proof            (modus-ponens tm-805 tm-73 ((Am (or (and A B) B)) (C Bm) (D (-> (or (not (not (or (and A B) B))) (or (and A B) B)) Bm))))
axioms-used      (tm-8 tm-4 tm-10)
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-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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-68714.        (((A -> B) or (((C and A) or A) -> B)) -> (((not (not ((C and A) or A))) or ((C and A) or A)) -> B)), M:tm-805, m:tm-73, u:((Am (or (and A B) B)) (C Bm) (D (-> (or (not (not (or (and A B) B))) (or (and A B) B)) Bm)))
================================================================
tm-name          tm-68715
in-theory        68715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((not (not D)) -> D) and (((C and A) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-805 tm-76 ((Am (-> (or (and A B) B) C)) (D (and (-> (not (not Bm)) Bm) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-10)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-68715.        (((A -> B) or (((C and A) or A) -> B)) -> (((not (not D)) -> D) and (((C and A) or A) -> B))), M:tm-805, m:tm-76, u:((Am (-> (or (and A B) B) C)) (D (and (-> (not (not Bm)) Bm) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68716
in-theory        68716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((not (not D)) -> D))
theorem-size     17
proof            (modus-ponens tm-805 tm-78 ((Am (-> (or (and A B) B) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-4 tm-1 tm-10)
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-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-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-68716.        (((A -> B) or (((C and A) or A) -> B)) -> ((not (not D)) -> D)), M:tm-805, m:tm-78, u:((Am (-> (or (and A B) B) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-68717
in-theory        68717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) or (((D and A) or A) -> (not (B -> (C -> B))))) -> (not ((D and A) or A)))
theorem-size     28
proof            (modus-ponens tm-805 tm-79 ((Am (or (and A B) B)) (C (not (-> Bm (-> Cm Bm)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-1)
proof-size       132
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-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-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-68717.        (((A -> (not (B -> (C -> B)))) or (((D and A) or A) -> (not (B -> (C -> B))))) -> (not ((D and A) or A))), M:tm-805, m:tm-79, u:((Am (or (and A B) B)) (C (not (-> Bm (-> Cm Bm)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68718
in-theory        68718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (F -> E))) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-83 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-68718.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (F -> E))) and (((C and A) or A) -> B))), M:tm-805, m:tm-83, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68719
in-theory        68719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (D -> B)))
theorem-size     21
proof            (modus-ponens tm-805 tm-84 ((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (-> Cm 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-68719.        (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (D -> B))), M:tm-805, m:tm-84, u:((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (-> Cm Bm))))
================================================================
tm-name          tm-68720
in-theory        68720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-805 tm-85 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-4 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-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-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-68720.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (F -> E)))), M:tm-805, m:tm-85, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-68721
in-theory        68721
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> B))
theorem-size     19
proof            (modus-ponens tm-805 tm-86 ((Am (-> (or (and A B) B) C)) (D (-> (or (and A B) B) C))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       117
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-68721.        (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> B)), M:tm-805, m:tm-86, u:((Am (-> (or (and A B) B) C)) (D (-> (or (and A B) B) C)))
================================================================
tm-name          tm-68722
in-theory        68722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((D and A) or A) -> (B -> C))) -> (((D and A) or A) -> (B -> C)))
theorem-size     25
proof            (modus-ponens tm-805 tm-87 ((Am (or (and A B) B)) (C (-> Bm Cm)) (D (-> (or (and A B) B) (-> Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-68722.        (((A -> (B -> C)) or (((D and A) or A) -> (B -> C))) -> (((D and A) or A) -> (B -> C))), M:tm-805, m:tm-87, u:((Am (or (and A B) B)) (C (-> Bm Cm)) (D (-> (or (and A B) B) (-> Bm Cm))))
================================================================
tm-name          tm-68723
in-theory        68723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> (D -> D)) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-95 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-2 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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-68723.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> (D -> D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-95, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68724
in-theory        68724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-805 tm-97 ((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
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-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-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-68724.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> (D -> D))), M:tm-805, m:tm-97, u:((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-68725
in-theory        68725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> ((C and A) or A)) -> D)) or (((C and A) or A) -> ((B -> ((C and A) or A)) -> D))) -> (((C and A) or A) -> D))
theorem-size     35
proof            (modus-ponens tm-805 tm-98 ((Am (or (and A B) B)) (C (-> (-> Bm (or (and A B) B)) Cm)) (D (-> (or (and A B) B) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-68725.        (((A -> ((B -> ((C and A) or A)) -> D)) or (((C and A) or A) -> ((B -> ((C and A) or A)) -> D))) -> (((C and A) or A) -> D)), M:tm-805, m:tm-98, u:((Am (or (and A B) B)) (C (-> (-> Bm (or (and A B) B)) Cm)) (D (-> (or (and A B) B) Cm)))
================================================================
tm-name          tm-68726
in-theory        68726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and A) or A) -> C)) or (((B and A) or A) -> (((B and A) or A) -> C))) -> (((B and A) or A) -> C))
theorem-size     31
proof            (modus-ponens tm-805 tm-99 ((Am (or (and A B) B)) (C (-> (or (and A B) B) Bm)) (D (-> (or (and A B) B) Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-68726.        (((A -> (((B and A) or A) -> C)) or (((B and A) or A) -> (((B and A) or A) -> C))) -> (((B and A) or A) -> C)), M:tm-805, m:tm-99, u:((Am (or (and A B) B)) (C (-> (or (and A B) B) Bm)) (D (-> (or (and A B) B) Bm)))
================================================================
tm-name          tm-68727
in-theory        68727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((C and A) or A) -> B)))
theorem-size     39
proof            (modus-ponens tm-805 tm-105 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-68727.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((C and A) or A) -> B))), M:tm-805, m:tm-105, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68728
in-theory        68728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-805 tm-107 ((Am (-> (or (and A B) B) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
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-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-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-68728.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-805, m:tm-107, u:((Am (-> (or (and A B) B) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-68729
in-theory        68729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or (((E and A) or A) -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not ((E and A) or A)))
theorem-size     44
proof            (modus-ponens tm-805 tm-109 ((Am (or (and A B) B)) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-2)
proof-size       172
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-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-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-68729.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or (((E and A) or A) -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not ((E and A) or A))), M:tm-805, m:tm-109, u:((Am (or (and A B) B)) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68730
in-theory        68730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((C and A) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-805 tm-113 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 tm-2)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-68730.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((C and A) or A) -> B))), M:tm-805, m:tm-113, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68731
in-theory        68731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) or (((E and A) or A) -> (B -> (C -> D)))) -> (((E and A) or A) -> ((B -> C) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-805 tm-114 ((Am (or (and A B) B)) (C (-> Bm (-> Cm Dm))) (D (-> (or (and A B) B) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
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-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-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-68731.        (((A -> (B -> (C -> D))) or (((E and A) or A) -> (B -> (C -> D)))) -> (((E and A) or A) -> ((B -> C) -> (B -> D)))), M:tm-805, m:tm-114, u:((Am (or (and A B) B)) (C (-> Bm (-> Cm Dm))) (D (-> (or (and A B) B) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-68732
in-theory        68732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-805 tm-115 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-68732.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-805, m:tm-115, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-68733
in-theory        68733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((C and A) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-805 tm-125 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-2 tm-3)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-68733.        (((A -> B) or (((C and A) or A) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((C and A) or A) -> B))), M:tm-805, m:tm-125, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68734
in-theory        68734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-805 tm-127 ((Am (-> (or (and A B) B) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2 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-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-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-68734.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-805, m:tm-127, u:((Am (-> (or (and A B) B) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-68735
in-theory        68735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) or (((D and A) or A) -> (not ((B and C) -> B)))) -> (not ((D and A) or A)))
theorem-size     28
proof            (modus-ponens tm-805 tm-130 ((Am (or (and A B) B)) (C (not (-> (and Bm Cm) Bm))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-3)
proof-size       132
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-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-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-68735.        (((A -> (not ((B and C) -> B))) or (((D and A) or A) -> (not ((B and C) -> B)))) -> (not ((D and A) or A))), M:tm-805, m:tm-130, u:((Am (or (and A B) B)) (C (not (-> (and Bm Cm) Bm))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68736
in-theory        68736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E and F) -> E)) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-134 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-68736.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E and F) -> E)) and (((C and A) or A) -> B))), M:tm-805, m:tm-134, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68737
in-theory        68737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) or (((D and A) or A) -> (B and C))) -> (((D and A) or A) -> B))
theorem-size     23
proof            (modus-ponens tm-805 tm-135 ((Am (or (and A B) B)) (C (and Bm Cm)) (D (-> (or (and A B) B) Bm))))
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-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-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-68737.        (((A -> (B and C)) or (((D and A) or A) -> (B and C))) -> (((D and A) or A) -> B)), M:tm-805, m:tm-135, u:((Am (or (and A B) B)) (C (and Bm Cm)) (D (-> (or (and A B) B) Bm)))
================================================================
tm-name          tm-68738
in-theory        68738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-805 tm-136 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-68738.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E and F) -> E))), M:tm-805, m:tm-136, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-68739
in-theory        68739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((C and A) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-805 tm-147 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
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-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-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-68739.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((C and A) or A) -> B))), M:tm-805, m:tm-147, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68740
in-theory        68740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-805 tm-149 ((Am (-> (or (and A B) B) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
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-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-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-68740.        (((A -> B) or (((C and A) or A) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-805, m:tm-149, u:((Am (-> (or (and A B) B) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-68741
in-theory        68741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) or (((D and A) or A) -> (not ((B and C) -> C)))) -> (not ((D and A) or A)))
theorem-size     28
proof            (modus-ponens tm-805 tm-153 ((Am (or (and A B) B)) (C (not (-> (and Bm Cm) Cm))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-1)
proof-size       132
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-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-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-68741.        (((A -> (not ((B and C) -> C))) or (((D and A) or A) -> (not ((B and C) -> C)))) -> (not ((D and A) or A))), M:tm-805, m:tm-153, u:((Am (or (and A B) B)) (C (not (-> (and Bm Cm) Cm))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68742
in-theory        68742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E and F) -> F)) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-157 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 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-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-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-68742.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E and F) -> F)) and (((C and A) or A) -> B))), M:tm-805, m:tm-157, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68743
in-theory        68743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) or (((D and A) or A) -> (B and C))) -> (((D and A) or A) -> C))
theorem-size     23
proof            (modus-ponens tm-805 tm-158 ((Am (or (and A B) B)) (C (and Bm Cm)) (D (-> (or (and A B) B) 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-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-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-68743.        (((A -> (B and C)) or (((D and A) or A) -> (B and C))) -> (((D and A) or A) -> C)), M:tm-805, m:tm-158, u:((Am (or (and A B) B)) (C (and Bm Cm)) (D (-> (or (and A B) B) Cm)))
================================================================
tm-name          tm-68744
in-theory        68744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-805 tm-159 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-4 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-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-1.            (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-68744.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E and F) -> F))), M:tm-805, m:tm-159, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-68745
in-theory        68745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and ((D and A) or A)))) or (((D and A) or A) -> (not ((B -> (C -> B)) and ((D and A) or A))))) -> (not ((D and A) or A)))
theorem-size     40
proof            (modus-ponens tm-805 tm-179 ((Am (or (and A B) B)) (C (not (and (-> Bm (-> Cm Bm)) (or (and A B) B)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-1)
proof-size       150
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-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-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-68745.        (((A -> (not ((B -> (C -> B)) and ((D and A) or A)))) or (((D and A) or A) -> (not ((B -> (C -> B)) and ((D and A) or A))))) -> (not ((D and A) or A))), M:tm-805, m:tm-179, u:((Am (or (and A B) B)) (C (not (and (-> Bm (-> Cm Bm)) (or (and A B) B)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68746
in-theory        68746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-183 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-68746.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-183, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68747
in-theory        68747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-805 tm-184 ((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-4 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-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-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-68747.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (F -> E)) and D))), M:tm-805, m:tm-184, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-68748
in-theory        68748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and A) or A)))) or (((E and A) or A) -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and A) or A))))) -> (not ((E and A) or A)))
theorem-size     56
proof            (modus-ponens tm-805 tm-206 ((Am (or (and A B) B)) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or (and A B) B)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-2)
proof-size       190
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-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-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-68748.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and A) or A)))) or (((E and A) or A) -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and A) or A))))) -> (not ((E and A) or A))), M:tm-805, m:tm-206, u:((Am (or (and A B) B)) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or (and A B) B)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68749
in-theory        68749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((C and A) or A) -> B)))
theorem-size     37
proof            (modus-ponens tm-805 tm-210 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-68749.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-210, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68750
in-theory        68750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-805 tm-211 ((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 tm-2)
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-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-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-68750.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-805, m:tm-211, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-68751
in-theory        68751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and ((D and A) or A)))) or (((D and A) or A) -> (not (((B and C) -> B) and ((D and A) or A))))) -> (not ((D and A) or A)))
theorem-size     40
proof            (modus-ponens tm-805 tm-235 ((Am (or (and A B) B)) (C (not (and (-> (and Bm Cm) Bm) (or (and A B) B)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-3)
proof-size       150
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-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-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-68751.        (((A -> (not (((B and C) -> B) and ((D and A) or A)))) or (((D and A) or A) -> (not (((B and C) -> B) and ((D and A) or A))))) -> (not ((D and A) or A))), M:tm-805, m:tm-235, u:((Am (or (and A B) B)) (C (not (and (-> (and Bm Cm) Bm) (or (and A B) B)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68752
in-theory        68752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (((E and F) -> E) and D)) and (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-239 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-3)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-68752.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (((E and F) -> E) and D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-239, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68753
in-theory        68753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (((E and F) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-805 tm-240 ((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 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-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-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-68753.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (((E and F) -> E) and D))), M:tm-805, m:tm-240, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-68754
in-theory        68754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and ((D and A) or A)))) or (((D and A) or A) -> (not (((B and C) -> C) and ((D and A) or A))))) -> (not ((D and A) or A)))
theorem-size     40
proof            (modus-ponens tm-805 tm-266 ((Am (or (and A B) B)) (C (not (and (-> (and Bm Cm) Cm) (or (and A B) B)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-5)
proof-size       150
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-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-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-68754.        (((A -> (not (((B and C) -> C) and ((D and A) or A)))) or (((D and A) or A) -> (not (((B and C) -> C) and ((D and A) or A))))) -> (not ((D and A) or A))), M:tm-805, m:tm-266, u:((Am (or (and A B) B)) (C (not (and (-> (and Bm Cm) Cm) (or (and A B) B)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68755
in-theory        68755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (((E and F) -> F) and D)) and (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-270 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5)
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-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-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-68755.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (((E and F) -> F) and D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-270, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68756
in-theory        68756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (((E and F) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-805 tm-271 ((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-4 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-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-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-68756.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (((E and F) -> F) and D))), M:tm-805, m:tm-271, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-68757
in-theory        68757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and ((D and A) or A)))) or (((D and A) or A) -> (not ((B -> (C -> (B and C))) and ((D and A) or A))))) -> (not ((D and A) or A)))
theorem-size     44
proof            (modus-ponens tm-805 tm-299 ((Am (or (and A B) B)) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or (and A B) B)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-5)
proof-size       160
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-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-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-68757.        (((A -> (not ((B -> (C -> (B and C))) and ((D and A) or A)))) or (((D and A) or A) -> (not ((B -> (C -> (B and C))) and ((D and A) or A))))) -> (not ((D and A) or A))), M:tm-805, m:tm-299, u:((Am (or (and A B) B)) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or (and A B) B)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68758
in-theory        68758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((C and A) or A) -> B)))
theorem-size     31
proof            (modus-ponens tm-805 tm-303 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       143
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-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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-68758.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-303, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68759
in-theory        68759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-805 tm-304 ((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
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-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-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-68759.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-805, m:tm-304, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-68760
in-theory        68760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (((C and A) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-805 tm-305 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (-> (or (and A B) B) C))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-68760.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (((C and A) or A) -> B)))), M:tm-805, m:tm-305, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (-> (or (and A B) B) C)))))
================================================================
tm-name          tm-68761
in-theory        68761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((D and A) or A) -> (B -> C))) -> ((((D and A) or A) -> (B -> C)) and ((((D and A) or A) -> B) -> (((D and A) or A) -> C))))
theorem-size     41
proof            (modus-ponens tm-805 tm-306 ((Am (or (and A B) B)) (C (-> Bm Cm)) (D (and (-> (or (and A B) B) (-> Bm Cm)) (-> (-> (or (and A B) B) Bm) (-> (or (and A B) B) Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-68761.        (((A -> (B -> C)) or (((D and A) or A) -> (B -> C))) -> ((((D and A) or A) -> (B -> C)) and ((((D and A) or A) -> B) -> (((D and A) or A) -> C)))), M:tm-805, m:tm-306, u:((Am (or (and A B) B)) (C (-> Bm Cm)) (D (and (-> (or (and A B) B) (-> Bm Cm)) (-> (-> (or (and A B) B) Bm) (-> (or (and A B) B) Cm)))))
================================================================
tm-name          tm-68762
in-theory        68762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> ((((C and A) or A) -> B) and D))))
theorem-size     31
proof            (modus-ponens tm-805 tm-309 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (and (-> (or (and A B) B) C) Bm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       141
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-68762.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> ((((C and A) or A) -> B) and D)))), M:tm-805, m:tm-309, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (and (-> (or (and A B) B) C) Bm)))))
================================================================
tm-name          tm-68763
in-theory        68763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((((C and A) or A) -> B) or D)))
theorem-size     29
proof            (modus-ponens tm-805 tm-310 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (or (-> (or (and A B) B) C) Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-6)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-68763.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((((C and A) or A) -> B) or D))), M:tm-805, m:tm-310, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (or (-> (or (and A B) B) C) Bm))))
================================================================
tm-name          tm-68764
in-theory        68764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D or (((C and A) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-805 tm-311 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (or Bm (-> (or (and A B) B) C))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-7)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-68764.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D or (((C and A) or A) -> B)))), M:tm-805, m:tm-311, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (or Bm (-> (or (and A B) B) C)))))
================================================================
tm-name          tm-68765
in-theory        68765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((B -> D) -> ((((C and A) or A) or B) -> D))))
theorem-size     33
proof            (modus-ponens tm-805 tm-312 ((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (-> Bm Cm) (-> (or (or (and A B) B) Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       157
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-68765.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((B -> D) -> ((((C and A) or A) or B) -> D)))), M:tm-805, m:tm-312, u:((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (-> Bm Cm) (-> (or (or (and A B) B) Bm) Cm)))))
================================================================
tm-name          tm-68766
in-theory        68766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((((C and A) or A) -> (not B)) -> (not ((C and A) or A)))))
theorem-size     35
proof            (modus-ponens tm-805 tm-313 ((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (-> (or (and A B) B) (not Bm)) (not (or (and A B) B)))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-9)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-68766.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((((C and A) or A) -> (not B)) -> (not ((C and A) or A))))), M:tm-805, m:tm-313, u:((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (-> (or (and A B) B) (not Bm)) (not (or (and A B) B))))))
================================================================
tm-name          tm-68767
in-theory        68767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-805 tm-315 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-68767.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (E -> D)))), M:tm-805, m:tm-315, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-68768
in-theory        68768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((C and A) or A) -> ((C and A) or A))))
theorem-size     31
proof            (modus-ponens tm-805 tm-316 ((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (or (and A B) B) (or (and A B) B))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-68768.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((C and A) or A) -> ((C and A) or A)))), M:tm-805, m:tm-316, u:((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (or (and A B) B) (or (and A B) B)))))
================================================================
tm-name          tm-68769
in-theory        68769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-805 tm-318 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-68769.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-805, m:tm-318, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-68770
in-theory        68770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D and E) -> D)))
theorem-size     25
proof            (modus-ponens tm-805 tm-320 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-68770.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D and E) -> D))), M:tm-805, m:tm-320, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-68771
in-theory        68771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D and E) -> E)))
theorem-size     25
proof            (modus-ponens tm-805 tm-322 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-68771.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D and E) -> E))), M:tm-805, m:tm-322, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-68772
in-theory        68772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (E -> D)) and (((C and A) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-805 tm-323 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> Bm (-> Cm Bm)) (-> (or (and A B) B) C))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-68772.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (E -> D)) and (((C and A) or A) -> B)))), M:tm-805, m:tm-323, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> Bm (-> Cm Bm)) (-> (or (and A B) B) C)))))
================================================================
tm-name          tm-68773
in-theory        68773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((C and A) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-805 tm-324 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (and A B) B) C))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-68773.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((C and A) or A) -> B)))), M:tm-805, m:tm-324, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (and A B) B) C)))))
================================================================
tm-name          tm-68774
in-theory        68774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((D and E) -> D) and (((C and A) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-805 tm-325 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> (and Bm Cm) Bm) (-> (or (and A B) B) C))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-68774.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((D and E) -> D) and (((C and A) or A) -> B)))), M:tm-805, m:tm-325, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> (and Bm Cm) Bm) (-> (or (and A B) B) C)))))
================================================================
tm-name          tm-68775
in-theory        68775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((D and E) -> E) and (((C and A) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-805 tm-326 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> (and Bm Cm) Cm) (-> (or (and A B) B) C))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-68775.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((D and E) -> E) and (((C and A) or A) -> B)))), M:tm-805, m:tm-326, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> (and Bm Cm) Cm) (-> (or (and A B) B) C)))))
================================================================
tm-name          tm-68776
in-theory        68776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (E -> (D and E))) and (((C and A) or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-805 tm-327 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (and A B) B) C))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-68776.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (E -> (D and E))) and (((C and A) or A) -> B)))), M:tm-805, m:tm-327, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (and A B) B) C)))))
================================================================
tm-name          tm-68777
in-theory        68777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((C and A) or A) -> (((C and A) or A) and B))))
theorem-size     33
proof            (modus-ponens tm-805 tm-328 ((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (or (and A B) B) (and (or (and A B) B) Bm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-68777.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((C and A) or A) -> (((C and A) or A) and B)))), M:tm-805, m:tm-328, u:((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (or (and A B) B) (and (or (and A B) B) Bm)))))
================================================================
tm-name          tm-68778
in-theory        68778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> (D -> (D and E))) and (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-338 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       143
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-68778.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> (D -> (D and E))) and (((C and A) or A) -> B))), M:tm-805, m:tm-338, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68779
in-theory        68779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-805 tm-340 ((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2 tm-5)
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-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-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-68779.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> (D -> (D and E)))), M:tm-805, m:tm-340, u:((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-68780
in-theory        68780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-805 tm-341 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-68780.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (E -> (D and E))))), M:tm-805, m:tm-341, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-68781
in-theory        68781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (((C and A) or A) and B)) -> D)) or (((C and A) or A) -> ((B -> (((C and A) or A) and B)) -> D))) -> (((C and A) or A) -> D))
theorem-size     39
proof            (modus-ponens tm-805 tm-349 ((Am (or (and A B) B)) (C (-> (-> Bm (and (or (and A B) B) Bm)) Cm)) (D (-> (or (and A B) B) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-5)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-68781.        (((A -> ((B -> (((C and A) or A) and B)) -> D)) or (((C and A) or A) -> ((B -> (((C and A) or A) and B)) -> D))) -> (((C and A) or A) -> D)), M:tm-805, m:tm-349, u:((Am (or (and A B) B)) (C (-> (-> Bm (and (or (and A B) B) Bm)) Cm)) (D (-> (or (and A B) B) Cm)))
================================================================
tm-name          tm-68782
in-theory        68782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) or (((D and A) or A) -> (not (B -> (C -> (B and C)))))) -> (not ((D and A) or A)))
theorem-size     32
proof            (modus-ponens tm-805 tm-350 ((Am (or (and A B) B)) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-5)
proof-size       142
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-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-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-68782.        (((A -> (not (B -> (C -> (B and C))))) or (((D and A) or A) -> (not (B -> (C -> (B and C)))))) -> (not ((D and A) or A))), M:tm-805, m:tm-350, u:((Am (or (and A B) B)) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68783
in-theory        68783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (F -> (E and F)))) and (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-354 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-68783.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (F -> (E and F)))) and (((C and A) or A) -> B))), M:tm-805, m:tm-354, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68784
in-theory        68784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (D -> (B and D))))
theorem-size     23
proof            (modus-ponens tm-805 tm-355 ((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (-> Cm (and Bm 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-68784.        (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (D -> (B and D)))), M:tm-805, m:tm-355, u:((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-68785
in-theory        68785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-805 tm-356 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-4 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-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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-68785.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (F -> (E and F))))), M:tm-805, m:tm-356, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-68786
in-theory        68786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> D)) or F) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-364 ((Am (-> (or (and A B) B) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6 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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-68786.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> D)) or F) and (((C and A) or A) -> B))), M:tm-805, m:tm-364, u:((Am (-> (or (and A B) B) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68787
in-theory        68787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-805 tm-365 ((Am (-> (or (and A B) B) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
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-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-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-68787.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> D)) or F)), M:tm-805, m:tm-365, u:((Am (-> (or (and A B) B) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-68788
in-theory        68788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((C and A) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-805 tm-373 ((Am (-> (or (and A B) B) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6 tm-2)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-68788.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((C and A) or A) -> B))), M:tm-805, m:tm-373, u:((Am (-> (or (and A B) B) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68789
in-theory        68789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-805 tm-374 ((Am (-> (or (and A B) B) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-4 tm-1 tm-6 tm-2)
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-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-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-68789.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-805, m:tm-374, u:((Am (-> (or (and A B) B) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-68790
in-theory        68790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D and E) -> D) or F) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-382 ((Am (-> (or (and A B) B) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6 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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-68790.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D and E) -> D) or F) and (((C and A) or A) -> B))), M:tm-805, m:tm-382, u:((Am (-> (or (and A B) B) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68791
in-theory        68791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D and E) -> D) or F))
theorem-size     19
proof            (modus-ponens tm-805 tm-383 ((Am (-> (or (and A B) B) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6 tm-3)
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-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-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-68791.        (((A -> B) or (((C and A) or A) -> B)) -> (((D and E) -> D) or F)), M:tm-805, m:tm-383, u:((Am (-> (or (and A B) B) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-68792
in-theory        68792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D and E) -> E) or F) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-391 ((Am (-> (or (and A B) B) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-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-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-68792.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D and E) -> E) or F) and (((C and A) or A) -> B))), M:tm-805, m:tm-391, u:((Am (-> (or (and A B) B) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68793
in-theory        68793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D and E) -> E) or F))
theorem-size     19
proof            (modus-ponens tm-805 tm-392 ((Am (-> (or (and A B) B) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
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-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-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-68793.        (((A -> B) or (((C and A) or A) -> B)) -> (((D and E) -> E) or F)), M:tm-805, m:tm-392, u:((Am (-> (or (and A B) B) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-68794
in-theory        68794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> (D and E))) or F) and (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-400 ((Am (-> (or (and A B) B) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-68794.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E -> (D and E))) or F) and (((C and A) or A) -> B))), M:tm-805, m:tm-400, u:((Am (-> (or (and A B) B) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68795
in-theory        68795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-805 tm-401 ((Am (-> (or (and A B) B) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6 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-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-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-68795.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (D and E))) or F)), M:tm-805, m:tm-401, u:((Am (-> (or (and A B) B) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-68796
in-theory        68796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (D or E)) or F) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-409 ((Am (-> (or (and A B) B) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-68796.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (D or E)) or F) and (((C and A) or A) -> B))), M:tm-805, m:tm-409, u:((Am (-> (or (and A B) B) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68797
in-theory        68797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (D or E)) or F))
theorem-size     19
proof            (modus-ponens tm-805 tm-410 ((Am (-> (or (and A B) B) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
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-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-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-68797.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (D or E)) or F)), M:tm-805, m:tm-410, u:((Am (-> (or (and A B) B) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-68798
in-theory        68798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (D or E)) and (((C and A) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-805 tm-443 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> Bm (or Bm Cm)) (-> (or (and A B) B) C))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-68798.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (D or E)) and (((C and A) or A) -> B)))), M:tm-805, m:tm-443, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> Bm (or Bm Cm)) (-> (or (and A B) B) C)))))
================================================================
tm-name          tm-68799
in-theory        68799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and ((D and A) or A)))) or (((D and A) or A) -> (not ((B -> (B or C)) and ((D and A) or A))))) -> (not ((D and A) or A)))
theorem-size     40
proof            (modus-ponens tm-805 tm-449 ((Am (or (and A B) B)) (C (not (and (-> Bm (or Bm Cm)) (or (and A B) B)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-6)
proof-size       150
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-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-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-68799.        (((A -> (not ((B -> (B or C)) and ((D and A) or A)))) or (((D and A) or A) -> (not ((B -> (B or C)) and ((D and A) or A))))) -> (not ((D and A) or A))), M:tm-805, m:tm-449, u:((Am (or (and A B) B)) (C (not (and (-> Bm (or Bm Cm)) (or (and A B) B)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68800
in-theory        68800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (E or F)) and D)) and (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-453 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-68800.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (E or F)) and D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-453, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68801
in-theory        68801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-805 tm-454 ((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 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-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-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-68801.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (E or F)) and D))), M:tm-805, m:tm-454, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-68802
in-theory        68802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (D or E))))
theorem-size     25
proof            (modus-ponens tm-805 tm-456 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-68802.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (D or E)))), M:tm-805, m:tm-456, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-68803
in-theory        68803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((((B and A) or A) or C) -> D)) or (((B and A) or A) -> ((((B and A) or A) or C) -> D))) -> (((B and A) or A) -> D))
theorem-size     35
proof            (modus-ponens tm-805 tm-464 ((Am (or (and A B) B)) (C (-> (or (or (and A B) B) Bm) Cm)) (D (-> (or (and A B) B) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-68803.        (((A -> ((((B and A) or A) or C) -> D)) or (((B and A) or A) -> ((((B and A) or A) or C) -> D))) -> (((B and A) or A) -> D)), M:tm-805, m:tm-464, u:((Am (or (and A B) B)) (C (-> (or (or (and A B) B) Bm) Cm)) (D (-> (or (and A B) B) Cm)))
================================================================
tm-name          tm-68804
in-theory        68804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) or (((D and A) or A) -> (not (B -> (B or C))))) -> (not ((D and A) or A)))
theorem-size     28
proof            (modus-ponens tm-805 tm-465 ((Am (or (and A B) B)) (C (not (-> Bm (or Bm Cm)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-6)
proof-size       132
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-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-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-68804.        (((A -> (not (B -> (B or C)))) or (((D and A) or A) -> (not (B -> (B or C))))) -> (not ((D and A) or A))), M:tm-805, m:tm-465, u:((Am (or (and A B) B)) (C (not (-> Bm (or Bm Cm)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68805
in-theory        68805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (E or F))) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-469 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-68805.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (E or F))) and (((C and A) or A) -> B))), M:tm-805, m:tm-469, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68806
in-theory        68806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (B or D)))
theorem-size     21
proof            (modus-ponens tm-805 tm-470 ((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (or Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-6)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-68806.        (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (B or D))), M:tm-805, m:tm-470, u:((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (or Bm Cm))))
================================================================
tm-name          tm-68807
in-theory        68807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-805 tm-471 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-68807.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (E or F)))), M:tm-805, m:tm-471, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-68808
in-theory        68808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D or (E -> (F -> E))) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-480 ((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7 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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-68808.        (((A -> B) or (((C and A) or A) -> B)) -> ((D or (E -> (F -> E))) and (((C and A) or A) -> B))), M:tm-805, m:tm-480, u:((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68809
in-theory        68809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D or (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-805 tm-481 ((Am (-> (or (and A B) B) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
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-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-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-68809.        (((A -> B) or (((C and A) or A) -> B)) -> (D or (E -> (F -> E)))), M:tm-805, m:tm-481, u:((Am (-> (or (and A B) B) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-68810
in-theory        68810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((C and A) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-805 tm-490 ((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7 tm-2)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-68810.        (((A -> B) or (((C and A) or A) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((C and A) or A) -> B))), M:tm-805, m:tm-490, u:((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68811
in-theory        68811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-805 tm-491 ((Am (-> (or (and A B) B) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7 tm-2)
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-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-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-68811.        (((A -> B) or (((C and A) or A) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-805, m:tm-491, u:((Am (-> (or (and A B) B) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-68812
in-theory        68812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D or ((E and F) -> E)) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-500 ((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7 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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-68812.        (((A -> B) or (((C and A) or A) -> B)) -> ((D or ((E and F) -> E)) and (((C and A) or A) -> B))), M:tm-805, m:tm-500, u:((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68813
in-theory        68813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D or ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-805 tm-501 ((Am (-> (or (and A B) B) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7 tm-3)
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-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-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-68813.        (((A -> B) or (((C and A) or A) -> B)) -> (D or ((E and F) -> E))), M:tm-805, m:tm-501, u:((Am (-> (or (and A B) B) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-68814
in-theory        68814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D or ((E and F) -> F)) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-510 ((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-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-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-68814.        (((A -> B) or (((C and A) or A) -> B)) -> ((D or ((E and F) -> F)) and (((C and A) or A) -> B))), M:tm-805, m:tm-510, u:((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68815
in-theory        68815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D or ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-805 tm-511 ((Am (-> (or (and A B) B) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
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-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-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-68815.        (((A -> B) or (((C and A) or A) -> B)) -> (D or ((E and F) -> F))), M:tm-805, m:tm-511, u:((Am (-> (or (and A B) B) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-68816
in-theory        68816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D or (E -> (F -> (E and F)))) and (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-520 ((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-68816.        (((A -> B) or (((C and A) or A) -> B)) -> ((D or (E -> (F -> (E and F)))) and (((C and A) or A) -> B))), M:tm-805, m:tm-520, u:((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68817
in-theory        68817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D or (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-805 tm-521 ((Am (-> (or (and A B) B) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7 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-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-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-68817.        (((A -> B) or (((C and A) or A) -> B)) -> (D or (E -> (F -> (E and F))))), M:tm-805, m:tm-521, u:((Am (-> (or (and A B) B) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-68818
in-theory        68818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D or (E -> (E or F))) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-530 ((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-68818.        (((A -> B) or (((C and A) or A) -> B)) -> ((D or (E -> (E or F))) and (((C and A) or A) -> B))), M:tm-805, m:tm-530, u:((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68819
in-theory        68819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D or (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-805 tm-531 ((Am (-> (or (and A B) B) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7 tm-6)
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-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-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-68819.        (((A -> B) or (((C and A) or A) -> B)) -> (D or (E -> (E or F)))), M:tm-805, m:tm-531, u:((Am (-> (or (and A B) B) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-68820
in-theory        68820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D or (E -> (F or E))) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-540 ((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-68820.        (((A -> B) or (((C and A) or A) -> B)) -> ((D or (E -> (F or E))) and (((C and A) or A) -> B))), M:tm-805, m:tm-540, u:((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68821
in-theory        68821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D or (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-805 tm-541 ((Am (-> (or (and A B) B) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
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-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-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-68821.        (((A -> B) or (((C and A) or A) -> B)) -> (D or (E -> (F or E)))), M:tm-805, m:tm-541, u:((Am (-> (or (and A B) B) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-68822
in-theory        68822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E or D)) or F) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-550 ((Am (-> (or (and A B) B) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-68822.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E or D)) or F) and (((C and A) or A) -> B))), M:tm-805, m:tm-550, u:((Am (-> (or (and A B) B) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68823
in-theory        68823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E or D)) or F))
theorem-size     19
proof            (modus-ponens tm-805 tm-551 ((Am (-> (or (and A B) B) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6 tm-7)
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-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-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-68823.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E or D)) or F)), M:tm-805, m:tm-551, u:((Am (-> (or (and A B) B) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-68824
in-theory        68824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (E or D)) and (((C and A) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-805 tm-595 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> Bm (or Cm Bm)) (-> (or (and A B) B) C))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-68824.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((D -> (E or D)) and (((C and A) or A) -> B)))), M:tm-805, m:tm-595, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (and (-> Bm (or Cm Bm)) (-> (or (and A B) B) C)))))
================================================================
tm-name          tm-68825
in-theory        68825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and ((D and A) or A)))) or (((D and A) or A) -> (not ((B -> (C or B)) and ((D and A) or A))))) -> (not ((D and A) or A)))
theorem-size     40
proof            (modus-ponens tm-805 tm-601 ((Am (or (and A B) B)) (C (not (and (-> Bm (or Cm Bm)) (or (and A B) B)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-7)
proof-size       150
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-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-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-68825.        (((A -> (not ((B -> (C or B)) and ((D and A) or A)))) or (((D and A) or A) -> (not ((B -> (C or B)) and ((D and A) or A))))) -> (not ((D and A) or A))), M:tm-805, m:tm-601, u:((Am (or (and A B) B)) (C (not (and (-> Bm (or Cm Bm)) (or (and A B) B)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68826
in-theory        68826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (F or E)) and D)) and (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-605 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-68826.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> ((E -> (F or E)) and D)) and (((C and A) or A) -> B))), M:tm-805, m:tm-605, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68827
in-theory        68827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     21
proof            (modus-ponens tm-805 tm-606 ((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 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-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-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-68827.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> ((E -> (F or E)) and D))), M:tm-805, m:tm-606, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-68828
in-theory        68828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (E or D))))
theorem-size     25
proof            (modus-ponens tm-805 tm-609 ((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-68828.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (D -> (E or D)))), M:tm-805, m:tm-609, u:((Am (-> (or (and A B) B) C)) (D (and (-> (or (and A B) B) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-68829
in-theory        68829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or ((C and A) or A)) -> D)) or (((C and A) or A) -> ((B or ((C and A) or A)) -> D))) -> (((C and A) or A) -> D))
theorem-size     35
proof            (modus-ponens tm-805 tm-617 ((Am (or (and A B) B)) (C (-> (or Bm (or (and A B) B)) Cm)) (D (-> (or (and A B) B) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-68829.        (((A -> ((B or ((C and A) or A)) -> D)) or (((C and A) or A) -> ((B or ((C and A) or A)) -> D))) -> (((C and A) or A) -> D)), M:tm-805, m:tm-617, u:((Am (or (and A B) B)) (C (-> (or Bm (or (and A B) B)) Cm)) (D (-> (or (and A B) B) Cm)))
================================================================
tm-name          tm-68830
in-theory        68830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) or (((D and A) or A) -> (not (B -> (C or B))))) -> (not ((D and A) or A)))
theorem-size     28
proof            (modus-ponens tm-805 tm-618 ((Am (or (and A B) B)) (C (not (-> Bm (or Cm Bm)))) (D (not (or (and A B) B)))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-7)
proof-size       132
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-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-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-68830.        (((A -> (not (B -> (C or B)))) or (((D and A) or A) -> (not (B -> (C or B))))) -> (not ((D and A) or A))), M:tm-805, m:tm-618, u:((Am (or (and A B) B)) (C (not (-> Bm (or Cm Bm)))) (D (not (or (and A B) B))))
================================================================
tm-name          tm-68831
in-theory        68831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (F or E))) and (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-805 tm-622 ((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-68831.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> (E -> (F or E))) and (((C and A) or A) -> B))), M:tm-805, m:tm-622, u:((Am (-> (or (and A B) B) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68832
in-theory        68832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (D or B)))
theorem-size     21
proof            (modus-ponens tm-805 tm-623 ((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (or Cm Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-7)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-68832.        (((A -> B) or (((C and A) or A) -> B)) -> (((C and A) or A) -> (D or B))), M:tm-805, m:tm-623, u:((Am (or (and A B) B)) (C Bm) (D (-> (or (and A B) B) (or Cm Bm))))
================================================================
tm-name          tm-68833
in-theory        68833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-805 tm-624 ((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-68833.        (((A -> B) or (((C and A) or A) -> B)) -> (D -> (E -> (F or E)))), M:tm-805, m:tm-624, u:((Am (-> (or (and A B) B) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-68834
in-theory        68834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((C and A) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-805 tm-665 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 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-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-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-68834.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((C and A) or A) -> B))), M:tm-805, m:tm-665, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68835
in-theory        68835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-805 tm-667 ((Am (-> (or (and A B) B) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       141
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-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-1.            (A -> (B -> A)), 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-68835.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-805, m:tm-667, u:((Am (-> (or (and A B) B) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-68836
in-theory        68836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((C and A) or A) -> B)))
theorem-size     45
proof            (modus-ponens tm-805 tm-708 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       197
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-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-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-68836.        (((A -> B) or (((C and A) or A) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((C and A) or A) -> B))), M:tm-805, m:tm-708, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68837
in-theory        68837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     37
proof            (modus-ponens tm-805 tm-710 ((Am (-> (or (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-4 tm-1 tm-2)
proof-size       185
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-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-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-68837.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-805, m:tm-710, u:((Am (-> (or (and A B) B) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-68838
in-theory        68838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((((C and A) or A) and D) or ((C and A) or A)) -> B)))
theorem-size     35
proof            (modus-ponens tm-805 tm-747 ((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (or (and (or (and A B) B) Cm) (or (and A B) B)) Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-68838.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((((C and A) or A) and D) or ((C and A) or A)) -> B))), M:tm-805, m:tm-747, u:((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (or (and (or (and A B) B) Cm) (or (and A B) B)) Bm))))
================================================================
tm-name          tm-68839
in-theory        68839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((C and A) or A) -> B)))
theorem-size     31
proof            (modus-ponens tm-805 tm-757 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 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-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-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-68839.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((C and A) or A) -> B))), M:tm-805, m:tm-757, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-68840
in-theory        68840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-805 tm-759 ((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
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-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-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-68840.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-805, m:tm-759, u:((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-68841
in-theory        68841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((D and ((C and A) or A)) or ((C and A) or A)) -> B)))
theorem-size     35
proof            (modus-ponens tm-805 tm-798 ((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (or (and Cm (or (and A B) B)) (or (and A B) B)) Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am 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-68841.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((D and ((C and A) or A)) or ((C and A) or A)) -> B))), M:tm-805, m:tm-798, u:((Am (or (and A B) B)) (C Bm) (D (and (-> (or (and A B) B) Bm) (-> (or (and Cm (or (and A B) B)) (or (and A B) B)) Bm))))
================================================================
tm-name          tm-68842
in-theory        68842
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((E and ((((A and B) or B) -> C) -> D)) or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))
theorem-size     59
proof            (modus-ponens tm-798 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-68842.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((E and ((((A and B) or B) -> C) -> D)) or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D))), M:tm-798, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68843
in-theory        68843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-757 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-4.            ((A and B) -> B), axiom
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-68843.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-757, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68844
in-theory        68844
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((((((A and B) or B) -> C) -> D) and E) or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))
theorem-size     59
proof            (modus-ponens tm-747 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-68844.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((((((A and B) or B) -> C) -> D) and E) or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D))), M:tm-747, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68845
in-theory        68845
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) -> (((F -> G) or (((E and F) or F) -> G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-708 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-68845.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H))), M:tm-708, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68846
in-theory        68846
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> (((A and B) or B) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> D)))
theorem-size     35
proof            (modus-ponens tm-703 tm-805 ((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or (and Am Bm) Bm) C)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or (and Am Bm) Bm) C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68846.        (((((A and B) or B) -> C) -> (((A and B) or B) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> D))), M:tm-703, m:tm-805, u:((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or (and Am Bm) Bm) C)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or (and Am Bm) Bm) C))))
================================================================
tm-name          tm-68847
in-theory        68847
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> (((A and B) or B) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> D))) and (((((A and B) or B) -> (C -> D)) or ((((A and B) or B) -> C) -> (((A and B) or B) -> D))) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> D))))
theorem-size     81
proof            (modus-ponens tm-697 tm-805 ((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or (and Am Bm) Bm) C)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or (and Am Bm) Bm) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68847.        ((((((A and B) or B) -> C) -> (((A and B) or B) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> D))) and (((((A and B) or B) -> (C -> D)) or ((((A and B) or B) -> C) -> (((A and B) or B) -> D))) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> D)))), M:tm-697, m:tm-805, u:((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or (and Am Bm) Bm) C)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or (and Am Bm) Bm) C))))
================================================================
tm-name          tm-68848
in-theory        68848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-665 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-68848.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-665, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68849
in-theory        68849
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((D or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))
theorem-size     49
proof            (modus-ponens tm-654 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (B Dm) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-68849.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((D or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D))), M:tm-654, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (B Dm) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68850
in-theory        68850
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> (E or (((B -> C) or (((A and B) or B) -> C)) -> D)))
theorem-size     25
proof            (modus-ponens tm-623 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-68850.        (((((A and B) or B) -> C) -> D) -> (E or (((B -> C) or (((A and B) or B) -> C)) -> D))), M:tm-623, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68851
in-theory        68851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-622 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-68851.        ((A -> (B -> (C or B))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-622, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68852
in-theory        68852
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or C) -> D) -> (E or (((B and C) or C) -> D)))) -> (((C -> D) or (((B and C) or C) -> D)) -> (E or (((B and C) or C) -> D))))
theorem-size     41
proof            (modus-ponens tm-619 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (Dm (or B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (or B (-> (or (and Am Bm) Bm) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 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-7.            (A -> (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-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-68852.        ((A or ((((B and C) or C) -> D) -> (E or (((B and C) or C) -> D)))) -> (((C -> D) or (((B and C) or C) -> D)) -> (E or (((B and C) or C) -> D)))), M:tm-619, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (Dm (or B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (or B (-> (or (and Am Bm) Bm) Cm)))))
================================================================
tm-name          tm-68853
in-theory        68853
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (F or E)))
theorem-size     29
proof            (modus-ponens tm-609 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-68853.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68854
in-theory        68854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-605 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-605.          (A -> ((B -> ((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-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-68854.        ((A -> ((B -> (C or B)) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-605, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68855
in-theory        68855
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (F or E)) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-595 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-68855.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (F or E)) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-595, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68856
in-theory        68856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-550 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-68856.        (((A -> (B or A)) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-550, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68857
in-theory        68857
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-540 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-68857.        ((A or (B -> (C or B))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-540, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68858
in-theory        68858
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-530 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-68858.        ((A or (B -> (B or C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-530, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68859
in-theory        68859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-520 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68859.        ((A or (B -> (C -> (B and C)))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-520, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68860
in-theory        68860
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-510 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-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-68860.        ((A or ((B and C) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-510, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68861
in-theory        68861
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-500 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-68861.        ((A or ((B and C) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-500, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68862
in-theory        68862
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-490 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68862.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H))), M:tm-490, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68863
in-theory        68863
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-480 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-68863.        ((A or (B -> (C -> B))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-480, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68864
in-theory        68864
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> ((((B -> C) or (((A and B) or B) -> C)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-470 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-68864.        (((((A and B) or B) -> C) -> D) -> ((((B -> C) or (((A and B) or B) -> C)) -> D) or E)), M:tm-470, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68865
in-theory        68865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-469 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-68865.        ((A -> (B -> (B or C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-469, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68866
in-theory        68866
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or C) -> D) -> ((((B and C) or C) -> D) or E))) -> (((C -> D) or (((B and C) or C) -> D)) -> ((((B and C) or C) -> D) or E)))
theorem-size     41
proof            (modus-ponens tm-466 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (Dm (or (-> (or (and Am Bm) Bm) Cm) B)) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (or (-> (or (and Am Bm) Bm) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 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-6.            (A -> (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-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-68866.        ((A or ((((B and C) or C) -> D) -> ((((B and C) or C) -> D) or E))) -> (((C -> D) or (((B and C) or C) -> D)) -> ((((B and C) or C) -> D) or E))), M:tm-466, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (Dm (or (-> (or (and Am Bm) Bm) Cm) B)) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (or (-> (or (and Am Bm) Bm) Cm) B))))
================================================================
tm-name          tm-68867
in-theory        68867
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (E or F)))
theorem-size     29
proof            (modus-ponens tm-456 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-68867.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68868
in-theory        68868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-453 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-453.          (A -> ((B -> ((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-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-68868.        ((A -> ((B -> (B or C)) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-453, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68869
in-theory        68869
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (E or F)) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-443 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-68869.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (E or F)) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-443, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68870
in-theory        68870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-409 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-68870.        (((A -> (A or B)) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-409, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68871
in-theory        68871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-400 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68871.        (((A -> (B -> (A and B))) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-400, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68872
in-theory        68872
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-391 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-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-68872.        ((((A and B) -> B) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-391, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68873
in-theory        68873
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-382 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-68873.        ((((A and B) -> A) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-382, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68874
in-theory        68874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-373 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68874.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H))), M:tm-373, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68875
in-theory        68875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-364 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-68875.        (((A -> (B -> A)) or C) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-364, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68876
in-theory        68876
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> (E -> ((((B -> C) or (((A and B) or B) -> C)) -> D) and E)))
theorem-size     27
proof            (modus-ponens tm-355 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-68876.        (((((A and B) or B) -> C) -> D) -> (E -> ((((B -> C) or (((A and B) or B) -> C)) -> D) and E))), M:tm-355, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68877
in-theory        68877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-354 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-68877.        ((A -> (B -> (C -> (B and C)))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-354, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68878
in-theory        68878
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or C) -> D) -> (E -> ((((B and C) or C) -> D) and E)))) -> (((C -> D) or (((B and C) or C) -> D)) -> (E -> ((((B and C) or C) -> D) and E))))
theorem-size     45
proof            (modus-ponens tm-351 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (Dm (-> B (and (-> (or (and Am Bm) Bm) Cm) B))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> B (and (-> (or (and Am Bm) Bm) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5 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-5.            (A -> (B -> (A and 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-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-68878.        ((A or ((((B and C) or C) -> D) -> (E -> ((((B and C) or C) -> D) and E)))) -> (((C -> D) or (((B and C) or C) -> D)) -> (E -> ((((B and C) or C) -> D) and E)))), M:tm-351, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (Dm (-> B (and (-> (or (and Am Bm) Bm) Cm) B))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> B (and (-> (or (and Am Bm) Bm) Cm) B)))))
================================================================
tm-name          tm-68879
in-theory        68879
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-341 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-68879.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68880
in-theory        68880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-338 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-68880.        (((A -> B) -> (A -> (A and B))) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F))), M:tm-338, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68881
in-theory        68881
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) or ((((A and B) or B) -> C) -> ((((A and B) or B) -> C) and D))) -> (((B -> C) or (((A and B) or B) -> C)) -> ((((A and B) or B) -> C) and D)))
theorem-size     49
proof            (modus-ponens tm-335 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (Dm (and (-> (or (and Am Bm) Bm) Cm) B)) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (and (-> (or (and Am Bm) Bm) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
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-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-68881.        ((((((A and B) or B) -> C) -> D) or ((((A and B) or B) -> C) -> ((((A and B) or B) -> C) and D))) -> (((B -> C) or (((A and B) or B) -> C)) -> ((((A and B) or B) -> C) and D))), M:tm-335, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (Dm (and (-> (or (and Am Bm) Bm) Cm) B)) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (and (-> (or (and Am Bm) Bm) Cm) B))))
================================================================
tm-name          tm-68882
in-theory        68882
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((((A and B) or B) -> C) -> D) -> (((((A and B) or B) -> C) -> D) and (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-328 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-68882.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((((A and B) or B) -> C) -> D) -> (((((A and B) or B) -> C) -> D) and (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-328, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68883
in-theory        68883
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (F -> (E and F))) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     55
proof            (modus-ponens tm-327 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-68883.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (F -> (E and F))) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-327, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68884
in-theory        68884
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((E and F) -> F) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-326 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-68884.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((E and F) -> F) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-326, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68885
in-theory        68885
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((E and F) -> E) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-325 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-68885.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((E and F) -> E) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-325, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68886
in-theory        68886
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-324 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-68886.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-324, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68887
in-theory        68887
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (F -> E)) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-323 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-68887.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (F -> E)) and (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-323, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68888
in-theory        68888
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E and F) -> F))
theorem-size     29
proof            (modus-ponens tm-322 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-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-68888.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68889
in-theory        68889
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E and F) -> E))
theorem-size     29
proof            (modus-ponens tm-320 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-68889.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68890
in-theory        68890
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-318 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-68890.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68891
in-theory        68891
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((((A and B) or B) -> C) -> D) -> ((((A and B) or B) -> C) -> D)))
theorem-size     43
proof            (modus-ponens tm-316 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-68891.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((((A and B) or B) -> C) -> D) -> ((((A and B) or B) -> C) -> D))), M:tm-316, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68892
in-theory        68892
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (F -> E)))
theorem-size     29
proof            (modus-ponens tm-315 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-68892.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68893
in-theory        68893
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((((((A and B) or B) -> C) -> D) -> (not (((B -> C) or (((A and B) or B) -> C)) -> D))) -> (not ((((A and B) or B) -> C) -> D))))
theorem-size     59
proof            (modus-ponens tm-313 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-68893.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((((((A and B) or B) -> C) -> D) -> (not (((B -> C) or (((A and B) or B) -> C)) -> D))) -> (not ((((A and B) or B) -> C) -> D)))), M:tm-313, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68894
in-theory        68894
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((((B -> C) or (((A and B) or B) -> C)) -> D) -> E) -> ((((((A and B) or B) -> C) -> D) or (((B -> C) or (((A and B) or B) -> C)) -> D)) -> E)))
theorem-size     65
proof            (modus-ponens tm-312 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
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-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-68894.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (((((B -> C) or (((A and B) or B) -> C)) -> D) -> E) -> ((((((A and B) or B) -> C) -> D) or (((B -> C) or (((A and B) or B) -> C)) -> D)) -> E))), M:tm-312, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68895
in-theory        68895
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E or (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-311 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-68895.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E or (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-311, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68896
in-theory        68896
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) or E))
theorem-size     49
proof            (modus-ponens tm-310 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-68896.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) or E)), M:tm-310, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68897
in-theory        68897
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and E)))
theorem-size     51
proof            (modus-ponens tm-309 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-68897.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and E))), M:tm-309, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68898
in-theory        68898
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((((((A and B) or B) -> C) -> D) -> ((B -> C) or (((A and B) or B) -> C))) -> (((((A and B) or B) -> C) -> D) -> D)))
theorem-size     57
proof            (modus-ponens tm-306 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68898.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and ((((((A and B) or B) -> C) -> D) -> ((B -> C) or (((A and B) or B) -> C))) -> (((((A and B) or B) -> C) -> D) -> D))), M:tm-306, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (C Dm))
================================================================
tm-name          tm-68899
in-theory        68899
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-305 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-68899.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) and (E -> (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)))), M:tm-305, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68900
in-theory        68900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-303 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68900.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-303, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68901
in-theory        68901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-270 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-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-68901.        ((A -> (((B and C) -> C) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-270, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68902
in-theory        68902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-239 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 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-239.          (A -> ((B -> (((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-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-68902.        ((A -> (((B and C) -> B) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-239, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68903
in-theory        68903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-210 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-68903.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H))), M:tm-210, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68904
in-theory        68904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-183 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-68904.        ((A -> ((B -> (C -> B)) and A)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-183, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68905
in-theory        68905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-157 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-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-68905.        ((A -> ((B and C) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-157, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68906
in-theory        68906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-147 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-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-68906.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-147, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68907
in-theory        68907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-134 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-68907.        ((A -> ((B and C) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-134, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68908
in-theory        68908
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-125 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-68908.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-125, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68909
in-theory        68909
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> (D -> E)) -> ((((B -> C) or (((A and B) or B) -> C)) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> E)))
theorem-size     39
proof            (modus-ponens tm-114 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) (-> C D))) (B (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68909.        (((((A and B) or B) -> C) -> (D -> E)) -> ((((B -> C) or (((A and B) or B) -> C)) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> E))), M:tm-114, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) (-> C D))) (B (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-68910
in-theory        68910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-113 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68910.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H))), M:tm-113, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68911
in-theory        68911
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or C) -> (D -> E)) -> ((((B and C) or C) -> D) -> (((B and C) or C) -> E)))) -> (((C -> (D -> E)) or (((B and C) or C) -> (D -> E))) -> ((((B and C) or C) -> D) -> (((B and C) or C) -> E))))
theorem-size     59
proof            (modus-ponens tm-110 tm-805 ((A (or (and Am Bm) Bm)) (Cm (-> B C)) (Dm (-> (-> (or (and Am Bm) Bm) B) (-> (or (and Am Bm) Bm) C))) (D (-> (or (-> Bm (-> B C)) (-> (or (and Am Bm) Bm) (-> B C))) (-> (-> (or (and Am Bm) Bm) B) (-> (or (and Am Bm) Bm) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-68911.        ((A or ((((B and C) or C) -> (D -> E)) -> ((((B and C) or C) -> D) -> (((B and C) or C) -> E)))) -> (((C -> (D -> E)) or (((B and C) or C) -> (D -> E))) -> ((((B and C) or C) -> D) -> (((B and C) or C) -> E)))), M:tm-110, m:tm-805, u:((A (or (and Am Bm) Bm)) (Cm (-> B C)) (Dm (-> (-> (or (and Am Bm) Bm) B) (-> (or (and Am Bm) Bm) C))) (D (-> (or (-> Bm (-> B C)) (-> (or (and Am Bm) Bm) (-> B C))) (-> (-> (or (and Am Bm) Bm) B) (-> (or (and Am Bm) Bm) C)))))
================================================================
tm-name          tm-68912
in-theory        68912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-105 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-68912.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-105, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68913
in-theory        68913
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> (C -> D)) -> (((A and B) or B) -> C)) or ((((A and B) or B) -> (C -> D)) -> (((A and B) or B) -> D))) -> (((B -> (C -> D)) or (((A and B) or B) -> (C -> D))) -> (((A and B) or B) -> D)))
theorem-size     59
proof            (modus-ponens tm-102 tm-805 ((A (or (and Am Bm) Bm)) (Cm (-> B C)) (Dm (-> (or (and Am Bm) Bm) C)) (D (-> (or (-> Bm (-> B C)) (-> (or (and Am Bm) Bm) (-> B C))) (-> (or (and Am Bm) Bm) C)))))
axioms-used      (tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-68913.        ((((((A and B) or B) -> (C -> D)) -> (((A and B) or B) -> C)) or ((((A and B) or B) -> (C -> D)) -> (((A and B) or B) -> D))) -> (((B -> (C -> D)) or (((A and B) or B) -> (C -> D))) -> (((A and B) or B) -> D))), M:tm-102, m:tm-805, u:((A (or (and Am Bm) Bm)) (Cm (-> B C)) (Dm (-> (or (and Am Bm) Bm) C)) (D (-> (or (-> Bm (-> B C)) (-> (or (and Am Bm) Bm) (-> B C))) (-> (or (and Am Bm) Bm) C))))
================================================================
tm-name          tm-68914
in-theory        68914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-95 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-68914.        (((A -> B) -> (A -> A)) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F))), M:tm-95, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68915
in-theory        68915
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) or ((((A and B) or B) -> C) -> (((A and B) or B) -> C))) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> C)))
theorem-size     45
proof            (modus-ponens tm-92 tm-805 ((Dm (-> (or (and Am Bm) Bm) Cm)) (A (-> (or (and Am Bm) Bm) Cm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or (and Am Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 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-1.            (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-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-68915.        ((((((A and B) or B) -> C) -> D) or ((((A and B) or B) -> C) -> (((A and B) or B) -> C))) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> C))), M:tm-92, m:tm-805, u:((Dm (-> (or (and Am Bm) Bm) Cm)) (A (-> (or (and Am Bm) Bm) Cm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or (and Am Bm) Bm) Cm))))
================================================================
tm-name          tm-68916
in-theory        68916
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> (E -> (((B -> C) or (((A and B) or B) -> C)) -> D)))
theorem-size     25
proof            (modus-ponens tm-84 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-68916.        (((((A and B) or B) -> C) -> D) -> (E -> (((B -> C) or (((A and B) or B) -> C)) -> D))), M:tm-84, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68917
in-theory        68917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-83 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-68917.        ((A -> (B -> (C -> B))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-83, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68918
in-theory        68918
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or C) -> D) -> (E -> (((B and C) or C) -> D)))) -> (((C -> D) or (((B and C) or C) -> D)) -> (E -> (((B and C) or C) -> D))))
theorem-size     41
proof            (modus-ponens tm-80 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (Dm (-> B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> B (-> (or (and Am Bm) Bm) Cm))))))
axioms-used      (tm-8 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-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-68918.        ((A or ((((B and C) or C) -> D) -> (E -> (((B and C) or C) -> D)))) -> (((C -> D) or (((B and C) or C) -> D)) -> (E -> (((B and C) or C) -> D)))), M:tm-80, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (Dm (-> B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> B (-> (or (and Am Bm) Bm) Cm)))))
================================================================
tm-name          tm-68919
in-theory        68919
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B and C) or C) -> D) -> E) -> (((C -> D) or (((B and C) or C) -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-76 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68919.        (((not (not A)) -> A) and (((((B and C) or C) -> D) -> E) -> (((C -> D) or (((B and C) or C) -> D)) -> E))), M:tm-76, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68920
in-theory        68920
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A and B) or B) -> C) -> D))) or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D))
theorem-size     35
proof            (modus-ponens tm-73 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-4)
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-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-68920.        (((not (not ((((A and B) or B) -> C) -> D))) or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D)), M:tm-73, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68921
in-theory        68921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-69 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68921.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F))), M:tm-69, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68922
in-theory        68922
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) or ((((A and B) or B) -> (not C)) -> (not ((A and B) or B)))) -> (((B -> (not C)) or (((A and B) or B) -> (not C))) -> (not ((A and B) or B))))
theorem-size     44
proof            (modus-ponens tm-66 tm-805 ((A (or (and Am Bm) Bm)) (Cm (not B)) (Dm (not (or (and Am Bm) Bm))) (C (-> (or (-> Bm (not B)) (-> (or (and Am Bm) Bm) (not B))) (not (or (and Am Bm) Bm))))))
axioms-used      (tm-8 tm-9 tm-4)
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-4.            ((A and B) -> B), axiom
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-68922.        (((((A and B) or B) -> C) or ((((A and B) or B) -> (not C)) -> (not ((A and B) or B)))) -> (((B -> (not C)) or (((A and B) or B) -> (not C))) -> (not ((A and B) or B)))), M:tm-66, m:tm-805, u:((A (or (and Am Bm) Bm)) (Cm (not B)) (Dm (not (or (and Am Bm) Bm))) (C (-> (or (-> Bm (not B)) (-> (or (and Am Bm) Bm) (not B))) (not (or (and Am Bm) Bm)))))
================================================================
tm-name          tm-68923
in-theory        68923
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> ((B -> C) or (((A and B) or B) -> C))) -> (((((A and B) or B) -> C) or ((B -> C) or (((A and B) or B) -> C))) -> ((B -> C) or (((A and B) or B) -> C))))
theorem-size     51
proof            (modus-ponens tm-55 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (Dm (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (B (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (C (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68923.        (((((A and B) or B) -> C) -> ((B -> C) or (((A and B) or B) -> C))) -> (((((A and B) or B) -> C) or ((B -> C) or (((A and B) or B) -> C))) -> ((B -> C) or (((A and B) or B) -> C)))), M:tm-55, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (Dm (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (B (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (C (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))))
================================================================
tm-name          tm-68924
in-theory        68924
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-54 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68924.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-54, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68925
in-theory        68925
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B and C) or C)) or ((((B and C) or C) -> D) -> ((A or ((B and C) or C)) -> D))) -> (((C -> D) or (((B and C) or C) -> D)) -> ((A or ((B and C) or C)) -> D)))
theorem-size     47
proof            (modus-ponens tm-51 tm-805 ((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or C (or (and Am Bm) Bm)) Cm)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or C (or (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68925.        (((A -> ((B and C) or C)) or ((((B and C) or C) -> D) -> ((A or ((B and C) or C)) -> D))) -> (((C -> D) or (((B and C) or C) -> D)) -> ((A or ((B and C) or C)) -> D))), M:tm-51, m:tm-805, u:((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or C (or (and Am Bm) Bm)) Cm)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or C (or (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-68926
in-theory        68926
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B and C) or C) -> D) -> (A and (((B and C) or C) -> D)))) -> (((C -> D) or (((B and C) or C) -> D)) -> (A and (((B and C) or C) -> D))))
theorem-size     41
proof            (modus-ponens tm-48 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (Dm (and B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (and B (-> (or (and Am Bm) Bm) Cm))))))
axioms-used      (tm-8 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-68926.        ((A or ((((B and C) or C) -> D) -> (A and (((B and C) or C) -> D)))) -> (((C -> D) or (((B and C) or C) -> D)) -> (A and (((B and C) or C) -> D)))), M:tm-48, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (Dm (and B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (and B (-> (or (and Am Bm) Bm) Cm)))))
================================================================
tm-name          tm-68927
in-theory        68927
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B and C) or C) -> D) -> E)) or ((((B and C) or C) -> D) -> E)) -> (((C -> D) or (((B and C) or C) -> D)) -> E))
theorem-size     35
proof            (modus-ponens tm-47 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-4)
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-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-68927.        (((A and ((((B and C) or C) -> D) -> E)) or ((((B and C) or C) -> D) -> E)) -> (((C -> D) or (((B and C) or C) -> D)) -> E)), M:tm-47, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68928
in-theory        68928
times-derived    2
----------------------------------------------------------------
theorem          (((((((A and B) or B) -> C) -> D) and E) or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D))
theorem-size     35
proof            (modus-ponens tm-46 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-4)
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-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-68928.        (((((((A and B) or B) -> C) -> D) and E) or ((((A and B) or B) -> C) -> D)) -> (((B -> C) or (((A and B) or B) -> C)) -> D)), M:tm-46, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68929
in-theory        68929
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) or B) -> (C -> D)) or ((((A and B) or B) -> C) -> (((A and B) or B) -> D))) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> D)))
theorem-size     45
proof            (modus-ponens tm-45 tm-805 ((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or (and Am Bm) Bm) C)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or (and Am Bm) Bm) C)))))
axioms-used      (tm-8 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-68929.        (((((A and B) or B) -> (C -> D)) or ((((A and B) or B) -> C) -> (((A and B) or B) -> D))) -> (((B -> C) or (((A and B) or B) -> C)) -> (((A and B) or B) -> D))), M:tm-45, m:tm-805, u:((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or (and Am Bm) Bm) C)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or (and Am Bm) Bm) C))))
================================================================
tm-name          tm-68930
in-theory        68930
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B and C) or C) -> D) -> A)) -> (((C -> D) or (((B and C) or C) -> D)) -> A))
theorem-size     25
proof            (modus-ponens tm-44 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (B Dm) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-68930.        ((A or ((((B and C) or C) -> D) -> A)) -> (((C -> D) or (((B and C) or C) -> D)) -> A)), M:tm-44, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (B Dm) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68931
in-theory        68931
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-42 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-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-68931.        ((A -> (B or A)) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F))), M:tm-42, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68932
in-theory        68932
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-32 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-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-68932.        ((A -> (A or B)) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F))), M:tm-32, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68933
in-theory        68933
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> (((((A and B) or B) -> C) -> D) and (((B -> C) or (((A and B) or B) -> C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-24 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) 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-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-68933.        (((((A and B) or B) -> C) -> D) -> (((((A and B) or B) -> C) -> D) and (((B -> C) or (((A and B) or B) -> C)) -> D))), M:tm-24, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68934
in-theory        68934
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-23 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68934.        ((A -> (B -> (A and B))) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F))), M:tm-23, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68935
in-theory        68935
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-22 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) 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-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-68935.        (((A and B) -> B) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F))), M:tm-22, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68936
in-theory        68936
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-21 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68936.        (((A and B) -> A) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F))), M:tm-21, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68937
in-theory        68937
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-20 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-68937.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-20, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68938
in-theory        68938
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-19 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and 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-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-68938.        ((A -> (B -> A)) and (((((C and D) or D) -> E) -> F) -> (((D -> E) or (((C and D) or D) -> E)) -> F))), M:tm-19, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68939
in-theory        68939
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> ((((A and B) or B) -> C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-68939.        (((((A and B) or B) -> C) -> D) -> ((((A and B) or B) -> C) -> D)), M:tm-12, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68940
in-theory        68940
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (not (((B -> C) or (((A and B) or B) -> C)) -> D))) -> (not ((((A and B) or B) -> C) -> D)))
theorem-size     35
proof            (modus-ponens tm-9 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-4)
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-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-68940.        ((((((A and B) or B) -> C) -> D) -> (not (((B -> C) or (((A and B) or B) -> C)) -> D))) -> (not ((((A and B) or B) -> C) -> D))), M:tm-9, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68941
in-theory        68941
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) or (((C and A) or A) -> B)) -> D) -> E) -> ((((((C and A) or A) -> B) -> D) or (((A -> B) or (((C and A) or A) -> B)) -> D)) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-4)
proof-size       119
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-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-68941.        (((((A -> B) or (((C and A) or A) -> B)) -> D) -> E) -> ((((((C and A) or A) -> B) -> D) or (((A -> B) or (((C and A) or A) -> B)) -> D)) -> E)), M:tm-8, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-68942
in-theory        68942
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B and C) or C) -> D) -> E) -> (((C -> D) or (((B and C) or C) -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-7 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68942.        (A or (((((B and C) or C) -> D) -> E) -> (((C -> D) or (((B and C) or C) -> D)) -> E))), M:tm-7, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68943
in-theory        68943
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) or E)
theorem-size     25
proof            (modus-ponens tm-6 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68943.        ((((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)) or E), M:tm-6, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68944
in-theory        68944
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B and C) or C) -> D) -> E) -> (((C -> D) or (((B and C) or C) -> D)) -> E)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-68944.        (A -> ((((((B and C) or C) -> D) -> E) -> (((C -> D) or (((B and C) or C) -> D)) -> E)) and A)), M:tm-5, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68945
in-theory        68945
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> D) -> ((B -> C) or (((A and B) or B) -> C))) -> (((((A and B) or B) -> C) -> D) -> D))
theorem-size     33
proof            (modus-ponens tm-2 tm-805 ((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (C 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-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-68945.        ((((((A and B) or B) -> C) -> D) -> ((B -> C) or (((A and B) or B) -> C))) -> (((((A and B) or B) -> C) -> D) -> D)), M:tm-2, m:tm-805, u:((A (-> (-> (or (and Am Bm) Bm) Cm) Dm)) (B (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm))) (C Dm))
================================================================
tm-name          tm-68946
in-theory        68946
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and C) or C) -> D) -> E) -> (((C -> D) or (((B and C) or C) -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-1 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       95
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-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-68946.        (A -> (((((B and C) or C) -> D) -> E) -> (((C -> D) or (((B and C) or C) -> D)) -> E))), M:tm-1, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-68947
in-theory        68947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-68947.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-757, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68948
in-theory        68948
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
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-4.            ((A and B) -> B), axiom
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-68948.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> (((H and F) or F) -> G)))), M:tm-708, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68949
in-theory        68949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
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-4.            ((A and B) -> B), axiom
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-68949.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-665, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68950
in-theory        68950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-68950.        ((A -> (B -> (C or B))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-622, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68951
in-theory        68951
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-68951.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F or E))), M:tm-609, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68952
in-theory        68952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-605.          (A -> ((B -> ((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-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-68952.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-605, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68953
in-theory        68953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F or E)) and (A or ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-68953.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F or E)) and (A or ((B -> C) -> (((D and B) or B) -> C))))), M:tm-595, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68954
in-theory        68954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-68954.        (((A -> (B or A)) or C) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-550, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68955
in-theory        68955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-68955.        ((A or (B -> (C or B))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-540, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68956
in-theory        68956
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-68956.        ((A or (B -> (B or C))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-530, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68957
in-theory        68957
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-68957.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-520, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68958
in-theory        68958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-68958.        ((A or ((B and C) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-510, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68959
in-theory        68959
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-68959.        ((A or ((B and C) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-500, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68960
in-theory        68960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68960.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (((H and F) or F) -> G)))), M:tm-490, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68961
in-theory        68961
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-68961.        ((A or (B -> (C -> B))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-480, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68962
in-theory        68962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68962.        ((A -> (B -> (B or C))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-469, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68963
in-theory        68963
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-68963.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (E or F))), M:tm-456, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68964
in-theory        68964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-453.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-68964.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-453, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68965
in-theory        68965
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (E or F)) and (A or ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68965.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (E or F)) and (A or ((B -> C) -> (((D and B) or B) -> C))))), M:tm-443, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68966
in-theory        68966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> B), axiom
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-68966.        (((A -> (A or B)) or C) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-409, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68967
in-theory        68967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-4.            ((A and B) -> B), axiom
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-68967.        (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-400, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68968
in-theory        68968
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-68968.        ((((A and B) -> B) or C) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-391, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68969
in-theory        68969
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-4.            ((A and B) -> B), axiom
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-68969.        ((((A and B) -> A) or C) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-382, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68970
in-theory        68970
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68970.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> (((H and F) or F) -> G)))), M:tm-373, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68971
in-theory        68971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-68971.        (((A -> (B -> A)) or C) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-364, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68972
in-theory        68972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-4.            ((A and B) -> B), axiom
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-68972.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-354, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68973
in-theory        68973
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> B), axiom
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-68973.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68974
in-theory        68974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> B), axiom
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-68974.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> (((F and D) or D) -> E)))), M:tm-338, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68975
in-theory        68975
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> (E and F))) and (A or ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-68975.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> (E and F))) and (A or ((B -> C) -> (((D and B) or B) -> C))))), M:tm-327, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68976
in-theory        68976
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (((E and F) -> F) and (A or ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-68976.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (((E and F) -> F) and (A or ((B -> C) -> (((D and B) or B) -> C))))), M:tm-326, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68977
in-theory        68977
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (((E and F) -> E) and (A or ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-68977.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (((E and F) -> E) and (A or ((B -> C) -> (((D and B) or B) -> C))))), M:tm-325, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68978
in-theory        68978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-68978.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> C) -> (((D and B) or B) -> C))))), M:tm-324, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68979
in-theory        68979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> E)) and (A or ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> B), axiom
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-68979.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> E)) and (A or ((B -> C) -> (((D and B) or B) -> C))))), M:tm-323, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68980
in-theory        68980
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-68980.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68981
in-theory        68981
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-68981.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68982
in-theory        68982
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-68982.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68983
in-theory        68983
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-68983.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68984
in-theory        68984
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E or (A or ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-68984.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E or (A or ((B -> C) -> (((D and B) or B) -> C))))), M:tm-311, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68985
in-theory        68985
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((A or ((B -> C) -> (((D and B) or B) -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-68985.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and ((A or ((B -> C) -> (((D and B) or B) -> C))) or E)), M:tm-310, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68986
in-theory        68986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> ((A or ((B -> C) -> (((D and B) or B) -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
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-68986.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> ((A or ((B -> C) -> (((D and B) or B) -> C))) and E))), M:tm-309, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68987
in-theory        68987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (A or ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (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-4.            ((A and B) -> B), axiom
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-68987.        ((A or ((B -> C) -> (((D and B) or B) -> C))) and (E -> (A or ((B -> C) -> (((D and B) or B) -> C))))), M:tm-305, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68988
in-theory        68988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-4.            ((A and B) -> B), axiom
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-68988.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-303, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68989
in-theory        68989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 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-270.          (A -> ((B -> (((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-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-68989.        ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-270, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68990
in-theory        68990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 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-239.          (A -> ((B -> (((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-4.            ((A and B) -> B), axiom
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-68990.        ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-239, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68991
in-theory        68991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> B), axiom
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-68991.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> (((H and F) or F) -> G)))), M:tm-210, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68992
in-theory        68992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-183.          (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-4.            ((A and B) -> B), axiom
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-68992.        ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-183, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68993
in-theory        68993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-68993.        ((A -> ((B and C) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-157, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68994
in-theory        68994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-68994.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-147, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68995
in-theory        68995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-68995.        ((A -> ((B and C) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-134, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68996
in-theory        68996
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-68996.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-125, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68997
in-theory        68997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-68997.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (((H and F) or F) -> G)))), M:tm-113, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68998
in-theory        68998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> B), axiom
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-68998.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-105, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-68999
in-theory        68999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> B), axiom
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-68999.        (((A -> B) -> (A -> A)) and (C or ((D -> E) -> (((F and D) or D) -> E)))), M:tm-95, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69000
in-theory        69000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-69000.        ((A -> (B -> (C -> B))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-83, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69001
in-theory        69001
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69001.        (((not (not A)) -> A) and (B or ((C -> D) -> (((E and C) or C) -> D)))), M:tm-76, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69002
in-theory        69002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69002.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> (((F and D) or D) -> E)))), M:tm-69, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69003
in-theory        69003
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-54.           (A -> (((B -> C) -> ((C -> 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-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-69003.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-54, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69004
in-theory        69004
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69004.        ((A -> (B or A)) and (C or ((D -> E) -> (((F and D) or D) -> E)))), M:tm-42, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69005
in-theory        69005
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69005.        ((A -> (A or B)) and (C or ((D -> E) -> (((F and D) or D) -> E)))), M:tm-32, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69006
in-theory        69006
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69006.        ((A -> (B -> (A and B))) and (C or ((D -> E) -> (((F and D) or D) -> E)))), M:tm-23, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69007
in-theory        69007
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-69007.        (((A and B) -> B) and (C or ((D -> E) -> (((F and D) or D) -> E)))), M:tm-22, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69008
in-theory        69008
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69008.        (((A and B) -> A) and (C or ((D -> E) -> (((F and D) or D) -> E)))), M:tm-21, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69009
in-theory        69009
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-4.            ((A and B) -> B), axiom
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-69009.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-20, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69010
in-theory        69010
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69010.        ((A -> (B -> A)) and (C or ((D -> E) -> (((F and D) or D) -> E)))), M:tm-19, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69011
in-theory        69011
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69011.        (A or (B or ((C -> D) -> (((E and C) or C) -> D)))), M:tm-7, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69012
in-theory        69012
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((D and B) or B) -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-6 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69012.        ((A or ((B -> C) -> (((D and B) or B) -> C))) or E), M:tm-6, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69013
in-theory        69013
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> D) -> (((E and C) or C) -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69013.        (A -> ((B or ((C -> D) -> (((E and C) or C) -> D))) and A)), M:tm-5, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69014
in-theory        69014
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-1 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69014.        (A -> (B or ((C -> D) -> (((E and C) or C) -> D)))), M:tm-1, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69015
in-theory        69015
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-795 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
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-69015.        (((A and B) or B) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-795, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69016
in-theory        69016
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> ((D and B) or B))) or ((B -> C) -> ((D and B) or B))) -> ((B -> C) -> C))
theorem-size     27
proof            (modus-ponens tm-794 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
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-69016.        (((A and ((B -> C) -> ((D and B) or B))) or ((B -> C) -> ((D and B) or B))) -> ((B -> C) -> C)), M:tm-794, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69017
in-theory        69017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-757 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-69017.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-757, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69018
in-theory        69018
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-744 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69018.        (((A and B) or A) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-744, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69019
in-theory        69019
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C and A) or A)) and D) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B))
theorem-size     27
proof            (modus-ponens tm-743 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-4.            ((A and B) -> B), axiom
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-69019.        (((((A -> B) -> ((C and A) or A)) and D) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B)), M:tm-743, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69020
in-theory        69020
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)) or H))
theorem-size     39
proof            (modus-ponens tm-708 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69020.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (((G and E) or E) -> F)) or H)), M:tm-708, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69021
in-theory        69021
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-694 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69021.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-694, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69022
in-theory        69022
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) or B) or ((B -> C) -> ((A and B) or B))) -> ((B -> C) -> C))
theorem-size     21
proof            (modus-ponens tm-692 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69022.        ((((A and B) or B) or ((B -> C) -> ((A and B) or B))) -> ((B -> C) -> C)), M:tm-692, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69023
in-theory        69023
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-690 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69023.        ((A -> (B or A)) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D))), M:tm-690, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69024
in-theory        69024
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-688 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69024.        ((A -> (A or B)) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D))), M:tm-688, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69025
in-theory        69025
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((C and A) or A)) -> (((A -> B) -> ((C and A) or A)) and ((A -> B) -> B)))
theorem-size     25
proof            (modus-ponens tm-686 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69025.        (((A -> B) -> ((C and A) or A)) -> (((A -> B) -> ((C and A) or A)) and ((A -> B) -> B))), M:tm-686, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69026
in-theory        69026
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D)))
theorem-size     23
proof            (modus-ponens tm-685 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-4.            ((A and B) -> B), axiom
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-69026.        ((A -> (B -> (A and B))) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D))), M:tm-685, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69027
in-theory        69027
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-684 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 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-4.            ((A and B) -> 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-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-69027.        (((A and B) -> B) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D))), M:tm-684, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69028
in-theory        69028
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-683 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69028.        (((A and B) -> A) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D))), M:tm-683, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69029
in-theory        69029
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-682 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69029.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-682, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69030
in-theory        69030
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-681 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69030.        ((A -> (B -> A)) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D))), M:tm-681, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69031
in-theory        69031
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> ((C and A) or A)))
theorem-size     19
proof            (modus-ponens tm-676 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69031.        (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> ((C and A) or A))), M:tm-676, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69032
in-theory        69032
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> (not ((A -> B) -> B))) -> (not ((A -> B) -> ((C and A) or A))))
theorem-size     27
proof            (modus-ponens tm-674 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-9 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-4.            ((A and B) -> B), axiom
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-69032.        ((((A -> B) -> ((C and A) or A)) -> (not ((A -> B) -> B))) -> (not ((A -> B) -> ((C and A) or A)))), M:tm-674, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69033
in-theory        69033
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> B) -> C) -> ((((A -> B) -> ((D and A) or A)) or ((A -> B) -> B)) -> C))
theorem-size     25
proof            (modus-ponens tm-673 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69033.        ((((A -> B) -> B) -> C) -> ((((A -> B) -> ((D and A) or A)) or ((A -> B) -> B)) -> C)), M:tm-673, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69034
in-theory        69034
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((D and B) or B)) -> ((B -> C) -> C)))
theorem-size     17
proof            (modus-ponens tm-672 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-4.            ((A and B) -> B), axiom
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-69034.        (A or (((B -> C) -> ((D and B) or B)) -> ((B -> C) -> C))), M:tm-672, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69035
in-theory        69035
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) or D)
theorem-size     17
proof            (modus-ponens tm-671 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-4.            ((A and B) -> B), axiom
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-69035.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) or D), M:tm-671, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69036
in-theory        69036
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((D and B) or B)) -> ((B -> C) -> C)) and A))
theorem-size     19
proof            (modus-ponens tm-670 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-4.            ((A and B) -> B), axiom
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-69036.        (A -> ((((B -> C) -> ((D and B) or B)) -> ((B -> C) -> C)) and A)), M:tm-670, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69037
in-theory        69037
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> (A -> B)) -> (((A -> B) -> ((C and A) or A)) -> B))
theorem-size     25
proof            (modus-ponens tm-669 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-4.            ((A and B) -> B), axiom
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-69037.        ((((A -> B) -> ((C and A) or A)) -> (A -> B)) -> (((A -> B) -> ((C and A) or A)) -> B)), M:tm-669, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69038
in-theory        69038
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((D and B) or B)) -> ((B -> C) -> C)))
theorem-size     17
proof            (modus-ponens tm-668 tm-807 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-4.            ((A and B) -> B), axiom
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-69038.        (A -> (((B -> C) -> ((D and B) or B)) -> ((B -> C) -> C))), M:tm-668, m:tm-807, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69039
in-theory        69039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-665 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69039.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-665, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69040
in-theory        69040
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-651 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> (-> B C) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69040.        ((A or (B -> A)) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-651, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> (-> B C) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69041
in-theory        69041
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-649 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69041.        ((A -> (B or A)) and (C -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-649, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69042
in-theory        69042
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-647 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69042.        ((A -> (A or B)) and (C -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-647, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69043
in-theory        69043
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> C) -> (((D and B) or B) -> C))))
theorem-size     15
proof            (modus-ponens tm-645 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-4.            ((A and B) -> B), axiom
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-69043.        (A -> (A and ((B -> C) -> (((D and B) or B) -> C)))), M:tm-645, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69044
in-theory        69044
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-644 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69044.        ((A -> (B -> (A and B))) and (C -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-644, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69045
in-theory        69045
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-643 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4 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-4.            ((A and B) -> 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-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-69045.        (((A and B) -> B) and (C -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-643, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69046
in-theory        69046
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-642 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69046.        (((A and B) -> A) and (C -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-642, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69047
in-theory        69047
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-641 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6 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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-4.            ((A and B) -> B), axiom
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-69047.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-641, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69048
in-theory        69048
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-640 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69048.        ((A -> (B -> A)) and (C -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-640, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69049
in-theory        69049
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (((D and B) or B) -> C)) -> E)) -> E)
theorem-size     17
proof            (modus-ponens tm-638 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> (and B (-> (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) C)) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-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-69049.        ((A and (((B -> C) -> (((D and B) or B) -> C)) -> E)) -> E), M:tm-638, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> (and B (-> (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) C)) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69050
in-theory        69050
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (((C and A) or A) -> B)) -> D) and E) -> D)
theorem-size     17
proof            (modus-ponens tm-636 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> (and (-> (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) B) C) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69050.        (((((A -> B) -> (((C and A) or A) -> B)) -> D) and E) -> D), M:tm-636, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> (and (-> (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) B) C) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69051
in-theory        69051
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C and A) or A) -> B) -> D)) -> ((A -> B) -> D))
theorem-size     19
proof            (modus-ponens tm-634 tm-807 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)) (Dm (-> (-> (-> Am Bm) (-> (-> (or (and Cm Am) Am) Bm) C)) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-4.            ((A and B) -> B), axiom
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-69051.        (((A -> B) -> ((((C and A) or A) -> B) -> D)) -> ((A -> B) -> D)), M:tm-634, m:tm-807, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)) (Dm (-> (-> (-> Am Bm) (-> (-> (or (and Cm Am) Am) Bm) C)) (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69052
in-theory        69052
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> C) -> (((D and B) or B) -> C)))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-631 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-9 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69052.        ((A -> (not ((B -> C) -> (((D and B) or B) -> C)))) -> (not A)), M:tm-631, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69053
in-theory        69053
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) -> D) -> ((E or ((A -> B) -> (((C and A) or A) -> B))) -> D))
theorem-size     29
proof            (modus-ponens tm-630 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69053.        ((((A -> B) -> (((C and A) or A) -> B)) -> D) -> ((E or ((A -> B) -> (((C and A) or A) -> B))) -> D)), M:tm-630, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69054
in-theory        69054
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-629 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69054.        (A or (B -> ((C -> D) -> (((E and C) or C) -> D)))), M:tm-629, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69055
in-theory        69055
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-628 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69055.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) or E), M:tm-628, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69056
in-theory        69056
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> D) -> (((E and C) or C) -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-627 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
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-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-4.            ((A and B) -> B), axiom
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-69056.        (A -> ((B -> ((C -> D) -> (((E and C) or C) -> D))) and A)), M:tm-627, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69057
in-theory        69057
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (A -> (((D and B) or B) -> C)))
theorem-size     15
proof            (modus-ponens tm-626 tm-807 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)) (Dm (-> C (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 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-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-4.            ((A and B) -> B), axiom
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-69057.        ((A -> (B -> C)) -> (A -> (((D and B) or B) -> C))), M:tm-626, m:tm-807, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)) (Dm (-> C (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69058
in-theory        69058
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-625 tm-807 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
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-69058.        (A -> (B -> ((C -> D) -> (((E and C) or C) -> D)))), M:tm-625, m:tm-807, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69059
in-theory        69059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-622 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-69059.        ((A -> (B -> (C or B))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-622, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69060
in-theory        69060
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-69060.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (F or E))), M:tm-609, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69061
in-theory        69061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-605 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 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-605.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-69061.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-605, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69062
in-theory        69062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (F or E)) and (((A -> B) -> (((C and A) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-595 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-69062.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (F or E)) and (((A -> B) -> (((C and A) or A) -> B)) or D))), M:tm-595, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69063
in-theory        69063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-550 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-69063.        (((A -> (B or A)) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-550, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69064
in-theory        69064
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-540 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> B), axiom
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-69064.        ((A or (B -> (C or B))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-540, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69065
in-theory        69065
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-530 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-69065.        ((A or (B -> (B or C))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-530, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69066
in-theory        69066
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-520 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-4.            ((A and B) -> B), axiom
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-69066.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-520, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69067
in-theory        69067
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-510 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-69067.        ((A or ((B and C) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-510, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69068
in-theory        69068
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-500 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-4.            ((A and B) -> B), axiom
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-69068.        ((A or ((B and C) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-500, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69069
in-theory        69069
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (((G and E) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-490 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69069.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (((G and E) or E) -> F)) or H)), M:tm-490, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69070
in-theory        69070
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-480 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-69070.        ((A or (B -> (C -> B))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-480, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69071
in-theory        69071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-469 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-69071.        ((A -> (B -> (B or C))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-469, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69072
in-theory        69072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-69072.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (E or F))), M:tm-456, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69073
in-theory        69073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-453 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
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-453.          (A -> ((B -> ((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-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-69073.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-453, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69074
in-theory        69074
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (E or F)) and (((A -> B) -> (((C and A) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-443 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-69074.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (E or F)) and (((A -> B) -> (((C and A) or A) -> B)) or D))), M:tm-443, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69075
in-theory        69075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-409 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-69075.        (((A -> (A or B)) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-409, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69076
in-theory        69076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-400 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-69076.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-400, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69077
in-theory        69077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-391 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-69077.        ((((A and B) -> B) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-391, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69078
in-theory        69078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-382 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-69078.        ((((A and B) -> A) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-382, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69079
in-theory        69079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (((G and E) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-373 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69079.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (((G and E) or E) -> F)) or H)), M:tm-373, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69080
in-theory        69080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-364 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-69080.        (((A -> (B -> A)) or C) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-364, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69081
in-theory        69081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-354 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-4.            ((A and B) -> B), axiom
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-69081.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-354, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69082
in-theory        69082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> B), axiom
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-69082.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69083
in-theory        69083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (((E and C) or C) -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-338 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> B), axiom
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-69083.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (((E and C) or C) -> D)) or F)), M:tm-338, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69084
in-theory        69084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (F -> (E and F))) and (((A -> B) -> (((C and A) or A) -> B)) or D)))
theorem-size     35
proof            (modus-ponens tm-327 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-69084.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (F -> (E and F))) and (((A -> B) -> (((C and A) or A) -> B)) or D))), M:tm-327, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69085
in-theory        69085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (((E and F) -> F) and (((A -> B) -> (((C and A) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-326 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-69085.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (((E and F) -> F) and (((A -> B) -> (((C and A) or A) -> B)) or D))), M:tm-326, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69086
in-theory        69086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (((E and F) -> E) and (((A -> B) -> (((C and A) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-325 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-69086.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (((E and F) -> E) and (((A -> B) -> (((C and A) or A) -> B)) or D))), M:tm-325, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69087
in-theory        69087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) -> (((C and A) or A) -> B)) or D)))
theorem-size     41
proof            (modus-ponens tm-324 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-69087.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) -> (((C and A) or A) -> B)) or D))), M:tm-324, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69088
in-theory        69088
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (F -> E)) and (((A -> B) -> (((C and A) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-323 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> B), axiom
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-69088.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (F -> E)) and (((A -> B) -> (((C and A) or A) -> B)) or D))), M:tm-323, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69089
in-theory        69089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-69089.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E and F) -> F)), M:tm-322, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69090
in-theory        69090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-69090.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E and F) -> E)), M:tm-320, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69091
in-theory        69091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-69091.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69092
in-theory        69092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-69092.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (F -> E))), M:tm-315, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69093
in-theory        69093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E or (((A -> B) -> (((C and A) or A) -> B)) or D)))
theorem-size     29
proof            (modus-ponens tm-311 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-69093.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E or (((A -> B) -> (((C and A) or A) -> B)) or D))), M:tm-311, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69094
in-theory        69094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((((A -> B) -> (((C and A) or A) -> B)) or D) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-69094.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and ((((A -> B) -> (((C and A) or A) -> B)) or D) or E)), M:tm-310, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69095
in-theory        69095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> ((((A -> B) -> (((C and A) or A) -> B)) or D) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
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-69095.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> ((((A -> B) -> (((C and A) or A) -> B)) or D) and E))), M:tm-309, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69096
in-theory        69096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (((A -> B) -> (((C and A) or A) -> B)) or D)))
theorem-size     29
proof            (modus-ponens tm-305 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (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-4.            ((A and B) -> B), axiom
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-69096.        ((((A -> B) -> (((C and A) or A) -> B)) or D) and (E -> (((A -> B) -> (((C and A) or A) -> B)) or D))), M:tm-305, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69097
in-theory        69097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-303 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-4.            ((A and B) -> B), axiom
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-69097.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-303, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69098
in-theory        69098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-270 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 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-270.          (A -> ((B -> (((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-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-69098.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-270, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69099
in-theory        69099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-239 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 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-239.          (A -> ((B -> (((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-4.            ((A and B) -> B), axiom
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-69099.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-239, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69100
in-theory        69100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (((G and E) or E) -> F)) or H))
theorem-size     31
proof            (modus-ponens tm-210 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> B), axiom
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-69100.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (((G and E) or E) -> F)) or H)), M:tm-210, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69101
in-theory        69101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-183 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 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-183.          (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-4.            ((A and B) -> B), axiom
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-69101.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-183, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69102
in-theory        69102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-157 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-69102.        ((A -> ((B and C) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-157, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69103
in-theory        69103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     29
proof            (modus-ponens tm-147 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-69103.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-147, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69104
in-theory        69104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-134 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-69104.        ((A -> ((B and C) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-134, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69105
in-theory        69105
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     29
proof            (modus-ponens tm-125 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-69105.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-125, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69106
in-theory        69106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (((G and E) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-113 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69106.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (((G and E) or E) -> F)) or H)), M:tm-113, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69107
in-theory        69107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     33
proof            (modus-ponens tm-105 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> B), axiom
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-69107.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-105, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69108
in-theory        69108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (((E and C) or C) -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-95 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> B), axiom
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-69108.        (((A -> B) -> (A -> A)) and (((C -> D) -> (((E and C) or C) -> D)) or F)), M:tm-95, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69109
in-theory        69109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-83 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-69109.        ((A -> (B -> (C -> B))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-83, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69110
in-theory        69110
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (((D and B) or B) -> C)) or E))
theorem-size     19
proof            (modus-ponens tm-76 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69110.        (((not (not A)) -> A) and (((B -> C) -> (((D and B) or B) -> C)) or E)), M:tm-76, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69111
in-theory        69111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (((E and C) or C) -> D)) or F))
theorem-size     25
proof            (modus-ponens tm-69 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69111.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (((E and C) or C) -> D)) or F)), M:tm-69, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69112
in-theory        69112
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-54 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-54.           (A -> (((B -> C) -> ((C -> 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-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-69112.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-54, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69113
in-theory        69113
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (((E and C) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-42 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69113.        ((A -> (B or A)) and (((C -> D) -> (((E and C) or C) -> D)) or F)), M:tm-42, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69114
in-theory        69114
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (((E and C) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-32 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69114.        ((A -> (A or B)) and (((C -> D) -> (((E and C) or C) -> D)) or F)), M:tm-32, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69115
in-theory        69115
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (((E and C) or C) -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-23 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69115.        ((A -> (B -> (A and B))) and (((C -> D) -> (((E and C) or C) -> D)) or F)), M:tm-23, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69116
in-theory        69116
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (((E and C) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-22 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-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-69116.        (((A and B) -> B) and (((C -> D) -> (((E and C) or C) -> D)) or F)), M:tm-22, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69117
in-theory        69117
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (((E and C) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-21 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69117.        (((A and B) -> A) and (((C -> D) -> (((E and C) or C) -> D)) or F)), M:tm-21, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69118
in-theory        69118
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-20 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-4.            ((A and B) -> B), axiom
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-69118.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-20, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69119
in-theory        69119
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (((E and C) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-19 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69119.        ((A -> (B -> A)) and (((C -> D) -> (((E and C) or C) -> D)) or F)), M:tm-19, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69120
in-theory        69120
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (((D and B) or B) -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-7 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-7 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69120.        (A or (((B -> C) -> (((D and B) or B) -> C)) or E)), M:tm-7, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69121
in-theory        69121
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) or D) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69121.        ((((A -> B) -> (((C and A) or A) -> B)) or D) or E), M:tm-6, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69122
in-theory        69122
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (((D and B) or B) -> C)) or E) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69122.        (A -> ((((B -> C) -> (((D and B) or B) -> C)) or E) and A)), M:tm-5, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69123
in-theory        69123
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (((D and B) or B) -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-1 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-1 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69123.        (A -> (((B -> C) -> (((D and B) or B) -> C)) or E)), M:tm-1, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69124
in-theory        69124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-69124.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-808, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-69125
in-theory        69125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69125.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-808, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-69126
in-theory        69126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((not (not D)) -> D))
theorem-size     17
proof            (modus-ponens tm-808 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-10.           ((not (not A)) -> A), axiom
tm-69126.        (((A -> B) -> (((C and A) or A) -> B)) and ((not (not D)) -> D)), M:tm-808, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-69127
in-theory        69127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-808 tm-11 ((A (-> Am (-> Bm (-> 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-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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-69127.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> E)))), M:tm-808, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-69128
in-theory        69128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-808 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-69128.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> D))), M:tm-808, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-69129
in-theory        69129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-808 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-69129.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-808, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-69130
in-theory        69130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-69130.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-808, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-69131
in-theory        69131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-808 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-69131.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-808, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-69132
in-theory        69132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-808 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-69132.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E and F) -> E))), M:tm-808, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-69133
in-theory        69133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-808 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-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-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-69133.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-808, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-69134
in-theory        69134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-808 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
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-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-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-69134.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E and F) -> F))), M:tm-808, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-69135
in-theory        69135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-69135.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> E)) and D))), M:tm-808, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-69136
in-theory        69136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-808 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-69136.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-808, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-69137
in-theory        69137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and F) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-69137.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and F) -> E) and D))), M:tm-808, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-69138
in-theory        69138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and F) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-69138.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and F) -> F) and D))), M:tm-808, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-69139
in-theory        69139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-69139.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-808, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-69140
in-theory        69140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-808 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-69140.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (D and E)))), M:tm-808, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-69141
in-theory        69141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-69141.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (E and F))))), M:tm-808, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-69142
in-theory        69142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-808 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-69142.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) or F)), M:tm-808, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-69143
in-theory        69143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-808 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-69143.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-808, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-69144
in-theory        69144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) or F))
theorem-size     19
proof            (modus-ponens tm-808 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-69144.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) or F)), M:tm-808, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-69145
in-theory        69145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) or F))
theorem-size     19
proof            (modus-ponens tm-808 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69145.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) or F)), M:tm-808, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-69146
in-theory        69146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-808 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-69146.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) or F)), M:tm-808, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-69147
in-theory        69147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) or F))
theorem-size     19
proof            (modus-ponens tm-808 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-69147.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) or F)), M:tm-808, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-69148
in-theory        69148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (E or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-69148.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (E or F)) and D))), M:tm-808, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-69149
in-theory        69149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-808 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-69149.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (E or F)))), M:tm-808, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-69150
in-theory        69150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-808 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-69150.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> E)))), M:tm-808, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-69151
in-theory        69151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-69151.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-808, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-69152
in-theory        69152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-808 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-69152.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E and F) -> E))), M:tm-808, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-69153
in-theory        69153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-808 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69153.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E and F) -> F))), M:tm-808, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-69154
in-theory        69154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-69154.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (E and F))))), M:tm-808, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-69155
in-theory        69155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-808 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-69155.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (E or F)))), M:tm-808, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-69156
in-theory        69156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-808 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-69156.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F or E)))), M:tm-808, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-69157
in-theory        69157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) or F))
theorem-size     19
proof            (modus-ponens tm-808 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-69157.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) or F)), M:tm-808, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-69158
in-theory        69158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F or E)) and D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-69158.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F or E)) and D))), M:tm-808, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-69159
in-theory        69159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-808 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-69159.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F or E)))), M:tm-808, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-69160
in-theory        69160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-808 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-69160.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-808, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-69161
in-theory        69161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-69161.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-808, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-69162
in-theory        69162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-808 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-69162.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-808, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-69163
in-theory        69163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-808 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-69163.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-808, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-69164
in-theory        69164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-808 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-69164.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-808, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-69165
in-theory        69165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-808 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-69165.        (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-808, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-69166
in-theory        69166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-808 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-69166.        (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-808, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-69167
in-theory        69167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-69167.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-808, 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-69168
in-theory        69168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69168.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-808, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-69169
in-theory        69169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-808 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69169.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-808, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-69170
in-theory        69170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-808 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-69170.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-808, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-69171
in-theory        69171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
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-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-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-69171.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-808, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-69172
in-theory        69172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69172.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-808, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-69173
in-theory        69173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69173.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> D))) -> (not D))), M:tm-808, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-69174
in-theory        69174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69174.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-808, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-69175
in-theory        69175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
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-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-69175.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-808, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-69176
in-theory        69176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69176.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-808, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-69177
in-theory        69177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69177.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-808, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-69178
in-theory        69178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69178.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (D or E))) -> (not D))), M:tm-808, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-69179
in-theory        69179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69179.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E or D))) -> (not D))), M:tm-808, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-69180
in-theory        69180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-808 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am 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-4.            ((A and B) -> B), axiom
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-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-69180.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-808, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-69181
in-theory        69181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-808 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69181.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-808, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-69182
in-theory        69182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-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-69182.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-808, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-69183
in-theory        69183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69183.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-808, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-69184
in-theory        69184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     25
proof            (modus-ponens tm-808 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69184.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-808, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-69185
in-theory        69185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-69185.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-808, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-69186
in-theory        69186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69186.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-808, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-69187
in-theory        69187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69187.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-808, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-69188
in-theory        69188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     23
proof            (modus-ponens tm-808 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69188.        (((A -> B) -> (((C and A) or A) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-808, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-69189
in-theory        69189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-808 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-69189.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-808, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-69190
in-theory        69190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-808 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69190.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((not (not E)) -> E))), M:tm-808, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-69191
in-theory        69191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((not (not D)) -> D) or E))
theorem-size     19
proof            (modus-ponens tm-808 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69191.        (((A -> B) -> (((C and A) or A) -> B)) and (((not (not D)) -> D) or E)), M:tm-808, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-69192
in-theory        69192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-69192.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((not (not E)) -> E) and D))), M:tm-808, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-69193
in-theory        69193
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     27
proof            (modus-ponens tm-808 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69193.        (((A -> B) -> (((C and A) or A) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-808, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-69194
in-theory        69194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-808 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69194.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((not (not E)) -> E))), M:tm-808, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-69195
in-theory        69195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69195.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-808, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-69196
in-theory        69196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-808 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
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-4.            ((A and B) -> B), axiom
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-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-69196.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-808, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-69197
in-theory        69197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69197.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (G -> F))))), M:tm-808, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-69198
in-theory        69198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (F -> E))) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69198.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (F -> E))) or G)), M:tm-808, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-69199
in-theory        69199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-69199.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-808, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-69200
in-theory        69200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-808 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-69200.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (F -> E)))), M:tm-808, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-69201
in-theory        69201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69201.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (G -> F))))), M:tm-808, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-69202
in-theory        69202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> D))
theorem-size     15
proof            (modus-ponens tm-808 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69202.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> D)), M:tm-808, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-69203
in-theory        69203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69203.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-808, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-69204
in-theory        69204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> (D and E)))
theorem-size     19
proof            (modus-ponens tm-808 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1 tm-3)
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69204.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> (D and E))), M:tm-808, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-69205
in-theory        69205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-808 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69205.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> E))), M:tm-808, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-69206
in-theory        69206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((not (not D)) -> (not (not D))))
theorem-size     19
proof            (modus-ponens tm-808 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69206.        (((A -> B) -> (((C and A) or A) -> B)) and ((not (not D)) -> (not (not D)))), M:tm-808, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-69207
in-theory        69207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-808 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69207.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-808, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-69208
in-theory        69208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-808 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69208.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-808, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-69209
in-theory        69209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-808 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69209.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> (E -> E)))), M:tm-808, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-69210
in-theory        69210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (D -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-808 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69210.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (D -> D)) or F)), M:tm-808, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-69211
in-theory        69211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-69211.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-808, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-69212
in-theory        69212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69212.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-808, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-69213
in-theory        69213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-808 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69213.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> (E -> E)))), M:tm-808, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-69214
in-theory        69214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-69214.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-808, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-69215
in-theory        69215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-808 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-69215.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D -> E)) -> (D -> E))), M:tm-808, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-69216
in-theory        69216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-808 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69216.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-808, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-69217
in-theory        69217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-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-69217.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-808, 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-69218
in-theory        69218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-69218.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-808, 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-69219
in-theory        69219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69219.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-808, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-69220
in-theory        69220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     33
proof            (modus-ponens tm-808 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69220.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-808, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-69221
in-theory        69221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     35
proof            (modus-ponens tm-808 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-69221.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-808, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-69222
in-theory        69222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-69222.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-808, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-69223
in-theory        69223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69223.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-808, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-69224
in-theory        69224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-808 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-69224.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-808, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-69225
in-theory        69225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-808 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69225.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-808, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-69226
in-theory        69226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-69226.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-808, 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-69227
in-theory        69227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-808 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69227.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-808, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-69228
in-theory        69228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     29
proof            (modus-ponens tm-808 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69228.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-808, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-69229
in-theory        69229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     31
proof            (modus-ponens tm-808 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-69229.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-808, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-69230
in-theory        69230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-808 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69230.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-808, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-69231
in-theory        69231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-808 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-69231.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-808, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-69232
in-theory        69232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) and D) -> E))
theorem-size     19
proof            (modus-ponens tm-808 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-69232.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) and D) -> E)), M:tm-808, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-69233
in-theory        69233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-808 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-69233.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-808, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-69234
in-theory        69234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     31
proof            (modus-ponens tm-808 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-3 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-69234.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-808, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-69235
in-theory        69235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-808 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-69235.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-808, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-69236
in-theory        69236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69236.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-808, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-69237
in-theory        69237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 tm-9 tm-2 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-4.            ((A and B) -> B), axiom
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-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-69237.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-808, 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-69238
in-theory        69238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-69238.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-808, 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-69239
in-theory        69239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-2 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-4.            ((A and B) -> B), axiom
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-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-69239.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-808, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-69240
in-theory        69240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     29
proof            (modus-ponens tm-808 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-2 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-4.            ((A and B) -> B), axiom
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-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-69240.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-808, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-69241
in-theory        69241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-808 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-69241.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-808, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-69242
in-theory        69242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-69242.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-808, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-69243
in-theory        69243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-2 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-4.            ((A and B) -> B), axiom
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-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-69243.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-808, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-69244
in-theory        69244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-808 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-69244.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-808, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-69245
in-theory        69245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     25
proof            (modus-ponens tm-808 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-69245.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-808, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-69246
in-theory        69246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 tm-9 tm-1 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-4.            ((A and B) -> B), axiom
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-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-69246.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-808, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-69247
in-theory        69247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-808 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-69247.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-808, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-69248
in-theory        69248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-808 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-1 tm-3)
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-4.            ((A and B) -> B), axiom
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-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-69248.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F and G) -> F)))), M:tm-808, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-69249
in-theory        69249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E and F) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-1 tm-3)
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-4.            ((A and B) -> B), axiom
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-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-69249.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E and F) -> E)) or G)), M:tm-808, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-69250
in-theory        69250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-69250.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-808, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-69251
in-theory        69251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-808 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1 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-4.            ((A and B) -> B), axiom
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-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-69251.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E and F)) -> (D -> E))), M:tm-808, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-69252
in-theory        69252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-808 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-3)
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-69252.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F and G) -> F)))), M:tm-808, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-69253
in-theory        69253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and (D -> E)) -> E))
theorem-size     19
proof            (modus-ponens tm-808 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-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-69253.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and (D -> E)) -> E)), M:tm-808, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-69254
in-theory        69254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-808 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69254.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-808, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-69255
in-theory        69255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     31
proof            (modus-ponens tm-808 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69255.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-808, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-69256
in-theory        69256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-808 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1 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-4.            ((A and B) -> B), axiom
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-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-69256.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-808, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-69257
in-theory        69257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-808 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-69257.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-808, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-69258
in-theory        69258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     27
proof            (modus-ponens tm-808 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69258.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-808, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-69259
in-theory        69259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-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-69259.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-808, 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-69260
in-theory        69260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-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-69260.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-808, 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-69261
in-theory        69261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69261.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-808, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-69262
in-theory        69262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-808 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69262.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-808, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-69263
in-theory        69263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-808 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-69263.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-808, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-69264
in-theory        69264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-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-69264.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-808, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-69265
in-theory        69265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69265.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-808, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-69266
in-theory        69266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-808 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69266.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-808, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-69267
in-theory        69267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-808 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-69267.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-808, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-69268
in-theory        69268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     25
proof            (modus-ponens tm-808 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-69268.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-808, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-69269
in-theory        69269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69269.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-808, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-69270
in-theory        69270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-808 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
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-4.            ((A and B) -> B), axiom
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-1.            (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-69270.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-808, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-69271
in-theory        69271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-808 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69271.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F and G) -> G)))), M:tm-808, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-69272
in-theory        69272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E and F) -> F)) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69272.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E and F) -> F)) or G)), M:tm-808, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-69273
in-theory        69273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69273.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-808, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-69274
in-theory        69274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-808 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69274.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E and F)) -> (D -> F))), M:tm-808, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-69275
in-theory        69275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-808 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (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-69275.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F and G) -> G)))), M:tm-808, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-69276
in-theory        69276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69276.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-808, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-69277
in-theory        69277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-69277.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-69278
in-theory        69278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-1.            (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-69278.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-808, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-69279
in-theory        69279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69279.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-808, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-69280
in-theory        69280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (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-69280.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-808, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-69281
in-theory        69281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69281.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-808, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-69282
in-theory        69282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69282.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-808, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-69283
in-theory        69283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (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-69283.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-808, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-69284
in-theory        69284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-808 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (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-69284.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-808, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-69285
in-theory        69285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (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-69285.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-808, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-69286
in-theory        69286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69286.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-808, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69287
in-theory        69287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-69287.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-808, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-69288
in-theory        69288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-69288.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-808, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-69289
in-theory        69289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-69289.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69290
in-theory        69290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-2 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-69290.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-808, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-69291
in-theory        69291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69291.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-808, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69292
in-theory        69292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-69292.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-808, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-69293
in-theory        69293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69293.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-808, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69294
in-theory        69294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69294.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-808, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-69295
in-theory        69295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69295.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-808, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-69296
in-theory        69296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (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-69296.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-808, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-69297
in-theory        69297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69297.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-808, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-69298
in-theory        69298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-808 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69298.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-808, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-69299
in-theory        69299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-69299.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-808, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-69300
in-theory        69300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69300.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-808, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-69301
in-theory        69301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69301.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-808, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-69302
in-theory        69302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69302.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-808, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-69303
in-theory        69303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-808 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69303.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-808, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-69304
in-theory        69304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-808 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69304.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-808, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-69305
in-theory        69305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69305.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-808, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-69306
in-theory        69306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69306.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-808, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-69307
in-theory        69307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69307.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-808, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-69308
in-theory        69308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69308.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-808, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-69309
in-theory        69309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69309.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-808, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-69310
in-theory        69310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-808 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69310.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-808, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-69311
in-theory        69311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69311.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-808, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-69312
in-theory        69312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     33
proof            (modus-ponens tm-808 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69312.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-808, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-69313
in-theory        69313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69313.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-808, 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-69314
in-theory        69314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69314.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-808, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-69315
in-theory        69315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 tm-2 tm-3)
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69315.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-808, 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-69316
in-theory        69316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-808 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69316.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-808, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-69317
in-theory        69317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69317.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-808, 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-69318
in-theory        69318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-808 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69318.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-808, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-69319
in-theory        69319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69319.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-808, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-69320
in-theory        69320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69320.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-808, 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-69321
in-theory        69321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-69321.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-808, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-69322
in-theory        69322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-808 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69322.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-808, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-69323
in-theory        69323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69323.        (((A -> B) -> (((C and A) 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-808, 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-69324
in-theory        69324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-808 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69324.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-808, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-69325
in-theory        69325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     31
proof            (modus-ponens tm-808 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69325.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-808, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-69326
in-theory        69326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     33
proof            (modus-ponens tm-808 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-69326.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-808, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-69327
in-theory        69327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-808 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69327.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-808, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-69328
in-theory        69328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69328.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-808, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-69329
in-theory        69329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-69329.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-69330
in-theory        69330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69330.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-808, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-69331
in-theory        69331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69331.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-808, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-69332
in-theory        69332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69332.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-808, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-69333
in-theory        69333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69333.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-808, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-69334
in-theory        69334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69334.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-808, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-69335
in-theory        69335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69335.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-808, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-69336
in-theory        69336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-808 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69336.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-808, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-69337
in-theory        69337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69337.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-808, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-69338
in-theory        69338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69338.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-808, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69339
in-theory        69339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-69339.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-808, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-69340
in-theory        69340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-69340.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-808, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-69341
in-theory        69341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69341.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69342
in-theory        69342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-69342.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-808, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-69343
in-theory        69343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69343.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-808, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69344
in-theory        69344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-69344.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-808, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-69345
in-theory        69345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69345.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-808, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69346
in-theory        69346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69346.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-808, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-69347
in-theory        69347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-69347.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-808, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-69348
in-theory        69348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69348.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-808, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-69349
in-theory        69349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69349.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-808, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-69350
in-theory        69350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-1.            (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-69350.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-808, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-69351
in-theory        69351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
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-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-69351.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-808, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-69352
in-theory        69352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69352.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-808, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-69353
in-theory        69353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-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-69353.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-808, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-69354
in-theory        69354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-808 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-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-69354.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-808, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-69355
in-theory        69355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-69355.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-808, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-69356
in-theory        69356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-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-69356.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-808, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-69357
in-theory        69357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B 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-69357.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-808, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-69358
in-theory        69358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 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       135
proof-steps      11
----------------------------------------------------------------
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-22.           (A -> (((B and C) -> C) and 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-69358.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-69359
in-theory        69359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69359.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-808, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-69360
in-theory        69360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69360.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-808, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-69361
in-theory        69361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69361.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-808, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-69362
in-theory        69362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and 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-69362.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-808, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-69363
in-theory        69363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and 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-69363.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-808, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-69364
in-theory        69364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 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       135
proof-steps      11
----------------------------------------------------------------
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-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-69364.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-808, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-69365
in-theory        69365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-808 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       129
proof-steps      11
----------------------------------------------------------------
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-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-69365.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-808, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-69366
in-theory        69366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69366.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-808, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-69367
in-theory        69367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B 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-69367.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-808, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69368
in-theory        69368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-808 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       135
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and C) -> C) and 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-69368.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-808, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-69369
in-theory        69369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       179
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and C) -> C) and 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-69369.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-808, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-69370
in-theory        69370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 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       159
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B 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-69370.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69371
in-theory        69371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       159
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and C) -> C) and 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-69371.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-808, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-69372
in-theory        69372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B 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-69372.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-808, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69373
in-theory        69373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       159
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and C) -> C) and 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-69373.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-808, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-69374
in-theory        69374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B 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-69374.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-808, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69375
in-theory        69375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 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       135
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B 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-69375.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-808, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-69376
in-theory        69376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       167
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and C) -> C) and 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-69376.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-808, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-69377
in-theory        69377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-808 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       135
proof-steps      13
----------------------------------------------------------------
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-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-69377.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-808, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-69378
in-theory        69378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-808 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       135
proof-steps      13
----------------------------------------------------------------
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-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-69378.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-808, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-69379
in-theory        69379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69379.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-808, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-69380
in-theory        69380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69380.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-808, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-69381
in-theory        69381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69381.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-808, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-69382
in-theory        69382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69382.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-808, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-69383
in-theory        69383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       139
proof-steps      11
----------------------------------------------------------------
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-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-69383.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-808, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-69384
in-theory        69384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-69384.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-808, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-69385
in-theory        69385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-808 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-69385.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-808, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-69386
in-theory        69386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-69386.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-808, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-69387
in-theory        69387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-69387.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-808, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-69388
in-theory        69388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-272 ((A (and (-> Am (-> Bm (and Am 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69388.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-808, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-69389
in-theory        69389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-69389.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-69390
in-theory        69390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-808 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69390.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-808, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-69391
in-theory        69391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-808 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69391.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-808, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-69392
in-theory        69392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69392.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-808, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-69393
in-theory        69393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69393.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-808, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-69394
in-theory        69394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69394.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-808, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-69395
in-theory        69395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69395.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-808, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-69396
in-theory        69396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69396.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-808, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-69397
in-theory        69397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-808 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69397.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-808, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-69398
in-theory        69398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69398.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-808, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69399
in-theory        69399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-69399.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-808, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-69400
in-theory        69400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-69400.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-808, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-69401
in-theory        69401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69401.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69402
in-theory        69402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-69402.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-808, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-69403
in-theory        69403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-808 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69403.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-808, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69404
in-theory        69404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-69404.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-808, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-69405
in-theory        69405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-808 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69405.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-808, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69406
in-theory        69406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69406.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-808, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-69407
in-theory        69407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-69407.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-808, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-69408
in-theory        69408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69408.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-808, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-69409
in-theory        69409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-808 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       143
proof-steps      13
----------------------------------------------------------------
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-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-69409.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-808, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-69410
in-theory        69410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69410.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-808, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-69411
in-theory        69411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-808 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       143
proof-steps      13
----------------------------------------------------------------
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-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-69411.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-808, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-69412
in-theory        69412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69412.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-808, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-69413
in-theory        69413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69413.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-808, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-69414
in-theory        69414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (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-69414.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-808, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-69415
in-theory        69415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69415.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-808, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-69416
in-theory        69416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4)
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-4.            ((A and B) -> B), axiom
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-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-69416.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-808, 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-69417
in-theory        69417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-808 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69417.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-808, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-69418
in-theory        69418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-808 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69418.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-808, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-69419
in-theory        69419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-69419.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-808, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-69420
in-theory        69420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-808 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
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-4.            ((A and B) -> B), axiom
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-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-69420.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-808, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-69421
in-theory        69421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> D))))
theorem-size     19
proof            (modus-ponens tm-808 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-69421.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> D)))), M:tm-808, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-69422
in-theory        69422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-69422.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-808, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-69423
in-theory        69423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> ((D and E) and D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-69423.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> ((D and E) and D))), M:tm-808, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-69424
in-theory        69424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> ((D and E) and E)))
theorem-size     21
proof            (modus-ponens tm-808 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69424.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> ((D and E) and E))), M:tm-808, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-69425
in-theory        69425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-69425.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (D and E))))), M:tm-808, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-69426
in-theory        69426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (D or E))))
theorem-size     19
proof            (modus-ponens tm-808 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-69426.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (D or E)))), M:tm-808, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-69427
in-theory        69427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E or D))))
theorem-size     19
proof            (modus-ponens tm-808 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-69427.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E or D)))), M:tm-808, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-69428
in-theory        69428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     29
proof            (modus-ponens tm-808 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69428.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-69429
in-theory        69429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-69429.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-808, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-69430
in-theory        69430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69430.        (((A -> B) -> (((C and A) or A) -> B)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-808, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-69431
in-theory        69431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (F -> E)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-69431.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (F -> E))))), M:tm-808, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-69432
in-theory        69432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-69432.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-808, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-69433
in-theory        69433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69433.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-808, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-69434
in-theory        69434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     29
proof            (modus-ponens tm-808 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-69434.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-808, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-69435
in-theory        69435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-69435.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-808, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-69436
in-theory        69436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E and F) -> E))))
theorem-size     21
proof            (modus-ponens tm-808 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1 tm-3)
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-69436.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E and F) -> E)))), M:tm-808, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-69437
in-theory        69437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69437.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-808, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-69438
in-theory        69438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E and F) -> F))))
theorem-size     21
proof            (modus-ponens tm-808 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-69438.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E and F) -> F)))), M:tm-808, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-69439
in-theory        69439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-69439.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-808, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-69440
in-theory        69440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     31
proof            (modus-ponens tm-808 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-69440.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-808, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-69441
in-theory        69441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-69441.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-808, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-69442
in-theory        69442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69442.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-808, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-69443
in-theory        69443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     25
proof            (modus-ponens tm-808 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-69443.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-808, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-69444
in-theory        69444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-69444.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-808, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-69445
in-theory        69445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-808 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-69445.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-808, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-69446
in-theory        69446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-808 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       143
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and C) -> C) and 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-69446.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-808, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-69447
in-theory        69447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-69447.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-808, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-69448
in-theory        69448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69448.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-808, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-69449
in-theory        69449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-69449.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-808, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-69450
in-theory        69450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-808 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69450.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-808, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-69451
in-theory        69451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-808 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69451.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-808, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-69452
in-theory        69452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-808 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69452.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-808, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-69453
in-theory        69453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-808 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69453.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-808, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-69454
in-theory        69454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-69454.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-808, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-69455
in-theory        69455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-808 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69455.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-808, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-69456
in-theory        69456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-808 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69456.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-808, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-69457
in-theory        69457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     23
proof            (modus-ponens tm-808 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-69457.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-808, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-69458
in-theory        69458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-808 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69458.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-808, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69459
in-theory        69459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 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       135
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B 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-69459.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-808, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69460
in-theory        69460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69460.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-808, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69461
in-theory        69461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69461.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-808, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-69462
in-theory        69462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (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-69462.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-808, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69463
in-theory        69463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-808 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69463.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-808, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-69464
in-theory        69464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-808 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-69464.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-808, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-69465
in-theory        69465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-808 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-69465.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-808, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-69466
in-theory        69466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69466.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-808, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-69467
in-theory        69467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> 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-69467.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-808, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-69468
in-theory        69468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-808 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69468.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-808, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-69469
in-theory        69469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     23
proof            (modus-ponens tm-808 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69469.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-808, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-69470
in-theory        69470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-69470.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-808, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-69471
in-theory        69471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-808 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69471.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-808, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-69472
in-theory        69472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-808 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> 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-69472.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-808, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-69473
in-theory        69473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-808 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69473.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-808, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-69474
in-theory        69474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69474.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-808, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-69475
in-theory        69475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69475.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-808, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-69476
in-theory        69476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69476.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-808, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-69477
in-theory        69477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69477.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-808, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-69478
in-theory        69478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69478.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (F -> E)) or G))), M:tm-808, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-69479
in-theory        69479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> D)) or F) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-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-69479.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> D)) or F) or G)), M:tm-808, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-69480
in-theory        69480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-69480.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-808, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-69481
in-theory        69481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69481.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> E)) or G))), M:tm-808, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-69482
in-theory        69482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69482.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-808, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-69483
in-theory        69483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       159
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69483.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-808, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-69484
in-theory        69484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69484.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-808, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-69485
in-theory        69485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69485.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-808, 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-69486
in-theory        69486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69486.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-808, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-69487
in-theory        69487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-808 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69487.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-808, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-69488
in-theory        69488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     29
proof            (modus-ponens tm-808 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-69488.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-808, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-69489
in-theory        69489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     31
proof            (modus-ponens tm-808 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-69489.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-808, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-69490
in-theory        69490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-808 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69490.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-808, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-69491
in-theory        69491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-808 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69491.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-808, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-69492
in-theory        69492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69492.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-808, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-69493
in-theory        69493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69493.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-808, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-69494
in-theory        69494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-6 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69494.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-808, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-69495
in-theory        69495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-6 tm-3)
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69495.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-808, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-69496
in-theory        69496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-6 tm-3)
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-4.            ((A and B) -> B), axiom
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-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-69496.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E and F) -> E) or G))), M:tm-808, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-69497
in-theory        69497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) -> D) or F) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-3)
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-69497.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) -> D) or F) or G)), M:tm-808, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-69498
in-theory        69498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-69498.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-808, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-69499
in-theory        69499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-6 tm-3)
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-4.            ((A and B) -> B), axiom
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-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-69499.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and F) -> E) or G))), M:tm-808, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-69500
in-theory        69500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-808 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69500.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-808, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-69501
in-theory        69501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69501.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-808, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-69502
in-theory        69502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69502.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-808, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-69503
in-theory        69503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69503.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-808, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-69504
in-theory        69504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69504.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-808, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-69505
in-theory        69505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69505.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E and F) -> F) or G))), M:tm-808, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-69506
in-theory        69506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) -> E) or F) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69506.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) -> E) or F) or G)), M:tm-808, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-69507
in-theory        69507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69507.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-808, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-69508
in-theory        69508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69508.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E and F) -> F) or G))), M:tm-808, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-69509
in-theory        69509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-808 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69509.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-808, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-69510
in-theory        69510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-808 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       135
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69510.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-808, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-69511
in-theory        69511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-808 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69511.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-808, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-69512
in-theory        69512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69512.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-808, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-69513
in-theory        69513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-808 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69513.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-808, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-69514
in-theory        69514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69514.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-808, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-69515
in-theory        69515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-808 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), 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-69515.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-808, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-69516
in-theory        69516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-69516.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-808, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-69517
in-theory        69517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69517.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-808, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-69518
in-theory        69518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-808 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69518.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-808, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-69519
in-theory        69519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69519.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-808, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-69520
in-theory        69520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69520.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-808, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-69521
in-theory        69521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69521.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-808, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-69522
in-theory        69522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69522.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-808, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-69523
in-theory        69523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69523.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (E or F)) or G))), M:tm-808, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-69524
in-theory        69524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (D or E)) or F) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A 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-69524.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (D or E)) or F) or G)), M:tm-808, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-69525
in-theory        69525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-69525.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-808, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-69526
in-theory        69526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69526.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (E or F)) or G))), M:tm-808, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-69527
in-theory        69527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69527.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-808, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-69528
in-theory        69528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-69528.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-69529
in-theory        69529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69529.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-808, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-69530
in-theory        69530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69530.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-808, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-69531
in-theory        69531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69531.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-808, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-69532
in-theory        69532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69532.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-808, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-69533
in-theory        69533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69533.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-808, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-69534
in-theory        69534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69534.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-808, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-69535
in-theory        69535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-808 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69535.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-808, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-69536
in-theory        69536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69536.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-808, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-69537
in-theory        69537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69537.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-808, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69538
in-theory        69538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-69538.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-808, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-69539
in-theory        69539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-69539.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-808, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-69540
in-theory        69540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69540.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69541
in-theory        69541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 tm-6 tm-2 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-69541.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-808, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-69542
in-theory        69542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-1 tm-3)
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69542.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-808, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69543
in-theory        69543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-69543.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-808, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-69544
in-theory        69544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69544.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-808, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69545
in-theory        69545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69545.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-808, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-69546
in-theory        69546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-69546.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-808, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-69547
in-theory        69547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69547.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-808, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-69548
in-theory        69548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69548.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-808, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-69549
in-theory        69549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69549.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-808, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-69550
in-theory        69550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-69550.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-808, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-69551
in-theory        69551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69551.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-808, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69552
in-theory        69552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69552.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-808, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-69553
in-theory        69553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-69553.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-808, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-69554
in-theory        69554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-3)
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69554.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-808, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-69555
in-theory        69555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69555.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-808, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-69556
in-theory        69556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-808 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69556.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-808, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-69557
in-theory        69557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69557.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-808, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-69558
in-theory        69558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69558.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-808, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-69559
in-theory        69559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-69559.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-808, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-69560
in-theory        69560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69560.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-808, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-69561
in-theory        69561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 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       135
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69561.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-808, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-69562
in-theory        69562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69562.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-808, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-69563
in-theory        69563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69563.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-808, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-69564
in-theory        69564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69564.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-808, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-69565
in-theory        69565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69565.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-808, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-69566
in-theory        69566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69566.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-808, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-69567
in-theory        69567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69567.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-808, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-69568
in-theory        69568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-808 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69568.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-808, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-69569
in-theory        69569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-69569.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-808, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-69570
in-theory        69570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69570.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-808, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-69571
in-theory        69571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69571.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-808, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69572
in-theory        69572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (E or F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-69572.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (E or F))))), M:tm-808, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-69573
in-theory        69573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69573.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-808, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69574
in-theory        69574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B 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-69574.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-808, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69575
in-theory        69575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69575.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-808, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69576
in-theory        69576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69576.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-808, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-69577
in-theory        69577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69577.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-808, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69578
in-theory        69578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-808 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69578.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-808, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-69579
in-theory        69579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-808 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-69579.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-808, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-69580
in-theory        69580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-69580.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-808, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-69581
in-theory        69581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69581.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-808, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-69582
in-theory        69582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-808 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-69582.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-808, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-69583
in-theory        69583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69583.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (F or G))))), M:tm-808, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-69584
in-theory        69584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (E or F))) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69584.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (E or F))) or G)), M:tm-808, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-69585
in-theory        69585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-69585.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-808, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-69586
in-theory        69586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-808 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-69586.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (E or F)))), M:tm-808, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-69587
in-theory        69587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-69587.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (F or G))))), M:tm-808, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-69588
in-theory        69588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69588.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-808, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69589
in-theory        69589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69589.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-808, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69590
in-theory        69590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69590.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-808, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69591
in-theory        69591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69591.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-808, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69592
in-theory        69592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69592.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-808, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-69593
in-theory        69593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69593.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-808, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69594
in-theory        69594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-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-69594.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or (F -> (G -> F))))), M:tm-808, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-69595
in-theory        69595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (F -> E))) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69595.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (F -> E))) or G)), M:tm-808, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-69596
in-theory        69596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-69596.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-808, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-69597
in-theory        69597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69597.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or (F -> (G -> F))))), M:tm-808, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-69598
in-theory        69598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69598.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69599
in-theory        69599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69599.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69600
in-theory        69600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       159
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69600.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69601
in-theory        69601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69601.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69602
in-theory        69602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69602.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-808, 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-69603
in-theory        69603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69603.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69604
in-theory        69604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-808 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-69604.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-808, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-69605
in-theory        69605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     29
proof            (modus-ponens tm-808 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69605.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-808, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-69606
in-theory        69606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     31
proof            (modus-ponens tm-808 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-69606.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-808, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-69607
in-theory        69607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-808 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69607.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-808, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-69608
in-theory        69608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-7 tm-3)
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69608.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-808, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69609
in-theory        69609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-808 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69609.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-808, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69610
in-theory        69610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69610.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-808, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69611
in-theory        69611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69611.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-808, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69612
in-theory        69612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-7 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69612.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-808, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-69613
in-theory        69613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-7 tm-3)
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69613.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-808, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69614
in-theory        69614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-808 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-3)
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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-69614.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or ((F and G) -> F)))), M:tm-808, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-69615
in-theory        69615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E and F) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-7 tm-3)
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-4.            ((A and B) -> B), axiom
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-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-69615.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E and F) -> E)) or G)), M:tm-808, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-69616
in-theory        69616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-69616.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-808, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-69617
in-theory        69617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-808 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-7 tm-3)
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-4.            ((A and B) -> B), axiom
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-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-69617.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or ((F and G) -> F)))), M:tm-808, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-69618
in-theory        69618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69618.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-808, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69619
in-theory        69619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-808 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69619.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-808, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69620
in-theory        69620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69620.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-808, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69621
in-theory        69621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69621.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-808, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69622
in-theory        69622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69622.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-808, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-69623
in-theory        69623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69623.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-808, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69624
in-theory        69624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-808 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69624.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or ((F and G) -> G)))), M:tm-808, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-69625
in-theory        69625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E and F) -> F)) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69625.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E and F) -> F)) or G)), M:tm-808, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-69626
in-theory        69626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69626.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-808, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-69627
in-theory        69627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-808 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69627.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or ((F and G) -> G)))), M:tm-808, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-69628
in-theory        69628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69628.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-808, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69629
in-theory        69629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-808 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69629.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-808, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69630
in-theory        69630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 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       135
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69630.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-808, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69631
in-theory        69631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69631.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-808, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69632
in-theory        69632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69632.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-808, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-69633
in-theory        69633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69633.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-808, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69634
in-theory        69634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-808 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), 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-69634.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-808, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-69635
in-theory        69635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     23
proof            (modus-ponens tm-808 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69635.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-808, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-69636
in-theory        69636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-69636.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-808, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-69637
in-theory        69637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-808 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69637.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-808, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-69638
in-theory        69638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69638.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-808, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69639
in-theory        69639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69639.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-808, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69640
in-theory        69640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69640.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-808, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69641
in-theory        69641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69641.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-808, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69642
in-theory        69642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69642.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-808, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-69643
in-theory        69643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69643.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-808, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69644
in-theory        69644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A 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-69644.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or (F -> (F or G))))), M:tm-808, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-69645
in-theory        69645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (E or F))) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69645.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (E or F))) or G)), M:tm-808, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-69646
in-theory        69646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-69646.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-808, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-69647
in-theory        69647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69647.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or (F -> (F or G))))), M:tm-808, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-69648
in-theory        69648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69648.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-808, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69649
in-theory        69649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69649.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-808, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69650
in-theory        69650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69650.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-808, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69651
in-theory        69651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69651.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-808, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69652
in-theory        69652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69652.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-808, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-69653
in-theory        69653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69653.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-808, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69654
in-theory        69654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B 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-69654.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or (F -> (G or F))))), M:tm-808, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-69655
in-theory        69655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (F or E))) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69655.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (F or E))) or G)), M:tm-808, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-69656
in-theory        69656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-69656.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-808, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-69657
in-theory        69657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69657.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or (F -> (G or F))))), M:tm-808, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-69658
in-theory        69658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69658.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-808, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-69659
in-theory        69659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-808 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69659.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-808, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-69660
in-theory        69660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69660.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-808, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-69661
in-theory        69661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69661.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-808, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-69662
in-theory        69662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69662.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-808, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-69663
in-theory        69663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69663.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-808, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-69664
in-theory        69664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69664.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> (F or E)) or G))), M:tm-808, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-69665
in-theory        69665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E or D)) or F) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B 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-69665.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E or D)) or F) or G)), M:tm-808, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-69666
in-theory        69666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-69666.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-808, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-69667
in-theory        69667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-808 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69667.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F or E)) or G))), M:tm-808, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-69668
in-theory        69668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69668.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-808, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-69669
in-theory        69669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-69669.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-69670
in-theory        69670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69670.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-808, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-69671
in-theory        69671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69671.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-808, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-69672
in-theory        69672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69672.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-808, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-69673
in-theory        69673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69673.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-808, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-69674
in-theory        69674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69674.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-808, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-69675
in-theory        69675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69675.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-808, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-69676
in-theory        69676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-808 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69676.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-808, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-69677
in-theory        69677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69677.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-808, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-69678
in-theory        69678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69678.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-808, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69679
in-theory        69679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-69679.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-808, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-69680
in-theory        69680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-69680.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-808, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-69681
in-theory        69681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69681.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69682
in-theory        69682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 tm-7 tm-2 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-69682.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-808, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-69683
in-theory        69683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-1 tm-3)
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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69683.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-808, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69684
in-theory        69684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-69684.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-808, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-69685
in-theory        69685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69685.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-808, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69686
in-theory        69686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69686.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-808, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-69687
in-theory        69687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-69687.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-808, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-69688
in-theory        69688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69688.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-808, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-69689
in-theory        69689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69689.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-808, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-69690
in-theory        69690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69690.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-808, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-69691
in-theory        69691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-69691.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-808, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-69692
in-theory        69692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69692.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-808, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69693
in-theory        69693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69693.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-808, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-69694
in-theory        69694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69694.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-808, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-69695
in-theory        69695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-6 tm-3)
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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69695.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-808, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-69696
in-theory        69696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69696.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-808, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-69697
in-theory        69697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-808 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69697.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-808, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-69698
in-theory        69698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69698.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-808, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-69699
in-theory        69699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69699.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-808, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-69700
in-theory        69700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69700.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-808, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69701
in-theory        69701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69701.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-808, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-69702
in-theory        69702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-69702.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-808, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-69703
in-theory        69703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-3)
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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69703.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-808, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-69704
in-theory        69704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-808 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69704.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-808, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-69705
in-theory        69705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-808 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69705.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-808, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-69706
in-theory        69706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69706.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-808, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-69707
in-theory        69707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69707.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-808, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69708
in-theory        69708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-808 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-69708.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-808, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-69709
in-theory        69709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69709.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-808, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-69710
in-theory        69710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-69710.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-808, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-69711
in-theory        69711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-69711.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-808, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-69712
in-theory        69712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and 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-69712.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-808, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-69713
in-theory        69713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 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       135
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and 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-69713.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-808, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-69714
in-theory        69714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-69714.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-808, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-69715
in-theory        69715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69715.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-808, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-69716
in-theory        69716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69716.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-808, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-69717
in-theory        69717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69717.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-808, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-69718
in-theory        69718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69718.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-808, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-69719
in-theory        69719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69719.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-808, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-69720
in-theory        69720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-808 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69720.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-808, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-69721
in-theory        69721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-69721.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-808, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-69722
in-theory        69722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69722.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-808, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-69723
in-theory        69723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69723.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-808, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69724
in-theory        69724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69724.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-808, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69725
in-theory        69725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (F or E)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-69725.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D and (E -> (F or E))))), M:tm-808, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-69726
in-theory        69726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69726.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-808, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69727
in-theory        69727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 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       127
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B 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-69727.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-808, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69728
in-theory        69728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69728.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-808, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69729
in-theory        69729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69729.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-808, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-69730
in-theory        69730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-69730.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-808, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-69731
in-theory        69731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-808 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69731.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-808, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-69732
in-theory        69732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-808 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-69732.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-808, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-69733
in-theory        69733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-69733.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-808, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-69734
in-theory        69734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69734.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-808, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-69735
in-theory        69735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-808 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-69735.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-808, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-69736
in-theory        69736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69736.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E -> (F -> (G or F))))), M:tm-808, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-69737
in-theory        69737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (F or E))) or G))
theorem-size     21
proof            (modus-ponens tm-808 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69737.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (F or E))) or G)), M:tm-808, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-69738
in-theory        69738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     23
proof            (modus-ponens tm-808 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-69738.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-808, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-69739
in-theory        69739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-808 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-69739.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> (D -> (F or E)))), M:tm-808, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-69740
in-theory        69740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-808 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-69740.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (F -> (G or F))))), M:tm-808, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-69741
in-theory        69741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69741.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-808, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-69742
in-theory        69742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     29
proof            (modus-ponens tm-808 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-69742.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-808, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-69743
in-theory        69743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69743.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-808, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-69744
in-theory        69744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69744.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-808, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-69745
in-theory        69745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69745.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-808, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-69746
in-theory        69746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     27
proof            (modus-ponens tm-808 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69746.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-808, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-69747
in-theory        69747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-808 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69747.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-808, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-69748
in-theory        69748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69748.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-808, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-69749
in-theory        69749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-808 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-69749.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (E -> E))), M:tm-808, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-69750
in-theory        69750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-808 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-69750.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-808, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-69751
in-theory        69751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-69751.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-69752
in-theory        69752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-808 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-2 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-69752.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-808, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-69753
in-theory        69753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69753.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-808, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-69754
in-theory        69754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-808 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-69754.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-808, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-69755
in-theory        69755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69755.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-808, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-69756
in-theory        69756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69756.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-808, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-69757
in-theory        69757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-69757.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-808, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-69758
in-theory        69758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69758.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-808, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-69759
in-theory        69759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69759.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-808, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-69760
in-theory        69760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-808 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69760.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-808, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-69761
in-theory        69761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-69761.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-808, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-69762
in-theory        69762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69762.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-808, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-69763
in-theory        69763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69763.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-808, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-69764
in-theory        69764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69764.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-808, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-69765
in-theory        69765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69765.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-808, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-69766
in-theory        69766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69766.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-808, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-69767
in-theory        69767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69767.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-808, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-69768
in-theory        69768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-69768.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-808, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-69769
in-theory        69769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-69769.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-808, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-69770
in-theory        69770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-808 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-69770.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-808, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-69771
in-theory        69771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B 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-69771.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-808, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-69772
in-theory        69772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 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       153
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B 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-69772.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-808, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-69773
in-theory        69773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-69773.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-808, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-69774
in-theory        69774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-69774.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-808, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-69775
in-theory        69775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (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-69775.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-808, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-69776
in-theory        69776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69776.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-808, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-69777
in-theory        69777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-808 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69777.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-808, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-69778
in-theory        69778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-69778.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-808, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-69779
in-theory        69779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-808 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69779.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-808, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-69780
in-theory        69780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-808 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69780.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-808, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-69781
in-theory        69781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-808 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-69781.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-808, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-69782
in-theory        69782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-808 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69782.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-808, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-69783
in-theory        69783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-808 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69783.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-808, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-69784
in-theory        69784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-808 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69784.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-808, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-69785
in-theory        69785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69785.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-808, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-69786
in-theory        69786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69786.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-808, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-69787
in-theory        69787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69787.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-808, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-69788
in-theory        69788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69788.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-808, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-69789
in-theory        69789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69789.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-808, 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-69790
in-theory        69790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69790.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-808, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-69791
in-theory        69791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69791.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-808, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-69792
in-theory        69792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     33
proof            (modus-ponens tm-808 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69792.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-808, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-69793
in-theory        69793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69793.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-808, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-69794
in-theory        69794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69794.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-808, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-69795
in-theory        69795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-808 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1 tm-3)
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69795.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-808, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-69796
in-theory        69796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-808 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69796.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-808, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-69797
in-theory        69797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69797.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-808, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-69798
in-theory        69798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69798.        (((A -> B) -> (((C and A) 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-808, 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-69799
in-theory        69799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69799.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-808, 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-69800
in-theory        69800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69800.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-808, 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-69801
in-theory        69801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69801.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-808, 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-69802
in-theory        69802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69802.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-808, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-69803
in-theory        69803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69803.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-808, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-69804
in-theory        69804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69804.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-808, 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-69805
in-theory        69805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69805.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-808, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-69806
in-theory        69806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69806.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-808, 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-69807
in-theory        69807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69807.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-808, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-69808
in-theory        69808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-69808.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-808, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-69809
in-theory        69809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69809.        (((A -> B) -> (((C and A) 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-808, 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-69810
in-theory        69810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-69810.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-808, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-69811
in-theory        69811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-69811.        (((A -> B) -> (((C and A) 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-808, 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-69812
in-theory        69812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-69812.        (((A -> B) -> (((C and A) 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-808, 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-69813
in-theory        69813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69813.        (((A -> B) -> (((C and A) 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-808, 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-69814
in-theory        69814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-69814.        (((A -> B) -> (((C and A) 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-808, 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-69815
in-theory        69815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       197
proof-steps      13
----------------------------------------------------------------
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-22.           (A -> (((B and C) -> C) and 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-69815.        (((A -> B) -> (((C and A) 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-808, 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-69816
in-theory        69816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-69816.        (((A -> B) -> (((C and A) 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-808, 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-69817
in-theory        69817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69817.        (((A -> B) -> (((C and A) 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-808, 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-69818
in-theory        69818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-69818.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-808, 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-69819
in-theory        69819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-808 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69819.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-808, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-69820
in-theory        69820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-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-69820.        (((A -> B) -> (((C and A) 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-808, 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-69821
in-theory        69821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-69821.        (((A -> B) -> (((C and A) 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-808, 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-69822
in-theory        69822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-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-69822.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-808, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-69823
in-theory        69823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-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-69823.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-808, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-69824
in-theory        69824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-69824.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-808, 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-69825
in-theory        69825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69825.        (((A -> B) -> (((C and A) 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-808, 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-69826
in-theory        69826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-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-69826.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-808, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-69827
in-theory        69827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69827.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> D))), M:tm-808, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-69828
in-theory        69828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-808 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-69828.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-808, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-69829
in-theory        69829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     23
proof            (modus-ponens tm-808 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69829.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-808, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-69830
in-theory        69830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     23
proof            (modus-ponens tm-808 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69830.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-808, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-69831
in-theory        69831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69831.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-808, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-69832
in-theory        69832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (D or F)))
theorem-size     21
proof            (modus-ponens tm-808 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69832.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (D or F))), M:tm-808, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-69833
in-theory        69833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F or D)))
theorem-size     21
proof            (modus-ponens tm-808 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69833.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F or D))), M:tm-808, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-69834
in-theory        69834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69834.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-808, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-69835
in-theory        69835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-808 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69835.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-808, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-69836
in-theory        69836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     23
proof            (modus-ponens tm-808 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69836.        (((A -> B) -> (((C and A) or A) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-808, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-69837
in-theory        69837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69837.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-808, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-69838
in-theory        69838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-69838.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-808, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-69839
in-theory        69839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-69839.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-808, 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-69840
in-theory        69840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69840.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-69841
in-theory        69841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-69841.        (((A -> B) -> (((C and A) or A) -> B)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-808, 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-69842
in-theory        69842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69842.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-808, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-69843
in-theory        69843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-69843.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-808, 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-69844
in-theory        69844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69844.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-808, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-69845
in-theory        69845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69845.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-808, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-69846
in-theory        69846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-69846.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-808, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-69847
in-theory        69847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69847.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-808, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-69848
in-theory        69848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69848.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-808, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-69849
in-theory        69849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69849.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-808, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-69850
in-theory        69850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-808 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-69850.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-808, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-69851
in-theory        69851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69851.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-808, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-69852
in-theory        69852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69852.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-808, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-69853
in-theory        69853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69853.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-808, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-69854
in-theory        69854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69854.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-808, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-69855
in-theory        69855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69855.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-808, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-69856
in-theory        69856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-69856.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-808, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-69857
in-theory        69857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-69857.        (((A -> B) -> (((C and A) 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-808, 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-69858
in-theory        69858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-808 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69858.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-808, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-69859
in-theory        69859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69859.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-808, 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-69860
in-theory        69860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69860.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-808, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-69861
in-theory        69861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69861.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-808, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-69862
in-theory        69862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69862.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-808, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-69863
in-theory        69863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-808 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-69863.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-808, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-69864
in-theory        69864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69864.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-808, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-69865
in-theory        69865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 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       147
proof-steps      13
----------------------------------------------------------------
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-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-69865.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-808, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-69866
in-theory        69866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> 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-69866.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-808, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-69867
in-theory        69867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 tm-2 tm-3)
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-69867.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-808, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-69868
in-theory        69868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-1.            (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-69868.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-808, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-69869
in-theory        69869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-808 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
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-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-69869.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-808, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-69870
in-theory        69870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-69870.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-808, 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-69871
in-theory        69871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69871.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-808, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-69872
in-theory        69872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-808 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-69872.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-808, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-69873
in-theory        69873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-69873.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-808, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69874
in-theory        69874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-808 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-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-69874.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-808, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-69875
in-theory        69875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69875.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-808, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-69876
in-theory        69876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-808 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
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-4.            ((A and B) -> B), axiom
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-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-69876.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> E))), M:tm-808, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-69877
in-theory        69877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-808 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       147
proof-steps      11
----------------------------------------------------------------
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-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-69877.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-808, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-69878
in-theory        69878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     23
proof            (modus-ponens tm-808 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       119
proof-steps      11
----------------------------------------------------------------
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-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-69878.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-808, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-69879
in-theory        69879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     23
proof            (modus-ponens tm-808 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69879.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-808, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-69880
in-theory        69880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69880.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-808, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-69881
in-theory        69881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-808 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
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-4.            ((A and B) -> B), axiom
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-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-69881.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (E or F))), M:tm-808, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-69882
in-theory        69882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-808 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
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-4.            ((A and B) -> B), axiom
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-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-69882.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F or E))), M:tm-808, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-69883
in-theory        69883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-808 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       143
proof-steps      11
----------------------------------------------------------------
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-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-69883.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-808, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-69884
in-theory        69884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-808 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       137
proof-steps      11
----------------------------------------------------------------
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-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-69884.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-808, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-69885
in-theory        69885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     23
proof            (modus-ponens tm-808 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       119
proof-steps      11
----------------------------------------------------------------
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-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-69885.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-808, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-69886
in-theory        69886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69886.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-808, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-69887
in-theory        69887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-808 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       143
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-69887.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-808, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-69888
in-theory        69888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       199
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-69888.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-808, 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-69889
in-theory        69889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 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       163
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-69889.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-69890
in-theory        69890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       175
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-69890.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-808, 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-69891
in-theory        69891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 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       131
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-69891.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-808, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-69892
in-theory        69892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       175
proof-steps      13
----------------------------------------------------------------
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-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-69892.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-808, 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-69893
in-theory        69893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (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-69893.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-808, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-69894
in-theory        69894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     25
proof            (modus-ponens tm-808 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       139
proof-steps      13
----------------------------------------------------------------
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-1.            (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-69894.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-808, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-69895
in-theory        69895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) 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-808 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       171
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-69895.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-808, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-69896
in-theory        69896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-808 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       139
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-69896.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-808, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-69897
in-theory        69897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     25
proof            (modus-ponens tm-808 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-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-69897.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-808, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-69898
in-theory        69898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     27
proof            (modus-ponens tm-808 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       147
proof-steps      13
----------------------------------------------------------------
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-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-69898.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-808, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-69899
in-theory        69899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-808 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       151
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-69899.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-808, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-69900
in-theory        69900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69900.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-808, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-69901
in-theory        69901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     25
proof            (modus-ponens tm-808 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-69901.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-808, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-69902
in-theory        69902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-69902.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-808, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-69903
in-theory        69903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     25
proof            (modus-ponens tm-808 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or 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-69903.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-808, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-69904
in-theory        69904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-69904.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-808, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-69905
in-theory        69905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-808 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-69905.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-808, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-69906
in-theory        69906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     49
proof            (modus-ponens tm-808 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-69906.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-808, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-69907
in-theory        69907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-808 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-69907.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-808, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-69908
in-theory        69908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-808 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-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-69908.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-808, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-69909
in-theory        69909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-808 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
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-69909.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-808, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-69910
in-theory        69910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-808 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
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-69910.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-808, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-69911
in-theory        69911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     25
proof            (modus-ponens tm-808 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
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-69911.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-808, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-69912
in-theory        69912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-69912.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-808, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-69913
in-theory        69913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-69913.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-808, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-69914
in-theory        69914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-808 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am 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-69914.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-808, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-69915
in-theory        69915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am 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-69915.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-808, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-69916
in-theory        69916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-69916.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-808, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-69917
in-theory        69917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-69917.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-808, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-69918
in-theory        69918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-808 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
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-69918.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-808, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-69919
in-theory        69919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-808 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-69919.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-808, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-69920
in-theory        69920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-808 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
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-69920.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-808, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-69921
in-theory        69921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-808 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-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-69921.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-808, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-69922
in-theory        69922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
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-69922.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-808, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-69923
in-theory        69923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-808 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
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-69923.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-808, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-69924
in-theory        69924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69924.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-808, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69925
in-theory        69925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((C and A) or A) -> B)))
theorem-size     31
proof            (modus-ponens tm-805 tm-808 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 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-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-5.            (A -> (B -> (A and B))), axiom
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-69925.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((C and A) or A) -> B))), M:tm-805, m:tm-808, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-69926
in-theory        69926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((E and A) or A) -> (((B -> C) -> (((D and B) or B) -> C)) and A)))
theorem-size     35
proof            (modus-ponens tm-798 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-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-69926.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((E and A) or A) -> (((B -> C) -> (((D and B) or B) -> C)) and A))), M:tm-798, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-69927
in-theory        69927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-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-69927.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-757, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69928
in-theory        69928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((A and C) or A) -> B)))
theorem-size     31
proof            (modus-ponens tm-754 tm-808 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 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-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A 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-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-69928.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((A and C) or A) -> B))), M:tm-754, m:tm-808, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-69929
in-theory        69929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((A and E) or A) -> (((B -> C) -> (((D and B) or B) -> C)) and A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-69929.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((A and E) or A) -> (((B -> C) -> (((D and B) or B) -> C)) and A))), M:tm-747, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-69930
in-theory        69930
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-69930.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E))), M:tm-708, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69931
in-theory        69931
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> (((G and E) or E) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-705 tm-808 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-69931.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> (((G and E) or E) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-808, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-69932
in-theory        69932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-703 tm-808 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-69932.        (((A -> B) -> (A -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-808, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-69933
in-theory        69933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-697 tm-808 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> A C))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-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-69933.        ((((A -> B) -> (A -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-808, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-69934
in-theory        69934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-69934.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-665, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69935
in-theory        69935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B or (A -> B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-662 tm-808 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or A (-> B A)) C)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((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-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-69935.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-808, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-69936
in-theory        69936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> B)))
theorem-size     19
proof            (modus-ponens tm-660 tm-808 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-69936.        ((A -> B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> B))), M:tm-660, m:tm-808, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A B))))
================================================================
tm-name          tm-69937
in-theory        69937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> B))))
theorem-size     41
proof            (modus-ponens tm-654 tm-808 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A B)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-69937.        (((A -> B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> B)))), M:tm-654, m:tm-808, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A B))))
================================================================
tm-name          tm-69938
in-theory        69938
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> D) -> (((E and C) or C) -> D)) and A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-69938.        (A -> (B or (((C -> D) -> (((E and C) or C) -> D)) and A))), M:tm-623, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-69939
in-theory        69939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-69939.        ((A -> (B -> (C or B))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-622, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69940
in-theory        69940
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> E) -> (((F and D) or D) -> E)) and (B -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-619 tm-808 ((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 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-7.            (A -> (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-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-69940.        ((A or (B -> (C or B))) -> (((D -> E) -> (((F and D) or D) -> E)) and (B -> (C or B)))), M:tm-619, m:tm-808, u:((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (or B A)))))
================================================================
tm-name          tm-69941
in-theory        69941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-69941.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (F or E))), M:tm-609, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69942
in-theory        69942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69942.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-605, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69943
in-theory        69943
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> (C or B)) and A)))
theorem-size     29
proof            (modus-ponens tm-602 tm-808 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 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-4.            ((A and B) -> B), axiom
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-69943.        ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-808, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-69944
in-theory        69944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (F or E)) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-69944.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (F or E)) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-595, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69945
in-theory        69945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-69945.        (((A -> (B or A)) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-550, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69946
in-theory        69946
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-69946.        ((A or (B -> (C or B))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-540, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69947
in-theory        69947
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-69947.        ((A or (B -> (B or C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-530, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69948
in-theory        69948
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69948.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-520, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69949
in-theory        69949
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 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-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-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-69949.        ((A or ((B and C) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-510, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69950
in-theory        69950
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-69950.        ((A or ((B and C) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-500, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69951
in-theory        69951
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69951.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E))), M:tm-490, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69952
in-theory        69952
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-69952.        ((A or (B -> (C -> B))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-480, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69953
in-theory        69953
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (((D and B) or B) -> C)) and A) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-69953.        (A -> ((((B -> C) -> (((D and B) or B) -> C)) and A) or E)), M:tm-470, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-69954
in-theory        69954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-69954.        ((A -> (B -> (B or C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-469, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69955
in-theory        69955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> E) -> (((F and D) or D) -> E)) and (B -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-466 tm-808 ((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 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-6.            (A -> (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-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-69955.        ((A or (B -> (B or C))) -> (((D -> E) -> (((F and D) or D) -> E)) and (B -> (B or C)))), M:tm-466, m:tm-808, u:((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (or A B)))))
================================================================
tm-name          tm-69956
in-theory        69956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-69956.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (E or F))), M:tm-456, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69957
in-theory        69957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69957.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-453, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69958
in-theory        69958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> (B or C)) and A)))
theorem-size     29
proof            (modus-ponens tm-450 tm-808 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 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-4.            ((A and B) -> B), axiom
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-69958.        ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-808, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-69959
in-theory        69959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (E or F)) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-69959.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (E or F)) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-443, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69960
in-theory        69960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-69960.        (((A -> (A or B)) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-409, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69961
in-theory        69961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69961.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-400, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69962
in-theory        69962
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 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-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-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-69962.        ((((A and B) -> B) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-391, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69963
in-theory        69963
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-69963.        ((((A and B) -> A) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-382, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69964
in-theory        69964
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69964.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E))), M:tm-373, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69965
in-theory        69965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-69965.        (((A -> (B -> A)) or C) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-364, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69966
in-theory        69966
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> (((E and C) or C) -> D)) and A) and B)))
theorem-size     19
proof            (modus-ponens tm-355 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-69966.        (A -> (B -> ((((C -> D) -> (((E and C) or C) -> D)) and A) and B))), M:tm-355, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-69967
in-theory        69967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69967.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-354, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69968
in-theory        69968
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> (((F and D) or D) -> E)) and (B -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-351 tm-808 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 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-4.            ((A and B) -> B), axiom
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-69968.        ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> (((F and D) or D) -> E)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-808, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-69969
in-theory        69969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-69969.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69970
in-theory        69970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-69970.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C))), M:tm-338, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69971
in-theory        69971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-335 tm-808 ((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 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-5.            (A -> (B -> (A and B))), axiom
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-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-69971.        (((A -> B) or (A -> (A and B))) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> (A and B)))), M:tm-335, m:tm-808, u:((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (and A B)))))
================================================================
tm-name          tm-69972
in-theory        69972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (A -> (A and (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-69972.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (A -> (A and (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-328, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-69973
in-theory        69973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-69973.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-327, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69974
in-theory        69974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((E and F) -> F) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-69974.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((E and F) -> F) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-326, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69975
in-theory        69975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((E and F) -> E) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-69975.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((E and F) -> E) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-325, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69976
in-theory        69976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-69976.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-324, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69977
in-theory        69977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (F -> E)) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-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-69977.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (F -> E)) and (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-323, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69978
in-theory        69978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-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-69978.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69979
in-theory        69979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-69979.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69980
in-theory        69980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-69980.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69981
in-theory        69981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (A -> A))
theorem-size     19
proof            (modus-ponens tm-316 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
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-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-69981.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (A -> A)), M:tm-316, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-69982
in-theory        69982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-69982.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69983
in-theory        69983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((A -> (not (((B -> C) -> (((D and B) or B) -> C)) and A))) -> (not A)))
theorem-size     35
proof            (modus-ponens tm-313 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-69983.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((A -> (not (((B -> C) -> (((D and B) or B) -> C)) and A))) -> (not A))), M:tm-313, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-69984
in-theory        69984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((((B -> C) -> (((D and B) or B) -> C)) and A) -> E) -> ((A or (((B -> C) -> (((D and B) or B) -> C)) and A)) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
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-312.          ((A -> B) -> ((A -> B) and ((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-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-69984.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (((((B -> C) -> (((D and B) or B) -> C)) and A) -> E) -> ((A or (((B -> C) -> (((D and B) or B) -> C)) and A)) -> E))), M:tm-312, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-69985
in-theory        69985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E or (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-69985.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E or (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-311, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69986
in-theory        69986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-69986.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) or E)), M:tm-310, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69987
in-theory        69987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-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-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-69987.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and E))), M:tm-309, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69988
in-theory        69988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-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-69988.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) and (E -> (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)))), M:tm-305, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69989
in-theory        69989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69989.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-303, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69990
in-theory        69990
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> (C -> (B and C))) and A)))
theorem-size     33
proof            (modus-ponens tm-300 tm-808 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-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-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-69990.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-808, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-69991
in-theory        69991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 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-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-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-69991.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-270, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69992
in-theory        69992
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((B and C) -> C) and A)))
theorem-size     29
proof            (modus-ponens tm-267 tm-808 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> (and A B) 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-4.            ((A and B) -> 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-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-69992.        ((A or (((B and C) -> C) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((B and C) -> C) and A))), M:tm-267, m:tm-808, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-69993
in-theory        69993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69993.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-239, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69994
in-theory        69994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((B and C) -> B) and A)))
theorem-size     29
proof            (modus-ponens tm-236 tm-808 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 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-4.            ((A and B) -> B), axiom
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-69994.        ((A or (((B and C) -> B) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((B and C) -> B) and A))), M:tm-236, m:tm-808, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-69995
in-theory        69995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-69995.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E))), M:tm-210, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69996
in-theory        69996
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> (((G and E) or E) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     45
proof            (modus-ponens tm-207 tm-808 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-69996.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> (((G and E) or E) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-808, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-69997
in-theory        69997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-69997.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-183, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-69998
in-theory        69998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> (C -> B)) and A)))
theorem-size     29
proof            (modus-ponens tm-180 tm-808 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 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-4.            ((A and B) -> B), axiom
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-69998.        ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-808, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-69999
in-theory        69999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-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-69999.        ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-157, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70000
in-theory        70000
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B and C) -> C)))
theorem-size     25
proof            (modus-ponens tm-154 tm-808 ((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 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-4.            ((A 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-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-70000.        ((A or ((B and C) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B and C) -> C))), M:tm-154, m:tm-808, u:((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (and A B) B))))
================================================================
tm-name          tm-70001
in-theory        70001
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 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-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-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-70001.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-147, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70002
in-theory        70002
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A and (B -> C)) -> C)))
theorem-size     35
proof            (modus-ponens tm-144 tm-808 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (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-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-70002.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-808, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-70003
in-theory        70003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-70003.        ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-134, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70004
in-theory        70004
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-131 tm-808 ((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 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-3.            ((A 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-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-70004.        ((A or ((B and C) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B and C) -> B))), M:tm-131, m:tm-808, u:((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (and A B) A))))
================================================================
tm-name          tm-70005
in-theory        70005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-70005.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-125, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70006
in-theory        70006
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((A -> B) and C) -> B)))
theorem-size     35
proof            (modus-ponens tm-122 tm-808 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-70006.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-808, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-70007
in-theory        70007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70007.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E))), M:tm-113, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70008
in-theory        70008
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> (((G and E) or E) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     41
proof            (modus-ponens tm-110 tm-808 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-70008.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> (((G and E) or E) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-808, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-70009
in-theory        70009
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-70009.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-105, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70010
in-theory        70010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-102 tm-808 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-70010.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-808, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-70011
in-theory        70011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-70011.        (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C))), M:tm-95, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70012
in-theory        70012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> A)))
theorem-size     23
proof            (modus-ponens tm-92 tm-808 ((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 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-1.            (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-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-70012.        (((A -> B) or (A -> A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> A))), M:tm-92, m:tm-808, u:((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A A))))
================================================================
tm-name          tm-70013
in-theory        70013
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> (((E and C) or C) -> D)) and A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-70013.        (A -> (B -> (((C -> D) -> (((E and C) or C) -> D)) and A))), M:tm-84, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-70014
in-theory        70014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70014.        ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-83, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70015
in-theory        70015
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> E) -> (((F and D) or D) -> E)) and (B -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-80 tm-808 ((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (-> B A))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-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-70015.        ((A or (B -> (C -> B))) -> (((D -> E) -> (((F and D) or D) -> E)) and (B -> (C -> B)))), M:tm-80, m:tm-808, u:((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (-> B A)))))
================================================================
tm-name          tm-70016
in-theory        70016
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> D) -> (((E and C) or C) -> D)) and B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70016.        (((not (not A)) -> A) and (B -> (((C -> D) -> (((E and C) or C) -> D)) and B))), M:tm-76, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70017
in-theory        70017
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> C) -> (((D and B) or B) -> C)) and A))
theorem-size     19
proof            (modus-ponens tm-73 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-70017.        (((not (not A)) or A) -> (((B -> C) -> (((D and B) or B) -> C)) and A)), M:tm-73, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-70018
in-theory        70018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70018.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C))), M:tm-69, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70019
in-theory        70019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> (((E and C) or C) -> D)) and ((A -> (not B)) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-66 tm-808 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-70019.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> (((E and C) or C) -> D)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-808, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-70020
in-theory        70020
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-70020.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-54, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70021
in-theory        70021
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-51 tm-808 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-70021.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-808, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-70022
in-theory        70022
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (B or A)))
theorem-size     21
proof            (modus-ponens tm-50 tm-808 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-70022.        ((A or (B or A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (B or A))), M:tm-50, m:tm-808, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-70023
in-theory        70023
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-49 tm-808 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-70023.        ((A or (A or B)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B))), M:tm-49, m:tm-808, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-70024
in-theory        70024
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> D) -> (((E and C) or C) -> D)) and (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-48 tm-808 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-70024.        ((A or (B -> (A and B))) -> (((C -> D) -> (((E and C) or C) -> D)) and (B -> (A and B)))), M:tm-48, m:tm-808, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-70025
in-theory        70025
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> D) -> (((E and C) or C) -> D)) and B))
theorem-size     19
proof            (modus-ponens tm-47 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-5)
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-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-70025.        (((A and B) or B) -> (((C -> D) -> (((E and C) or C) -> D)) and B)), M:tm-47, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-70026
in-theory        70026
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> D) -> (((E and C) or C) -> D)) and A))
theorem-size     19
proof            (modus-ponens tm-46 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-70026.        (((A and B) or A) -> (((C -> D) -> (((E and C) or C) -> D)) and A)), M:tm-46, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-70027
in-theory        70027
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-45 tm-808 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-70027.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-808, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-70028
in-theory        70028
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (B -> A)))
theorem-size     21
proof            (modus-ponens tm-44 tm-808 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-70028.        ((A or (B -> A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (B -> A))), M:tm-44, m:tm-808, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A B))))
================================================================
tm-name          tm-70029
in-theory        70029
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70029.        ((A -> (B or A)) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C))), M:tm-42, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70030
in-theory        70030
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70030.        ((A -> (A or B)) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C))), M:tm-32, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70031
in-theory        70031
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> C) -> (((D and B) or B) -> C)) and A)))
theorem-size     17
proof            (modus-ponens tm-24 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70031.        (A -> (A and (((B -> C) -> (((D and B) or B) -> C)) and A))), M:tm-24, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-70032
in-theory        70032
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70032.        ((A -> (B -> (A and B))) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C))), M:tm-23, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70033
in-theory        70033
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-70033.        (((A and B) -> B) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C))), M:tm-22, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70034
in-theory        70034
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70034.        (((A and B) -> A) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C))), M:tm-21, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70035
in-theory        70035
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70035.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-20, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70036
in-theory        70036
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70036.        ((A -> (B -> A)) and (C -> (((D -> E) -> (((F and D) or D) -> E)) and C))), M:tm-19, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70037
in-theory        70037
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> C) -> (((D and B) or B) -> C)) and A))) -> (not A))
theorem-size     19
proof            (modus-ponens tm-9 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-9 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70037.        ((A -> (not (((B -> C) -> (((D and B) or B) -> C)) and A))) -> (not A)), M:tm-9, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-70038
in-theory        70038
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (((C and A) or A) -> B)) and D) -> E) -> ((D or (((A -> B) -> (((C and A) or A) -> B)) and D)) -> E))
theorem-size     33
proof            (modus-ponens tm-8 tm-808 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
axioms-used      (tm-8 tm-5 tm-4)
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-4.            ((A and B) -> B), axiom
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-70038.        (((((A -> B) -> (((C and A) or A) -> B)) and D) -> E) -> ((D or (((A -> B) -> (((C and A) or A) -> B)) and D)) -> E)), M:tm-8, m:tm-808, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))
================================================================
tm-name          tm-70039
in-theory        70039
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> D) -> (((E and C) or C) -> D)) and B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-7 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70039.        (A or (B -> (((C -> D) -> (((E and C) or C) -> D)) and B))), M:tm-7, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70040
in-theory        70040
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-6 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70040.        ((A -> (((B -> C) -> (((D and B) or B) -> C)) and A)) or E), M:tm-6, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70041
in-theory        70041
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> D) -> (((E and C) or C) -> D)) and B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70041.        (A -> ((B -> (((C -> D) -> (((E and C) or C) -> D)) and B)) and A)), M:tm-5, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70042
in-theory        70042
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> (((E and C) or C) -> D)) and B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-1 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70042.        (A -> (B -> (((C -> D) -> (((E and C) or C) -> D)) and B))), M:tm-1, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-70043
in-theory        70043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-808 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-70043.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-808, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70044
in-theory        70044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((D and ((A -> B) -> ((C and A) or A))) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B)))
theorem-size     43
proof            (modus-ponens tm-798 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) 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-4.            ((A and B) -> B), axiom
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-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-70044.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((D and ((A -> B) -> ((C and A) or A))) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B))), M:tm-798, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70045
in-theory        70045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-757 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70045.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-757, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70046
in-theory        70046
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((((A -> B) -> ((C and A) or A)) and D) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B)))
theorem-size     43
proof            (modus-ponens tm-747 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-70046.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((((A -> B) -> ((C and A) or A)) and D) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B))), M:tm-747, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70047
in-theory        70047
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)) -> ((E -> F) -> F)))
theorem-size     41
proof            (modus-ponens tm-708 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-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-70047.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F))), M:tm-708, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70048
in-theory        70048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-665 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-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-70048.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-665, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70049
in-theory        70049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((C and A) or A) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B)))
theorem-size     37
proof            (modus-ponens tm-654 tm-809 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-70049.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((C and A) or A) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B))), M:tm-654, m:tm-809, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70050
in-theory        70050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C and A) or A)) -> (D or ((A -> B) -> B)))
theorem-size     17
proof            (modus-ponens tm-623 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70050.        (((A -> B) -> ((C and A) or A)) -> (D or ((A -> B) -> B))), M:tm-623, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70051
in-theory        70051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-622 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-70051.        ((A -> (B -> (C or B))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-622, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70052
in-theory        70052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70052.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (E or D))), M:tm-609, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70053
in-theory        70053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-605 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-70053.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-605, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70054
in-theory        70054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (E or D)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-595 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-70054.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (E or D)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))), M:tm-595, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70055
in-theory        70055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-550 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70055.        (((A -> (B or A)) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-550, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70056
in-theory        70056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-540 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70056.        ((A or (B -> (C or B))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-540, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70057
in-theory        70057
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-530 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70057.        ((A or (B -> (B or C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-530, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70058
in-theory        70058
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-520 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-4.            ((A and B) -> B), axiom
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-70058.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-520, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70059
in-theory        70059
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-510 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-70059.        ((A or ((B and C) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-510, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70060
in-theory        70060
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-500 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70060.        ((A or ((B and C) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-500, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70061
in-theory        70061
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-490 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70061.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F))), M:tm-490, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70062
in-theory        70062
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-480 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70062.        ((A or (B -> (C -> B))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-480, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70063
in-theory        70063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C and A) or A)) -> (((A -> B) -> B) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70063.        (((A -> B) -> ((C and A) or A)) -> (((A -> B) -> B) or D)), M:tm-470, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70064
in-theory        70064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-469 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-70064.        ((A -> (B -> (B or C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-469, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70065
in-theory        70065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70065.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (D or E))), M:tm-456, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70066
in-theory        70066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-453 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-70066.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-453, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70067
in-theory        70067
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (D or E)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-443 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-70067.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (D or E)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))), M:tm-443, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70068
in-theory        70068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-409 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70068.        (((A -> (A or B)) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-409, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70069
in-theory        70069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-400 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-4.            ((A and B) -> B), axiom
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-70069.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-400, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70070
in-theory        70070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-391 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-70070.        ((((A and B) -> B) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-391, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70071
in-theory        70071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-382 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70071.        ((((A and B) -> A) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-382, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70072
in-theory        70072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-373 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70072.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F))), M:tm-373, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70073
in-theory        70073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-364 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70073.        (((A -> (B -> A)) or C) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-364, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70074
in-theory        70074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C and A) or A)) -> (D -> (((A -> B) -> B) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-70074.        (((A -> B) -> ((C and A) or A)) -> (D -> (((A -> B) -> B) and D))), M:tm-355, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70075
in-theory        70075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-354 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-4.            ((A and B) -> B), axiom
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-70075.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-354, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70076
in-theory        70076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-70076.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70077
in-theory        70077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D)))
theorem-size     25
proof            (modus-ponens tm-338 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-70077.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D))), M:tm-338, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70078
in-theory        70078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((A -> B) -> ((C and A) or A)) -> (((A -> B) -> ((C and A) or A)) and ((A -> B) -> B))))
theorem-size     41
proof            (modus-ponens tm-328 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
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-328.          ((A -> 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-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-70078.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((A -> B) -> ((C and A) or A)) -> (((A -> B) -> ((C and A) or A)) and ((A -> B) -> B)))), M:tm-328, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70079
in-theory        70079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (E -> (D and E))) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))))
theorem-size     39
proof            (modus-ponens tm-327 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-70079.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (E -> (D and E))) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))), M:tm-327, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70080
in-theory        70080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((D and E) -> E) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-326 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-70080.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((D and E) -> E) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))), M:tm-326, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70081
in-theory        70081
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((D and E) -> D) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-325 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-70081.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((D and E) -> D) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))), M:tm-325, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70082
in-theory        70082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))))
theorem-size     45
proof            (modus-ponens tm-324 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-70082.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))), M:tm-324, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70083
in-theory        70083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (E -> D)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-323 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-70083.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (E -> D)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))), M:tm-323, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70084
in-theory        70084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-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-70084.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70085
in-theory        70085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-70085.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70086
in-theory        70086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-70086.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70087
in-theory        70087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> ((C and A) or A))))
theorem-size     35
proof            (modus-ponens tm-316 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-70087.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> ((C and A) or A)))), M:tm-316, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70088
in-theory        70088
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70088.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70089
in-theory        70089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((C and A) or A)) -> (not ((A -> B) -> B))) -> (not ((A -> B) -> ((C and A) or A)))))
theorem-size     43
proof            (modus-ponens tm-313 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-70089.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((C and A) or A)) -> (not ((A -> B) -> B))) -> (not ((A -> B) -> ((C and A) or A))))), M:tm-313, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70090
in-theory        70090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> B) -> D) -> ((((A -> B) -> ((C and A) or A)) or ((A -> B) -> B)) -> D)))
theorem-size     41
proof            (modus-ponens tm-312 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-70090.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> B) -> D) -> ((((A -> B) -> ((C and A) or A)) or ((A -> B) -> B)) -> D))), M:tm-312, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70091
in-theory        70091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D or (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))))
theorem-size     33
proof            (modus-ponens tm-311 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-70091.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D or (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))), M:tm-311, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70092
in-theory        70092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-70092.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) or D)), M:tm-310, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70093
in-theory        70093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-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-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-70093.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and D))), M:tm-309, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70094
in-theory        70094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((C and A) or A)) -> (A -> B)) -> (((A -> B) -> ((C and A) or A)) -> B)))
theorem-size     41
proof            (modus-ponens tm-306 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> Am Bm)) (C Bm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-70094.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((C and A) or A)) -> (A -> B)) -> (((A -> B) -> ((C and A) or A)) -> B))), M:tm-306, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> Am Bm)) (C Bm))
================================================================
tm-name          tm-70095
in-theory        70095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))))
theorem-size     33
proof            (modus-ponens tm-305 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-70095.        ((((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)) and (D -> (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))), M:tm-305, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70096
in-theory        70096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-303 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 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-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-70096.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-303, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70097
in-theory        70097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-270 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-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-70097.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-270, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70098
in-theory        70098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-239 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 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-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-70098.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-239, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70099
in-theory        70099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-210 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-70099.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F))), M:tm-210, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70100
in-theory        70100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-183 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-4.            ((A and B) -> B), axiom
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-70100.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-183, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70101
in-theory        70101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-157 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-70101.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-157, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70102
in-theory        70102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-147 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-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-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-70102.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-147, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70103
in-theory        70103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-134 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-70103.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-134, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70104
in-theory        70104
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-125 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70104.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-125, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70105
in-theory        70105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((D and A) or A)) -> (((A -> (B -> C)) -> B) -> ((A -> (B -> C)) -> C)))
theorem-size     27
proof            (modus-ponens tm-114 tm-809 ((A (-> (-> Am (-> C D)) (or (and Cm Am) Am))) (B (-> Am (-> C D))) (Bm (-> C D))))
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-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-70105.        (((A -> (B -> C)) -> ((D and A) or A)) -> (((A -> (B -> C)) -> B) -> ((A -> (B -> C)) -> C))), M:tm-114, m:tm-809, u:((A (-> (-> Am (-> C D)) (or (and Cm Am) Am))) (B (-> Am (-> C D))) (Bm (-> C D)))
================================================================
tm-name          tm-70106
in-theory        70106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-113 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70106.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F))), M:tm-113, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70107
in-theory        70107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     35
proof            (modus-ponens tm-105 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-70107.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-105, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70108
in-theory        70108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D)))
theorem-size     23
proof            (modus-ponens tm-95 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70108.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D))), M:tm-95, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70109
in-theory        70109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C and A) or A)) -> (D -> ((A -> B) -> B)))
theorem-size     17
proof            (modus-ponens tm-84 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70109.        (((A -> B) -> ((C and A) or A)) -> (D -> ((A -> B) -> B))), M:tm-84, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70110
in-theory        70110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-83 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-70110.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-83, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70111
in-theory        70111
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((D and B) or B)) -> ((B -> C) -> C)))
theorem-size     21
proof            (modus-ponens tm-76 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 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-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-70111.        (((not (not A)) -> A) and (((B -> C) -> ((D and B) or B)) -> ((B -> C) -> C))), M:tm-76, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70112
in-theory        70112
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> ((C and A) or A)))) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B))
theorem-size     27
proof            (modus-ponens tm-73 tm-809 ((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-4)
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-4.            ((A and B) -> B), axiom
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-70112.        (((not (not ((A -> B) -> ((C and A) or A)))) or ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B)), M:tm-73, m:tm-809, u:((A (-> (-> Am Bm) (or (and Cm Am) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-70113
in-theory        70113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and A) or A))) -> ((B and A) or A)) -> (not (A -> (not ((B and A) or A)))))
theorem-size     24
proof            (modus-ponens tm-70 tm-809 ((B (or (and Cm Am) Am)) (A (-> Am (not (or (and Cm Am) Am)))) (Bm (not (or (and Cm Am) Am)))))
axioms-used      (tm-2 tm-9 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70113.        (((A -> (not ((B and A) or A))) -> ((B and A) or A)) -> (not (A -> (not ((B and A) or A))))), M:tm-70, m:tm-809, u:((B (or (and Cm Am) Am)) (A (-> Am (not (or (and Cm Am) Am)))) (Bm (not (or (and Cm Am) Am))))
================================================================
tm-name          tm-70114
in-theory        70114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D)))
theorem-size     27
proof            (modus-ponens tm-69 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 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-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-70114.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((E and C) or C)) -> ((C -> D) -> D))), M:tm-69, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70115
in-theory        70115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-54 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-70115.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-54, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-70116
in-theory        70116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
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-70116.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-808, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70117
in-theory        70117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-805 tm-810 ((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-4 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-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-1.            (A -> (B -> A)), axiom
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-70117.        (((A -> B) or (((C and A) or A) -> B)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-805, m:tm-810, u:((Am (-> (or (and A B) B) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70118
in-theory        70118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((E and A) or A) -> ((B -> C) -> (((D and B) or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-810 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
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-70118.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((E and A) or A) -> ((B -> C) -> (((D and B) or B) -> C)))), M:tm-798, m:tm-810, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70119
in-theory        70119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-70119.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-757, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70120
in-theory        70120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-754 tm-810 ((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-70120.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-754, m:tm-810, u:((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70121
in-theory        70121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((A and E) or A) -> ((B -> C) -> (((D and B) or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-810 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-70121.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((A and E) or A) -> ((B -> C) -> (((D and B) or B) -> C)))), M:tm-747, m:tm-810, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70122
in-theory        70122
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70122.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> (((H and F) or F) -> G)))), M:tm-708, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70123
in-theory        70123
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     37
proof            (modus-ponens tm-705 tm-810 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) 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-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-70123.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> (((G and E) or E) -> F))), M:tm-705, m:tm-810, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70124
in-theory        70124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-703 tm-810 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 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-12.           ((A -> B) -> (A -> A)), M: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-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-70124.        (((A -> B) -> (A -> C)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-703, m:tm-810, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70125
in-theory        70125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> E) -> (((F and D) or D) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     45
proof            (modus-ponens tm-697 tm-810 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-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-70125.        ((((A -> B) -> (A -> C)) -> ((D -> E) -> (((F and D) or D) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-697, m:tm-810, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70126
in-theory        70126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70126.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-665, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70127
in-theory        70127
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-662 tm-810 ((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 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-4.            ((A and B) -> B), axiom
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-70127.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-662, m:tm-810, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70128
in-theory        70128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     15
proof            (modus-ponens tm-660 tm-810 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 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-12.           ((A -> B) -> (A -> A)), M: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-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-70128.        ((A -> B) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-660, m:tm-810, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70129
in-theory        70129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> D) -> (((E and C) or C) -> D))) and ((B or (A -> B)) -> ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     33
proof            (modus-ponens tm-654 tm-810 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-70129.        (((A -> B) -> ((C -> D) -> (((E and C) or C) -> D))) and ((B or (A -> B)) -> ((C -> D) -> (((E and C) or C) -> D)))), M:tm-654, m:tm-810, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70130
in-theory        70130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70130.        ((A -> (B -> (C or B))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-622, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70131
in-theory        70131
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-619 tm-810 ((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 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-7.            (A -> (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-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-70131.        ((A or (B -> (C or B))) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-619, m:tm-810, u:((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70132
in-theory        70132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70132.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F or E))), M:tm-609, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70133
in-theory        70133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 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-605.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-70133.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-605, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70134
in-theory        70134
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-602 tm-810 ((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-7 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-7.            (A -> (B or 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-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-70134.        ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-602, m:tm-810, u:((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70135
in-theory        70135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F or E)) and (A -> ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-70135.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F or E)) and (A -> ((B -> C) -> (((D and B) or B) -> C))))), M:tm-595, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70136
in-theory        70136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-4.            ((A and B) -> B), axiom
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-70136.        (((A -> (B or A)) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-550, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70137
in-theory        70137
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> B), axiom
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-70137.        ((A or (B -> (C or B))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-540, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70138
in-theory        70138
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-4.            ((A and B) -> B), axiom
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-70138.        ((A or (B -> (B or C))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-530, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70139
in-theory        70139
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-4.            ((A and B) -> B), axiom
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-70139.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-520, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70140
in-theory        70140
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-70140.        ((A or ((B and C) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-510, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70141
in-theory        70141
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-4.            ((A and B) -> B), axiom
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-70141.        ((A or ((B and C) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-500, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70142
in-theory        70142
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70142.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (((H and F) or F) -> G)))), M:tm-490, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70143
in-theory        70143
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-70143.        ((A or (B -> (C -> B))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-480, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70144
in-theory        70144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70144.        ((A -> (B -> (B or C))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-469, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70145
in-theory        70145
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-466 tm-810 ((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-6 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-6.            (A -> (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-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-70145.        ((A or (B -> (B or C))) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-466, m:tm-810, u:((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70146
in-theory        70146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70146.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (E or F))), M:tm-456, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70147
in-theory        70147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 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-453.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-70147.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-453, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70148
in-theory        70148
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-450 tm-810 ((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-6 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-6.            (A -> (A or 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-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-70148.        ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-450, m:tm-810, u:((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70149
in-theory        70149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (E or F)) and (A -> ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-70149.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (E or F)) and (A -> ((B -> C) -> (((D and B) or B) -> C))))), M:tm-443, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70150
in-theory        70150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> B), axiom
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-70150.        (((A -> (A or B)) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-409, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70151
in-theory        70151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-4.            ((A and B) -> B), axiom
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-70151.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-400, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70152
in-theory        70152
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-70152.        ((((A and B) -> B) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-391, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70153
in-theory        70153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-4.            ((A and B) -> B), axiom
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-70153.        ((((A and B) -> A) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-382, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70154
in-theory        70154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70154.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> (((H and F) or F) -> G)))), M:tm-373, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70155
in-theory        70155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-70155.        (((A -> (B -> A)) or C) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-364, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70156
in-theory        70156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-70156.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-354, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70157
in-theory        70157
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-351 tm-810 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
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-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-70157.        ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-351, m:tm-810, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70158
in-theory        70158
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (A and C)))
theorem-size     11
proof            (modus-ponens tm-349 tm-810 ((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (or (and Dm Bm) Bm) (and Am Bm)))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-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-70158.        (A -> (((B and C) or C) -> (A and C))), M:tm-349, m:tm-810, u:((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (or (and Dm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-70159
in-theory        70159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-70159.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70160
in-theory        70160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) -> D) -> (((A -> B) -> (((C and A) or A) -> B)) and D))
theorem-size     27
proof            (modus-ponens tm-339 tm-810 ((Am (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B)) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-4.            ((A and B) -> B), axiom
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-70160.        ((((A -> B) -> (((C and A) or A) -> B)) -> D) -> (((A -> B) -> (((C and A) or A) -> B)) and D)), M:tm-339, m:tm-810, u:((Am (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B)) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70161
in-theory        70161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> B), axiom
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-70161.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-338, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70162
in-theory        70162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     21
proof            (modus-ponens tm-335 tm-810 ((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
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-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-70162.        (((A -> B) or (A -> (A and B))) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-335, m:tm-810, u:((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70163
in-theory        70163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (A -> (A and ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-810 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) 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-328.          ((A -> 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-4.            ((A and B) -> B), axiom
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-70163.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (A -> (A and ((B -> C) -> (((D and B) or B) -> C))))), M:tm-328, m:tm-810, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70164
in-theory        70164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> (E and F))) and (A -> ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-70164.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> (E and F))) and (A -> ((B -> C) -> (((D and B) or B) -> C))))), M:tm-327, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70165
in-theory        70165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((E and F) -> F) and (A -> ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-70165.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((E and F) -> F) and (A -> ((B -> C) -> (((D and B) or B) -> C))))), M:tm-326, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70166
in-theory        70166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((E and F) -> E) and (A -> ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-70166.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((E and F) -> E) and (A -> ((B -> C) -> (((D and B) or B) -> C))))), M:tm-325, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70167
in-theory        70167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-70167.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> C) -> (((D and B) or B) -> C))))), M:tm-324, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70168
in-theory        70168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> E)) and (A -> ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-70168.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> E)) and (A -> ((B -> C) -> (((D and B) or B) -> C))))), M:tm-323, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70169
in-theory        70169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-70169.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70170
in-theory        70170
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (((D and B) or B) -> C)) -> E)) -> ((B -> C) -> (((D and B) or B) -> C))) and ((A and (((B -> C) -> (((D and B) or B) -> C)) -> E)) -> E))
theorem-size     45
proof            (modus-ponens tm-321 tm-810 ((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) C))) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-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-70170.        (((A and (((B -> C) -> (((D and B) or B) -> C)) -> E)) -> ((B -> C) -> (((D and B) or B) -> C))) and ((A and (((B -> C) -> (((D and B) or B) -> C)) -> E)) -> E)), M:tm-321, m:tm-810, u:((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) C))) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70171
in-theory        70171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-70171.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70172
in-theory        70172
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (((C and A) or A) -> B)) -> D) and E) -> ((A -> B) -> (((C and A) or A) -> B))) and (((((A -> B) -> (((C and A) or A) -> B)) -> D) and E) -> D))
theorem-size     45
proof            (modus-ponens tm-319 tm-810 ((Am (and (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B) C)) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-4.            ((A and B) -> B), axiom
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-70172.        ((((((A -> B) -> (((C and A) or A) -> B)) -> D) and E) -> ((A -> B) -> (((C and A) or A) -> B))) and (((((A -> B) -> (((C and A) or A) -> B)) -> D) and E) -> D)), M:tm-319, m:tm-810, u:((Am (and (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B) C)) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70173
in-theory        70173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-70173.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70174
in-theory        70174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((((C and A) or A) -> B) -> D)) -> ((A -> B) -> (((C and A) or A) -> B))) and (((A -> B) -> ((((C and A) or A) -> B) -> D)) -> ((A -> B) -> D)))
theorem-size     45
proof            (modus-ponens tm-317 tm-810 ((Am (-> (-> Bm Cm) (-> (-> (or (and Dm Bm) Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or (and Dm Bm) Bm) Cm))))
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-13.           (((A -> (B -> C)) -> (A -> 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-4.            ((A and B) -> B), axiom
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-70174.        ((((A -> B) -> ((((C and A) or A) -> B) -> D)) -> ((A -> B) -> (((C and A) or A) -> B))) and (((A -> B) -> ((((C and A) or A) -> B) -> D)) -> ((A -> B) -> D))), M:tm-317, m:tm-810, u:((Am (-> (-> Bm Cm) (-> (-> (or (and Dm Bm) Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-70175
in-theory        70175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-810 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
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-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-70175.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (A -> A)), M:tm-316, m:tm-810, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70176
in-theory        70176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70176.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70177
in-theory        70177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((A -> (not ((B -> C) -> (((D and B) or B) -> C)))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-810 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-4.            ((A and B) -> B), axiom
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-70177.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((A -> (not ((B -> C) -> (((D and B) or B) -> C)))) -> (not A))), M:tm-313, m:tm-810, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70178
in-theory        70178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((((B -> C) -> (((D and B) or B) -> C)) -> E) -> ((A or ((B -> C) -> (((D and B) or B) -> C))) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-810 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
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-312.          ((A -> B) -> ((A -> B) and ((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-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-70178.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((((B -> C) -> (((D and B) or B) -> C)) -> E) -> ((A or ((B -> C) -> (((D and B) or B) -> C))) -> E))), M:tm-312, m:tm-810, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70179
in-theory        70179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E or (A -> ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-70179.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E or (A -> ((B -> C) -> (((D and B) or B) -> C))))), M:tm-311, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70180
in-theory        70180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((A -> ((B -> C) -> (((D and B) or B) -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-70180.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((A -> ((B -> C) -> (((D and B) or B) -> C))) or E)), M:tm-310, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70181
in-theory        70181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> ((A -> ((B -> C) -> (((D and B) or B) -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-4.            ((A and B) -> B), axiom
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-70181.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> ((A -> ((B -> C) -> (((D and B) or B) -> C))) and E))), M:tm-309, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70182
in-theory        70182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((A -> (B -> C)) -> (A -> (((D and B) or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-810 ((A Am) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 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-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-70182.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and ((A -> (B -> C)) -> (A -> (((D and B) or B) -> C)))), M:tm-306, m:tm-810, u:((A Am) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-70183
in-theory        70183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (A -> ((B -> C) -> (((D and B) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-70183.        ((A -> ((B -> C) -> (((D and B) or B) -> C))) and (E -> (A -> ((B -> C) -> (((D and B) or B) -> C))))), M:tm-305, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70184
in-theory        70184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-4.            ((A and B) -> B), axiom
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-70184.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-303, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70185
in-theory        70185
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-300 tm-810 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70185.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-300, m:tm-810, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70186
in-theory        70186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 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-270.          (A -> ((B -> (((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-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-70186.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-270, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70187
in-theory        70187
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-267 tm-810 ((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
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-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-70187.        ((A or (((B and C) -> C) and A)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-267, m:tm-810, u:((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70188
in-theory        70188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 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-239.          (A -> ((B -> (((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-4.            ((A and B) -> B), axiom
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-70188.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-239, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70189
in-theory        70189
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-236 tm-810 ((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-3 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-3.            ((A and B) -> 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-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-70189.        ((A or (((B and C) -> B) and A)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-236, m:tm-810, u:((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70190
in-theory        70190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> B), axiom
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-70190.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> (((H and F) or F) -> G)))), M:tm-210, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70191
in-theory        70191
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-207 tm-810 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
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-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-70191.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> (((G and E) or E) -> F))), M:tm-207, m:tm-810, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70192
in-theory        70192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-183.          (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-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-70192.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-183, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70193
in-theory        70193
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-180 tm-810 ((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
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-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-70193.        ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-180, m:tm-810, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70194
in-theory        70194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-70194.        ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-157, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70195
in-theory        70195
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-154 tm-810 ((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 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-4.            ((A 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-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-70195.        ((A or ((B and C) -> C)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-154, m:tm-810, u:((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70196
in-theory        70196
times-derived    1
----------------------------------------------------------------
theorem          ((A and (B -> C)) -> (((D and B) or B) -> C))
theorem-size     13
proof            (modus-ponens tm-152 tm-810 ((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-4 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-4.            ((A 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-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-70196.        ((A and (B -> C)) -> (((D and B) or B) -> C)), M:tm-152, m:tm-810, u:((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-70197
in-theory        70197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-70197.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-147, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70198
in-theory        70198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-144 tm-810 ((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 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-1.            (A -> (B -> A)), axiom
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-70198.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-144, m:tm-810, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70199
in-theory        70199
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (((D and B) or B) -> C)) -> E)) -> ((B -> C) -> (((D and B) or B) -> C)))
theorem-size     27
proof            (modus-ponens tm-142 tm-810 ((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) C))) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-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-70199.        ((A and (((B -> C) -> (((D and B) or B) -> C)) -> E)) -> ((B -> C) -> (((D and B) or B) -> C))), M:tm-142, m:tm-810, u:((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) C))) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70200
in-theory        70200
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (((D and B) or B) -> C)) -> (B -> C))) -> (((D and B) or B) -> C))
theorem-size     25
proof            (modus-ponens tm-141 tm-810 ((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-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-70200.        ((A and (((B -> C) -> (((D and B) or B) -> C)) -> (B -> C))) -> (((D and B) or B) -> C)), M:tm-141, m:tm-810, u:((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-70201
in-theory        70201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-70201.        ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-134, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70202
in-theory        70202
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-131 tm-810 ((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3 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-4.            ((A and B) -> B), axiom
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-70202.        ((A or ((B and C) -> B)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-131, m:tm-810, u:((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70203
in-theory        70203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and C) -> (((D and A) or A) -> B))
theorem-size     13
proof            (modus-ponens tm-129 tm-810 ((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70203.        (((A -> B) and C) -> (((D and A) or A) -> B)), M:tm-129, m:tm-810, u:((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-70204
in-theory        70204
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-70204.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-125, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70205
in-theory        70205
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-122 tm-810 ((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-70205.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-122, m:tm-810, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70206
in-theory        70206
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (((C and A) or A) -> B)) -> D) and E) -> ((A -> B) -> (((C and A) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-120 tm-810 ((Am (and (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B) C)) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-3 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-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-4.            ((A and B) -> B), axiom
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-70206.        (((((A -> B) -> (((C and A) or A) -> B)) -> D) and E) -> ((A -> B) -> (((C and A) or A) -> B))), M:tm-120, m:tm-810, u:((Am (and (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B) C)) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70207
in-theory        70207
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (((C and A) or A) -> B)) -> (A -> B)) and D) -> (((C and A) or A) -> B))
theorem-size     25
proof            (modus-ponens tm-119 tm-810 ((Am (and (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-3 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70207.        (((((A -> B) -> (((C and A) or A) -> B)) -> (A -> B)) and D) -> (((C and A) or A) -> B)), M:tm-119, m:tm-810, u:((Am (and (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-70208
in-theory        70208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70208.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (((H and F) or F) -> G)))), M:tm-113, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70209
in-theory        70209
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-110 tm-810 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-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-70209.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> (((G and E) or E) -> F))), M:tm-110, m:tm-810, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70210
in-theory        70210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))
theorem-size     19
proof            (modus-ponens tm-108 tm-810 ((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (or (and Dm (-> A B)) (-> A B)) (-> A 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-4.            ((A and B) -> B), axiom
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-70210.        ((A -> (B -> C)) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))), M:tm-108, m:tm-810, u:((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (or (and Dm (-> A B)) (-> A B)) (-> A C))))
================================================================
tm-name          tm-70211
in-theory        70211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) -> ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B))
theorem-size     27
proof            (modus-ponens tm-106 tm-810 ((Am (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> Bm Cm) (or (and Dm Bm) Bm)))) (A (-> Bm Cm)) (B (or (and Dm Bm) Bm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70211.        ((((A -> B) -> (((C and A) or A) -> B)) -> ((A -> B) -> ((C and A) or A))) -> ((A -> B) -> B)), M:tm-106, m:tm-810, u:((Am (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> Bm Cm) (or (and Dm Bm) Bm)))) (A (-> Bm Cm)) (B (or (and Dm Bm) Bm)) (C Cm))
================================================================
tm-name          tm-70212
in-theory        70212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> B), axiom
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-70212.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-105, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70213
in-theory        70213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-102 tm-810 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70213.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-102, m:tm-810, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70214
in-theory        70214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C and A) or A) -> B) -> D)) -> ((A -> B) -> (((C and A) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-100 tm-810 ((Am (-> (-> Bm Cm) (-> (-> (or (and Dm Bm) Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-1 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-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-4.            ((A and B) -> B), axiom
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-70214.        (((A -> B) -> ((((C and A) or A) -> B) -> D)) -> ((A -> B) -> (((C and A) or A) -> B))), M:tm-100, m:tm-810, u:((Am (-> (-> Bm Cm) (-> (-> (or (and Dm Bm) Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-70215
in-theory        70215
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> A))
theorem-size     9
proof            (modus-ponens tm-98 tm-810 ((Cm Am) (B Bm) (A Am) (C (-> (or (and Dm Bm) Bm) Am))))
axioms-used      (tm-2 tm-1 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-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-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-70215.        (A -> (((B and C) or C) -> A)), M:tm-98, m:tm-810, u:((Cm Am) (B Bm) (A Am) (C (-> (or (and Dm Bm) Bm) Am)))
================================================================
tm-name          tm-70216
in-theory        70216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) -> D) -> ((A -> B) -> (((C and A) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-96 tm-810 ((Am (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B)) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
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-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-4.            ((A and B) -> B), axiom
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-70216.        ((((A -> B) -> (((C and A) or A) -> B)) -> D) -> ((A -> B) -> (((C and A) or A) -> B))), M:tm-96, m:tm-810, u:((Am (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B)) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70217
in-theory        70217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-70217.        (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-95, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70218
in-theory        70218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-92 tm-810 ((Am (-> A A)) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 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-1.            (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-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-70218.        (((A -> B) or (A -> A)) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-92, m:tm-810, u:((Am (-> A A)) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70219
in-theory        70219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70219.        ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-83, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70220
in-theory        70220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-80 tm-810 ((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-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-70220.        ((A or (B -> (C -> B))) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-80, m:tm-810, u:((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70221
in-theory        70221
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> B) -> (((C and A) or A) -> B)) -> D))) -> D)
theorem-size     17
proof            (modus-ponens tm-77 tm-810 ((Am (not (not (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B)))) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70221.        ((not (not (((A -> B) -> (((C and A) or A) -> B)) -> D))) -> D), M:tm-77, m:tm-810, u:((Am (not (not (-> (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) B)))) (A (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70222
in-theory        70222
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70222.        (((not (not A)) -> A) and (B -> ((C -> D) -> (((E and C) or C) -> D)))), M:tm-76, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70223
in-theory        70223
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> C) -> (((D and B) or B) -> C)))
theorem-size     17
proof            (modus-ponens tm-73 tm-810 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70223.        (((not (not A)) or A) -> ((B -> C) -> (((D and B) or B) -> C))), M:tm-73, m:tm-810, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70224
in-theory        70224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-70224.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-69, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70225
in-theory        70225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-66 tm-810 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-9 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-70225.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-66, m:tm-810, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70226
in-theory        70226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A or (B -> C)) -> (((D and B) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-55 tm-810 ((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70226.        ((A -> (B -> C)) -> ((A or (B -> C)) -> (((D and B) or B) -> C))), M:tm-55, m:tm-810, u:((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-70227
in-theory        70227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-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-70227.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-54, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-70228
in-theory        70228
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-51 tm-810 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70228.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-51, m:tm-810, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70229
in-theory        70229
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-50 tm-810 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70229.        ((A or (B or A)) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-50, m:tm-810, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70230
in-theory        70230
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-49 tm-810 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70230.        ((A or (A or B)) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-49, m:tm-810, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70231
in-theory        70231
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-48 tm-810 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
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-4.            ((A and B) -> B), axiom
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-70231.        ((A or (B -> (A and B))) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-48, m:tm-810, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-70232
in-theory        70232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70232.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-808, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70233
in-theory        70233
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (B -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-798 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70233.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (B -> (A and B))))), M:tm-798, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70234
in-theory        70234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70234.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-757, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70235
in-theory        70235
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (C -> (B -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-747 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-70235.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (C -> (B -> (A and B))))), M:tm-747, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70236
in-theory        70236
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70236.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F))))), M:tm-708, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70237
in-theory        70237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70237.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-665, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70238
in-theory        70238
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D -> (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-623 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70238.        ((A or (B -> (A and B))) -> (C or (D -> (B -> (A and B))))), M:tm-623, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70239
in-theory        70239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70239.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-622, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70240
in-theory        70240
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70240.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (E or D))), M:tm-609, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70241
in-theory        70241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70241.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-605, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70242
in-theory        70242
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-70242.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))))), M:tm-595, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70243
in-theory        70243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70243.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-550, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70244
in-theory        70244
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70244.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-540, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70245
in-theory        70245
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70245.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-530, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70246
in-theory        70246
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70246.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-520, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70247
in-theory        70247
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70247.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-510, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70248
in-theory        70248
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70248.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-500, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70249
in-theory        70249
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70249.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F))))), M:tm-490, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70250
in-theory        70250
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70250.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-480, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70251
in-theory        70251
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (B -> (A and B))) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70251.        ((A or (B -> (A and B))) -> ((C -> (B -> (A and B))) or D)), M:tm-470, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70252
in-theory        70252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70252.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-469, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70253
in-theory        70253
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70253.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (D or E))), M:tm-456, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70254
in-theory        70254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70254.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-453, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70255
in-theory        70255
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-70255.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))))), M:tm-443, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70256
in-theory        70256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70256.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-409, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70257
in-theory        70257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70257.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-400, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70258
in-theory        70258
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70258.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-391, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70259
in-theory        70259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70259.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-382, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70260
in-theory        70260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70260.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F))))), M:tm-373, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70261
in-theory        70261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70261.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-364, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70262
in-theory        70262
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (B -> (A and B))) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70262.        ((A or (B -> (A and B))) -> (C -> ((D -> (B -> (A and B))) and C))), M:tm-355, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70263
in-theory        70263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70263.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-354, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70264
in-theory        70264
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70264.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70265
in-theory        70265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70265.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D))))), M:tm-338, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70266
in-theory        70266
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (B -> (A and B))))))
theorem-size     39
proof            (modus-ponens tm-328 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-70266.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (B -> (A and B)))))), M:tm-328, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70267
in-theory        70267
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-70267.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))))), M:tm-327, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70268
in-theory        70268
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-70268.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))))), M:tm-326, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70269
in-theory        70269
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-70269.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))))), M:tm-325, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70270
in-theory        70270
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-70270.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))))), M:tm-324, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70271
in-theory        70271
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-70271.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))))), M:tm-323, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70272
in-theory        70272
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70272.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D and E) -> E)), M:tm-322, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70273
in-theory        70273
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am 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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70273.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D and E) -> D)), M:tm-320, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70274
in-theory        70274
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70274.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70275
in-theory        70275
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     31
proof            (modus-ponens tm-316 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-70275.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70276
in-theory        70276
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70276.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (E -> D))), M:tm-315, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70277
in-theory        70277
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (C -> (B -> (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-313 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-70277.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (C -> (B -> (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70278
in-theory        70278
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((C -> (B -> (A and B))) -> D) -> (((A or (B -> (A and B))) or (C -> (B -> (A and B)))) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-70278.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((C -> (B -> (A and B))) -> D) -> (((A or (B -> (A and B))) or (C -> (B -> (A and B)))) -> D))), M:tm-312, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70279
in-theory        70279
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D or ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-7.            (A -> (B or 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-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-70279.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D or ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))))), M:tm-311, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70280
in-theory        70280
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-6.            (A -> (A or 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-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-70280.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) or D)), M:tm-310, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70281
in-theory        70281
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-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-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-70281.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and D))), M:tm-309, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70282
in-theory        70282
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (B -> (A and B)))))
theorem-size     39
proof            (modus-ponens tm-306 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Bm (and 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-70282.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (B -> (A and B))))), M:tm-306, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Bm (and Am Bm))))
================================================================
tm-name          tm-70283
in-theory        70283
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-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-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-70283.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (D -> ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))))), M:tm-305, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70284
in-theory        70284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70284.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-303, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70285
in-theory        70285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70285.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-270, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70286
in-theory        70286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70286.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-239, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70287
in-theory        70287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70287.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F))))), M:tm-210, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70288
in-theory        70288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70288.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-183, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70289
in-theory        70289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70289.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-157, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70290
in-theory        70290
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70290.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-147, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70291
in-theory        70291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70291.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-134, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70292
in-theory        70292
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70292.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-125, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70293
in-theory        70293
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> B) -> (C -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-114 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C Bm) (D (and Am Bm))))
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-14.           (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-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-70293.        ((A or (B -> (A and B))) -> ((C -> B) -> (C -> (A and B)))), M:tm-114, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C Bm) (D (and Am Bm)))
================================================================
tm-name          tm-70294
in-theory        70294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70294.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F))))), M:tm-113, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70295
in-theory        70295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70295.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-105, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70296
in-theory        70296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70296.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D))))), M:tm-95, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70297
in-theory        70297
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-84 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70297.        ((A or (B -> (A and B))) -> (C -> (D -> (B -> (A and B))))), M:tm-84, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70298
in-theory        70298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70298.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-83, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70299
in-theory        70299
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70299.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (C -> (B and C))))), M:tm-76, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70300
in-theory        70300
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-73 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-5 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-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-70300.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (B -> (A and B)))), M:tm-73, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70301
in-theory        70301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70301.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D))))), M:tm-69, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70302
in-theory        70302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70302.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-54, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70303
in-theory        70303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-50 tm-811 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-70303.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (A -> (B and A)))), M:tm-50, m:tm-811, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70304
in-theory        70304
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (C -> (B -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-49 tm-811 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       105
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-48.           (((A -> (B and 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-70304.        ((A or (A or (B -> (A and B)))) -> (C -> (B -> (A and B)))), M:tm-49, m:tm-811, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70305
in-theory        70305
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (C -> (B and C))))
theorem-size     25
proof            (modus-ponens tm-47 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-5 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-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-70305.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (C -> (B and C)))), M:tm-47, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70306
in-theory        70306
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-46 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
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-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-70306.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (B -> (A and B)))), M:tm-46, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70307
in-theory        70307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70307.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D))))), M:tm-42, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70308
in-theory        70308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70308.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D))))), M:tm-32, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70309
in-theory        70309
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-24 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-70309.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (B -> (A and B))))), M:tm-24, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70310
in-theory        70310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70310.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D))))), M:tm-23, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70311
in-theory        70311
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70311.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D))))), M:tm-22, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70312
in-theory        70312
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70312.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D))))), M:tm-21, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70313
in-theory        70313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70313.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-20, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70314
in-theory        70314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70314.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (D -> (C and D))))), M:tm-19, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70315
in-theory        70315
times-derived    24
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (A or (B -> (A and B))))
theorem-size     15
proof            (modus-ponens tm-12 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-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-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-70315.        ((A or (B -> (A and B))) -> (A or (B -> (A and B)))), M:tm-12, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70316
in-theory        70316
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (C -> (B -> (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-9 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5 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-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-70316.        (((A or (B -> (A and B))) -> (not (C -> (B -> (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70317
in-theory        70317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C and B))) -> D) -> (((C or (B -> (C and B))) or (A -> (B -> (C and B)))) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-5 tm-1)
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-48.           (((A -> (B and 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-70317.        (((A -> (B -> (C and B))) -> D) -> (((C or (B -> (C and B))) or (A -> (B -> (C and B)))) -> D)), M:tm-8, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70318
in-theory        70318
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (D -> (C -> (B and C)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-1)
proof-size       79
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-48.           (((A -> (B and 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-70318.        (A or ((B or (C -> (B and C))) -> (D -> (C -> (B and C))))), M:tm-7, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70319
in-theory        70319
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-1)
proof-size       79
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-48.           (((A -> (B and 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-70319.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) or D), M:tm-6, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70320
in-theory        70320
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (D -> (C -> (B and C)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70320.        (A -> (((B or (C -> (B and C))) -> (D -> (C -> (B and C)))) and A)), M:tm-5, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70321
in-theory        70321
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-2 tm-811 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-8 tm-5 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-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-70321.        (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (B -> (A and B)))), M:tm-2, m:tm-811, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Bm (and Am Bm))))
================================================================
tm-name          tm-70322
in-theory        70322
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (D -> (C -> (B and C)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       79
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70322.        (A -> ((B or (C -> (B and C))) -> (D -> (C -> (B and C))))), M:tm-1, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70323
in-theory        70323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     29
proof            (modus-ponens tm-808 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70323.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-808, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70324
in-theory        70324
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C))))
theorem-size     45
proof            (modus-ponens tm-798 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70324.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C)))), M:tm-798, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70325
in-theory        70325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-70325.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-757, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70326
in-theory        70326
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C))))
theorem-size     45
proof            (modus-ponens tm-747 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-70326.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C)))), M:tm-747, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70327
in-theory        70327
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-70327.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G)))), M:tm-708, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70328
in-theory        70328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-70328.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-665, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70329
in-theory        70329
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D -> ((B -> (A and B)) and D))))
theorem-size     19
proof            (modus-ponens tm-623 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-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-70329.        ((A or (B -> (A and B))) -> (C or (D -> ((B -> (A and B)) and D)))), M:tm-623, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70330
in-theory        70330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-48.           (((A -> (B and 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-70330.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-622, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70331
in-theory        70331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C or (A or (B -> (A and B))))))
theorem-size     23
proof            (modus-ponens tm-617 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (and (-> Bm (and Am Bm)) (or B (or Am (-> Bm (and Am Bm))))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-7.            (A -> (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-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-70331.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C or (A or (B -> (A and B)))))), M:tm-617, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (and (-> Bm (and Am Bm)) (or B (or Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-70332
in-theory        70332
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70332.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (E or D))), M:tm-609, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70333
in-theory        70333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-70333.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-605, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70334
in-theory        70334
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-70334.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))))), M:tm-595, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70335
in-theory        70335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-48.           (((A -> (B and 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-70335.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-550, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70336
in-theory        70336
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-70336.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-540, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70337
in-theory        70337
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-48.           (((A -> (B and 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-70337.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-530, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70338
in-theory        70338
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-70338.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-520, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70339
in-theory        70339
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-48.           (((A -> (B and 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-70339.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-510, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70340
in-theory        70340
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-48.           (((A -> (B and 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-70340.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-500, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70341
in-theory        70341
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-48.           (((A -> (B and 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-70341.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G)))), M:tm-490, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70342
in-theory        70342
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-48.           (((A -> (B and 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-70342.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-480, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70343
in-theory        70343
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> ((B -> (A and B)) and C)) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-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-70343.        ((A or (B -> (A and B))) -> ((C -> ((B -> (A and B)) and C)) or D)), M:tm-470, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70344
in-theory        70344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-48.           (((A -> (B and 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-70344.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-469, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70345
in-theory        70345
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((A or (B -> (A and B))) or C)))
theorem-size     23
proof            (modus-ponens tm-464 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (and (-> Bm (and Am Bm)) (or (or Am (-> Bm (and Am Bm))) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-6.            (A -> (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-48.           (((A -> (B and 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-70345.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((A or (B -> (A and B))) or C))), M:tm-464, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (and (-> Bm (and Am Bm)) (or (or Am (-> Bm (and Am Bm))) B))))
================================================================
tm-name          tm-70346
in-theory        70346
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70346.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (D or E))), M:tm-456, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70347
in-theory        70347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-70347.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-453, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70348
in-theory        70348
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-70348.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))))), M:tm-443, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70349
in-theory        70349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-70349.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-409, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70350
in-theory        70350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-70350.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-400, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70351
in-theory        70351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-48.           (((A -> (B and 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-70351.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-391, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70352
in-theory        70352
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-48.           (((A -> (B and 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-70352.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-382, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70353
in-theory        70353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-48.           (((A -> (B and 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-70353.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G)))), M:tm-373, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70354
in-theory        70354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-48.           (((A -> (B and 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-70354.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-364, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70355
in-theory        70355
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> ((B -> (A and B)) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-355 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70355.        ((A or (B -> (A and B))) -> (C -> ((D -> ((B -> (A and B)) and D)) and C))), M:tm-355, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70356
in-theory        70356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-70356.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-354, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70357
in-theory        70357
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> ((A or (B -> (A and B))) and C))))
theorem-size     25
proof            (modus-ponens tm-349 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (and (-> Bm (and Am Bm)) (-> B (and (or Am (-> Bm (and Am Bm))) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
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-48.           (((A -> (B and 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-70357.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> ((A or (B -> (A and B))) and C)))), M:tm-349, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (and (-> Bm (and Am Bm)) (-> B (and (or Am (-> Bm (and Am Bm))) B)))))
================================================================
tm-name          tm-70358
in-theory        70358
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70358.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70359
in-theory        70359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-48.           (((A -> (B and 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-70359.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E)))), M:tm-338, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70360
in-theory        70360
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> ((B -> (A and B)) and C)))))
theorem-size     43
proof            (modus-ponens tm-328 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (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-328.          ((A -> 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-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-70360.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> ((B -> (A and B)) and C))))), M:tm-328, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70361
in-theory        70361
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-70361.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))))), M:tm-327, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70362
in-theory        70362
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-70362.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))))), M:tm-326, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70363
in-theory        70363
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-70363.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))))), M:tm-325, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70364
in-theory        70364
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-70364.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))))), M:tm-324, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70365
in-theory        70365
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-70365.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))))), M:tm-323, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70366
in-theory        70366
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70366.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D and E) -> E)), M:tm-322, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70367
in-theory        70367
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70367.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D and E) -> D)), M:tm-320, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70368
in-theory        70368
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-70368.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70369
in-theory        70369
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-316 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-70369.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70370
in-theory        70370
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70370.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (E -> D))), M:tm-315, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70371
in-theory        70371
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((A or (B -> (A and B))) -> (not (C -> ((B -> (A and B)) and C)))) -> (not (A or (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-313 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-70371.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((A or (B -> (A and B))) -> (not (C -> ((B -> (A and B)) and C)))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70372
in-theory        70372
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((C -> ((B -> (A and B)) and C)) -> D) -> (((A or (B -> (A and B))) or (C -> ((B -> (A and B)) and C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-312 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-70372.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((C -> ((B -> (A and B)) and C)) -> D) -> (((A or (B -> (A and B))) or (C -> ((B -> (A and B)) and C))) -> D))), M:tm-312, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70373
in-theory        70373
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D or ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-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-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-70373.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D or ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))))), M:tm-311, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70374
in-theory        70374
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-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-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-70374.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) or D)), M:tm-310, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70375
in-theory        70375
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
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-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-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-70375.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and D))), M:tm-309, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70376
in-theory        70376
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> ((B -> (A and B)) and C))))
theorem-size     43
proof            (modus-ponens tm-306 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (and (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-70376.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> ((B -> (A and B)) and C)))), M:tm-306, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (and (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70377
in-theory        70377
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-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-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-70377.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (D -> ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))))), M:tm-305, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70378
in-theory        70378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-70378.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-303, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70379
in-theory        70379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-48.           (((A -> (B and 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-70379.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-270, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70380
in-theory        70380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-48.           (((A -> (B and 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-70380.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-239, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70381
in-theory        70381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-70381.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G)))), M:tm-210, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70382
in-theory        70382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-70382.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-183, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70383
in-theory        70383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-48.           (((A -> (B and 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-70383.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-157, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70384
in-theory        70384
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-70384.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-147, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70385
in-theory        70385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-48.           (((A -> (B and 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-70385.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-134, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70386
in-theory        70386
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-70386.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-125, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70387
in-theory        70387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70387.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G)))), M:tm-113, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70388
in-theory        70388
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-70388.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-105, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70389
in-theory        70389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (A or (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-99 tm-812 ((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (and (-> Bm (and Am Bm)) (or Am (-> Bm (and Am Bm)))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-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-70389.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (A or (B -> (A and B))))), M:tm-99, m:tm-812, u:((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (and (-> Bm (and Am Bm)) (or Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70390
in-theory        70390
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (A or (B -> (A and B))))))
theorem-size     23
proof            (modus-ponens tm-98 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (and (-> Bm (and Am Bm)) (-> B (or Am (-> Bm (and Am 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-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-70390.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (A or (B -> (A and B)))))), M:tm-98, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (and (-> Bm (and Am Bm)) (-> B (or Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-70391
in-theory        70391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-70391.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E)))), M:tm-95, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70392
in-theory        70392
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> ((B -> (A and B)) and D))))
theorem-size     19
proof            (modus-ponens tm-84 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 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-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-70392.        ((A or (B -> (A and B))) -> (C -> (D -> ((B -> (A and B)) and D)))), M:tm-84, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70393
in-theory        70393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-70393.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-83, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70394
in-theory        70394
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> ((C -> (B and C)) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-8)
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-48.           (((A -> (B and 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-70394.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> ((C -> (B and C)) and D)))), M:tm-76, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70395
in-theory        70395
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C)))
theorem-size     27
proof            (modus-ponens tm-73 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-8 tm-10 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-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-70395.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C))), M:tm-73, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70396
in-theory        70396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-48.           (((A -> (B and 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-70396.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E)))), M:tm-69, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70397
in-theory        70397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-70397.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-54, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70398
in-theory        70398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> ((A -> (B and A)) and C)))
theorem-size     23
proof            (modus-ponens tm-50 tm-812 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-8 tm-7 tm-5)
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-48.           (((A -> (B and 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-70398.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> ((A -> (B and A)) and C))), M:tm-50, m:tm-812, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70399
in-theory        70399
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C)))
theorem-size     19
proof            (modus-ponens tm-49 tm-812 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-70399.        ((A or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C))), M:tm-49, m:tm-812, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70400
in-theory        70400
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> ((C -> (B and C)) and D)))
theorem-size     27
proof            (modus-ponens tm-47 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70400.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> ((C -> (B and C)) and D))), M:tm-47, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70401
in-theory        70401
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> ((B -> (A and B)) and D)))
theorem-size     27
proof            (modus-ponens tm-46 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70401.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> ((B -> (A and B)) and D))), M:tm-46, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70402
in-theory        70402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-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-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-70402.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E)))), M:tm-42, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70403
in-theory        70403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-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-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-70403.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E)))), M:tm-32, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70404
in-theory        70404
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> ((B -> (A and B)) and C))))
theorem-size     25
proof            (modus-ponens tm-24 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and 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-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-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-70404.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> ((B -> (A and B)) and C)))), M:tm-24, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70405
in-theory        70405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-70405.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E)))), M:tm-23, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70406
in-theory        70406
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-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-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-70406.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E)))), M:tm-22, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70407
in-theory        70407
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-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-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-70407.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E)))), M:tm-21, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70408
in-theory        70408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-70408.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-20, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70409
in-theory        70409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) 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-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-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-70409.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> ((D -> (C and D)) and E)))), M:tm-19, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70410
in-theory        70410
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (C -> ((B -> (A and B)) and C)))) -> (not (A or (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-9 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-9 tm-8 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-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-70410.        (((A or (B -> (A and B))) -> (not (C -> ((B -> (A and B)) and C)))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70411
in-theory        70411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C and B)) and A)) -> D) -> (((C or (B -> (C and B))) or (A -> ((B -> (C and B)) and A))) -> D))
theorem-size     31
proof            (modus-ponens tm-8 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
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-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-70411.        (((A -> ((B -> (C and B)) and A)) -> D) -> (((C or (B -> (C and B))) or (A -> ((B -> (C and B)) and A))) -> D)), M:tm-8, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70412
in-theory        70412
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (D -> ((C -> (B and C)) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-7 tm-8 tm-5)
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-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-70412.        (A or ((B or (C -> (B and C))) -> (D -> ((C -> (B and C)) and D)))), M:tm-7, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70413
in-theory        70413
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-6 tm-8 tm-5)
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-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-70413.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) or D), M:tm-6, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70414
in-theory        70414
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (D -> ((C -> (B and C)) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-70414.        (A -> (((B or (C -> (B and C))) -> (D -> ((C -> (B and C)) and D))) and A)), M:tm-5, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70415
in-theory        70415
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> ((B -> (A and B)) and C)))
theorem-size     25
proof            (modus-ponens tm-2 tm-812 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (and (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-8 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-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-70415.        (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> ((B -> (A and B)) and C))), M:tm-2, m:tm-812, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (and (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70416
in-theory        70416
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (D -> ((C -> (B and C)) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       85
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-48.           (((A -> (B and 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-70416.        (A -> ((B or (C -> (B and C))) -> (D -> ((C -> (B and C)) and D)))), M:tm-1, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70417
in-theory        70417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     27
proof            (modus-ponens tm-808 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70417.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-808, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70418
in-theory        70418
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C)))
theorem-size     41
proof            (modus-ponens tm-798 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70418.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C))), M:tm-798, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70419
in-theory        70419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     27
proof            (modus-ponens tm-757 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70419.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-757, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70420
in-theory        70420
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C)))
theorem-size     41
proof            (modus-ponens tm-747 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-70420.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C))), M:tm-747, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70421
in-theory        70421
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G)))
theorem-size     41
proof            (modus-ponens tm-708 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70421.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G))), M:tm-708, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70422
in-theory        70422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     29
proof            (modus-ponens tm-665 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70422.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-665, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70423
in-theory        70423
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or ((B -> (A and B)) or D)))
theorem-size     17
proof            (modus-ponens tm-623 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70423.        ((A or (B -> (A and B))) -> (C or ((B -> (A and B)) or D))), M:tm-623, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70424
in-theory        70424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-622 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70424.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-622, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70425
in-theory        70425
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70425.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (E or D))), M:tm-609, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70426
in-theory        70426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     25
proof            (modus-ponens tm-605 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-605.          (A -> ((B -> ((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-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-70426.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-605, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70427
in-theory        70427
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))))
theorem-size     37
proof            (modus-ponens tm-595 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-70427.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)))), M:tm-595, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70428
in-theory        70428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-550 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-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-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-70428.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-550, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70429
in-theory        70429
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-540 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-48.           (((A -> (B and 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-70429.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-540, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70430
in-theory        70430
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-530 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-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-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-70430.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-530, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70431
in-theory        70431
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     25
proof            (modus-ponens tm-520 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-48.           (((A -> (B and 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-70431.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-520, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70432
in-theory        70432
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-510 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-48.           (((A -> (B and 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-70432.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-510, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70433
in-theory        70433
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-500 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-48.           (((A -> (B and 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-70433.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-500, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70434
in-theory        70434
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G)))
theorem-size     31
proof            (modus-ponens tm-490 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-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-70434.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G))), M:tm-490, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70435
in-theory        70435
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-480 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-48.           (((A -> (B and 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-70435.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-480, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70436
in-theory        70436
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((B -> (A and B)) or C) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70436.        ((A or (B -> (A and B))) -> (((B -> (A and B)) or C) or D)), M:tm-470, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70437
in-theory        70437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-469 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70437.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-469, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70438
in-theory        70438
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70438.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (D or E))), M:tm-456, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70439
in-theory        70439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     25
proof            (modus-ponens tm-453 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70439.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-453, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70440
in-theory        70440
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))))
theorem-size     37
proof            (modus-ponens tm-443 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-70440.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)))), M:tm-443, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70441
in-theory        70441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-409 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-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-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-70441.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-409, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70442
in-theory        70442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     25
proof            (modus-ponens tm-400 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-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-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-70442.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-400, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70443
in-theory        70443
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-391 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-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-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-70443.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-391, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70444
in-theory        70444
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-382 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-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-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-70444.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-382, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70445
in-theory        70445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G)))
theorem-size     31
proof            (modus-ponens tm-373 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-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-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-70445.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G))), M:tm-373, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70446
in-theory        70446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-364 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70446.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-364, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70447
in-theory        70447
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((B -> (A and B)) or D) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-70447.        ((A or (B -> (A and B))) -> (C -> (((B -> (A and B)) or D) and C))), M:tm-355, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70448
in-theory        70448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     25
proof            (modus-ponens tm-354 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-48.           (((A -> (B and 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-70448.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-354, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70449
in-theory        70449
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-70449.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70450
in-theory        70450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E)))
theorem-size     25
proof            (modus-ponens tm-338 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-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-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-70450.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E))), M:tm-338, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70451
in-theory        70451
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((B -> (A and B)) or C))))
theorem-size     39
proof            (modus-ponens tm-328 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-70451.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((B -> (A and B)) or C)))), M:tm-328, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70452
in-theory        70452
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))))
theorem-size     39
proof            (modus-ponens tm-327 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-70452.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)))), M:tm-327, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70453
in-theory        70453
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((D and E) -> E) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))))
theorem-size     37
proof            (modus-ponens tm-326 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-70453.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((D and E) -> E) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)))), M:tm-326, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70454
in-theory        70454
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((D and E) -> D) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))))
theorem-size     37
proof            (modus-ponens tm-325 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-70454.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((D and E) -> D) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)))), M:tm-325, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70455
in-theory        70455
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))))
theorem-size     45
proof            (modus-ponens tm-324 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-70455.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)))), M:tm-324, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70456
in-theory        70456
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))))
theorem-size     37
proof            (modus-ponens tm-323 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-70456.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)))), M:tm-323, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70457
in-theory        70457
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-70457.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D and E) -> E)), M:tm-322, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70458
in-theory        70458
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-70458.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D and E) -> D)), M:tm-320, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70459
in-theory        70459
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-70459.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70460
in-theory        70460
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     31
proof            (modus-ponens tm-316 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-70460.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70461
in-theory        70461
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70461.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (E -> D))), M:tm-315, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70462
in-theory        70462
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((A or (B -> (A and B))) -> (not ((B -> (A and B)) or C))) -> (not (A or (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-313 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
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-48.           (((A -> (B and 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-70462.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((A or (B -> (A and B))) -> (not ((B -> (A and B)) or C))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70463
in-theory        70463
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((((B -> (A and B)) or C) -> D) -> (((A or (B -> (A and B))) or ((B -> (A and B)) or C)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-70463.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((((B -> (A and B)) or C) -> D) -> (((A or (B -> (A and B))) or ((B -> (A and B)) or C)) -> D))), M:tm-312, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70464
in-theory        70464
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D or ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))))
theorem-size     33
proof            (modus-ponens tm-311 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-70464.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D or ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)))), M:tm-311, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70465
in-theory        70465
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-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-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-70465.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) or D)), M:tm-310, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70466
in-theory        70466
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 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-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-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-70466.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and D))), M:tm-309, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70467
in-theory        70467
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))))
theorem-size     33
proof            (modus-ponens tm-305 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-70467.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (D -> ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)))), M:tm-305, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70468
in-theory        70468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     27
proof            (modus-ponens tm-303 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-70468.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-303, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70469
in-theory        70469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     25
proof            (modus-ponens tm-270 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 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-270.          (A -> ((B -> (((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-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-70469.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-270, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70470
in-theory        70470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     25
proof            (modus-ponens tm-239 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 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-239.          (A -> ((B -> (((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-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-70470.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-239, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70471
in-theory        70471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G)))
theorem-size     33
proof            (modus-ponens tm-210 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-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-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-70471.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G))), M:tm-210, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70472
in-theory        70472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     25
proof            (modus-ponens tm-183 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 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-183.          (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-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-70472.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-183, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70473
in-theory        70473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-157 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-70473.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-157, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70474
in-theory        70474
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     31
proof            (modus-ponens tm-147 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-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-70474.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-147, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70475
in-theory        70475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-134 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-70475.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-134, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70476
in-theory        70476
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     31
proof            (modus-ponens tm-125 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-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-70476.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-125, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70477
in-theory        70477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G)))
theorem-size     31
proof            (modus-ponens tm-113 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-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-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-70477.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G))), M:tm-113, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70478
in-theory        70478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     35
proof            (modus-ponens tm-105 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-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-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-70478.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-105, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70479
in-theory        70479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E)))
theorem-size     23
proof            (modus-ponens tm-95 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-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-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-70479.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E))), M:tm-95, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70480
in-theory        70480
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) or D)))
theorem-size     17
proof            (modus-ponens tm-84 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-70480.        ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) or D))), M:tm-84, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70481
in-theory        70481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     23
proof            (modus-ponens tm-83 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70481.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-83, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70482
in-theory        70482
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((C -> (B and C)) or D)))
theorem-size     21
proof            (modus-ponens tm-76 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-48.           (((A -> (B and 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-70482.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((C -> (B and C)) or D))), M:tm-76, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70483
in-theory        70483
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C))
theorem-size     25
proof            (modus-ponens tm-73 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
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-48.           (((A -> (B and 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-70483.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C)), M:tm-73, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70484
in-theory        70484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E)))
theorem-size     27
proof            (modus-ponens tm-69 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-48.           (((A -> (B and 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-70484.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E))), M:tm-69, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70485
in-theory        70485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     29
proof            (modus-ponens tm-54 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70485.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-54, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70486
in-theory        70486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((A -> (B and A)) or C))
theorem-size     21
proof            (modus-ponens tm-50 tm-813 ((A Am) (B (-> Bm (and Am Bm))) (C (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-48.           (((A -> (B and 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-70486.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((A -> (B and A)) or C)), M:tm-50, m:tm-813, u:((A Am) (B (-> Bm (and Am Bm))) (C (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70487
in-theory        70487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C))
theorem-size     17
proof            (modus-ponens tm-49 tm-813 ((A Am) (B (-> Bm (and Am Bm))) (C (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       105
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70487.        ((A or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C)), M:tm-49, m:tm-813, u:((A Am) (B (-> Bm (and Am Bm))) (C (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70488
in-theory        70488
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((C -> (B and C)) or D))
theorem-size     25
proof            (modus-ponens tm-47 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-48.           (((A -> (B and 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-70488.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((C -> (B and C)) or D)), M:tm-47, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70489
in-theory        70489
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or D))
theorem-size     25
proof            (modus-ponens tm-46 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
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-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-70489.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or D)), M:tm-46, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70490
in-theory        70490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E)))
theorem-size     21
proof            (modus-ponens tm-42 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-48.           (((A -> (B and 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-70490.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E))), M:tm-42, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70491
in-theory        70491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E)))
theorem-size     21
proof            (modus-ponens tm-32 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70491.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E))), M:tm-32, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70492
in-theory        70492
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((B -> (A and B)) or C)))
theorem-size     23
proof            (modus-ponens tm-24 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-70492.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((B -> (A and B)) or C))), M:tm-24, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70493
in-theory        70493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E)))
theorem-size     23
proof            (modus-ponens tm-23 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-70493.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E))), M:tm-23, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70494
in-theory        70494
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E)))
theorem-size     21
proof            (modus-ponens tm-22 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-48.           (((A -> (B and 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-70494.        (((A and B) -> B) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E))), M:tm-22, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70495
in-theory        70495
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E)))
theorem-size     21
proof            (modus-ponens tm-21 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-48.           (((A -> (B and 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-70495.        (((A and B) -> A) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E))), M:tm-21, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70496
in-theory        70496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     29
proof            (modus-ponens tm-20 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-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-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-70496.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-20, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70497
in-theory        70497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E)))
theorem-size     21
proof            (modus-ponens tm-19 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-48.           (((A -> (B and 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-70497.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((D -> (C and D)) or E))), M:tm-19, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70498
in-theory        70498
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not ((B -> (A and B)) or C))) -> (not (A or (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-9 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-9 tm-8 tm-5 tm-6)
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-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-70498.        (((A or (B -> (A and B))) -> (not ((B -> (A and B)) or C))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70499
in-theory        70499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) or C) -> D) -> (((B or (A -> (B and A))) or ((A -> (B and A)) or C)) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-813 ((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-70499.        ((((A -> (B and A)) or C) -> D) -> (((B or (A -> (B and A))) or ((A -> (B and A)) or C)) -> D)), M:tm-8, m:tm-813, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70500
in-theory        70500
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> ((C -> (B and C)) or D)))
theorem-size     17
proof            (modus-ponens tm-7 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-7 tm-8 tm-5 tm-6)
proof-size       79
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-48.           (((A -> (B and 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-70500.        (A or ((B or (C -> (B and C))) -> ((C -> (B and C)) or D))), M:tm-7, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70501
in-theory        70501
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       79
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70501.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) or D), M:tm-6, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70502
in-theory        70502
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> ((C -> (B and C)) or D)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-70502.        (A -> (((B or (C -> (B and C))) -> ((C -> (B and C)) or D)) and A)), M:tm-5, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70503
in-theory        70503
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> ((C -> (B and C)) or D)))
theorem-size     17
proof            (modus-ponens tm-1 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-1 tm-8 tm-5 tm-6)
proof-size       79
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-48.           (((A -> (B and 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-70503.        (A -> ((B or (C -> (B and C))) -> ((C -> (B and C)) or D))), M:tm-1, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70504
in-theory        70504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70504.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-808, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70505
in-theory        70505
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C or (B -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-798 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70505.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C or (B -> (A and B))))), M:tm-798, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70506
in-theory        70506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70506.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-757, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70507
in-theory        70507
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (C or (B -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-747 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-70507.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (C or (B -> (A and B))))), M:tm-747, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70508
in-theory        70508
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G or (F -> (E and F)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70508.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G or (F -> (E and F))))), M:tm-708, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70509
in-theory        70509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70509.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-665, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70510
in-theory        70510
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D or (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-623 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70510.        ((A or (B -> (A and B))) -> (C or (D or (B -> (A and B))))), M:tm-623, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70511
in-theory        70511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70511.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-622, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70512
in-theory        70512
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70512.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (E or D))), M:tm-609, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70513
in-theory        70513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70513.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-605, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70514
in-theory        70514
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (C or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-70514.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (C or (B -> (A and B)))))), M:tm-595, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70515
in-theory        70515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-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-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-70515.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-550, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70516
in-theory        70516
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-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-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-70516.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-540, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70517
in-theory        70517
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-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-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-70517.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-530, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70518
in-theory        70518
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-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-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-70518.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-520, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70519
in-theory        70519
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-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-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-70519.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-510, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70520
in-theory        70520
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-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-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-70520.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-500, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70521
in-theory        70521
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G or (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-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-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-70521.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G or (F -> (E and F))))), M:tm-490, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70522
in-theory        70522
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70522.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-480, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70523
in-theory        70523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or (B -> (A and B))) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70523.        ((A or (B -> (A and B))) -> ((C or (B -> (A and B))) or D)), M:tm-470, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70524
in-theory        70524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70524.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-469, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70525
in-theory        70525
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70525.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (D or E))), M:tm-456, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70526
in-theory        70526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-453.          (A -> ((B -> ((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-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-70526.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-453, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70527
in-theory        70527
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (C or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-70527.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (C or (B -> (A and B)))))), M:tm-443, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70528
in-theory        70528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-48.           (((A -> (B and 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-70528.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-409, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70529
in-theory        70529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-48.           (((A -> (B and 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-70529.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-400, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70530
in-theory        70530
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-48.           (((A -> (B and 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-70530.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-391, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70531
in-theory        70531
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-48.           (((A -> (B and 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-70531.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-382, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70532
in-theory        70532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G or (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-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-70532.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G or (F -> (E and F))))), M:tm-373, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70533
in-theory        70533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-48.           (((A -> (B and 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-70533.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-364, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70534
in-theory        70534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D or (B -> (A and B))) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-70534.        ((A or (B -> (A and B))) -> (C -> ((D or (B -> (A and B))) and C))), M:tm-355, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70535
in-theory        70535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-48.           (((A -> (B and 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-70535.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-354, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70536
in-theory        70536
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-70536.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70537
in-theory        70537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E or (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-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-70537.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E or (D -> (C and D))))), M:tm-338, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70538
in-theory        70538
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C or (B -> (A and B))))))
theorem-size     39
proof            (modus-ponens tm-328 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-70538.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C or (B -> (A and B)))))), M:tm-328, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70539
in-theory        70539
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (C or (B -> (A and B))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-70539.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (C or (B -> (A and B)))))), M:tm-327, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70540
in-theory        70540
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (C or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-70540.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (C or (B -> (A and B)))))), M:tm-326, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70541
in-theory        70541
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (C or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-70541.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (C or (B -> (A and B)))))), M:tm-325, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70542
in-theory        70542
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (C or (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-70542.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (C or (B -> (A and B)))))), M:tm-324, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70543
in-theory        70543
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (C or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-70543.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (C or (B -> (A and B)))))), M:tm-323, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70544
in-theory        70544
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-70544.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D and E) -> E)), M:tm-322, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70545
in-theory        70545
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-70545.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D and E) -> D)), M:tm-320, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70546
in-theory        70546
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-70546.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70547
in-theory        70547
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     31
proof            (modus-ponens tm-316 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-70547.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70548
in-theory        70548
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70548.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (E -> D))), M:tm-315, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70549
in-theory        70549
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (C or (B -> (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-313 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
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-48.           (((A -> (B and 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-70549.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (C or (B -> (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70550
in-theory        70550
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((C or (B -> (A and B))) -> D) -> (((A or (B -> (A and B))) or (C or (B -> (A and B)))) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-70550.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((C or (B -> (A and B))) -> D) -> (((A or (B -> (A and B))) or (C or (B -> (A and B)))) -> D))), M:tm-312, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70551
in-theory        70551
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D or ((A or (B -> (A and B))) -> (C or (B -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-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-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-70551.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D or ((A or (B -> (A and B))) -> (C or (B -> (A and B)))))), M:tm-311, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70552
in-theory        70552
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-70552.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) or D)), M:tm-310, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70553
in-theory        70553
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-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-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-70553.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and D))), M:tm-309, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70554
in-theory        70554
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> ((A or (B -> (A and B))) -> (C or (B -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-70554.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (D -> ((A or (B -> (A and B))) -> (C or (B -> (A and B)))))), M:tm-305, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70555
in-theory        70555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-70555.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-303, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70556
in-theory        70556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-270.          (A -> ((B -> (((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-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-70556.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-270, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70557
in-theory        70557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-239.          (A -> ((B -> (((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-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-70557.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-239, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70558
in-theory        70558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G or (F -> (E and F)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-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-70558.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G or (F -> (E and F))))), M:tm-210, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70559
in-theory        70559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-183.          (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-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-70559.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-183, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70560
in-theory        70560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-70560.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-157, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70561
in-theory        70561
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-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-70561.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-147, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70562
in-theory        70562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-70562.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-134, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70563
in-theory        70563
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-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-70563.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-125, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70564
in-theory        70564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G or (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-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-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-70564.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G or (F -> (E and F))))), M:tm-113, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70565
in-theory        70565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-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-70565.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-105, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70566
in-theory        70566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E or (D -> (C and D)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-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-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-70566.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E or (D -> (C and D))))), M:tm-95, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70567
in-theory        70567
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D or (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-84 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-70567.        ((A or (B -> (A and B))) -> (C -> (D or (B -> (A and B))))), M:tm-84, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70568
in-theory        70568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70568.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-83, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70569
in-theory        70569
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D or (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-48.           (((A -> (B and 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-70569.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D or (C -> (B and C))))), M:tm-76, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70570
in-theory        70570
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C or (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-73 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
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-48.           (((A -> (B and 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-70570.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C or (B -> (A and B)))), M:tm-73, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70571
in-theory        70571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E or (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-48.           (((A -> (B and 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-70571.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E or (D -> (C and D))))), M:tm-69, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70572
in-theory        70572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-70572.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-54, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70573
in-theory        70573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C or (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-50 tm-814 ((A Am) (B (-> Bm (and Am Bm))) (C (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-7 tm-5)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70573.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C or (A -> (B and A)))), M:tm-50, m:tm-814, u:((A Am) (B (-> Bm (and Am Bm))) (C (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70574
in-theory        70574
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (C or (B -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-49 tm-814 ((A Am) (B (-> Bm (and Am Bm))) (C (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       105
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-48.           (((A -> (B and 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-70574.        ((A or (A or (B -> (A and B)))) -> (C or (B -> (A and B)))), M:tm-49, m:tm-814, u:((A Am) (B (-> Bm (and Am Bm))) (C (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70575
in-theory        70575
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D or (C -> (B and C))))
theorem-size     25
proof            (modus-ponens tm-47 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-48.           (((A -> (B and 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-70575.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D or (C -> (B and C)))), M:tm-47, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70576
in-theory        70576
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D or (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-46 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
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-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-70576.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D or (B -> (A and B)))), M:tm-46, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70577
in-theory        70577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E or (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70577.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E or (D -> (C and D))))), M:tm-42, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70578
in-theory        70578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E or (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-48.           (((A -> (B and 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-70578.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E or (D -> (C and D))))), M:tm-32, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70579
in-theory        70579
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C or (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-24 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-70579.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C or (B -> (A and B))))), M:tm-24, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70580
in-theory        70580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E or (D -> (C and D)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-70580.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E or (D -> (C and D))))), M:tm-23, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70581
in-theory        70581
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (E or (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-48.           (((A -> (B and 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-70581.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (E or (D -> (C and D))))), M:tm-22, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70582
in-theory        70582
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (E or (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-48.           (((A -> (B and 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-70582.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (E or (D -> (C and D))))), M:tm-21, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70583
in-theory        70583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-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-70583.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-20, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70584
in-theory        70584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E or (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-48.           (((A -> (B and 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-70584.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E or (D -> (C and D))))), M:tm-19, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70585
in-theory        70585
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (C or (B -> (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-9 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-7)
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-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-70585.        (((A or (B -> (A and B))) -> (not (C or (B -> (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70586
in-theory        70586
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C and B))) -> D) -> (((C or (B -> (C and B))) or (A or (B -> (C and B)))) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-814 ((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-5 tm-7)
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-48.           (((A -> (B and 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-70586.        (((A or (B -> (C and B))) -> D) -> (((C or (B -> (C and B))) or (A or (B -> (C and B)))) -> D)), M:tm-8, m:tm-814, u:((A (or Am (-> Bm (and Am Bm)))) (B (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-70587
in-theory        70587
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (D or (C -> (B and C)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       79
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70587.        (A or ((B or (C -> (B and C))) -> (D or (C -> (B and C))))), M:tm-7, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70588
in-theory        70588
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-7)
proof-size       79
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-48.           (((A -> (B and 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-70588.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) or D), M:tm-6, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70589
in-theory        70589
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (D or (C -> (B and C)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-70589.        (A -> (((B or (C -> (B and C))) -> (D or (C -> (B and C)))) and A)), M:tm-5, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70590
in-theory        70590
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (D or (C -> (B and C)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-7)
proof-size       79
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-48.           (((A -> (B and 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-70590.        (A -> ((B or (C -> (B and C))) -> (D or (C -> (B and C))))), M:tm-1, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70591
in-theory        70591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-808 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70591.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-808, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70592
in-theory        70592
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))
theorem-size     53
proof            (modus-ponens tm-798 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70592.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))), M:tm-798, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70593
in-theory        70593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-757 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-70593.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-757, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70594
in-theory        70594
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))
theorem-size     53
proof            (modus-ponens tm-747 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70594.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))), M:tm-747, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70595
in-theory        70595
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-708 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-70595.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G)))), M:tm-708, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70596
in-theory        70596
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-665 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-70596.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-665, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70597
in-theory        70597
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (((A and B) -> D) -> ((B or (A and B)) -> D))))
theorem-size     23
proof            (modus-ponens tm-623 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
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-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-70597.        ((A or (B -> (A and B))) -> (C or (((A and B) -> D) -> ((B or (A and B)) -> D)))), M:tm-623, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70598
in-theory        70598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-622 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-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-70598.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-622, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70599
in-theory        70599
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-609 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70599.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (E or D))), M:tm-609, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70600
in-theory        70600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-605 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-70600.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-605, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70601
in-theory        70601
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70601.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-595, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70602
in-theory        70602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-550 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-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-70602.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-550, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70603
in-theory        70603
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-540 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-70603.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-540, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70604
in-theory        70604
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-530 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-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-70604.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-530, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70605
in-theory        70605
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-520 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-70605.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-520, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70606
in-theory        70606
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-510 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-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-70606.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-510, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70607
in-theory        70607
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-500 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-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-70607.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-500, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70608
in-theory        70608
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-490 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-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-70608.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G)))), M:tm-490, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70609
in-theory        70609
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-480 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-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-70609.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-480, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70610
in-theory        70610
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((A and B) -> C) -> ((B or (A and B)) -> C)) or D))
theorem-size     23
proof            (modus-ponens tm-470 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
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-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-70610.        ((A or (B -> (A and B))) -> ((((A and B) -> C) -> ((B or (A and B)) -> C)) or D)), M:tm-470, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70611
in-theory        70611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-469 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-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-70611.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-469, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70612
in-theory        70612
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-456 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70612.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (D or E))), M:tm-456, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70613
in-theory        70613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-453 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-70613.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-453, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70614
in-theory        70614
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70614.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-443, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70615
in-theory        70615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-409 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-70615.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-409, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70616
in-theory        70616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-400 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-70616.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-400, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70617
in-theory        70617
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-391 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-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-70617.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-391, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70618
in-theory        70618
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-382 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-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-70618.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-382, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70619
in-theory        70619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-373 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-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-70619.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G)))), M:tm-373, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70620
in-theory        70620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-364 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-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-70620.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-364, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70621
in-theory        70621
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((((A and B) -> D) -> ((B or (A and B)) -> D)) and C)))
theorem-size     25
proof            (modus-ponens tm-355 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-70621.        ((A or (B -> (A and B))) -> (C -> ((((A and B) -> D) -> ((B or (A and B)) -> D)) and C))), M:tm-355, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70622
in-theory        70622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-354 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-70622.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-354, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70623
in-theory        70623
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B or (A and B)) -> ((A or (B -> (A and B))) and (A and B))))
theorem-size     25
proof            (modus-ponens tm-349 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (and Am Bm)) (Cm (and (or Am (-> Bm (and Am Bm))) (and Am Bm))) (C (-> (or Bm (and Am Bm)) (and (or Am (-> Bm (and Am Bm))) (and Am Bm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-48.           (((A -> (B and 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-70623.        ((A or (B -> (A and B))) -> ((B or (A and B)) -> ((A or (B -> (A and B))) and (A and B)))), M:tm-349, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (and Am Bm)) (Cm (and (or Am (-> Bm (and Am Bm))) (and Am Bm))) (C (-> (or Bm (and Am Bm)) (and (or Am (-> Bm (and Am Bm))) (and Am Bm)))))
================================================================
tm-name          tm-70624
in-theory        70624
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-341 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-70624.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70625
in-theory        70625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E))))
theorem-size     31
proof            (modus-ponens tm-338 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-70625.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E)))), M:tm-338, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70626
in-theory        70626
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     51
proof            (modus-ponens tm-328 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and 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-328.          ((A -> 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-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-70626.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-328, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70627
in-theory        70627
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70627.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-327, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70628
in-theory        70628
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70628.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-326, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70629
in-theory        70629
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70629.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-325, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70630
in-theory        70630
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-70630.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-324, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70631
in-theory        70631
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70631.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-323, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70632
in-theory        70632
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-322 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-70632.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70633
in-theory        70633
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-320 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-70633.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70634
in-theory        70634
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-318 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-70634.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70635
in-theory        70635
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-316 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-70635.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70636
in-theory        70636
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-315 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70636.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70637
in-theory        70637
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((A or (B -> (A and B))) -> (not (((A and B) -> C) -> ((B or (A and B)) -> C)))) -> (not (A or (B -> (A and B))))))
theorem-size     53
proof            (modus-ponens tm-313 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
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-48.           (((A -> (B and 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-70637.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((A or (B -> (A and B))) -> (not (((A and B) -> C) -> ((B or (A and B)) -> C)))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70638
in-theory        70638
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((((A and B) -> C) -> ((B or (A and B)) -> C)) -> D) -> (((A or (B -> (A and B))) or (((A and B) -> C) -> ((B or (A and B)) -> C))) -> D)))
theorem-size     61
proof            (modus-ponens tm-312 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70638.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((((A and B) -> C) -> ((B or (A and B)) -> C)) -> D) -> (((A or (B -> (A and B))) or (((A and B) -> C) -> ((B or (A and B)) -> C))) -> D))), M:tm-312, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70639
in-theory        70639
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D or ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70639.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D or ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-311, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70640
in-theory        70640
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) or D))
theorem-size     45
proof            (modus-ponens tm-310 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70640.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) or D)), M:tm-310, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70641
in-theory        70641
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and D)))
theorem-size     47
proof            (modus-ponens tm-309 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70641.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and D))), M:tm-309, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70642
in-theory        70642
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((A or (B -> (A and B))) -> ((A and B) -> C)) -> ((A or (B -> (A and B))) -> ((B or (A and B)) -> C))))
theorem-size     51
proof            (modus-ponens tm-306 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Am Bm) Cm)) (C (-> (or Bm (and Am Bm)) Cm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-70642.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((A or (B -> (A and B))) -> ((A and B) -> C)) -> ((A or (B -> (A and B))) -> ((B or (A and B)) -> C)))), M:tm-306, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Am Bm) Cm)) (C (-> (or Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70643
in-theory        70643
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-48.           (((A -> (B and 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-70643.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (D -> ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))), M:tm-305, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70644
in-theory        70644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-303 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-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-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-70644.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-303, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70645
in-theory        70645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-270 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-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-70645.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-270, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70646
in-theory        70646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-239 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-3 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-239.          (A -> ((B -> (((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-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-70646.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-239, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70647
in-theory        70647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G))))
theorem-size     39
proof            (modus-ponens tm-210 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-70647.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G)))), M:tm-210, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70648
in-theory        70648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-183 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-70648.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-183, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70649
in-theory        70649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-157 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-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-70649.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-157, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70650
in-theory        70650
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     37
proof            (modus-ponens tm-147 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-70650.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-147, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70651
in-theory        70651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-134 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-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-70651.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-134, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70652
in-theory        70652
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     37
proof            (modus-ponens tm-125 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-70652.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-125, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70653
in-theory        70653
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((A and B) -> C) -> (B or (A and B))) -> (((A and B) -> C) -> C)))
theorem-size     27
proof            (modus-ponens tm-114 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Am Bm) Cm)) (C (or Bm (and Am Bm))) (D Cm)))
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-14.           (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-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-70653.        ((A or (B -> (A and B))) -> ((((A and B) -> C) -> (B or (A and B))) -> (((A and B) -> C) -> C))), M:tm-114, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Am Bm) Cm)) (C (or Bm (and Am Bm))) (D Cm))
================================================================
tm-name          tm-70654
in-theory        70654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-113 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-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-70654.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G)))), M:tm-113, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70655
in-theory        70655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     41
proof            (modus-ponens tm-105 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-70655.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-105, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70656
in-theory        70656
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B or (A and B)) -> (A or (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-98 tm-815 ((Cm (or Am (-> Bm (and Am Bm)))) (B (and Am Bm)) (A (or Am (-> Bm (and Am Bm)))) (C (-> (or Bm (and Am Bm)) (or Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 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-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-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-70656.        ((A or (B -> (A and B))) -> ((B or (A and B)) -> (A or (B -> (A and B))))), M:tm-98, m:tm-815, u:((Cm (or Am (-> Bm (and Am Bm)))) (B (and Am Bm)) (A (or Am (-> Bm (and Am Bm)))) (C (-> (or Bm (and Am Bm)) (or Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70657
in-theory        70657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E))))
theorem-size     29
proof            (modus-ponens tm-95 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-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-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-70657.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E)))), M:tm-95, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70658
in-theory        70658
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((A and B) -> D) -> ((B or (A and B)) -> D))))
theorem-size     23
proof            (modus-ponens tm-84 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-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-70658.        ((A or (B -> (A and B))) -> (C -> (((A and B) -> D) -> ((B or (A and B)) -> D)))), M:tm-84, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70659
in-theory        70659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-83 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-70659.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-83, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70660
in-theory        70660
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((B and C) -> D) -> ((C or (B and C)) -> D))))
theorem-size     27
proof            (modus-ponens tm-76 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-8)
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-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-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-70660.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((B and C) -> D) -> ((C or (B and C)) -> D)))), M:tm-76, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70661
in-theory        70661
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-73 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70661.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))), M:tm-73, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70662
in-theory        70662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E))))
theorem-size     33
proof            (modus-ponens tm-69 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-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-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-70662.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E)))), M:tm-69, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70663
in-theory        70663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-54 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-70663.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-54, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70664
in-theory        70664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((B and A) -> C) -> ((A or (B and A)) -> C)))
theorem-size     27
proof            (modus-ponens tm-50 tm-815 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       129
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-48.           (((A -> (B and 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-70664.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((B and A) -> C) -> ((A or (B and A)) -> C))), M:tm-50, m:tm-815, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70665
in-theory        70665
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-49 tm-815 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       125
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-48.           (((A -> (B and 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-70665.        ((A or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))), M:tm-49, m:tm-815, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70666
in-theory        70666
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((B and C) -> D) -> ((C or (B and C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-47 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70666.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((B and C) -> D) -> ((C or (B and C)) -> D))), M:tm-47, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70667
in-theory        70667
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((A and B) -> D) -> ((B or (A and B)) -> D)))
theorem-size     31
proof            (modus-ponens tm-46 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70667.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((A and B) -> D) -> ((B or (A and B)) -> D))), M:tm-46, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70668
in-theory        70668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-42 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-70668.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E)))), M:tm-42, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70669
in-theory        70669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-32 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-70669.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E)))), M:tm-32, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70670
in-theory        70670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((A and B) -> C) -> ((B or (A and B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-24 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70670.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((A and B) -> C) -> ((B or (A and B)) -> C)))), M:tm-24, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70671
in-theory        70671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E))))
theorem-size     29
proof            (modus-ponens tm-23 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-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-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-70671.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E)))), M:tm-23, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70672
in-theory        70672
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-22 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-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-70672.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E)))), M:tm-22, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70673
in-theory        70673
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-21 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-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-70673.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E)))), M:tm-21, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70674
in-theory        70674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-20 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and 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-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-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-70674.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-20, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70675
in-theory        70675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-19 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-70675.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((C and D) -> E) -> ((D or (C and D)) -> E)))), M:tm-19, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70676
in-theory        70676
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (((A and B) -> C) -> ((B or (A and B)) -> C)))) -> (not (A or (B -> (A and B)))))
theorem-size     31
proof            (modus-ponens tm-9 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-70676.        (((A or (B -> (A and B))) -> (not (((A and B) -> C) -> ((B or (A and B)) -> C)))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70677
in-theory        70677
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> C) -> ((B or (A and B)) -> C)) -> D) -> (((A or (B -> (A and B))) or (((A and B) -> C) -> ((B or (A and B)) -> C))) -> D))
theorem-size     39
proof            (modus-ponens tm-8 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-8 tm-5)
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-48.           (((A -> (B and 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-70677.        (((((A and B) -> C) -> ((B or (A and B)) -> C)) -> D) -> (((A or (B -> (A and B))) or (((A and B) -> C) -> ((B or (A and B)) -> C))) -> D)), M:tm-8, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-70678
in-theory        70678
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (((B and C) -> D) -> ((C or (B and C)) -> D))))
theorem-size     23
proof            (modus-ponens tm-7 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       99
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-48.           (((A -> (B and 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-70678.        (A or ((B or (C -> (B and C))) -> (((B and C) -> D) -> ((C or (B and C)) -> D)))), M:tm-7, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70679
in-theory        70679
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) or D)
theorem-size     23
proof            (modus-ponens tm-6 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       99
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-48.           (((A -> (B and 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-70679.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) or D), M:tm-6, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70680
in-theory        70680
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (((B and C) -> D) -> ((C or (B and C)) -> D))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
proof-size       103
proof-steps      7
----------------------------------------------------------------
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-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-70680.        (A -> (((B or (C -> (B and C))) -> (((B and C) -> D) -> ((C or (B and C)) -> D))) and A)), M:tm-5, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70681
in-theory        70681
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((A and B) -> C)) -> ((A or (B -> (A and B))) -> ((B or (A and B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-2 tm-815 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Am Bm) Cm)) (C (-> (or Bm (and Am Bm)) Cm))))
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-48.           (((A -> (B and 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-70681.        (((A or (B -> (A and B))) -> ((A and B) -> C)) -> ((A or (B -> (A and B))) -> ((B or (A and B)) -> C))), M:tm-2, m:tm-815, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Am Bm) Cm)) (C (-> (or Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-70682
in-theory        70682
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (((B and C) -> D) -> ((C or (B and C)) -> D))))
theorem-size     23
proof            (modus-ponens tm-1 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       99
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-48.           (((A -> (B and 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-70682.        (A -> ((B or (C -> (B and C))) -> (((B and C) -> D) -> ((C or (B and C)) -> D)))), M:tm-1, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-70683
in-theory        70683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-808 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9)
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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70683.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-808, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70684
in-theory        70684
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((C and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B))))
theorem-size     45
proof            (modus-ponens tm-798 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70684.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((C and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B)))), M:tm-798, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70685
in-theory        70685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-757 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
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-48.           (((A -> (B and 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-70685.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-757, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70686
in-theory        70686
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B))))
theorem-size     45
proof            (modus-ponens tm-747 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-70686.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B)))), M:tm-747, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70687
in-theory        70687
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F))))
theorem-size     43
proof            (modus-ponens tm-708 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
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-48.           (((A -> (B and 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-70687.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F)))), M:tm-708, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70688
in-theory        70688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-665 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
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-48.           (((A -> (B and 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-70688.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-665, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70689
in-theory        70689
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or ((B -> (not (A and B))) -> (not B))))
theorem-size     19
proof            (modus-ponens tm-623 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 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-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-70689.        ((A or (B -> (A and B))) -> (C or ((B -> (not (A and B))) -> (not B)))), M:tm-623, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70690
in-theory        70690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-622 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-9)
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-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-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-70690.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-622, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70691
in-theory        70691
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (D or C)))
theorem-size     23
proof            (modus-ponens tm-609 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-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-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-70691.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (D or C))), M:tm-609, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70692
in-theory        70692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-605 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
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-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-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-70692.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-605, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70693
in-theory        70693
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (D or C)) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-70693.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (D or C)) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))))), M:tm-595, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70694
in-theory        70694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-550 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-9)
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-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-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-70694.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-550, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70695
in-theory        70695
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-540 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
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-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-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-70695.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-540, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70696
in-theory        70696
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-530 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-9)
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-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-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-70696.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-530, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70697
in-theory        70697
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-520 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
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-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-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-70697.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-520, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70698
in-theory        70698
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-510 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-9)
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-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-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-70698.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-510, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70699
in-theory        70699
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-500 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-9)
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-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-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-70699.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-500, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70700
in-theory        70700
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-490 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-9)
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-48.           (((A -> (B and 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-70700.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F)))), M:tm-490, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70701
in-theory        70701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-480 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-9)
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-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-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-70701.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-480, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70702
in-theory        70702
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((B -> (not (A and B))) -> (not B)) or C))
theorem-size     19
proof            (modus-ponens tm-470 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 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-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-70702.        ((A or (B -> (A and B))) -> (((B -> (not (A and B))) -> (not B)) or C)), M:tm-470, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70703
in-theory        70703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-469 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-9)
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-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-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-70703.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-469, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70704
in-theory        70704
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (C or D)))
theorem-size     23
proof            (modus-ponens tm-456 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-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-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-70704.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (C or D))), M:tm-456, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70705
in-theory        70705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-453 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
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-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-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-70705.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-453, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70706
in-theory        70706
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (C or D)) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-70706.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (C or D)) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))))), M:tm-443, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70707
in-theory        70707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-409 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
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-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-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-70707.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-409, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70708
in-theory        70708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-400 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
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-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-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-70708.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-400, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70709
in-theory        70709
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-391 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-9)
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-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-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-70709.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-391, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70710
in-theory        70710
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-382 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-9)
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-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-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-70710.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-382, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70711
in-theory        70711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-373 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-9)
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-48.           (((A -> (B and 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-70711.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F)))), M:tm-373, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70712
in-theory        70712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-364 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-9)
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-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-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-70712.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-364, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70713
in-theory        70713
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((B -> (not (A and B))) -> (not B)) and C)))
theorem-size     21
proof            (modus-ponens tm-355 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-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-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-70713.        ((A or (B -> (A and B))) -> (C -> (((B -> (not (A and B))) -> (not B)) and C))), M:tm-355, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70714
in-theory        70714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-354 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
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-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-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-70714.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-354, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70715
in-theory        70715
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (D -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-341 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-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-70715.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70716
in-theory        70716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-338 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-70716.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D)))), M:tm-338, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70717
in-theory        70717
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((B -> (not (A and B))) -> (not B)))))
theorem-size     43
proof            (modus-ponens tm-328 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-70717.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((B -> (not (A and B))) -> (not B))))), M:tm-328, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70718
in-theory        70718
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (D -> (C and D))) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-70718.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (D -> (C and D))) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))))), M:tm-327, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70719
in-theory        70719
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((C and D) -> D) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-70719.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((C and D) -> D) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))))), M:tm-326, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70720
in-theory        70720
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((C and D) -> C) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-70720.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((C and D) -> C) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))))), M:tm-325, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70721
in-theory        70721
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-70721.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))))), M:tm-324, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70722
in-theory        70722
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (D -> C)) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-70722.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (D -> C)) and ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))))), M:tm-323, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70723
in-theory        70723
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C and D) -> D))
theorem-size     23
proof            (modus-ponens tm-322 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-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-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-70723.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C and D) -> D)), M:tm-322, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70724
in-theory        70724
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C and D) -> C))
theorem-size     23
proof            (modus-ponens tm-320 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-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-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-70724.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C and D) -> C)), M:tm-320, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70725
in-theory        70725
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-318 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-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-70725.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70726
in-theory        70726
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-316 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-70726.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70727
in-theory        70727
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (D -> C)))
theorem-size     23
proof            (modus-ponens tm-315 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-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-70727.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (D -> C))), M:tm-315, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70728
in-theory        70728
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((A or (B -> (A and B))) -> (not ((B -> (not (A and B))) -> (not B)))) -> (not (A or (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-313 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70728.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((A or (B -> (A and B))) -> (not ((B -> (not (A and B))) -> (not B)))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70729
in-theory        70729
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((((B -> (not (A and B))) -> (not B)) -> C) -> (((A or (B -> (A and B))) or ((B -> (not (A and B))) -> (not B))) -> C)))
theorem-size     49
proof            (modus-ponens tm-312 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-70729.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((((B -> (not (A and B))) -> (not B)) -> C) -> (((A or (B -> (A and B))) or ((B -> (not (A and B))) -> (not B))) -> C))), M:tm-312, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70730
in-theory        70730
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C or ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-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-70730.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C or ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))))), M:tm-311, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70731
in-theory        70731
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) or C))
theorem-size     37
proof            (modus-ponens tm-310 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-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-70731.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) or C)), M:tm-310, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70732
in-theory        70732
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and C)))
theorem-size     39
proof            (modus-ponens tm-309 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-70732.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and C))), M:tm-309, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70733
in-theory        70733
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((A or (B -> (A and B))) -> (B -> (not (A and B)))) -> ((A or (B -> (A and B))) -> (not B))))
theorem-size     43
proof            (modus-ponens tm-306 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (not (and Am Bm)))) (C (not Bm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-70733.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((A or (B -> (A and B))) -> (B -> (not (A and B)))) -> ((A or (B -> (A and B))) -> (not B)))), M:tm-306, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (not (and Am Bm)))) (C (not Bm)))
================================================================
tm-name          tm-70734
in-theory        70734
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-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-70734.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (C -> ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))))), M:tm-305, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70735
in-theory        70735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-303 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-9)
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-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-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-70735.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-303, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70736
in-theory        70736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-270 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-9)
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-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-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-70736.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-270, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70737
in-theory        70737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-239 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-9)
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-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-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-70737.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-239, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70738
in-theory        70738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F))))
theorem-size     35
proof            (modus-ponens tm-210 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-70738.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F)))), M:tm-210, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70739
in-theory        70739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-183 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
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-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-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-70739.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-183, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70740
in-theory        70740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-157 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-9)
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-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-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-70740.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-157, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70741
in-theory        70741
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-147 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-70741.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-147, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70742
in-theory        70742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-134 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-9)
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-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-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-70742.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-134, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70743
in-theory        70743
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-125 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-70743.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-125, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70744
in-theory        70744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-113 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-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-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-70744.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F)))), M:tm-113, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70745
in-theory        70745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     37
proof            (modus-ponens tm-105 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-70745.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-105, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70746
in-theory        70746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-95 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-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-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-70746.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D)))), M:tm-95, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70747
in-theory        70747
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((B -> (not (A and B))) -> (not B))))
theorem-size     19
proof            (modus-ponens tm-84 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-70747.        ((A or (B -> (A and B))) -> (C -> ((B -> (not (A and B))) -> (not B)))), M:tm-84, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70748
in-theory        70748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-83 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
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-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-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-70748.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-83, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70749
in-theory        70749
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((C -> (not (B and C))) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-76 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-9)
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-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-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-70749.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((C -> (not (B and C))) -> (not C)))), M:tm-76, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70750
in-theory        70750
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B)))
theorem-size     27
proof            (modus-ponens tm-73 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-8 tm-10 tm-5 tm-9)
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-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-70750.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B))), M:tm-73, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70751
in-theory        70751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-69 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-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-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-70751.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D)))), M:tm-69, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70752
in-theory        70752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-54 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-70752.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-54, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70753
in-theory        70753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((A -> (not (B and A))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-50 tm-816 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-8 tm-7 tm-5 tm-9)
proof-size       119
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-48.           (((A -> (B and 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-70753.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((A -> (not (B and A))) -> (not A))), M:tm-50, m:tm-816, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70754
in-theory        70754
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-816 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-9)
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-48.           (((A -> (B and 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-70754.        ((A or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B))), M:tm-49, m:tm-816, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70755
in-theory        70755
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((C -> (not (B and C))) -> (not C)))
theorem-size     27
proof            (modus-ponens tm-47 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-8 tm-4 tm-5 tm-9)
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-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-70755.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((C -> (not (B and C))) -> (not C))), M:tm-47, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70756
in-theory        70756
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B)))
theorem-size     27
proof            (modus-ponens tm-46 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-8 tm-3 tm-5 tm-9)
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-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-70756.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B))), M:tm-46, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70757
in-theory        70757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-42 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
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-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-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-70757.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D)))), M:tm-42, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70758
in-theory        70758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-32 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
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-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-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-70758.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D)))), M:tm-32, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70759
in-theory        70759
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((B -> (not (A and B))) -> (not B))))
theorem-size     25
proof            (modus-ponens tm-24 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-70759.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((B -> (not (A and B))) -> (not B)))), M:tm-24, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70760
in-theory        70760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-23 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 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-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-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-70760.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D)))), M:tm-23, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70761
in-theory        70761
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-22 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-9)
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-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-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-70761.        (((A and B) -> B) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D)))), M:tm-22, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70762
in-theory        70762
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-21 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-9)
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-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-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-70762.        (((A and B) -> A) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D)))), M:tm-21, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70763
in-theory        70763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-20 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
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-48.           (((A -> (B and 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-70763.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-20, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70764
in-theory        70764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-19 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
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-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-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-70764.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((D -> (not (C and D))) -> (not D)))), M:tm-19, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70765
in-theory        70765
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not ((B -> (not (A and B))) -> (not B)))) -> (not (A or (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-9 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-9 tm-8 tm-5)
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-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-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-70765.        (((A or (B -> (A and B))) -> (not ((B -> (not (A and B))) -> (not B)))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70766
in-theory        70766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (B and A))) -> (not A)) -> C) -> (((B or (A -> (B and A))) or ((A -> (not (B and A))) -> (not A))) -> C))
theorem-size     31
proof            (modus-ponens tm-8 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       109
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-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-70766.        ((((A -> (not (B and A))) -> (not A)) -> C) -> (((B or (A -> (B and A))) or ((A -> (not (B and A))) -> (not A))) -> C)), M:tm-8, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-70767
in-theory        70767
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> ((C -> (not (B and C))) -> (not C))))
theorem-size     19
proof            (modus-ponens tm-7 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-7 tm-8 tm-5 tm-9)
proof-size       89
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-48.           (((A -> (B and 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-70767.        (A or ((B or (C -> (B and C))) -> ((C -> (not (B and C))) -> (not C)))), M:tm-7, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70768
in-theory        70768
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) or C)
theorem-size     19
proof            (modus-ponens tm-6 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-6 tm-8 tm-5 tm-9)
proof-size       89
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-48.           (((A -> (B and 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-70768.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) or C), M:tm-6, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70769
in-theory        70769
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> ((C -> (not (B and C))) -> (not C))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-70769.        (A -> (((B or (C -> (B and C))) -> ((C -> (not (B and C))) -> (not C))) and A)), M:tm-5, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70770
in-theory        70770
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (not (A and B)))) -> ((A or (B -> (A and B))) -> (not B)))
theorem-size     25
proof            (modus-ponens tm-2 tm-816 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (not (and Am Bm)))) (C (not Bm))))
axioms-used      (tm-2 tm-8 tm-5 tm-9)
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-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-70770.        (((A or (B -> (A and B))) -> (B -> (not (A and B)))) -> ((A or (B -> (A and B))) -> (not B))), M:tm-2, m:tm-816, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (not (and Am Bm)))) (C (not Bm)))
================================================================
tm-name          tm-70771
in-theory        70771
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> ((C -> (not (B and C))) -> (not C))))
theorem-size     19
proof            (modus-ponens tm-1 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-1 tm-8 tm-5 tm-9)
proof-size       89
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-48.           (((A -> (B and 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-70771.        (A -> ((B or (C -> (B and C))) -> ((C -> (not (B and C))) -> (not C)))), M:tm-1, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-70772
in-theory        70772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70772.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-808, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70773
in-theory        70773
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (D -> C))))
theorem-size     37
proof            (modus-ponens tm-798 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70773.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (D -> C)))), M:tm-798, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70774
in-theory        70774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> 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-48.           (((A -> (B and 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-70774.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-757, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70775
in-theory        70775
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (C -> (D -> C))))
theorem-size     37
proof            (modus-ponens tm-747 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-70775.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (C -> (D -> C)))), M:tm-747, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70776
in-theory        70776
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> 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-48.           (((A -> (B and 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-70776.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H -> G)))), M:tm-708, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70777
in-theory        70777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> 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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70777.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-665, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70778
in-theory        70778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70778.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-622, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70779
in-theory        70779
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D or (A or (B -> (A and B))))))
theorem-size     19
proof            (modus-ponens tm-617 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (-> Dm (or B (or Am (-> Bm (and Am Bm))))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (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-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-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-70779.        ((A or (B -> (A and B))) -> (C -> (D or (A or (B -> (A and B)))))), M:tm-617, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (-> Dm (or B (or Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-70780
in-theory        70780
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70780.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70781
in-theory        70781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-48.           (((A -> (B and 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-70781.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-605, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70782
in-theory        70782
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and 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-70782.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (C -> (D -> C))))), M:tm-595, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70783
in-theory        70783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-48.           (((A -> (B and 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-70783.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-550, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70784
in-theory        70784
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-48.           (((A -> (B and 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-70784.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-540, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70785
in-theory        70785
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-48.           (((A -> (B and 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-70785.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-530, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70786
in-theory        70786
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-48.           (((A -> (B and 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-70786.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-520, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70787
in-theory        70787
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-48.           (((A -> (B and 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-70787.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-510, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70788
in-theory        70788
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-48.           (((A -> (B and 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-70788.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-500, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70789
in-theory        70789
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-48.           (((A -> (B and 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-70789.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> G)))), M:tm-490, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70790
in-theory        70790
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70790.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-480, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70791
in-theory        70791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70791.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-469, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70792
in-theory        70792
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((A or (B -> (A and B))) or D)))
theorem-size     19
proof            (modus-ponens tm-464 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (-> Dm (or (or Am (-> Bm (and Am Bm))) B)))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70792.        ((A or (B -> (A and B))) -> (C -> ((A or (B -> (A and B))) or D))), M:tm-464, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (-> Dm (or (or Am (-> Bm (and Am Bm))) B))))
================================================================
tm-name          tm-70793
in-theory        70793
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70793.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70794
in-theory        70794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-48.           (((A -> (B and 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-70794.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-453, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70795
in-theory        70795
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and 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-70795.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (C -> (D -> C))))), M:tm-443, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70796
in-theory        70796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-48.           (((A -> (B and 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-70796.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-409, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70797
in-theory        70797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-48.           (((A -> (B and 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-70797.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-400, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70798
in-theory        70798
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-48.           (((A -> (B and 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-70798.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-391, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70799
in-theory        70799
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-48.           (((A -> (B and 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-70799.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-382, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70800
in-theory        70800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-48.           (((A -> (B and 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-70800.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H -> G)))), M:tm-373, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70801
in-theory        70801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70801.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-364, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70802
in-theory        70802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70802.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-354, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70803
in-theory        70803
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> ((A or (B -> (A and B))) and D))))
theorem-size     21
proof            (modus-ponens tm-349 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (-> Dm (-> B (and (or Am (-> Bm (and Am Bm))) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       167
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70803.        ((A or (B -> (A and B))) -> (C -> (D -> ((A or (B -> (A and B))) and D)))), M:tm-349, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (-> Dm (-> B (and (or Am (-> Bm (and Am Bm))) B)))))
================================================================
tm-name          tm-70804
in-theory        70804
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-70804.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70805
in-theory        70805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-48.           (((A -> (B and 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-70805.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F -> E)))), M:tm-338, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70806
in-theory        70806
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     35
proof            (modus-ponens tm-328 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm 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-328.          ((A -> 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-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-70806.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D -> C))))), M:tm-328, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70807
in-theory        70807
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (C -> (D -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and 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-70807.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (C -> (D -> C))))), M:tm-327, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70808
in-theory        70808
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and 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-70808.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (C -> (D -> C))))), M:tm-326, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70809
in-theory        70809
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and 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-70809.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (C -> (D -> C))))), M:tm-325, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70810
in-theory        70810
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (C -> (D -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-70810.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (C -> (D -> C))))), M:tm-324, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70811
in-theory        70811
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70811.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (C -> (D -> C))))), M:tm-323, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70812
in-theory        70812
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70812.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70813
in-theory        70813
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70813.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70814
in-theory        70814
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-70814.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70815
in-theory        70815
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-316 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-70815.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70816
in-theory        70816
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70816.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70817
in-theory        70817
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((A or (B -> (A and B))) -> (not (C -> (D -> C)))) -> (not (A or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-313 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-70817.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((A or (B -> (A and B))) -> (not (C -> (D -> C)))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70818
in-theory        70818
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> (((A or (B -> (A and B))) or (C -> (D -> C))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm 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-48.           (((A -> (B and 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-70818.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> (((A or (B -> (A and B))) or (C -> (D -> C))) -> E))), M:tm-312, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70819
in-theory        70819
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E or ((A or (B -> (A and B))) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and 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-70819.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E or ((A or (B -> (A and B))) -> (C -> (D -> C))))), M:tm-311, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70820
in-theory        70820
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((A or (B -> (A and B))) -> (C -> (D -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm 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-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-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-70820.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((A or (B -> (A and B))) -> (C -> (D -> C))) or E)), M:tm-310, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70821
in-theory        70821
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (((A or (B -> (A and B))) -> (C -> (D -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and 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-70821.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> (((A or (B -> (A and B))) -> (C -> (D -> C))) and E))), M:tm-309, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70822
in-theory        70822
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D -> C))))
theorem-size     35
proof            (modus-ponens tm-306 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Dm 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-70822.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D -> C)))), M:tm-306, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-70823
in-theory        70823
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> ((A or (B -> (A and B))) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm 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-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-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-70823.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (E -> ((A or (B -> (A and B))) -> (C -> (D -> C))))), M:tm-305, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70824
in-theory        70824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-70824.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-303, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70825
in-theory        70825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-48.           (((A -> (B and 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-70825.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-270, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70826
in-theory        70826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 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-48.           (((A -> (B and 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-70826.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-239, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70827
in-theory        70827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-48.           (((A -> (B and 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-70827.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (H -> G)))), M:tm-210, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70828
in-theory        70828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70828.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-183, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70829
in-theory        70829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70829.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-157, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70830
in-theory        70830
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and 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-70830.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-147, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70831
in-theory        70831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70831.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-134, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70832
in-theory        70832
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-48.           (((A -> (B and 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-70832.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-125, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70833
in-theory        70833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70833.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> G)))), M:tm-113, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70834
in-theory        70834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-70834.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-105, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70835
in-theory        70835
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (A or (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-99 tm-817 ((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (-> Dm (or Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-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-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-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-70835.        ((A or (B -> (A and B))) -> (C -> (A or (B -> (A and B))))), M:tm-99, m:tm-817, u:((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (-> Dm (or Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-70836
in-theory        70836
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> (A or (B -> (A and B))))))
theorem-size     19
proof            (modus-ponens tm-98 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (-> Dm (-> B (or Am (-> Bm (and Am Bm))))))))
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-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-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-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-70836.        ((A or (B -> (A and B))) -> (C -> (D -> (A or (B -> (A and B)))))), M:tm-98, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (-> Dm (-> B (or Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-70837
in-theory        70837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70837.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (F -> E)))), M:tm-95, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70838
in-theory        70838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70838.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-83, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70839
in-theory        70839
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 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-48.           (((A -> (B and 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-70839.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (E -> D)))), M:tm-76, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70840
in-theory        70840
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (D -> C)))
theorem-size     23
proof            (modus-ponens tm-73 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
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-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-70840.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (D -> C))), M:tm-73, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70841
in-theory        70841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 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-48.           (((A -> (B and 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-70841.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (F -> E)))), M:tm-69, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70842
in-theory        70842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> 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-48.           (((A -> (B and 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-70842.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-54, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70843
in-theory        70843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-50 tm-817 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
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-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-70843.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (D -> C))), M:tm-50, m:tm-817, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70844
in-theory        70844
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-817 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       113
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-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-70844.        ((A or (A or (B -> (A and B)))) -> (C -> (D -> C))), M:tm-49, m:tm-817, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70845
in-theory        70845
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-47 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
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-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-70845.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (E -> D))), M:tm-47, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70846
in-theory        70846
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-46 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
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-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-70846.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (E -> D))), M:tm-46, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70847
in-theory        70847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm 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-42.           (A -> ((B -> (C or B)) and A)), 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-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-70847.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (F -> E)))), M:tm-42, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70848
in-theory        70848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm 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-32.           (A -> ((B -> (B or C)) and A)), 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-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-70848.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (F -> E)))), M:tm-32, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70849
in-theory        70849
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D -> C))))
theorem-size     21
proof            (modus-ponens tm-24 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
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-48.           (((A -> (B and 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-70849.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D -> C)))), M:tm-24, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70850
in-theory        70850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-70850.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F -> E)))), M:tm-23, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70851
in-theory        70851
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-48.           (((A -> (B and 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-70851.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (F -> E)))), M:tm-22, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70852
in-theory        70852
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 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-48.           (((A -> (B and 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-70852.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (F -> E)))), M:tm-21, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70853
in-theory        70853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-70853.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-20, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70854
in-theory        70854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm 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-19.           (A -> ((B -> (C -> B)) and 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-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-70854.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (F -> E)))), M:tm-19, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70855
in-theory        70855
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (C -> (D -> C)))) -> (not (A or (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-9 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-5 tm-1)
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-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-70855.        (((A or (B -> (A and B))) -> (not (C -> (D -> C)))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70856
in-theory        70856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (((D or (E -> (D and E))) or (A -> (B -> A))) -> C))
theorem-size     23
proof            (modus-ponens tm-8 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm 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-48.           (((A -> (B and 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-70856.        (((A -> (B -> A)) -> C) -> (((D or (E -> (D and E))) or (A -> (B -> A))) -> C)), M:tm-8, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-70857
in-theory        70857
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-8 tm-5 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-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-70857.        (A or ((B or (C -> (B and C))) -> (D -> (E -> D)))), M:tm-7, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70858
in-theory        70858
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-5 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-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-70858.        (((A or (B -> (A and B))) -> (C -> (D -> C))) or E), M:tm-6, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70859
in-theory        70859
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (D -> (E -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-817 ((A (-> (or Am (-> Bm (and 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-48.           (((A -> (B and 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-70859.        (A -> (((B or (C -> (B and C))) -> (D -> (E -> D))) and A)), M:tm-5, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70860
in-theory        70860
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D -> C)))
theorem-size     21
proof            (modus-ponens tm-2 tm-817 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-8 tm-5 tm-1)
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-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-70860.        (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D -> C))), M:tm-2, m:tm-817, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-70861
in-theory        70861
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
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-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-70861.        (A -> ((B or (C -> (B and C))) -> (D -> (E -> D)))), M:tm-1, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-70862
in-theory        70862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-808 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70862.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-808, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70863
in-theory        70863
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (((C and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (B -> B)))
theorem-size     33
proof            (modus-ponens tm-798 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-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-70863.        (((A or (B -> (A and B))) -> (B -> B)) and (((C and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (B -> B))), M:tm-798, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70864
in-theory        70864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-757 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-48.           (((A -> (B and 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-70864.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-757, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70865
in-theory        70865
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (B -> B)))
theorem-size     33
proof            (modus-ponens tm-747 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm 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-48.           (((A -> (B and 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-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-70865.        (((A or (B -> (A and B))) -> (B -> B)) and ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (B -> B))), M:tm-747, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70866
in-theory        70866
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (F -> F)))
theorem-size     37
proof            (modus-ponens tm-708 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-48.           (((A -> (B and 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-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-70866.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (F -> F))), M:tm-708, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70867
in-theory        70867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-665 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm 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-48.           (((A -> (B and 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-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-70867.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-665, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70868
in-theory        70868
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (B -> B)))
theorem-size     13
proof            (modus-ponens tm-623 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70868.        ((A or (B -> (A and B))) -> (C or (B -> B))), M:tm-623, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70869
in-theory        70869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-622 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70869.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-622, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70870
in-theory        70870
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-70870.        (((A or (B -> (A and B))) -> (B -> B)) and (C -> (D or C))), M:tm-609, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70871
in-theory        70871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-605 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70871.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-605, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70872
in-theory        70872
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (D or C)) and ((A or (B -> (A and B))) -> (B -> B))))
theorem-size     29
proof            (modus-ponens tm-595 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (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-70872.        (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (D or C)) and ((A or (B -> (A and B))) -> (B -> B)))), M:tm-595, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70873
in-theory        70873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-550 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70873.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-550, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70874
in-theory        70874
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-540 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70874.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-540, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70875
in-theory        70875
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-530 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70875.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-530, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70876
in-theory        70876
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-520 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70876.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-520, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70877
in-theory        70877
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-510 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70877.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-510, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70878
in-theory        70878
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-500 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70878.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-500, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70879
in-theory        70879
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (F -> F)))
theorem-size     27
proof            (modus-ponens tm-490 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-1.            (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-70879.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (F -> F))), M:tm-490, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70880
in-theory        70880
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-480 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70880.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-480, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70881
in-theory        70881
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> B) or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70881.        ((A or (B -> (A and B))) -> ((B -> B) or C)), M:tm-470, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70882
in-theory        70882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-469 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70882.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-469, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70883
in-theory        70883
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-70883.        (((A or (B -> (A and B))) -> (B -> B)) and (C -> (C or D))), M:tm-456, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70884
in-theory        70884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-453 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70884.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-453, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70885
in-theory        70885
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (C or D)) and ((A or (B -> (A and B))) -> (B -> B))))
theorem-size     29
proof            (modus-ponens tm-443 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (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-70885.        (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (C or D)) and ((A or (B -> (A and B))) -> (B -> B)))), M:tm-443, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70886
in-theory        70886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-409 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70886.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-409, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70887
in-theory        70887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-400 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70887.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-400, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70888
in-theory        70888
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-391 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70888.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-391, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70889
in-theory        70889
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-382 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70889.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-382, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70890
in-theory        70890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (F -> F)))
theorem-size     27
proof            (modus-ponens tm-373 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-1.            (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-70890.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (F -> F))), M:tm-373, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70891
in-theory        70891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-364 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70891.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-364, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70892
in-theory        70892
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((B -> B) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-70892.        ((A or (B -> (A and B))) -> (C -> ((B -> B) and C))), M:tm-355, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70893
in-theory        70893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-354 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70893.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-354, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70894
in-theory        70894
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-70894.        (((A or (B -> (A and B))) -> (B -> B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70895
in-theory        70895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-338 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (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-70895.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (D -> D))), M:tm-338, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70896
in-theory        70896
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (B -> B))))
theorem-size     31
proof            (modus-ponens tm-328 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
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-48.           (((A -> (B and 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-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-70896.        (((A or (B -> (A and B))) -> (B -> B)) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (B -> B)))), M:tm-328, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70897
in-theory        70897
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (D -> (C and D))) and ((A or (B -> (A and B))) -> (B -> B))))
theorem-size     31
proof            (modus-ponens tm-327 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (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-70897.        (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (D -> (C and D))) and ((A or (B -> (A and B))) -> (B -> B)))), M:tm-327, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70898
in-theory        70898
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (((C and D) -> D) and ((A or (B -> (A and B))) -> (B -> B))))
theorem-size     29
proof            (modus-ponens tm-326 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (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-70898.        (((A or (B -> (A and B))) -> (B -> B)) and (((C and D) -> D) and ((A or (B -> (A and B))) -> (B -> B)))), M:tm-326, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70899
in-theory        70899
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (((C and D) -> C) and ((A or (B -> (A and B))) -> (B -> B))))
theorem-size     29
proof            (modus-ponens tm-325 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (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-70899.        (((A or (B -> (A and B))) -> (B -> B)) and (((C and D) -> C) and ((A or (B -> (A and B))) -> (B -> B)))), M:tm-325, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70900
in-theory        70900
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> (A and B))) -> (B -> B))))
theorem-size     37
proof            (modus-ponens tm-324 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (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-70900.        (((A or (B -> (A and B))) -> (B -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> (A and B))) -> (B -> B)))), M:tm-324, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70901
in-theory        70901
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (D -> C)) and ((A or (B -> (A and B))) -> (B -> B))))
theorem-size     29
proof            (modus-ponens tm-323 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-70901.        (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (D -> C)) and ((A or (B -> (A and B))) -> (B -> B)))), M:tm-323, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70902
in-theory        70902
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm 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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70902.        (((A or (B -> (A and B))) -> (B -> B)) and ((C and D) -> D)), M:tm-322, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70903
in-theory        70903
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-70903.        (((A or (B -> (A and B))) -> (B -> B)) and ((C and D) -> C)), M:tm-320, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70904
in-theory        70904
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-70904.        (((A or (B -> (A and B))) -> (B -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70905
in-theory        70905
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-316 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-70905.        (((A or (B -> (A and B))) -> (B -> B)) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70906
in-theory        70906
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 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-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-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-70906.        (((A or (B -> (A and B))) -> (B -> B)) and (C -> (D -> C))), M:tm-315, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70907
in-theory        70907
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (((A or (B -> (A and B))) -> (not (B -> B))) -> (not (A or (B -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-313 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
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-48.           (((A -> (B and 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-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-70907.        (((A or (B -> (A and B))) -> (B -> B)) and (((A or (B -> (A and B))) -> (not (B -> B))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70908
in-theory        70908
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (((B -> B) -> C) -> (((A or (B -> (A and B))) or (B -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-312 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm 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-312.          ((A -> B) -> ((A -> B) and ((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-1.            (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-70908.        (((A or (B -> (A and B))) -> (B -> B)) and (((B -> B) -> C) -> (((A or (B -> (A and B))) or (B -> B)) -> C))), M:tm-312, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70909
in-theory        70909
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (C or ((A or (B -> (A and B))) -> (B -> B))))
theorem-size     25
proof            (modus-ponens tm-311 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-1.            (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-70909.        (((A or (B -> (A and B))) -> (B -> B)) and (C or ((A or (B -> (A and B))) -> (B -> B)))), M:tm-311, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70910
in-theory        70910
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (((A or (B -> (A and B))) -> (B -> B)) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-1.            (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-70910.        (((A or (B -> (A and B))) -> (B -> B)) and (((A or (B -> (A and B))) -> (B -> B)) or C)), M:tm-310, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70911
in-theory        70911
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (C -> (((A or (B -> (A and B))) -> (B -> B)) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm 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-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-1.            (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-70911.        (((A or (B -> (A and B))) -> (B -> B)) and (C -> (((A or (B -> (A and B))) -> (B -> B)) and C))), M:tm-309, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70912
in-theory        70912
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (((A or (B -> (A and B))) -> B) -> ((A or (B -> (A and B))) -> B)))
theorem-size     31
proof            (modus-ponens tm-306 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B Bm) (C 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (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-70912.        (((A or (B -> (A and B))) -> (B -> B)) and (((A or (B -> (A and B))) -> B) -> ((A or (B -> (A and B))) -> B))), M:tm-306, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B Bm) (C Bm))
================================================================
tm-name          tm-70913
in-theory        70913
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (C -> ((A or (B -> (A and B))) -> (B -> B))))
theorem-size     25
proof            (modus-ponens tm-305 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm 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-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-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-70913.        (((A or (B -> (A and B))) -> (B -> B)) and (C -> ((A or (B -> (A and B))) -> (B -> B)))), M:tm-305, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70914
in-theory        70914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-303 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70914.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-303, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70915
in-theory        70915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-270 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70915.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-270, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70916
in-theory        70916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-239 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70916.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-239, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70917
in-theory        70917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (F -> F)))
theorem-size     29
proof            (modus-ponens tm-210 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (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-70917.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (F -> F))), M:tm-210, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70918
in-theory        70918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-183 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70918.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-183, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70919
in-theory        70919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-157 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70919.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-157, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70920
in-theory        70920
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     27
proof            (modus-ponens tm-147 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-1.            (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-70920.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-147, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70921
in-theory        70921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-134 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70921.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-134, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70922
in-theory        70922
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     27
proof            (modus-ponens tm-125 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-1.            (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-70922.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-125, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70923
in-theory        70923
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> (((B -> C) -> B) -> ((B -> C) -> C)))
theorem-size     23
proof            (modus-ponens tm-114 tm-818 ((A (or Am (-> (-> C D) (and Am (-> C D))))) (B (-> C D)) (Bm (-> C D))))
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-14.           (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-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-70923.        ((A or ((B -> C) -> (A and (B -> C)))) -> (((B -> C) -> B) -> ((B -> C) -> C))), M:tm-114, m:tm-818, u:((A (or Am (-> (-> C D) (and Am (-> C D))))) (B (-> C D)) (Bm (-> C D)))
================================================================
tm-name          tm-70924
in-theory        70924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (F -> F)))
theorem-size     27
proof            (modus-ponens tm-113 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-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-70924.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (F -> F))), M:tm-113, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70925
in-theory        70925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     31
proof            (modus-ponens tm-105 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (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-70925.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-105, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70926
in-theory        70926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-95 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-1 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-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-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-70926.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (D -> D))), M:tm-95, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70927
in-theory        70927
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (B -> B)))
theorem-size     13
proof            (modus-ponens tm-84 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-70927.        ((A or (B -> (A and B))) -> (C -> (B -> B))), M:tm-84, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70928
in-theory        70928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-83 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70928.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-83, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70929
in-theory        70929
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (C -> C)))
theorem-size     17
proof            (modus-ponens tm-76 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-10 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70929.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (C -> C))), M:tm-76, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70930
in-theory        70930
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (B -> B))
theorem-size     21
proof            (modus-ponens tm-73 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-10 tm-5 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-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-70930.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (B -> B)), M:tm-73, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70931
in-theory        70931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-69 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-9 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70931.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (D -> D))), M:tm-69, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70932
in-theory        70932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-54 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-48.           (((A -> (B and 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-70932.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-54, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70933
in-theory        70933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (A -> A))
theorem-size     17
proof            (modus-ponens tm-50 tm-818 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm Bm))))
axioms-used      (tm-8 tm-7 tm-5 tm-2 tm-1)
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-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-70933.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (A -> A)), M:tm-50, m:tm-818, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm Bm)))
================================================================
tm-name          tm-70934
in-theory        70934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (B -> B))
theorem-size     13
proof            (modus-ponens tm-49 tm-818 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm Bm))))
axioms-used      (tm-8 tm-6 tm-5 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-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-70934.        ((A or (A or (B -> (A and B)))) -> (B -> B)), M:tm-49, m:tm-818, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm Bm)))
================================================================
tm-name          tm-70935
in-theory        70935
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (C -> C))
theorem-size     21
proof            (modus-ponens tm-47 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-4 tm-5 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-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-70935.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (C -> C)), M:tm-47, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70936
in-theory        70936
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (B -> B))
theorem-size     21
proof            (modus-ponens tm-46 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-3 tm-5 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-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-70936.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (B -> B)), M:tm-46, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70937
in-theory        70937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-42 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm 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-42.           (A -> ((B -> (C or B)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70937.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (D -> D))), M:tm-42, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70938
in-theory        70938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-32 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm 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-32.           (A -> ((B -> (B or C)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70938.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (D -> D))), M:tm-32, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70939
in-theory        70939
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (B -> B)))
theorem-size     19
proof            (modus-ponens tm-24 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
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-48.           (((A -> (B and 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-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-70939.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (B -> B))), M:tm-24, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70940
in-theory        70940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-23 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70940.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (D -> D))), M:tm-23, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70941
in-theory        70941
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-22 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70941.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (D -> D))), M:tm-22, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70942
in-theory        70942
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-21 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-70942.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (D -> D))), M:tm-21, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70943
in-theory        70943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-20 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (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-70943.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-20, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70944
in-theory        70944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-19 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm 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-19.           (A -> ((B -> (C -> B)) and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70944.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (D -> D))), M:tm-19, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70945
in-theory        70945
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (B -> B))) -> (not (A or (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-9 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
axioms-used      (tm-9 tm-8 tm-5 tm-2 tm-1)
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-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-70945.        (((A or (B -> (A and B))) -> (not (B -> B))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70946
in-theory        70946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> (((C or (A -> (C and A))) or (A -> A)) -> B))
theorem-size     19
proof            (modus-ponens tm-8 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-5 tm-2 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-48.           (((A -> (B and 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-70946.        (((A -> A) -> B) -> (((C or (A -> (C and A))) or (A -> A)) -> B)), M:tm-8, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm Bm)))
================================================================
tm-name          tm-70947
in-theory        70947
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-7 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-7 tm-8 tm-5 tm-2 tm-1)
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-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-70947.        (A or ((B or (C -> (B and C))) -> (C -> C))), M:tm-7, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70948
in-theory        70948
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-6 tm-8 tm-5 tm-2 tm-1)
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-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-70948.        (((A or (B -> (A and B))) -> (B -> B)) or C), M:tm-6, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70949
in-theory        70949
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (C -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-70949.        (A -> (((B or (C -> (B and C))) -> (C -> C)) and A)), M:tm-5, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70950
in-theory        70950
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> B) -> ((A or (B -> (A and B))) -> B))
theorem-size     19
proof            (modus-ponens tm-2 tm-818 ((A (or Am (-> Bm (and Am Bm)))) (B Bm) (C Bm)))
axioms-used      (tm-2 tm-8 tm-5 tm-1)
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-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-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-70950.        (((A or (B -> (A and B))) -> B) -> ((A or (B -> (A and B))) -> B)), M:tm-2, m:tm-818, u:((A (or Am (-> Bm (and Am Bm)))) (B Bm) (C Bm))
================================================================
tm-name          tm-70951
in-theory        70951
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-1 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-1 tm-8 tm-5 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-70951.        (A -> ((B or (C -> (B and C))) -> (C -> C))), M:tm-1, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-70952
in-theory        70952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-70952.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70953
in-theory        70953
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     53
proof            (modus-ponens tm-798 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-14.           (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-70953.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-798, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-70954
in-theory        70954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70954.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70955
in-theory        70955
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A or (B -> (A and B))) and F) or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     53
proof            (modus-ponens tm-747 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
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-48.           (((A -> (B and 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-14.           (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-70955.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A or (B -> (A and B))) and F) or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-747, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-70956
in-theory        70956
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-48.           (((A -> (B and 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-14.           (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-70956.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70957
in-theory        70957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm 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-48.           (((A -> (B and 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-14.           (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-70957.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70958
in-theory        70958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70958.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70959
in-theory        70959
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-14.           (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-70959.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70960
in-theory        70960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-48.           (((A -> (B and 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-70960.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70961
in-theory        70961
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70961.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70962
in-theory        70962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70962.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70963
in-theory        70963
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70963.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70964
in-theory        70964
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70964.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70965
in-theory        70965
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-48.           (((A -> (B and 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-70965.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70966
in-theory        70966
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70966.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70967
in-theory        70967
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70967.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70968
in-theory        70968
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
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-48.           (((A -> (B and 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-14.           (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-70968.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70969
in-theory        70969
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70969.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70970
in-theory        70970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70970.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70971
in-theory        70971
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-14.           (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-70971.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70972
in-theory        70972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-48.           (((A -> (B and 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-70972.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70973
in-theory        70973
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70973.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70974
in-theory        70974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70974.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70975
in-theory        70975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-48.           (((A -> (B and 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-70975.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70976
in-theory        70976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70976.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70977
in-theory        70977
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70977.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70978
in-theory        70978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
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-48.           (((A -> (B and 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-14.           (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-70978.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70979
in-theory        70979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-70979.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70980
in-theory        70980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-48.           (((A -> (B and 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-14.           (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-70980.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70981
in-theory        70981
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-70981.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70982
in-theory        70982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70982.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70983
in-theory        70983
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     51
proof            (modus-ponens tm-328 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
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-328.          ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70983.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-328, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-70984
in-theory        70984
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70984.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70985
in-theory        70985
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70985.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70986
in-theory        70986
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70986.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70987
in-theory        70987
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70987.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70988
in-theory        70988
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-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-14.           (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-70988.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70989
in-theory        70989
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-70989.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70990
in-theory        70990
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-70990.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70991
in-theory        70991
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-70991.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70992
in-theory        70992
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-316 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-14.           (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-70992.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-70993
in-theory        70993
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-14.           (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-70993.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70994
in-theory        70994
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> (A and B))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B -> (A and B))))))
theorem-size     53
proof            (modus-ponens tm-313 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70994.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> (A and B))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-70995
in-theory        70995
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> (((A or (B -> (A and B))) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     61
proof            (modus-ponens tm-312 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70995.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> (((A or (B -> (A and B))) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-312, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-70996
in-theory        70996
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70996.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70997
in-theory        70997
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70997.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70998
in-theory        70998
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70998.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-70999
in-theory        70999
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> (A and B))) -> (C -> (D -> E))) -> ((A or (B -> (A and B))) -> ((C -> D) -> (C -> E)))))
theorem-size     51
proof            (modus-ponens tm-306 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-70999.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> (A and B))) -> (C -> (D -> E))) -> ((A or (B -> (A and B))) -> ((C -> D) -> (C -> E))))), M:tm-306, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-71000
in-theory        71000
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-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-14.           (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-71000.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71001
in-theory        71001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-71001.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71002
in-theory        71002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-48.           (((A -> (B and 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-71002.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71003
in-theory        71003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-48.           (((A -> (B and 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-71003.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71004
in-theory        71004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-71004.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71005
in-theory        71005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-48.           (((A -> (B and 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-14.           (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-71005.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71006
in-theory        71006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-48.           (((A -> (B and 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-14.           (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-71006.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71007
in-theory        71007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-71007.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71008
in-theory        71008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-48.           (((A -> (B and 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-14.           (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-71008.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71009
in-theory        71009
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-71009.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71010
in-theory        71010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-71010.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71011
in-theory        71011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-71011.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71012
in-theory        71012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-14.           (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-71012.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71013
in-theory        71013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-71013.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71014
in-theory        71014
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 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-48.           (((A -> (B and 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-71014.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71015
in-theory        71015
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-73 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 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-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-71015.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-73, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-71016
in-theory        71016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 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-48.           (((A -> (B and 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-71016.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71017
in-theory        71017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-71017.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71018
in-theory        71018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-50 tm-819 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 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-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-71018.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-50, m:tm-819, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-71019
in-theory        71019
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-49 tm-819 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-2)
proof-size       145
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-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-71019.        ((A or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-49, m:tm-819, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-71020
in-theory        71020
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-47 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 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-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-71020.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-47, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-71021
in-theory        71021
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-46 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 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-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-71021.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-46, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-71022
in-theory        71022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-48.           (((A -> (B and 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-71022.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71023
in-theory        71023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-48.           (((A -> (B and 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-71023.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71024
in-theory        71024
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-24 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
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-48.           (((A -> (B and 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-14.           (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-71024.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-24, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-71025
in-theory        71025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-71025.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71026
in-theory        71026
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-48.           (((A -> (B and 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-71026.        (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71027
in-theory        71027
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-48.           (((A -> (B and 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-71027.        (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71028
in-theory        71028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-71028.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71029
in-theory        71029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-48.           (((A -> (B and 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-14.           (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-71029.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71030
in-theory        71030
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B -> (A and B)))))
theorem-size     31
proof            (modus-ponens tm-9 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-9 tm-8 tm-5 tm-1 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-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-71030.        (((A or (B -> (A and B))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-71031
in-theory        71031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or (F -> (E and F))) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     39
proof            (modus-ponens tm-8 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-71031.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or (F -> (E and F))) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-71032
in-theory        71032
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-1 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-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-71032.        (A or ((B or (C -> (B and C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71033
in-theory        71033
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-1 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-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-71033.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71034
in-theory        71034
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-819 ((A (-> (or Am (-> Bm (and 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-48.           (((A -> (B and 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-71034.        (A -> (((B or (C -> (B and C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71035
in-theory        71035
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> E))) -> ((A or (B -> (A and B))) -> ((C -> D) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-2 tm-819 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-8 tm-5 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-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-14.           (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-71035.        (((A or (B -> (A and B))) -> (C -> (D -> E))) -> ((A or (B -> (A and B))) -> ((C -> D) -> (C -> E)))), M:tm-2, m:tm-819, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-71036
in-theory        71036
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-8 tm-5 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-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-14.           (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-71036.        (A -> ((B or (C -> (B and C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-71037
in-theory        71037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-808 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71037.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-808, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71038
in-theory        71038
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C and D) -> C)))
theorem-size     37
proof            (modus-ponens tm-798 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71038.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C and D) -> C))), M:tm-798, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71039
in-theory        71039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-757 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm 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-48.           (((A -> (B and 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-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-71039.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-757, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71040
in-theory        71040
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C and D) -> C)))
theorem-size     37
proof            (modus-ponens tm-747 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (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-71040.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C and D) -> C))), M:tm-747, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71041
in-theory        71041
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-708 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-71041.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G and H) -> G))), M:tm-708, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71042
in-theory        71042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-665 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm 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-48.           (((A -> (B and 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-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-71042.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-665, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71043
in-theory        71043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-622 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-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-3.            ((A 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-71043.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-622, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71044
in-theory        71044
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-71044.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71045
in-theory        71045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-605 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71045.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-605, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71046
in-theory        71046
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-595 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71046.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C and D) -> C)))), M:tm-595, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71047
in-theory        71047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-550 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71047.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-550, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71048
in-theory        71048
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-540 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71048.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-540, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71049
in-theory        71049
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-530 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71049.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-530, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71050
in-theory        71050
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-520 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71050.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-520, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71051
in-theory        71051
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-510 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71051.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-510, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71052
in-theory        71052
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-500 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-48.           (((A -> (B and 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-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-71052.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-500, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71053
in-theory        71053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-490 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71053.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> G))), M:tm-490, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71054
in-theory        71054
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-480 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-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-3.            ((A 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-71054.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-480, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71055
in-theory        71055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-469 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-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-3.            ((A 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-71055.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-469, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71056
in-theory        71056
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-71056.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71057
in-theory        71057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-453 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71057.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-453, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71058
in-theory        71058
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-443 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71058.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C and D) -> C)))), M:tm-443, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71059
in-theory        71059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-409 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71059.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-409, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71060
in-theory        71060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-400 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71060.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-400, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71061
in-theory        71061
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-391 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71061.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-391, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71062
in-theory        71062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-382 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-48.           (((A -> (B and 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-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-71062.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-382, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71063
in-theory        71063
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-373 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71063.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G and H) -> G))), M:tm-373, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71064
in-theory        71064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-364 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-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-3.            ((A 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-71064.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-364, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71065
in-theory        71065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-354 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-3.            ((A 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-71065.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-354, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71066
in-theory        71066
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A 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-71066.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71067
in-theory        71067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-338 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71067.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E and F) -> E))), M:tm-338, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71068
in-theory        71068
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C and D) -> C))))
theorem-size     35
proof            (modus-ponens tm-328 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
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-328.          ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71068.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C and D) -> C)))), M:tm-328, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71069
in-theory        71069
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C and D) -> C))))
theorem-size     35
proof            (modus-ponens tm-327 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71069.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C and D) -> C)))), M:tm-327, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71070
in-theory        71070
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-326 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71070.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C and D) -> C)))), M:tm-326, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71071
in-theory        71071
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-325 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-71071.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C and D) -> C)))), M:tm-325, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71072
in-theory        71072
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C and D) -> C))))
theorem-size     41
proof            (modus-ponens tm-324 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71072.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C and D) -> C)))), M:tm-324, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71073
in-theory        71073
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-323 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A 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-71073.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C and D) -> C)))), M:tm-323, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71074
in-theory        71074
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-71074.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71075
in-theory        71075
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-71075.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71076
in-theory        71076
times-derived    1
----------------------------------------------------------------
theorem          (((A or (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-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-71076.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71077
in-theory        71077
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-316 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-3.            ((A 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-71077.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71078
in-theory        71078
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-71078.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71079
in-theory        71079
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((A or (B -> (A and B))) -> (not ((C and D) -> C))) -> (not (A or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-313 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71079.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((A or (B -> (A and B))) -> (not ((C and D) -> C))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71080
in-theory        71080
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> (((A or (B -> (A and B))) or ((C and D) -> C)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) 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-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71080.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> (((A or (B -> (A and B))) or ((C and D) -> C)) -> E))), M:tm-312, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71081
in-theory        71081
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E or ((A or (B -> (A and B))) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-311 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71081.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E or ((A or (B -> (A and B))) -> ((C and D) -> C)))), M:tm-311, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71082
in-theory        71082
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((A or (B -> (A and B))) -> ((C and D) -> C)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71082.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((A or (B -> (A and B))) -> ((C and D) -> C)) or E)), M:tm-310, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71083
in-theory        71083
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (((A or (B -> (A and B))) -> ((C and D) -> C)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71083.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> (((A or (B -> (A and B))) -> ((C and D) -> C)) and E))), M:tm-309, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71084
in-theory        71084
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((A or (B -> (A and B))) -> (C and D)) -> ((A or (B -> (A and B))) -> C)))
theorem-size     35
proof            (modus-ponens tm-306 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (and Cm Dm)) (C 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71084.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((A or (B -> (A and B))) -> (C and D)) -> ((A or (B -> (A and B))) -> C))), M:tm-306, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-71085
in-theory        71085
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> ((A or (B -> (A and B))) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-305 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) 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-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-3.            ((A 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-71085.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (E -> ((A or (B -> (A and B))) -> ((C and D) -> C)))), M:tm-305, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71086
in-theory        71086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-303 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71086.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-303, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71087
in-theory        71087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-270 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71087.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-270, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71088
in-theory        71088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-239 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 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-48.           (((A -> (B and 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-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-71088.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-239, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71089
in-theory        71089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-210 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71089.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G and H) -> G))), M:tm-210, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71090
in-theory        71090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-183 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-3.            ((A 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-71090.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-183, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71091
in-theory        71091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-157 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-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-3.            ((A 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-71091.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-157, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71092
in-theory        71092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-147 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71092.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-147, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71093
in-theory        71093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-134 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-71093.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-134, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71094
in-theory        71094
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-125 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-71094.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-125, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71095
in-theory        71095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-113 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-71095.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> G))), M:tm-113, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71096
in-theory        71096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-105 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71096.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-105, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71097
in-theory        71097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-95 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-71097.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E and F) -> E))), M:tm-95, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71098
in-theory        71098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-83 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 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-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-3.            ((A 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-71098.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-83, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71099
in-theory        71099
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-76 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71099.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D and E) -> D))), M:tm-76, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71100
in-theory        71100
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C and D) -> C))
theorem-size     23
proof            (modus-ponens tm-73 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 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-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-71100.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C and D) -> C)), M:tm-73, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71101
in-theory        71101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-69 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71101.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E and F) -> E))), M:tm-69, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71102
in-theory        71102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-54 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-71102.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-54, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71103
in-theory        71103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-50 tm-820 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 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-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-71103.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C and D) -> C)), M:tm-50, m:tm-820, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71104
in-theory        71104
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-49 tm-820 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-3)
proof-size       113
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-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-71104.        ((A or (A or (B -> (A and B)))) -> ((C and D) -> C)), M:tm-49, m:tm-820, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71105
in-theory        71105
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-47 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 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-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-71105.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D and E) -> D)), M:tm-47, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71106
in-theory        71106
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-46 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
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-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-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-71106.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D and E) -> D)), M:tm-46, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71107
in-theory        71107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-42 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) 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-42.           (A -> ((B -> (C or B)) and A)), 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71107.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E and F) -> E))), M:tm-42, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71108
in-theory        71108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-32 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) 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-32.           (A -> ((B -> (B or C)) and A)), 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71108.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E and F) -> E))), M:tm-32, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71109
in-theory        71109
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C and D) -> C)))
theorem-size     21
proof            (modus-ponens tm-24 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
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-48.           (((A -> (B and 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-71109.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C and D) -> C))), M:tm-24, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71110
in-theory        71110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-23 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71110.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E and F) -> E))), M:tm-23, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71111
in-theory        71111
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-22 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71111.        (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E and F) -> E))), M:tm-22, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71112
in-theory        71112
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-21 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 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-48.           (((A -> (B and 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-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-71112.        (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E and F) -> E))), M:tm-21, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71113
in-theory        71113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-20 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-71113.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-20, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71114
in-theory        71114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-19 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) 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-19.           (A -> ((B -> (C -> B)) and 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-3.            ((A 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-71114.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E and F) -> E))), M:tm-19, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71115
in-theory        71115
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not ((C and D) -> C))) -> (not (A or (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-9 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-9 tm-8 tm-5 tm-1 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-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-71115.        (((A or (B -> (A and B))) -> (not ((C and D) -> C))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71116
in-theory        71116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (((D or (E -> (D and E))) or ((A and B) -> A)) -> C))
theorem-size     23
proof            (modus-ponens tm-8 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) 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-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-71116.        ((((A and B) -> A) -> C) -> (((D or (E -> (D and E))) or ((A and B) -> A)) -> C)), M:tm-8, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-71117
in-theory        71117
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-7 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-8 tm-5 tm-1 tm-3)
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-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-71117.        (A or ((B or (C -> (B and C))) -> ((D and E) -> D))), M:tm-7, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71118
in-theory        71118
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-8 tm-5 tm-1 tm-3)
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-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-71118.        (((A or (B -> (A and B))) -> ((C and D) -> C)) or E), M:tm-6, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71119
in-theory        71119
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> ((D and E) -> D)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-820 ((A (-> (or Am (-> Bm (and 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-48.           (((A -> (B and 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-71119.        (A -> (((B or (C -> (B and C))) -> ((D and E) -> D)) and A)), M:tm-5, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71120
in-theory        71120
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C and D)) -> ((A or (B -> (A and B))) -> C))
theorem-size     21
proof            (modus-ponens tm-2 tm-820 ((A (or Am (-> Bm (and Am Bm)))) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-3)
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-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-71120.        (((A or (B -> (A and B))) -> (C and D)) -> ((A or (B -> (A and B))) -> C)), M:tm-2, m:tm-820, u:((A (or Am (-> Bm (and Am Bm)))) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-71121
in-theory        71121
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-1 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-8 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
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-3.            ((A 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-71121.        (A -> ((B or (C -> (B and C))) -> ((D and E) -> D))), M:tm-1, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-71122
in-theory        71122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-808 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-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-71122.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-808, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71123
in-theory        71123
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C and D) -> D)))
theorem-size     37
proof            (modus-ponens tm-798 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-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-71123.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C and D) -> D))), M:tm-798, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71124
in-theory        71124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-757 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 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-48.           (((A -> (B and 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-71124.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-757, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71125
in-theory        71125
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C and D) -> D)))
theorem-size     37
proof            (modus-ponens tm-747 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71125.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C and D) -> D))), M:tm-747, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71126
in-theory        71126
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-708 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-71126.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G and H) -> H))), M:tm-708, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71127
in-theory        71127
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-665 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-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-71127.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-665, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71128
in-theory        71128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-622 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-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-4.            ((A 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-71128.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-622, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71129
in-theory        71129
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-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-71129.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71130
in-theory        71130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-605 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71130.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-605, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71131
in-theory        71131
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-595 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71131.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C and D) -> D)))), M:tm-595, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71132
in-theory        71132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-550 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71132.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-550, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71133
in-theory        71133
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-540 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71133.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-540, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71134
in-theory        71134
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-530 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71134.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-530, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71135
in-theory        71135
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-520 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71135.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-520, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71136
in-theory        71136
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-510 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-48.           (((A -> (B and 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-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-71136.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-510, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71137
in-theory        71137
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-500 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71137.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-500, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71138
in-theory        71138
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-490 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71138.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> H))), M:tm-490, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71139
in-theory        71139
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-480 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-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-4.            ((A 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-71139.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-480, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71140
in-theory        71140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-469 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-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-4.            ((A 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-71140.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-469, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71141
in-theory        71141
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-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-71141.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71142
in-theory        71142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-453 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71142.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-453, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71143
in-theory        71143
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-443 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71143.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C and D) -> D)))), M:tm-443, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71144
in-theory        71144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-409 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71144.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-409, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71145
in-theory        71145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-400 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71145.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-400, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71146
in-theory        71146
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-391 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-48.           (((A -> (B and 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-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-71146.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-391, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71147
in-theory        71147
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-382 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71147.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-382, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71148
in-theory        71148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-373 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71148.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G and H) -> H))), M:tm-373, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71149
in-theory        71149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-364 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-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-4.            ((A 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-71149.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-364, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71150
in-theory        71150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-354 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-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-4.            ((A 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-71150.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-354, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71151
in-theory        71151
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A 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-71151.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71152
in-theory        71152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-338 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71152.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E and F) -> F))), M:tm-338, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71153
in-theory        71153
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C and D) -> D))))
theorem-size     35
proof            (modus-ponens tm-328 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
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-328.          ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71153.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C and D) -> D)))), M:tm-328, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71154
in-theory        71154
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C and D) -> D))))
theorem-size     35
proof            (modus-ponens tm-327 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71154.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C and D) -> D)))), M:tm-327, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71155
in-theory        71155
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-326 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-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-71155.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C and D) -> D)))), M:tm-326, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71156
in-theory        71156
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-325 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71156.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C and D) -> D)))), M:tm-325, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71157
in-theory        71157
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C and D) -> D))))
theorem-size     41
proof            (modus-ponens tm-324 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71157.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C and D) -> D)))), M:tm-324, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71158
in-theory        71158
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-323 tm-821 ((A (-> (or Am (-> Bm (and Am 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A 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-71158.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C and D) -> D)))), M:tm-323, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71159
in-theory        71159
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am 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-71159.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71160
in-theory        71160
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-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-71160.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71161
in-theory        71161
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A 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-71161.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71162
in-theory        71162
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-316 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-4.            ((A 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-71162.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71163
in-theory        71163
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-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-71163.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71164
in-theory        71164
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((A or (B -> (A and B))) -> (not ((C and D) -> D))) -> (not (A or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-313 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71164.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((A or (B -> (A and B))) -> (not ((C and D) -> D))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71165
in-theory        71165
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> (((A or (B -> (A and B))) or ((C and D) -> D)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
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-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71165.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> (((A or (B -> (A and B))) or ((C and D) -> D)) -> E))), M:tm-312, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71166
in-theory        71166
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E or ((A or (B -> (A and B))) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-311 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71166.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E or ((A or (B -> (A and B))) -> ((C and D) -> D)))), M:tm-311, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71167
in-theory        71167
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((A or (B -> (A and B))) -> ((C and D) -> D)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71167.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((A or (B -> (A and B))) -> ((C and D) -> D)) or E)), M:tm-310, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71168
in-theory        71168
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (((A or (B -> (A and B))) -> ((C and D) -> D)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71168.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> (((A or (B -> (A and B))) -> ((C and D) -> D)) and E))), M:tm-309, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71169
in-theory        71169
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((A or (B -> (A and B))) -> (C and D)) -> ((A or (B -> (A and B))) -> D)))
theorem-size     35
proof            (modus-ponens tm-306 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (and Cm Dm)) (C Dm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71169.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((A or (B -> (A and B))) -> (C and D)) -> ((A or (B -> (A and B))) -> D))), M:tm-306, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-71170
in-theory        71170
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> ((A or (B -> (A and B))) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-305 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) 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-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-4.            ((A 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-71170.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (E -> ((A or (B -> (A and B))) -> ((C and D) -> D)))), M:tm-305, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71171
in-theory        71171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-303 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71171.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-303, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71172
in-theory        71172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-270 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 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-48.           (((A -> (B and 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-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-71172.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-270, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71173
in-theory        71173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-239 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71173.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-239, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71174
in-theory        71174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-210 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71174.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G and H) -> H))), M:tm-210, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71175
in-theory        71175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-183 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-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-4.            ((A 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-71175.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-183, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71176
in-theory        71176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-157 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am 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-71176.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-157, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71177
in-theory        71177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-147 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-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-71177.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-147, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71178
in-theory        71178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-134 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-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-4.            ((A 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-71178.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-134, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71179
in-theory        71179
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-125 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71179.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-125, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71180
in-theory        71180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-113 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-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-71180.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> H))), M:tm-113, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71181
in-theory        71181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     33
proof            (modus-ponens tm-105 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71181.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-105, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71182
in-theory        71182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-95 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-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-71182.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E and F) -> F))), M:tm-95, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71183
in-theory        71183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-83 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-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-4.            ((A 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-71183.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-83, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71184
in-theory        71184
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-76 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71184.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D and E) -> E))), M:tm-76, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71185
in-theory        71185
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C and D) -> D))
theorem-size     23
proof            (modus-ponens tm-73 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 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-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-71185.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C and D) -> D)), M:tm-73, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71186
in-theory        71186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-69 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71186.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E and F) -> F))), M:tm-69, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71187
in-theory        71187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-54 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-71187.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-54, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71188
in-theory        71188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-50 tm-821 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 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-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-71188.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C and D) -> D)), M:tm-50, m:tm-821, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71189
in-theory        71189
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-49 tm-821 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-4)
proof-size       113
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-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-71189.        ((A or (A or (B -> (A and B)))) -> ((C and D) -> D)), M:tm-49, m:tm-821, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71190
in-theory        71190
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-47 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
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-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-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-71190.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D and E) -> E)), M:tm-47, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71191
in-theory        71191
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-46 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 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-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-71191.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D and E) -> E)), M:tm-46, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71192
in-theory        71192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-42 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71192.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E and F) -> F))), M:tm-42, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71193
in-theory        71193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-32 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71193.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E and F) -> F))), M:tm-32, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71194
in-theory        71194
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C and D) -> D)))
theorem-size     21
proof            (modus-ponens tm-24 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
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-48.           (((A -> (B and 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-71194.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C and D) -> D))), M:tm-24, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71195
in-theory        71195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-23 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71195.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E and F) -> F))), M:tm-23, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71196
in-theory        71196
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-22 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 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-48.           (((A -> (B and 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-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-71196.        (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E and F) -> F))), M:tm-22, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71197
in-theory        71197
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-21 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71197.        (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E and F) -> F))), M:tm-21, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71198
in-theory        71198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-20 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-71198.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-20, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71199
in-theory        71199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-19 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
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-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-4.            ((A 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-71199.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E and F) -> F))), M:tm-19, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71200
in-theory        71200
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not ((C and D) -> D))) -> (not (A or (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-9 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-9 tm-8 tm-5 tm-1 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-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-71200.        (((A or (B -> (A and B))) -> (not ((C and D) -> D))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71201
in-theory        71201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (((D or (E -> (D and E))) or ((A and B) -> B)) -> C))
theorem-size     23
proof            (modus-ponens tm-8 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
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-4.            ((A 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-71201.        ((((A and B) -> B) -> C) -> (((D or (E -> (D and E))) or ((A and B) -> B)) -> C)), M:tm-8, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-71202
in-theory        71202
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-7 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-8 tm-5 tm-1 tm-4)
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-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-71202.        (A or ((B or (C -> (B and C))) -> ((D and E) -> E))), M:tm-7, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71203
in-theory        71203
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-8 tm-5 tm-1 tm-4)
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-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-71203.        (((A or (B -> (A and B))) -> ((C and D) -> D)) or E), M:tm-6, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71204
in-theory        71204
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> ((D and E) -> E)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-821 ((A (-> (or Am (-> Bm (and 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-48.           (((A -> (B and 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-71204.        (A -> (((B or (C -> (B and C))) -> ((D and E) -> E)) and A)), M:tm-5, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71205
in-theory        71205
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C and D)) -> ((A or (B -> (A and B))) -> D))
theorem-size     21
proof            (modus-ponens tm-2 tm-821 ((A (or Am (-> Bm (and Am Bm)))) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-4)
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-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-71205.        (((A or (B -> (A and B))) -> (C and D)) -> ((A or (B -> (A and B))) -> D)), M:tm-2, m:tm-821, u:((A (or Am (-> Bm (and Am Bm)))) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-71206
in-theory        71206
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-1 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-8 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
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-4.            ((A 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-71206.        (A -> ((B or (C -> (B and C))) -> ((D and E) -> E))), M:tm-1, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-71207
in-theory        71207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71207.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-808, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71208
in-theory        71208
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-798 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71208.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B))))), M:tm-798, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71209
in-theory        71209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-71209.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-757, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71210
in-theory        71210
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-747 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-71210.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B))))), M:tm-747, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71211
in-theory        71211
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71211.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F))))), M:tm-708, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71212
in-theory        71212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-71212.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-665, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71213
in-theory        71213
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or ((D -> (E -> D)) and (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-623 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-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-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-71213.        ((A or (B -> (A and B))) -> (C or ((D -> (E -> D)) and (B -> (A and B))))), M:tm-623, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71214
in-theory        71214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-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-71214.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-622, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71215
in-theory        71215
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-71215.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (F or E))), M:tm-609, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71216
in-theory        71216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-71216.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-605, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71217
in-theory        71217
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (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-71217.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-595, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71218
in-theory        71218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-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-1.            (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-71218.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-550, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71219
in-theory        71219
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-71219.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-540, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71220
in-theory        71220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-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-1.            (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-71220.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-530, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71221
in-theory        71221
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-71221.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-520, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71222
in-theory        71222
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-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-1.            (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-71222.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-510, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71223
in-theory        71223
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-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-1.            (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-71223.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-500, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71224
in-theory        71224
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-1.            (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-71224.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F))))), M:tm-490, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71225
in-theory        71225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-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-71225.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-480, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71226
in-theory        71226
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D -> C)) and (B -> (A and B))) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-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-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-71226.        ((A or (B -> (A and B))) -> (((C -> (D -> C)) and (B -> (A and B))) or E)), M:tm-470, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71227
in-theory        71227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-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-71227.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-469, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71228
in-theory        71228
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-71228.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (E or F))), M:tm-456, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71229
in-theory        71229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-71229.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-453, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71230
in-theory        71230
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (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-71230.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-443, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71231
in-theory        71231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-71231.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-409, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71232
in-theory        71232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-71232.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-400, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71233
in-theory        71233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-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-1.            (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-71233.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-391, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71234
in-theory        71234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-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-1.            (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-71234.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-382, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71235
in-theory        71235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-1.            (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-71235.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F))))), M:tm-373, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71236
in-theory        71236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-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-71236.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-364, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71237
in-theory        71237
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D -> (E -> D)) and (B -> (A and B))) and C)))
theorem-size     23
proof            (modus-ponens tm-355 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
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-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-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-71237.        ((A or (B -> (A and B))) -> (C -> (((D -> (E -> D)) and (B -> (A and B))) and C))), M:tm-355, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71238
in-theory        71238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-71238.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-354, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71239
in-theory        71239
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-71239.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71240
in-theory        71240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (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-71240.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D))))), M:tm-338, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71241
in-theory        71241
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-328 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-71241.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-328, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71242
in-theory        71242
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (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-71242.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-327, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71243
in-theory        71243
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71243.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-326, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71244
in-theory        71244
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am 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-48.           (((A -> (B and 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-71244.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-325, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71245
in-theory        71245
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (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-71245.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-324, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71246
in-theory        71246
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-71246.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-323, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71247
in-theory        71247
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-71247.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E and F) -> F)), M:tm-322, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71248
in-theory        71248
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-71248.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E and F) -> E)), M:tm-320, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71249
in-theory        71249
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-71249.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71250
in-theory        71250
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-71250.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71251
in-theory        71251
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-71251.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (F -> E))), M:tm-315, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71252
in-theory        71252
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not ((C -> (D -> C)) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-313 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-71252.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not ((C -> (D -> C)) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71253
in-theory        71253
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((((C -> (D -> C)) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or ((C -> (D -> C)) and (B -> (A and B)))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am 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-312.          ((A -> B) -> ((A -> B) and ((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-1.            (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-71253.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((((C -> (D -> C)) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or ((C -> (D -> C)) and (B -> (A and B)))) -> E))), M:tm-312, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71254
in-theory        71254
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-7.            (A -> (B or 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-1.            (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-71254.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-311, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71255
in-theory        71255
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-6.            (A -> (A or 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-1.            (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-71255.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) or E)), M:tm-310, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71256
in-theory        71256
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and 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-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-1.            (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-71256.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and E))), M:tm-309, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71257
in-theory        71257
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and 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-1.            (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-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-71257.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))))), M:tm-305, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71258
in-theory        71258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-1.            (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-71258.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-303, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71259
in-theory        71259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-1.            (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-71259.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-270, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71260
in-theory        71260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-1.            (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-71260.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-239, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71261
in-theory        71261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (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-71261.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F))))), M:tm-210, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71262
in-theory        71262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-71262.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-183, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71263
in-theory        71263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-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-71263.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-157, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71264
in-theory        71264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-1.            (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-71264.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-147, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71265
in-theory        71265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-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-71265.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-134, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71266
in-theory        71266
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-1.            (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-71266.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-125, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71267
in-theory        71267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-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-71267.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F))))), M:tm-113, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71268
in-theory        71268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (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-71268.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-105, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71269
in-theory        71269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-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-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-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-71269.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D))))), M:tm-95, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71270
in-theory        71270
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (E -> D)) and (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-84 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 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-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-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-71270.        ((A or (B -> (A and B))) -> (C -> ((D -> (E -> D)) and (B -> (A and B))))), M:tm-84, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71271
in-theory        71271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-71271.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-83, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71272
in-theory        71272
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (E -> D)) and (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-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-1.            (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-71272.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (E -> D)) and (C -> (B and C))))), M:tm-76, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71273
in-theory        71273
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-73 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 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-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-71273.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B)))), M:tm-73, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71274
in-theory        71274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-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-1.            (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-71274.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D))))), M:tm-69, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71275
in-theory        71275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-71275.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-54, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71276
in-theory        71276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (D -> C)) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-50 tm-822 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-7 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-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-71276.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (D -> C)) and (A -> (B and A)))), M:tm-50, m:tm-822, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71277
in-theory        71277
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-49 tm-822 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
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-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-71277.        ((A or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B)))), M:tm-49, m:tm-822, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71278
in-theory        71278
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (E -> D)) and (C -> (B and C))))
theorem-size     29
proof            (modus-ponens tm-47 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 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-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-71278.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (E -> D)) and (C -> (B and C)))), M:tm-47, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71279
in-theory        71279
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (E -> D)) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-46 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
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-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-71279.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (E -> D)) and (B -> (A and B)))), M:tm-46, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71280
in-theory        71280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-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-1.            (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-71280.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D))))), M:tm-42, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71281
in-theory        71281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-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-1.            (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-71281.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D))))), M:tm-32, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71282
in-theory        71282
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> C)) and (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-24 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and 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-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-1.            (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-71282.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> C)) and (B -> (A and B))))), M:tm-24, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71283
in-theory        71283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-1.            (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-71283.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D))))), M:tm-23, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71284
in-theory        71284
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-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-1.            (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-71284.        (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D))))), M:tm-22, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71285
in-theory        71285
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-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-1.            (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-71285.        (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D))))), M:tm-21, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71286
in-theory        71286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-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-1.            (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-71286.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-20, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71287
in-theory        71287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
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-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-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-71287.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> E)) and (D -> (C and D))))), M:tm-19, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71288
in-theory        71288
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not ((C -> (D -> C)) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-9 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-1)
proof-size       117
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-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-71288.        (((A or (B -> (A and B))) -> (not ((C -> (D -> C)) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71289
in-theory        71289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or ((A -> (B -> A)) and (C -> (D and C)))) -> E))
theorem-size     35
proof            (modus-ponens tm-8 tm-822 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-5 tm-1)
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-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-71289.        ((((A -> (B -> A)) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or ((A -> (B -> A)) and (C -> (D and C)))) -> E)), M:tm-8, m:tm-822, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71290
in-theory        71290
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> ((D -> (E -> D)) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-1.            (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-71290.        (A or ((B or (C -> (B and C))) -> ((D -> (E -> D)) and (C -> (B and C))))), M:tm-7, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71291
in-theory        71291
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-1.            (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-71291.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) or E), M:tm-6, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71292
in-theory        71292
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> ((D -> (E -> D)) and (C -> (B and C)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am 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-48.           (((A -> (B and 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-71292.        (A -> (((B or (C -> (B and C))) -> ((D -> (E -> D)) and (C -> (B and C)))) and A)), M:tm-5, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71293
in-theory        71293
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> ((D -> (E -> D)) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-71293.        (A -> ((B or (C -> (B and C))) -> ((D -> (E -> D)) and (C -> (B and C))))), M:tm-1, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71294
in-theory        71294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-808 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71294.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-808, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71295
in-theory        71295
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((F and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))
theorem-size     65
proof            (modus-ponens tm-798 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71295.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((F and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))), M:tm-798, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71296
in-theory        71296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71296.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-757, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71297
in-theory        71297
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and F) or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))
theorem-size     65
proof            (modus-ponens tm-747 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-20.           (A -> (((B -> (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-71297.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and F) or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))), M:tm-747, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71298
in-theory        71298
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71298.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F))))), M:tm-708, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71299
in-theory        71299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71299.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-665, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71300
in-theory        71300
times-derived    1
----------------------------------------------------------------
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-623 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-20.           (A -> (((B -> (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-71300.        ((A or (B -> (A and B))) -> (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (A and B))))), M:tm-623, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71301
in-theory        71301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71301.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-622, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71302
in-theory        71302
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71302.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (G or F))), M:tm-609, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71303
in-theory        71303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71303.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-605, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71304
in-theory        71304
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (G or F)) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71304.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (G or F)) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-595, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71305
in-theory        71305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71305.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-550, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71306
in-theory        71306
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71306.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-540, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71307
in-theory        71307
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71307.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-530, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71308
in-theory        71308
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71308.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-520, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71309
in-theory        71309
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71309.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-510, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71310
in-theory        71310
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71310.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-500, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71311
in-theory        71311
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71311.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F))))), M:tm-490, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71312
in-theory        71312
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71312.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-480, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71313
in-theory        71313
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))) or F))
theorem-size     29
proof            (modus-ponens tm-470 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-20.           (A -> (((B -> (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-71313.        ((A or (B -> (A and B))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))) or F)), M:tm-470, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71314
in-theory        71314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71314.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-469, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71315
in-theory        71315
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71315.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (F or G))), M:tm-456, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71316
in-theory        71316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71316.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-453, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71317
in-theory        71317
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (F or G)) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71317.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (F or G)) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-443, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71318
in-theory        71318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71318.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-409, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71319
in-theory        71319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71319.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-400, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71320
in-theory        71320
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71320.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-391, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71321
in-theory        71321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71321.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-382, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71322
in-theory        71322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71322.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F))))), M:tm-373, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71323
in-theory        71323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71323.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-364, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71324
in-theory        71324
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (A and B))) and C)))
theorem-size     31
proof            (modus-ponens tm-355 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71324.        ((A or (B -> (A and B))) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (A and B))) and C))), M:tm-355, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71325
in-theory        71325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71325.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-354, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71326
in-theory        71326
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71326.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71327
in-theory        71327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-20.           (A -> (((B -> (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-71327.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D))))), M:tm-338, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71328
in-theory        71328
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     63
proof            (modus-ponens tm-328 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-20.           (A -> (((B -> (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-71328.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-328, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71329
in-theory        71329
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (G -> (F and G))) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71329.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (G -> (F and G))) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-327, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71330
in-theory        71330
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((F and G) -> G) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71330.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((F and G) -> G) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-326, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71331
in-theory        71331
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((F and G) -> F) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71331.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((F and G) -> F) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-325, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71332
in-theory        71332
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-71332.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-324, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71333
in-theory        71333
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (G -> F)) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71333.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (G -> F)) and ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-323, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71334
in-theory        71334
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71334.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F and G) -> G)), M:tm-322, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71335
in-theory        71335
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71335.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F and G) -> F)), M:tm-320, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71336
in-theory        71336
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71336.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71337
in-theory        71337
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     43
proof            (modus-ponens tm-316 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-20.           (A -> (((B -> (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-71337.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71338
in-theory        71338
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71338.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (G -> F))), M:tm-315, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71339
in-theory        71339
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     65
proof            (modus-ponens tm-313 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-20.           (A -> (((B -> (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-71339.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71340
in-theory        71340
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))) -> F) -> (((A or (B -> (A and B))) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) -> F)))
theorem-size     79
proof            (modus-ponens tm-312 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-20.           (A -> (((B -> (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-71340.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))) -> F) -> (((A or (B -> (A and B))) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) -> F))), M:tm-312, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71341
in-theory        71341
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F or ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71341.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F or ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-311, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71342
in-theory        71342
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71342.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) or F)), M:tm-310, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71343
in-theory        71343
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71343.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and F))), M:tm-309, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71344
in-theory        71344
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71344.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (F -> ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))), M:tm-305, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71345
in-theory        71345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-48.           (((A -> (B and 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-71345.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-303, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71346
in-theory        71346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71346.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-270, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71347
in-theory        71347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71347.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-239, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71348
in-theory        71348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-71348.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F))))), M:tm-210, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71349
in-theory        71349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71349.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-183, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71350
in-theory        71350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71350.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-157, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71351
in-theory        71351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71351.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-147, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71352
in-theory        71352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71352.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-134, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71353
in-theory        71353
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71353.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-125, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71354
in-theory        71354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71354.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F))))), M:tm-113, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71355
in-theory        71355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71355.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-105, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71356
in-theory        71356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-71356.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D))))), M:tm-95, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71357
in-theory        71357
times-derived    1
----------------------------------------------------------------
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-84 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-20.           (A -> (((B -> (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-71357.        ((A or (B -> (A and B))) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (A and B))))), M:tm-84, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71358
in-theory        71358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71358.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-83, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71359
in-theory        71359
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
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-48.           (((A -> (B and 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-71359.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C))))), M:tm-76, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71360
in-theory        71360
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))
theorem-size     37
proof            (modus-ponens tm-73 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-5 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-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-71360.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))), M:tm-73, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71361
in-theory        71361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
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-48.           (((A -> (B and 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-71361.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D))))), M:tm-69, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71362
in-theory        71362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71362.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-54, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71363
in-theory        71363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A))))
theorem-size     33
proof            (modus-ponens tm-50 tm-823 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
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-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-71363.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A)))), M:tm-50, m:tm-823, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71364
in-theory        71364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-49 tm-823 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       161
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-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-71364.        ((A or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))), M:tm-49, m:tm-823, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71365
in-theory        71365
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C))))
theorem-size     37
proof            (modus-ponens tm-47 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-5 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-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-71365.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C)))), M:tm-47, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71366
in-theory        71366
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (A and B))))
theorem-size     37
proof            (modus-ponens tm-46 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
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-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-71366.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (A and B)))), M:tm-46, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71367
in-theory        71367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71367.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D))))), M:tm-42, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71368
in-theory        71368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71368.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D))))), M:tm-32, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71369
in-theory        71369
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))
theorem-size     35
proof            (modus-ponens tm-24 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-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-20.           (A -> (((B -> (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-71369.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))), M:tm-24, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71370
in-theory        71370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-48.           (((A -> (B and 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-71370.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D))))), M:tm-23, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71371
in-theory        71371
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71371.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D))))), M:tm-22, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71372
in-theory        71372
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-71372.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D))))), M:tm-21, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71373
in-theory        71373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-71373.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-20, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71374
in-theory        71374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71374.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> (C and D))))), M:tm-19, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71375
in-theory        71375
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-9 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5 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-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-71375.        (((A or (B -> (A and B))) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71376
in-theory        71376
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E and D))) -> F) -> (((E or (D -> (E and D))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E and D)))) -> F))
theorem-size     51
proof            (modus-ponens tm-8 tm-823 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-5 tm-2)
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-48.           (((A -> (B and 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-71376.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E and D))) -> F) -> (((E or (D -> (E and D))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E and D)))) -> F)), M:tm-8, m:tm-823, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71377
in-theory        71377
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-2)
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-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-71377.        (A or ((B or (C -> (B and C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C))))), M:tm-7, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71378
in-theory        71378
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) or F)
theorem-size     29
proof            (modus-ponens tm-6 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-2)
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-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-71378.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) or F), M:tm-6, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71379
in-theory        71379
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-71379.        (A -> (((B or (C -> (B and C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C)))) and A)), M:tm-5, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71380
in-theory        71380
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5 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-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-71380.        (A -> ((B or (C -> (B and C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> (B and C))))), M:tm-1, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71381
in-theory        71381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71381.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-808, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71382
in-theory        71382
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-798 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71382.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B))))), M:tm-798, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71383
in-theory        71383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-71383.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-757, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71384
in-theory        71384
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-747 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-71384.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B))))), M:tm-747, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71385
in-theory        71385
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71385.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F))))), M:tm-708, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71386
in-theory        71386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-71386.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-665, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71387
in-theory        71387
times-derived    1
----------------------------------------------------------------
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-623 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> 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-71387.        ((A or (B -> (A and B))) -> (C or (((D and E) -> D) and (B -> (A and B))))), M:tm-623, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71388
in-theory        71388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> 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-71388.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-622, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71389
in-theory        71389
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> 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-71389.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (F or E))), M:tm-609, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71390
in-theory        71390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> 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-71390.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-605, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71391
in-theory        71391
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-3.            ((A and B) -> 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-71391.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))))), M:tm-595, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71392
in-theory        71392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-3.            ((A and B) -> 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-71392.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-550, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71393
in-theory        71393
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-3.            ((A and B) -> 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-71393.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-540, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71394
in-theory        71394
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-3.            ((A and B) -> 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-71394.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-530, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71395
in-theory        71395
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> 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-71395.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-520, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71396
in-theory        71396
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-3.            ((A and B) -> 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-71396.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-510, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71397
in-theory        71397
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-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-71397.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-500, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71398
in-theory        71398
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-3.            ((A and B) -> 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-71398.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F))))), M:tm-490, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71399
in-theory        71399
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and B) -> 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-71399.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-480, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71400
in-theory        71400
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C and D) -> C) and (B -> (A and B))) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> 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-71400.        ((A or (B -> (A and B))) -> ((((C and D) -> C) and (B -> (A and B))) or E)), M:tm-470, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71401
in-theory        71401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> 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-71401.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-469, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71402
in-theory        71402
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> 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-71402.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (E or F))), M:tm-456, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71403
in-theory        71403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> 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-71403.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-453, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71404
in-theory        71404
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-3.            ((A and B) -> 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-71404.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))))), M:tm-443, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71405
in-theory        71405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-3.            ((A and B) -> 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-71405.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-409, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71406
in-theory        71406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> 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-71406.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-400, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71407
in-theory        71407
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-3.            ((A and B) -> 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-71407.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-391, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71408
in-theory        71408
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-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-71408.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-382, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71409
in-theory        71409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-3.            ((A and B) -> 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-71409.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F))))), M:tm-373, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71410
in-theory        71410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and B) -> 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-71410.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-364, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71411
in-theory        71411
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((((D and E) -> D) and (B -> (A and B))) and C)))
theorem-size     23
proof            (modus-ponens tm-355 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-3.            ((A and B) -> 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-71411.        ((A or (B -> (A and B))) -> (C -> ((((D and E) -> D) and (B -> (A and B))) and C))), M:tm-355, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71412
in-theory        71412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-3.            ((A and B) -> 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-71412.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-354, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71413
in-theory        71413
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A and B) -> 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-71413.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71414
in-theory        71414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-3.            ((A and B) -> 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-71414.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D))))), M:tm-338, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71415
in-theory        71415
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and D) -> C) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-328 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and 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-328.          ((A -> 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-3.            ((A and B) -> 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-71415.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and D) -> C) and (B -> (A and B)))))), M:tm-328, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71416
in-theory        71416
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-3.            ((A and B) -> 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-71416.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))))), M:tm-327, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71417
in-theory        71417
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-3.            ((A and B) -> 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-71417.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))))), M:tm-326, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71418
in-theory        71418
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-71418.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))))), M:tm-325, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71419
in-theory        71419
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-3.            ((A and B) -> 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-71419.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))))), M:tm-324, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71420
in-theory        71420
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am 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-48.           (((A -> (B and 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-71420.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))))), M:tm-323, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71421
in-theory        71421
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> 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-71421.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E and F) -> F)), M:tm-322, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71422
in-theory        71422
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-71422.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E and F) -> E)), M:tm-320, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71423
in-theory        71423
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-3.            ((A and B) -> 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-71423.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71424
in-theory        71424
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and 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-48.           (((A -> (B and 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-71424.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71425
in-theory        71425
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> 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-71425.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (F -> E))), M:tm-315, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71426
in-theory        71426
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (((C and D) -> C) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-313 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-3.            ((A and B) -> 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-71426.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (((C and D) -> C) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71427
in-theory        71427
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((((C and D) -> C) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or (((C and D) -> C) and (B -> (A and B)))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-3.            ((A and B) -> 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-71427.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((((C and D) -> C) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or (((C and D) -> C) and (B -> (A and B)))) -> E))), M:tm-312, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71428
in-theory        71428
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-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-3.            ((A and B) -> 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-71428.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))))), M:tm-311, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71429
in-theory        71429
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-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-3.            ((A and B) -> 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-71429.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) or E)), M:tm-310, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71430
in-theory        71430
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-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-3.            ((A and B) -> 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-71430.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and E))), M:tm-309, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71431
in-theory        71431
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am 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-48.           (((A -> (B and 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-71431.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))))), M:tm-305, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71432
in-theory        71432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-3.            ((A and B) -> 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-71432.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-303, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71433
in-theory        71433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-3.            ((A and B) -> 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-71433.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-270, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71434
in-theory        71434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-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-71434.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-239, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71435
in-theory        71435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-3.            ((A and B) -> 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-71435.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F))))), M:tm-210, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71436
in-theory        71436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-3.            ((A and B) -> 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-71436.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-183, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71437
in-theory        71437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> 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-71437.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-157, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71438
in-theory        71438
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-3.            ((A and B) -> 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-71438.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-147, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71439
in-theory        71439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-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-71439.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-134, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71440
in-theory        71440
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-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-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-71440.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-125, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71441
in-theory        71441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-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-3.            ((A and B) -> 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-71441.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F))))), M:tm-113, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71442
in-theory        71442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-3.            ((A and B) -> 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-71442.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-105, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71443
in-theory        71443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-3.            ((A and B) -> 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-71443.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D))))), M:tm-95, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71444
in-theory        71444
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D and E) -> D) and (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-84 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> 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-71444.        ((A or (B -> (A and B))) -> (C -> (((D and E) -> D) and (B -> (A and B))))), M:tm-84, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71445
in-theory        71445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> 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-71445.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-83, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71446
in-theory        71446
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((D and E) -> D) and (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-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-3.            ((A and B) -> 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-71446.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((D and E) -> D) and (C -> (B and C))))), M:tm-76, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71447
in-theory        71447
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-73 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-3)
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-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-71447.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B)))), M:tm-73, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71448
in-theory        71448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-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-3.            ((A and B) -> 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-71448.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D))))), M:tm-69, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71449
in-theory        71449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-71449.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-54, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71450
in-theory        71450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((C and D) -> C) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-50 tm-824 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
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-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-71450.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((C and D) -> C) and (A -> (B and A)))), M:tm-50, m:tm-824, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71451
in-theory        71451
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-49 tm-824 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5 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-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-71451.        ((A or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B)))), M:tm-49, m:tm-824, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71452
in-theory        71452
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((D and E) -> D) and (C -> (B and C))))
theorem-size     29
proof            (modus-ponens tm-47 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-3)
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-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-71452.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((D and E) -> D) and (C -> (B and C)))), M:tm-47, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71453
in-theory        71453
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((D and E) -> D) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-46 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
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-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-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-71453.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((D and E) -> D) and (B -> (A and B)))), M:tm-46, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71454
in-theory        71454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-3.            ((A and B) -> 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-71454.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D))))), M:tm-42, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71455
in-theory        71455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-3.            ((A and B) -> 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-71455.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D))))), M:tm-32, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71456
in-theory        71456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and D) -> C) and (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-24 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-71456.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and D) -> C) and (B -> (A and B))))), M:tm-24, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71457
in-theory        71457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-3.            ((A and B) -> 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-71457.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D))))), M:tm-23, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71458
in-theory        71458
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 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-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-3.            ((A and B) -> 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-71458.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D))))), M:tm-22, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71459
in-theory        71459
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-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-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-71459.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D))))), M:tm-21, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71460
in-theory        71460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-3.            ((A and B) -> 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-71460.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-20, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71461
in-theory        71461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-19.           (A -> ((B -> (C -> B)) and 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-3.            ((A and B) -> 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-71461.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((E and F) -> E) and (D -> (C and D))))), M:tm-19, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71462
in-theory        71462
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (((C and D) -> C) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-9 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-3)
proof-size       117
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-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-71462.        (((A or (B -> (A and B))) -> (not (((C and D) -> C) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71463
in-theory        71463
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or (((A and B) -> A) and (C -> (D and C)))) -> E))
theorem-size     35
proof            (modus-ponens tm-8 tm-824 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-5 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-3.            ((A and B) -> 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-71463.        (((((A and B) -> A) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or (((A and B) -> A) and (C -> (D and C)))) -> E)), M:tm-8, m:tm-824, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71464
in-theory        71464
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (((D and E) -> D) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> 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-71464.        (A or ((B or (C -> (B and C))) -> (((D and E) -> D) and (C -> (B and C))))), M:tm-7, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71465
in-theory        71465
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> 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-71465.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) or E), M:tm-6, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71466
in-theory        71466
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (((D and E) -> D) and (C -> (B and C)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71466.        (A -> (((B or (C -> (B and C))) -> (((D and E) -> D) and (C -> (B and C)))) and A)), M:tm-5, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71467
in-theory        71467
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (((D and E) -> D) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> 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-71467.        (A -> ((B or (C -> (B and C))) -> (((D and E) -> D) and (C -> (B and C))))), M:tm-1, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71468
in-theory        71468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71468.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-808, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71469
in-theory        71469
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-798 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71469.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B))))), M:tm-798, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71470
in-theory        71470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-71470.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-757, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71471
in-theory        71471
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-747 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-4.            ((A and B) -> 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-71471.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B))))), M:tm-747, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71472
in-theory        71472
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71472.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F))))), M:tm-708, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71473
in-theory        71473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-71473.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-665, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71474
in-theory        71474
times-derived    1
----------------------------------------------------------------
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-623 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> 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-71474.        ((A or (B -> (A and B))) -> (C or (((D and E) -> E) and (B -> (A and B))))), M:tm-623, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71475
in-theory        71475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-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-4.            ((A and B) -> 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-71475.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-622, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71476
in-theory        71476
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> 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-71476.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (F or E))), M:tm-609, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71477
in-theory        71477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> 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-71477.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-605, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71478
in-theory        71478
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> 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-71478.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))))), M:tm-595, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71479
in-theory        71479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-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-4.            ((A and B) -> 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-71479.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-550, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71480
in-theory        71480
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> 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-71480.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-540, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71481
in-theory        71481
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-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-4.            ((A and B) -> 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-71481.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-530, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71482
in-theory        71482
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> 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-71482.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-520, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71483
in-theory        71483
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-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-71483.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-510, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71484
in-theory        71484
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-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-4.            ((A and B) -> 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-71484.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-500, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71485
in-theory        71485
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-4.            ((A and B) -> 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-71485.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F))))), M:tm-490, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71486
in-theory        71486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-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-4.            ((A and B) -> 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-71486.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-480, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71487
in-theory        71487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C and D) -> D) and (B -> (A and B))) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> 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-71487.        ((A or (B -> (A and B))) -> ((((C and D) -> D) and (B -> (A and B))) or E)), M:tm-470, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71488
in-theory        71488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-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-4.            ((A and B) -> 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-71488.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-469, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71489
in-theory        71489
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> 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-71489.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (E or F))), M:tm-456, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71490
in-theory        71490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> 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-71490.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-453, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71491
in-theory        71491
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> 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-71491.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))))), M:tm-443, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71492
in-theory        71492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> 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-71492.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-409, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71493
in-theory        71493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> 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-71493.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-400, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71494
in-theory        71494
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-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-71494.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-391, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71495
in-theory        71495
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-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-4.            ((A and B) -> 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-71495.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-382, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71496
in-theory        71496
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-4.            ((A and B) -> 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-71496.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F))))), M:tm-373, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71497
in-theory        71497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-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-4.            ((A and B) -> 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-71497.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-364, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71498
in-theory        71498
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((((D and E) -> E) and (B -> (A and B))) and C)))
theorem-size     23
proof            (modus-ponens tm-355 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-4.            ((A and B) -> 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-71498.        ((A or (B -> (A and B))) -> (C -> ((((D and E) -> E) and (B -> (A and B))) and C))), M:tm-355, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71499
in-theory        71499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-4.            ((A and B) -> 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-71499.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-354, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71500
in-theory        71500
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> 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-71500.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71501
in-theory        71501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-4.            ((A and B) -> 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-71501.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D))))), M:tm-338, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71502
in-theory        71502
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and D) -> D) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-328 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-4.            ((A and B) -> 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-71502.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and D) -> D) and (B -> (A and B)))))), M:tm-328, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71503
in-theory        71503
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> 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-71503.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))))), M:tm-327, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71504
in-theory        71504
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-71504.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))))), M:tm-326, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71505
in-theory        71505
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> 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-71505.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))))), M:tm-325, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71506
in-theory        71506
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-71506.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))))), M:tm-324, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71507
in-theory        71507
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71507.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))))), M:tm-323, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71508
in-theory        71508
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-71508.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E and F) -> F)), M:tm-322, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71509
in-theory        71509
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> 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-71509.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E and F) -> E)), M:tm-320, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71510
in-theory        71510
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A and B) -> 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-71510.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71511
in-theory        71511
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-4.            ((A and B) -> 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-71511.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71512
in-theory        71512
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> 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-71512.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (F -> E))), M:tm-315, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71513
in-theory        71513
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (((C and D) -> D) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-313 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-4.            ((A and B) -> 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-71513.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not (((C and D) -> D) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71514
in-theory        71514
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((((C and D) -> D) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or (((C and D) -> D) and (B -> (A and B)))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-4.            ((A and B) -> 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-71514.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((((C and D) -> D) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or (((C and D) -> D) and (B -> (A and B)))) -> E))), M:tm-312, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71515
in-theory        71515
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> 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-71515.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))))), M:tm-311, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71516
in-theory        71516
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> 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-71516.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) or E)), M:tm-310, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71517
in-theory        71517
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-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-4.            ((A and B) -> 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-71517.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and E))), M:tm-309, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71518
in-theory        71518
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71518.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))))), M:tm-305, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71519
in-theory        71519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-4.            ((A and B) -> 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-71519.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-303, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71520
in-theory        71520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-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-71520.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-270, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71521
in-theory        71521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-4.            ((A and B) -> 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-71521.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-239, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71522
in-theory        71522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> 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-71522.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F))))), M:tm-210, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71523
in-theory        71523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-4.            ((A and B) -> 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-71523.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-183, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71524
in-theory        71524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-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-71524.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-157, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71525
in-theory        71525
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-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-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-71525.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-147, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71526
in-theory        71526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-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-4.            ((A and B) -> 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-71526.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-134, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71527
in-theory        71527
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> 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-71527.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-125, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71528
in-theory        71528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-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-4.            ((A and B) -> 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-71528.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F))))), M:tm-113, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71529
in-theory        71529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> 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-71529.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-105, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71530
in-theory        71530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> 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-71530.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D))))), M:tm-95, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71531
in-theory        71531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D and E) -> E) and (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-84 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> 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-71531.        ((A or (B -> (A and B))) -> (C -> (((D and E) -> E) and (B -> (A and B))))), M:tm-84, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71532
in-theory        71532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-4.            ((A and B) -> 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-71532.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-83, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71533
in-theory        71533
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((D and E) -> E) and (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-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-4.            ((A and B) -> 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-71533.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((D and E) -> E) and (C -> (B and C))))), M:tm-76, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71534
in-theory        71534
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-73 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-4)
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-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-71534.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B)))), M:tm-73, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71535
in-theory        71535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-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-4.            ((A and B) -> 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-71535.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D))))), M:tm-69, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71536
in-theory        71536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-71536.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-54, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71537
in-theory        71537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((C and D) -> D) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-50 tm-825 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
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-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-71537.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((C and D) -> D) and (A -> (B and A)))), M:tm-50, m:tm-825, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71538
in-theory        71538
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-49 tm-825 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
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-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-71538.        ((A or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B)))), M:tm-49, m:tm-825, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71539
in-theory        71539
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((D and E) -> E) and (C -> (B and C))))
theorem-size     29
proof            (modus-ponens tm-47 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-5)
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-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-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-71539.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((D and E) -> E) and (C -> (B and C)))), M:tm-47, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71540
in-theory        71540
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((D and E) -> E) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-46 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
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-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-71540.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((D and E) -> E) and (B -> (A and B)))), M:tm-46, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71541
in-theory        71541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-4.            ((A and B) -> 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-71541.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D))))), M:tm-42, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71542
in-theory        71542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-4.            ((A and B) -> 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-71542.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D))))), M:tm-32, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71543
in-theory        71543
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and D) -> D) and (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-24 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-71543.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and D) -> D) and (B -> (A and B))))), M:tm-24, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71544
in-theory        71544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-4.            ((A and B) -> 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-71544.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D))))), M:tm-23, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71545
in-theory        71545
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
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-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-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-71545.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D))))), M:tm-22, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71546
in-theory        71546
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-4.            ((A and B) -> 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-71546.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D))))), M:tm-21, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71547
in-theory        71547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-4.            ((A and B) -> 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-71547.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-20, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71548
in-theory        71548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
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-19.           (A -> ((B -> (C -> B)) and 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-4.            ((A and B) -> 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-71548.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((E and F) -> F) and (D -> (C and D))))), M:tm-19, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71549
in-theory        71549
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (((C and D) -> D) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-9 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-4)
proof-size       117
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-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-71549.        (((A or (B -> (A and B))) -> (not (((C and D) -> D) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71550
in-theory        71550
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or (((A and B) -> B) and (C -> (D and C)))) -> E))
theorem-size     35
proof            (modus-ponens tm-8 tm-825 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-5 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-4.            ((A and B) -> 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-71550.        (((((A and B) -> B) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or (((A and B) -> B) and (C -> (D and C)))) -> E)), M:tm-8, m:tm-825, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71551
in-theory        71551
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (((D and E) -> E) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> 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-71551.        (A or ((B or (C -> (B and C))) -> (((D and E) -> E) and (C -> (B and C))))), M:tm-7, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71552
in-theory        71552
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> 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-71552.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) or E), M:tm-6, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71553
in-theory        71553
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (((D and E) -> E) and (C -> (B and C)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71553.        (A -> (((B or (C -> (B and C))) -> (((D and E) -> E) and (C -> (B and C)))) and A)), M:tm-5, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71554
in-theory        71554
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (((D and E) -> E) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> 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-71554.        (A -> ((B or (C -> (B and C))) -> (((D and E) -> E) and (C -> (B and C))))), M:tm-1, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71555
in-theory        71555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71555.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-808, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71556
in-theory        71556
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))
theorem-size     53
proof            (modus-ponens tm-798 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71556.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))), M:tm-798, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71557
in-theory        71557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-71557.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-757, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71558
in-theory        71558
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))
theorem-size     53
proof            (modus-ponens tm-747 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-71558.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))), M:tm-747, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71559
in-theory        71559
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71559.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F))))), M:tm-708, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71560
in-theory        71560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-71560.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-665, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71561
in-theory        71561
times-derived    1
----------------------------------------------------------------
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-623 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-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-71561.        ((A or (B -> (A and B))) -> (C or ((D -> (E -> (D and E))) and (B -> (A and B))))), M:tm-623, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71562
in-theory        71562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-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-71562.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-622, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71563
in-theory        71563
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-71563.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (F or E))), M:tm-609, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71564
in-theory        71564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-71564.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-605, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71565
in-theory        71565
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-71565.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-595, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71566
in-theory        71566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-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-71566.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-550, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71567
in-theory        71567
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-71567.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-540, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71568
in-theory        71568
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-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-71568.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-530, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71569
in-theory        71569
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-71569.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-520, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71570
in-theory        71570
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-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-71570.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-510, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71571
in-theory        71571
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-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-71571.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-500, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71572
in-theory        71572
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-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-71572.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F))))), M:tm-490, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71573
in-theory        71573
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-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-71573.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-480, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71574
in-theory        71574
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D -> (C and D))) and (B -> (A and B))) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-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-71574.        ((A or (B -> (A and B))) -> (((C -> (D -> (C and D))) and (B -> (A and B))) or E)), M:tm-470, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71575
in-theory        71575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-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-71575.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-469, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71576
in-theory        71576
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-71576.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (E or F))), M:tm-456, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71577
in-theory        71577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-71577.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-453, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71578
in-theory        71578
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-71578.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-443, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71579
in-theory        71579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-71579.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-409, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71580
in-theory        71580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-71580.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-400, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71581
in-theory        71581
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-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-71581.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-391, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71582
in-theory        71582
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-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-71582.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-382, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71583
in-theory        71583
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-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-71583.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F))))), M:tm-373, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71584
in-theory        71584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-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-71584.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-364, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71585
in-theory        71585
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D -> (E -> (D and E))) and (B -> (A and B))) and C)))
theorem-size     25
proof            (modus-ponens tm-355 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
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-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-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-71585.        ((A or (B -> (A and B))) -> (C -> (((D -> (E -> (D and E))) and (B -> (A and B))) and C))), M:tm-355, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71586
in-theory        71586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-71586.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-354, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71587
in-theory        71587
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-71587.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71588
in-theory        71588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-71588.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D))))), M:tm-338, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71589
in-theory        71589
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     51
proof            (modus-ponens tm-328 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-71589.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-328, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71590
in-theory        71590
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-71590.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-327, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71591
in-theory        71591
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-71591.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-326, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71592
in-theory        71592
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-71592.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-325, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71593
in-theory        71593
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-71593.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-324, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71594
in-theory        71594
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71594.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-323, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71595
in-theory        71595
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-71595.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E and F) -> F)), M:tm-322, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71596
in-theory        71596
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-71596.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E and F) -> E)), M:tm-320, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71597
in-theory        71597
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-71597.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71598
in-theory        71598
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-316 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-71598.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71599
in-theory        71599
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-71599.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (F -> E))), M:tm-315, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71600
in-theory        71600
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not ((C -> (D -> (C and D))) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     53
proof            (modus-ponens tm-313 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-71600.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not ((C -> (D -> (C and D))) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71601
in-theory        71601
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((((C -> (D -> (C and D))) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or ((C -> (D -> (C and D))) and (B -> (A and B)))) -> E)))
theorem-size     61
proof            (modus-ponens tm-312 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-71601.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((((C -> (D -> (C and D))) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or ((C -> (D -> (C and D))) and (B -> (A and B)))) -> E))), M:tm-312, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71602
in-theory        71602
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-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-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-71602.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-311, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71603
in-theory        71603
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-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-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-71603.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) or E)), M:tm-310, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71604
in-theory        71604
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-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-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-71604.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and E))), M:tm-309, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71605
in-theory        71605
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71605.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))), M:tm-305, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71606
in-theory        71606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8)
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-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-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-71606.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-303, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71607
in-theory        71607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-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-71607.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-270, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71608
in-theory        71608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-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-71608.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-239, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71609
in-theory        71609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-71609.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F))))), M:tm-210, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71610
in-theory        71610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-71610.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-183, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71611
in-theory        71611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-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-71611.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-157, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71612
in-theory        71612
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-71612.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-147, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71613
in-theory        71613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-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-71613.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-134, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71614
in-theory        71614
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-71614.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-125, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71615
in-theory        71615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-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-71615.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F))))), M:tm-113, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71616
in-theory        71616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-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-71616.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-105, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71617
in-theory        71617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-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-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-71617.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D))))), M:tm-95, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71618
in-theory        71618
times-derived    1
----------------------------------------------------------------
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-84 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-71618.        ((A or (B -> (A and B))) -> (C -> ((D -> (E -> (D and E))) and (B -> (A and B))))), M:tm-84, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71619
in-theory        71619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-71619.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-83, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71620
in-theory        71620
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (E -> (D and E))) and (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8)
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-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-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-71620.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (E -> (D and E))) and (C -> (B and C))))), M:tm-76, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71621
in-theory        71621
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-73 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       143
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-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-71621.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))), M:tm-73, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71622
in-theory        71622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8)
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-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-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-71622.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D))))), M:tm-69, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71623
in-theory        71623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-71623.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-54, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71624
in-theory        71624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (D -> (C and D))) and (A -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-50 tm-826 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-71624.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (D -> (C and D))) and (A -> (B and A)))), M:tm-50, m:tm-826, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71625
in-theory        71625
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-49 tm-826 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       137
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-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-71625.        ((A or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))), M:tm-49, m:tm-826, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71626
in-theory        71626
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (E -> (D and E))) and (C -> (B and C))))
theorem-size     31
proof            (modus-ponens tm-47 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       143
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-48.           (((A -> (B and 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-71626.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (E -> (D and E))) and (C -> (B and C)))), M:tm-47, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71627
in-theory        71627
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (E -> (D and E))) and (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-46 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
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-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-71627.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (E -> (D and E))) and (B -> (A and B)))), M:tm-46, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71628
in-theory        71628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-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-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-71628.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D))))), M:tm-42, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71629
in-theory        71629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-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-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-71629.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D))))), M:tm-32, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71630
in-theory        71630
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> (C and D))) and (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-24 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-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-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-71630.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D -> (C and D))) and (B -> (A and B))))), M:tm-24, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71631
in-theory        71631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8)
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-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-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-71631.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D))))), M:tm-23, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71632
in-theory        71632
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-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-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-71632.        (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D))))), M:tm-22, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71633
in-theory        71633
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-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-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-71633.        (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D))))), M:tm-21, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71634
in-theory        71634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 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-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-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-71634.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-20, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71635
in-theory        71635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
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-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-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-71635.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (F -> (E and F))) and (D -> (C and D))))), M:tm-19, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71636
in-theory        71636
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not ((C -> (D -> (C and D))) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     31
proof            (modus-ponens tm-9 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5)
proof-size       125
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-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-71636.        (((A or (B -> (A and B))) -> (not ((C -> (D -> (C and D))) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71637
in-theory        71637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or ((A -> (B -> (A and B))) and (C -> (D and C)))) -> E))
theorem-size     39
proof            (modus-ponens tm-8 tm-826 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-71637.        ((((A -> (B -> (A and B))) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or ((A -> (B -> (A and B))) and (C -> (D and C)))) -> E)), M:tm-8, m:tm-826, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71638
in-theory        71638
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> ((D -> (E -> (D and E))) and (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-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-71638.        (A or ((B or (C -> (B and C))) -> ((D -> (E -> (D and E))) and (C -> (B and C))))), M:tm-7, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71639
in-theory        71639
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-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-71639.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) or E), M:tm-6, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71640
in-theory        71640
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> ((D -> (E -> (D and E))) and (C -> (B and C)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-71640.        (A -> (((B or (C -> (B and C))) -> ((D -> (E -> (D and E))) and (C -> (B and C)))) and A)), M:tm-5, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71641
in-theory        71641
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> ((D -> (E -> (D and E))) and (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-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-71641.        (A -> ((B or (C -> (B and C))) -> ((D -> (E -> (D and E))) and (C -> (B and C))))), M:tm-1, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71642
in-theory        71642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71642.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-808, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71643
in-theory        71643
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((C and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (B -> (B and (A and B)))))
theorem-size     41
proof            (modus-ponens tm-798 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-71643.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((C and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (B -> (B and (A and B))))), M:tm-798, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71644
in-theory        71644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71644.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-757, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71645
in-theory        71645
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (B -> (B and (A and B)))))
theorem-size     41
proof            (modus-ponens tm-747 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and 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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-71645.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (B -> (B and (A and B))))), M:tm-747, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71646
in-theory        71646
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (F -> (F and (E and F)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71646.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (F -> (F and (E and F))))), M:tm-708, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71647
in-theory        71647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71647.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-665, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71648
in-theory        71648
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (B -> (B and (A and B)))))
theorem-size     17
proof            (modus-ponens tm-623 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-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-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-71648.        ((A or (B -> (A and B))) -> (C or (B -> (B and (A and B))))), M:tm-623, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71649
in-theory        71649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71649.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-622, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71650
in-theory        71650
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (D or C)))
theorem-size     21
proof            (modus-ponens tm-609 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-71650.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (D or C))), M:tm-609, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71651
in-theory        71651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71651.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-605, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71652
in-theory        71652
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (D or C)) and ((A or (B -> (A and B))) -> (B -> (B and (A and B))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-71652.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (D or C)) and ((A or (B -> (A and B))) -> (B -> (B and (A and B)))))), M:tm-595, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71653
in-theory        71653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71653.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-550, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71654
in-theory        71654
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71654.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-540, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71655
in-theory        71655
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71655.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-530, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71656
in-theory        71656
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71656.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-520, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71657
in-theory        71657
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71657.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-510, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71658
in-theory        71658
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71658.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-500, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71659
in-theory        71659
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (F -> (F and (E and F)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-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-71659.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (F -> (F and (E and F))))), M:tm-490, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71660
in-theory        71660
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71660.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-480, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71661
in-theory        71661
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (B and (A and B))) or C))
theorem-size     17
proof            (modus-ponens tm-470 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-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-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-71661.        ((A or (B -> (A and B))) -> ((B -> (B and (A and B))) or C)), M:tm-470, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71662
in-theory        71662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71662.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-469, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71663
in-theory        71663
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (C or D)))
theorem-size     21
proof            (modus-ponens tm-456 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-71663.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (C or D))), M:tm-456, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71664
in-theory        71664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71664.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-453, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71665
in-theory        71665
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (C or D)) and ((A or (B -> (A and B))) -> (B -> (B and (A and B))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-71665.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (C or D)) and ((A or (B -> (A and B))) -> (B -> (B and (A and B)))))), M:tm-443, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71666
in-theory        71666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71666.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-409, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71667
in-theory        71667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71667.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-400, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71668
in-theory        71668
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71668.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-391, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71669
in-theory        71669
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71669.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-382, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71670
in-theory        71670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (F -> (F and (E and F)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-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-71670.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (F -> (F and (E and F))))), M:tm-373, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71671
in-theory        71671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71671.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-364, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71672
in-theory        71672
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((B -> (B and (A and B))) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
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-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-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-71672.        ((A or (B -> (A and B))) -> (C -> ((B -> (B and (A and B))) and C))), M:tm-355, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71673
in-theory        71673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71673.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-354, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71674
in-theory        71674
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (D -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-341 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-71674.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71675
in-theory        71675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (D -> (D and (C and D)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-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-71675.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (D -> (D and (C and D))))), M:tm-338, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71676
in-theory        71676
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (B -> (B and (A and B))))))
theorem-size     39
proof            (modus-ponens tm-328 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-71676.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (B -> (B and (A and B)))))), M:tm-328, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71677
in-theory        71677
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (D -> (C and D))) and ((A or (B -> (A and B))) -> (B -> (B and (A and B))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-71677.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (D -> (C and D))) and ((A or (B -> (A and B))) -> (B -> (B and (A and B)))))), M:tm-327, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71678
in-theory        71678
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((C and D) -> D) and ((A or (B -> (A and B))) -> (B -> (B and (A and B))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-71678.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((C and D) -> D) and ((A or (B -> (A and B))) -> (B -> (B and (A and B)))))), M:tm-326, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71679
in-theory        71679
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((C and D) -> C) and ((A or (B -> (A and B))) -> (B -> (B and (A and B))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-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-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-71679.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((C and D) -> C) and ((A or (B -> (A and B))) -> (B -> (B and (A and B)))))), M:tm-325, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71680
in-theory        71680
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> (A and B))) -> (B -> (B and (A and B))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-71680.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> (A and B))) -> (B -> (B and (A and B)))))), M:tm-324, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71681
in-theory        71681
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (D -> C)) and ((A or (B -> (A and B))) -> (B -> (B and (A and B))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-71681.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (D -> C)) and ((A or (B -> (A and B))) -> (B -> (B and (A and B)))))), M:tm-323, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71682
in-theory        71682
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C and D) -> D))
theorem-size     21
proof            (modus-ponens tm-322 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-71682.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C and D) -> D)), M:tm-322, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71683
in-theory        71683
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C and D) -> C))
theorem-size     21
proof            (modus-ponens tm-320 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-71683.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C and D) -> C)), M:tm-320, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71684
in-theory        71684
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-318 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-71684.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71685
in-theory        71685
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     31
proof            (modus-ponens tm-316 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-71685.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71686
in-theory        71686
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (D -> C)))
theorem-size     21
proof            (modus-ponens tm-315 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-71686.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (D -> C))), M:tm-315, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71687
in-theory        71687
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((A or (B -> (A and B))) -> (not (B -> (B and (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-313 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-71687.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((A or (B -> (A and B))) -> (not (B -> (B and (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71688
in-theory        71688
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((B -> (B and (A and B))) -> C) -> (((A or (B -> (A and B))) or (B -> (B and (A and B)))) -> C)))
theorem-size     43
proof            (modus-ponens tm-312 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-71688.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((B -> (B and (A and B))) -> C) -> (((A or (B -> (A and B))) or (B -> (B and (A and B)))) -> C))), M:tm-312, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71689
in-theory        71689
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C or ((A or (B -> (A and B))) -> (B -> (B and (A and B))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-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-71689.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C or ((A or (B -> (A and B))) -> (B -> (B and (A and B)))))), M:tm-311, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71690
in-theory        71690
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) or C))
theorem-size     33
proof            (modus-ponens tm-310 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-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-71690.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) or C)), M:tm-310, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71691
in-theory        71691
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and C)))
theorem-size     35
proof            (modus-ponens tm-309 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-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-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-71691.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and C))), M:tm-309, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71692
in-theory        71692
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((A or (B -> (A and B))) -> B) -> ((A or (B -> (A and B))) -> (B and (A and B)))))
theorem-size     39
proof            (modus-ponens tm-306 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B Bm) (C (and Bm (and Am Bm)))))
axioms-used      (tm-2 tm-5 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-71692.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((A or (B -> (A and B))) -> B) -> ((A or (B -> (A and B))) -> (B and (A and B))))), M:tm-306, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B Bm) (C (and Bm (and Am Bm))))
================================================================
tm-name          tm-71693
in-theory        71693
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> ((A or (B -> (A and B))) -> (B -> (B and (A and B))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-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-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-71693.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (C -> ((A or (B -> (A and B))) -> (B -> (B and (A and B)))))), M:tm-305, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71694
in-theory        71694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71694.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-303, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71695
in-theory        71695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71695.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-270, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71696
in-theory        71696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71696.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-239, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71697
in-theory        71697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (F -> (F and (E and F)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-71697.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (F -> (F and (E and F))))), M:tm-210, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71698
in-theory        71698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71698.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-183, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71699
in-theory        71699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71699.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-157, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71700
in-theory        71700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-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-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-71700.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-147, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71701
in-theory        71701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71701.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-134, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71702
in-theory        71702
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-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-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-71702.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-125, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71703
in-theory        71703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (F -> (F and (E and F)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-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-71703.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (F -> (F and (E and F))))), M:tm-113, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71704
in-theory        71704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-71704.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-105, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71705
in-theory        71705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (D -> (D and (C and D)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-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-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-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-71705.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (D -> (D and (C and D))))), M:tm-95, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71706
in-theory        71706
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (B -> (B and (A and B)))))
theorem-size     17
proof            (modus-ponens tm-84 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 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-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-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-71706.        ((A or (B -> (A and B))) -> (C -> (B -> (B and (A and B))))), M:tm-84, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71707
in-theory        71707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71707.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-83, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71708
in-theory        71708
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (C -> (C and (B and C)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71708.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (C -> (C and (B and C))))), M:tm-76, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71709
in-theory        71709
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (B -> (B and (A and B))))
theorem-size     25
proof            (modus-ponens tm-73 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-2)
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-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-71709.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (B -> (B and (A and B)))), M:tm-73, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71710
in-theory        71710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (D -> (D and (C and D)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71710.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (D -> (D and (C and D))))), M:tm-69, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71711
in-theory        71711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-71711.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-54, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71712
in-theory        71712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (A -> (A and (B and A))))
theorem-size     21
proof            (modus-ponens tm-50 tm-827 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-8 tm-7 tm-5 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-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-71712.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (A -> (A and (B and A)))), M:tm-50, m:tm-827, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71713
in-theory        71713
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (B -> (B and (A and B))))
theorem-size     17
proof            (modus-ponens tm-49 tm-827 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
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-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-71713.        ((A or (A or (B -> (A and B)))) -> (B -> (B and (A and B)))), M:tm-49, m:tm-827, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71714
in-theory        71714
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (C -> (C and (B and C))))
theorem-size     25
proof            (modus-ponens tm-47 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
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-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-71714.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (C -> (C and (B and C)))), M:tm-47, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71715
in-theory        71715
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (B -> (B and (A and B))))
theorem-size     25
proof            (modus-ponens tm-46 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
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-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-71715.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (B -> (B and (A and B)))), M:tm-46, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71716
in-theory        71716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (D -> (D and (C and D)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71716.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (D -> (D and (C and D))))), M:tm-42, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71717
in-theory        71717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (D -> (D and (C and D)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71717.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (D -> (D and (C and D))))), M:tm-32, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71718
in-theory        71718
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (B -> (B and (A and B)))))
theorem-size     23
proof            (modus-ponens tm-24 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-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-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-71718.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (B -> (B and (A and B))))), M:tm-24, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71719
in-theory        71719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (D -> (D and (C and D)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71719.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (D -> (D and (C and D))))), M:tm-23, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71720
in-theory        71720
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (D -> (D and (C and D)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71720.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (D -> (D and (C and D))))), M:tm-22, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71721
in-theory        71721
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (D -> (D and (C and D)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71721.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (D -> (D and (C and D))))), M:tm-21, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71722
in-theory        71722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-71722.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-20, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71723
in-theory        71723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (D -> (D and (C and D)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
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-19.           (A -> ((B -> (C -> B)) and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71723.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (D -> (D and (C and D))))), M:tm-19, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71724
in-theory        71724
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (B -> (B and (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-9 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-2)
proof-size       117
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-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-71724.        (((A or (B -> (A and B))) -> (not (B -> (B and (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71725
in-theory        71725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and (B and A))) -> C) -> (((B or (A -> (B and A))) or (A -> (A and (B and A)))) -> C))
theorem-size     27
proof            (modus-ponens tm-8 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-71725.        (((A -> (A and (B and A))) -> C) -> (((B or (A -> (B and A))) or (A -> (A and (B and A)))) -> C)), M:tm-8, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-71726
in-theory        71726
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (C -> (C and (B and C)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71726.        (A or ((B or (C -> (B and C))) -> (C -> (C and (B and C))))), M:tm-7, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71727
in-theory        71727
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) or C)
theorem-size     17
proof            (modus-ponens tm-6 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71727.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) or C), M:tm-6, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71728
in-theory        71728
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (C -> (C and (B and C)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-71728.        (A -> (((B or (C -> (B and C))) -> (C -> (C and (B and C)))) and A)), M:tm-5, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71729
in-theory        71729
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> B) -> ((A or (B -> (A and B))) -> (B and (A and B))))
theorem-size     23
proof            (modus-ponens tm-2 tm-827 ((A (or Am (-> Bm (and Am Bm)))) (B Bm) (C (and Bm (and Am Bm)))))
axioms-used      (tm-2 tm-8 tm-5)
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-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-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-71729.        (((A or (B -> (A and B))) -> B) -> ((A or (B -> (A and B))) -> (B and (A and B)))), M:tm-2, m:tm-827, u:((A (or Am (-> Bm (and Am Bm)))) (B Bm) (C (and Bm (and Am Bm))))
================================================================
tm-name          tm-71730
in-theory        71730
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (C -> (C and (B and C)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-71730.        (A -> ((B or (C -> (B and C))) -> (C -> (C and (B and C))))), M:tm-1, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-71731
in-theory        71731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-808 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71731.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-808, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71732
in-theory        71732
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (D -> (C and D)))))
theorem-size     41
proof            (modus-ponens tm-798 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71732.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (D -> (C and D))))), M:tm-798, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71733
in-theory        71733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-71733.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-757, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71734
in-theory        71734
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (C -> (D -> (C and D)))))
theorem-size     41
proof            (modus-ponens tm-747 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
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-48.           (((A -> (B and 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-71734.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (C -> (D -> (C and D))))), M:tm-747, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71735
in-theory        71735
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-48.           (((A -> (B and 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-71735.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H))))), M:tm-708, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71736
in-theory        71736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71736.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-665, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71737
in-theory        71737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71737.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-622, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71738
in-theory        71738
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D or (A or (B -> (A and B)))) and C)))
theorem-size     21
proof            (modus-ponens tm-617 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (-> Dm (and (or B (or Am (-> Bm (and Am Bm)))) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       167
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-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-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-71738.        ((A or (B -> (A and B))) -> (C -> ((D or (A or (B -> (A and B)))) and C))), M:tm-617, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (-> Dm (and (or B (or Am (-> Bm (and Am Bm)))) Dm))))
================================================================
tm-name          tm-71739
in-theory        71739
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-71739.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71740
in-theory        71740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> 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-71740.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-605, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71741
in-theory        71741
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> 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-71741.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))))), M:tm-595, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71742
in-theory        71742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-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-1.            (A -> (B -> 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-71742.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-550, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71743
in-theory        71743
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> 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-71743.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-540, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71744
in-theory        71744
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-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-1.            (A -> (B -> 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-71744.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-530, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71745
in-theory        71745
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> 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-71745.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-520, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71746
in-theory        71746
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-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-1.            (A -> (B -> 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-71746.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-510, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71747
in-theory        71747
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-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-1.            (A -> (B -> 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-71747.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-500, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71748
in-theory        71748
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-1.            (A -> (B -> 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-71748.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H))))), M:tm-490, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71749
in-theory        71749
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71749.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-480, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71750
in-theory        71750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71750.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-469, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71751
in-theory        71751
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((A or (B -> (A and B))) or D) and C)))
theorem-size     21
proof            (modus-ponens tm-464 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (-> Dm (and (or (or Am (-> Bm (and Am Bm))) B) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       167
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-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-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-71751.        ((A or (B -> (A and B))) -> (C -> (((A or (B -> (A and B))) or D) and C))), M:tm-464, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (-> Dm (and (or (or Am (-> Bm (and Am Bm))) B) Dm))))
================================================================
tm-name          tm-71752
in-theory        71752
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-71752.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71753
in-theory        71753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> 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-71753.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-453, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71754
in-theory        71754
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> 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-71754.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))))), M:tm-443, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71755
in-theory        71755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> 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-71755.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-409, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71756
in-theory        71756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> 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-71756.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-400, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71757
in-theory        71757
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-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-1.            (A -> (B -> 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-71757.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-391, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71758
in-theory        71758
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-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-1.            (A -> (B -> 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-71758.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-382, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71759
in-theory        71759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-1.            (A -> (B -> 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-71759.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H))))), M:tm-373, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71760
in-theory        71760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71760.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-364, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71761
in-theory        71761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-71761.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-354, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71762
in-theory        71762
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> ((A or (B -> (A and B))) and D)) and C)))
theorem-size     23
proof            (modus-ponens tm-349 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (-> Dm (and (-> B (and (or Am (-> Bm (and Am Bm))) B)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       175
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-71762.        ((A or (B -> (A and B))) -> (C -> ((D -> ((A or (B -> (A and B))) and D)) and C))), M:tm-349, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (-> Dm (and (-> B (and (or Am (-> Bm (and Am Bm))) B)) Dm))))
================================================================
tm-name          tm-71763
in-theory        71763
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-71763.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71764
in-theory        71764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (A -> (B -> 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-71764.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F))))), M:tm-338, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71765
in-theory        71765
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     39
proof            (modus-ponens tm-328 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
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-328.          ((A -> 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-1.            (A -> (B -> 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-71765.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-328, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71766
in-theory        71766
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> 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-71766.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))))), M:tm-327, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71767
in-theory        71767
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> 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-71767.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))))), M:tm-326, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71768
in-theory        71768
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> 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-71768.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))))), M:tm-325, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71769
in-theory        71769
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> 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-71769.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))))), M:tm-324, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71770
in-theory        71770
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-71770.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))))), M:tm-323, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71771
in-theory        71771
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71771.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71772
in-theory        71772
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71772.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71773
in-theory        71773
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71773.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71774
in-theory        71774
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     31
proof            (modus-ponens tm-316 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-71774.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71775
in-theory        71775
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-71775.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71776
in-theory        71776
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((A or (B -> (A and B))) -> (not (C -> (D -> (C and D))))) -> (not (A or (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-313 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> 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-71776.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((A or (B -> (A and B))) -> (not (C -> (D -> (C and D))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71777
in-theory        71777
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> (((A or (B -> (A and B))) or (C -> (D -> (C and D)))) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> 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-71777.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> (((A or (B -> (A and B))) or (C -> (D -> (C and D)))) -> E))), M:tm-312, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71778
in-theory        71778
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E or ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-1.            (A -> (B -> 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-71778.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E or ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))))), M:tm-311, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71779
in-theory        71779
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-1.            (A -> (B -> 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-71779.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71780
in-theory        71780
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-1.            (A -> (B -> 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-71780.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71781
in-theory        71781
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D -> (C and D)))))
theorem-size     39
proof            (modus-ponens tm-306 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Dm (and 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> 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-71781.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D -> (C and D))))), M:tm-306, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-71782
in-theory        71782
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-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-71782.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (E -> ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))))), M:tm-305, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71783
in-theory        71783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-1.            (A -> (B -> 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-71783.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-303, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71784
in-theory        71784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-1.            (A -> (B -> 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-71784.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-270, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71785
in-theory        71785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-1.            (A -> (B -> 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-71785.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-239, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71786
in-theory        71786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (A -> (B -> 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-71786.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H))))), M:tm-210, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71787
in-theory        71787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71787.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-183, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71788
in-theory        71788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71788.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-157, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71789
in-theory        71789
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-1.            (A -> (B -> 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-71789.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-147, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71790
in-theory        71790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 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-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-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-71790.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-134, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71791
in-theory        71791
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-1.            (A -> (B -> 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-71791.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-125, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71792
in-theory        71792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71792.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H))))), M:tm-113, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71793
in-theory        71793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (A -> (B -> 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-71793.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-105, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71794
in-theory        71794
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((A or (B -> (A and B))) and C)))
theorem-size     19
proof            (modus-ponens tm-99 tm-828 ((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (-> Dm (and (or Am (-> Bm (and Am Bm))) Dm)))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-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-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-71794.        ((A or (B -> (A and B))) -> (C -> ((A or (B -> (A and B))) and C))), M:tm-99, m:tm-828, u:((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (-> Dm (and (or Am (-> Bm (and Am Bm))) Dm))))
================================================================
tm-name          tm-71795
in-theory        71795
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (A or (B -> (A and B)))) and C)))
theorem-size     21
proof            (modus-ponens tm-98 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (-> Dm (and (-> B (or Am (-> Bm (and Am 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-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-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-71795.        ((A or (B -> (A and B))) -> (C -> ((D -> (A or (B -> (A and B)))) and C))), M:tm-98, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (-> Dm (and (-> B (or Am (-> Bm (and Am Bm)))) Dm))))
================================================================
tm-name          tm-71796
in-theory        71796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71796.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F))))), M:tm-95, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71797
in-theory        71797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-71797.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-83, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71798
in-theory        71798
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-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-1.            (A -> (B -> 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-71798.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (E -> (D and E))))), M:tm-76, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71799
in-theory        71799
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (D -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-73 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
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-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-71799.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (D -> (C and D)))), M:tm-73, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71800
in-theory        71800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-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-1.            (A -> (B -> 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-71800.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F))))), M:tm-69, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71801
in-theory        71801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-71801.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-54, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71802
in-theory        71802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-50 tm-828 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
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-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-71802.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (D -> (C and D)))), M:tm-50, m:tm-828, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71803
in-theory        71803
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-49 tm-828 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       121
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-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-71803.        ((A or (A or (B -> (A and B)))) -> (C -> (D -> (C and D)))), M:tm-49, m:tm-828, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71804
in-theory        71804
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-47 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-4 tm-5 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-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-71804.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (E -> (D and E)))), M:tm-47, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71805
in-theory        71805
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-46 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
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-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-71805.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (E -> (D and E)))), M:tm-46, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71806
in-theory        71806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-1.            (A -> (B -> 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-71806.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F))))), M:tm-42, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71807
in-theory        71807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-1.            (A -> (B -> 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-71807.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F))))), M:tm-32, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71808
in-theory        71808
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D -> (C and D)))))
theorem-size     23
proof            (modus-ponens tm-24 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
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-48.           (((A -> (B and 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-71808.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D -> (C and D))))), M:tm-24, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71809
in-theory        71809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-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-1.            (A -> (B -> 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-71809.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F))))), M:tm-23, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71810
in-theory        71810
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-1.            (A -> (B -> 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-71810.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F))))), M:tm-22, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71811
in-theory        71811
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-1.            (A -> (B -> 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-71811.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F))))), M:tm-21, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71812
in-theory        71812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (A -> (B -> 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-71812.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-20, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71813
in-theory        71813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-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-71813.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (F -> (E and F))))), M:tm-19, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71814
in-theory        71814
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (C -> (D -> (C and D))))) -> (not (A or (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-9 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-1)
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-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-71814.        (((A or (B -> (A and B))) -> (not (C -> (D -> (C and D))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71815
in-theory        71815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (((D or (E -> (D and E))) or (A -> (B -> (A and B)))) -> C))
theorem-size     27
proof            (modus-ponens tm-8 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-1)
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-1.            (A -> (B -> 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-71815.        (((A -> (B -> (A and B))) -> C) -> (((D or (E -> (D and E))) or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-71816
in-theory        71816
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-1)
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-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-71816.        (A or ((B or (C -> (B and C))) -> (D -> (E -> (D and E))))), M:tm-7, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71817
in-theory        71817
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-1)
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-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-71817.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71818
in-theory        71818
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (D -> (E -> (D and E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-828 ((A (-> (or Am (-> Bm (and 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-48.           (((A -> (B and 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-71818.        (A -> (((B or (C -> (B and C))) -> (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71819
in-theory        71819
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-2 tm-828 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1)
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-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-71819.        (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D -> (C and D)))), M:tm-2, m:tm-828, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-71820
in-theory        71820
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-8 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-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-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-71820.        (A -> ((B or (C -> (B and C))) -> (D -> (E -> (D and E))))), M:tm-1, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-71821
in-theory        71821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71821.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-808, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71822
in-theory        71822
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-798 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71822.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B))))), M:tm-798, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71823
in-theory        71823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-71823.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-757, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71824
in-theory        71824
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-747 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-6.            (A -> (A or 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-71824.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B))))), M:tm-747, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71825
in-theory        71825
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71825.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F))))), M:tm-708, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71826
in-theory        71826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-71826.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-665, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71827
in-theory        71827
times-derived    1
----------------------------------------------------------------
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-623 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or 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-71827.        ((A or (B -> (A and B))) -> (C or ((D -> (D or E)) and (B -> (A and B))))), M:tm-623, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71828
in-theory        71828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-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-6.            (A -> (A or 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-71828.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-622, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71829
in-theory        71829
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or 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-71829.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (F or E))), M:tm-609, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71830
in-theory        71830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-71830.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-605, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71831
in-theory        71831
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or 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-71831.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))))), M:tm-595, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71832
in-theory        71832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-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-71832.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-550, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71833
in-theory        71833
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-71833.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-540, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71834
in-theory        71834
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-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-71834.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-530, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71835
in-theory        71835
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-71835.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-520, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71836
in-theory        71836
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-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-6.            (A -> (A or 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-71836.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-510, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71837
in-theory        71837
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-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-6.            (A -> (A or 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-71837.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-500, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71838
in-theory        71838
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-6.            (A -> (A or 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-71838.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F))))), M:tm-490, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71839
in-theory        71839
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-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-6.            (A -> (A or 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-71839.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-480, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71840
in-theory        71840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (C or D)) and (B -> (A and B))) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-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-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-71840.        ((A or (B -> (A and B))) -> (((C -> (C or D)) and (B -> (A and B))) or E)), M:tm-470, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71841
in-theory        71841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-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-71841.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-469, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71842
in-theory        71842
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-71842.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (E or F))), M:tm-456, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71843
in-theory        71843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-71843.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-453, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71844
in-theory        71844
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-71844.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))))), M:tm-443, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71845
in-theory        71845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-71845.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-409, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71846
in-theory        71846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-71846.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-400, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71847
in-theory        71847
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-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-71847.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-391, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71848
in-theory        71848
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-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-71848.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-382, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71849
in-theory        71849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-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-71849.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F))))), M:tm-373, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71850
in-theory        71850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-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-71850.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-364, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71851
in-theory        71851
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D -> (D or E)) and (B -> (A and B))) and C)))
theorem-size     23
proof            (modus-ponens tm-355 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-6.            (A -> (A or 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-71851.        ((A or (B -> (A and B))) -> (C -> (((D -> (D or E)) and (B -> (A and B))) and C))), M:tm-355, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71852
in-theory        71852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-6.            (A -> (A or 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-71852.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-354, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71853
in-theory        71853
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or 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-71853.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71854
in-theory        71854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-6.            (A -> (A or 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-71854.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D))))), M:tm-338, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71855
in-theory        71855
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-328 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-6.            (A -> (A or 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-71855.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (C or D)) and (B -> (A and B)))))), M:tm-328, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71856
in-theory        71856
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or 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-71856.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))))), M:tm-327, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71857
in-theory        71857
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or 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-71857.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))))), M:tm-326, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71858
in-theory        71858
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or 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-71858.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))))), M:tm-325, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71859
in-theory        71859
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-6.            (A -> (A or 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-71859.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))))), M:tm-324, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71860
in-theory        71860
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or 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-71860.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))))), M:tm-323, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71861
in-theory        71861
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or 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-71861.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E and F) -> F)), M:tm-322, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71862
in-theory        71862
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or 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-71862.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E and F) -> E)), M:tm-320, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71863
in-theory        71863
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-6.            (A -> (A or 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-71863.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71864
in-theory        71864
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-6.            (A -> (A or 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-71864.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71865
in-theory        71865
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or 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-71865.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (F -> E))), M:tm-315, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71866
in-theory        71866
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not ((C -> (C or D)) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-313 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-6.            (A -> (A or 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-71866.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not ((C -> (C or D)) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71867
in-theory        71867
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((((C -> (C or D)) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or ((C -> (C or D)) and (B -> (A and B)))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-6.            (A -> (A or 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-71867.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((((C -> (C or D)) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or ((C -> (C or D)) and (B -> (A and B)))) -> E))), M:tm-312, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71868
in-theory        71868
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-71868.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))))), M:tm-311, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71869
in-theory        71869
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
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-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-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-71869.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) or E)), M:tm-310, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71870
in-theory        71870
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-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-6.            (A -> (A or 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-71870.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and E))), M:tm-309, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71871
in-theory        71871
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-6.            (A -> (A or 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-71871.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))))), M:tm-305, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71872
in-theory        71872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-6.            (A -> (A or 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-71872.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-303, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71873
in-theory        71873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-6.            (A -> (A or 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-71873.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-270, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71874
in-theory        71874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-6.            (A -> (A or 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-71874.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-239, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71875
in-theory        71875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-6.            (A -> (A or 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-71875.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F))))), M:tm-210, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71876
in-theory        71876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-6.            (A -> (A or 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-71876.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-183, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71877
in-theory        71877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-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-6.            (A -> (A or 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-71877.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-157, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71878
in-theory        71878
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-6.            (A -> (A or 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-71878.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-147, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71879
in-theory        71879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-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-6.            (A -> (A or 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-71879.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-134, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71880
in-theory        71880
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-6.            (A -> (A or 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-71880.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-125, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71881
in-theory        71881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-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-6.            (A -> (A or 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-71881.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F))))), M:tm-113, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71882
in-theory        71882
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-6.            (A -> (A or 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-71882.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-105, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71883
in-theory        71883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-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-6.            (A -> (A or 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-71883.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D))))), M:tm-95, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71884
in-theory        71884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (D or E)) and (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-84 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or 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-71884.        ((A or (B -> (A and B))) -> (C -> ((D -> (D or E)) and (B -> (A and B))))), M:tm-84, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71885
in-theory        71885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-6.            (A -> (A or 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-71885.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-83, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71886
in-theory        71886
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (D or E)) and (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-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-6.            (A -> (A or 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-71886.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (D or E)) and (C -> (B and C))))), M:tm-76, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71887
in-theory        71887
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-73 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
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-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-71887.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B)))), M:tm-73, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71888
in-theory        71888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-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-6.            (A -> (A or 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-71888.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D))))), M:tm-69, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71889
in-theory        71889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-71889.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-54, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71890
in-theory        71890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (C or D)) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-50 tm-829 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-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-71890.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (C or D)) and (A -> (B and A)))), M:tm-50, m:tm-829, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71891
in-theory        71891
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-49 tm-829 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-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-71891.        ((A or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B)))), M:tm-49, m:tm-829, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71892
in-theory        71892
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (D or E)) and (C -> (B and C))))
theorem-size     29
proof            (modus-ponens tm-47 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-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-71892.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (D or E)) and (C -> (B and C)))), M:tm-47, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71893
in-theory        71893
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (D or E)) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-46 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
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-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-71893.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (D or E)) and (B -> (A and B)))), M:tm-46, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71894
in-theory        71894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-71894.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D))))), M:tm-42, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71895
in-theory        71895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
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-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-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-71895.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D))))), M:tm-32, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71896
in-theory        71896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (C or D)) and (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-24 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
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-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-6.            (A -> (A or 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-71896.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (C or D)) and (B -> (A and B))))), M:tm-24, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71897
in-theory        71897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-6.            (A -> (A or 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-71897.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D))))), M:tm-23, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71898
in-theory        71898
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-6.            (A -> (A or 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-71898.        (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D))))), M:tm-22, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71899
in-theory        71899
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-6.            (A -> (A or 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-71899.        (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D))))), M:tm-21, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71900
in-theory        71900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-6.            (A -> (A or 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-71900.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-20, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71901
in-theory        71901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-6.            (A -> (A or 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-71901.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (E or F)) and (D -> (C and D))))), M:tm-19, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71902
in-theory        71902
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not ((C -> (C or D)) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-9 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-6)
proof-size       117
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-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-71902.        (((A or (B -> (A and B))) -> (not ((C -> (C or D)) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71903
in-theory        71903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or ((A -> (A or B)) and (C -> (D and C)))) -> E))
theorem-size     35
proof            (modus-ponens tm-8 tm-829 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-5 tm-6)
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-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-71903.        ((((A -> (A or B)) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or ((A -> (A or B)) and (C -> (D and C)))) -> E)), M:tm-8, m:tm-829, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-71904
in-theory        71904
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> ((D -> (D or E)) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or 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-71904.        (A or ((B or (C -> (B and C))) -> ((D -> (D or E)) and (C -> (B and C))))), M:tm-7, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71905
in-theory        71905
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-71905.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) or E), M:tm-6, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71906
in-theory        71906
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> ((D -> (D or E)) and (C -> (B and C)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-71906.        (A -> (((B or (C -> (B and C))) -> ((D -> (D or E)) and (C -> (B and C)))) and A)), M:tm-5, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71907
in-theory        71907
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> ((D -> (D or E)) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or 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-71907.        (A -> ((B or (C -> (B and C))) -> ((D -> (D or E)) and (C -> (B and C))))), M:tm-1, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71908
in-theory        71908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-808 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71908.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-808, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71909
in-theory        71909
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (C or D))))
theorem-size     37
proof            (modus-ponens tm-798 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71909.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (C or D)))), M:tm-798, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71910
in-theory        71910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 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-48.           (((A -> (B and 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-71910.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-757, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71911
in-theory        71911
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (C -> (C or D))))
theorem-size     37
proof            (modus-ponens tm-747 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71911.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (C -> (C or D)))), M:tm-747, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71912
in-theory        71912
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-71912.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (G or H)))), M:tm-708, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71913
in-theory        71913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
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-48.           (((A -> (B and 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-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-71913.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-665, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71914
in-theory        71914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-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-6.            (A -> (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-71914.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-622, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71915
in-theory        71915
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or (A or (B -> (A and B)))) or D))
theorem-size     19
proof            (modus-ponens tm-617 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (or (or B (or Am (-> Bm (and Am Bm)))) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-6)
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-7.            (A -> (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-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-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-71915.        ((A or (B -> (A and B))) -> ((C or (A or (B -> (A and B)))) or D)), M:tm-617, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (or (or B (or Am (-> Bm (and Am Bm)))) Dm)))
================================================================
tm-name          tm-71916
in-theory        71916
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-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-6.            (A -> (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-71916.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71917
in-theory        71917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71917.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-605, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71918
in-theory        71918
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71918.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (C -> (C or D))))), M:tm-595, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71919
in-theory        71919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-48.           (((A -> (B and 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-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-71919.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-550, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71920
in-theory        71920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71920.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-540, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71921
in-theory        71921
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-48.           (((A -> (B and 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-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-71921.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-530, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71922
in-theory        71922
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71922.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-520, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71923
in-theory        71923
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71923.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-510, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71924
in-theory        71924
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71924.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-500, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71925
in-theory        71925
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71925.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (G or H)))), M:tm-490, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71926
in-theory        71926
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-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-6.            (A -> (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-71926.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-480, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71927
in-theory        71927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and 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-71927.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-469, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71928
in-theory        71928
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((A or (B -> (A and B))) or C) or D))
theorem-size     19
proof            (modus-ponens tm-464 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (or (or (or Am (-> Bm (and Am Bm))) B) Dm))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and 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-71928.        ((A or (B -> (A and B))) -> (((A or (B -> (A and B))) or C) or D)), M:tm-464, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (or (or (or Am (-> Bm (and Am Bm))) B) Dm)))
================================================================
tm-name          tm-71929
in-theory        71929
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-71929.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71930
in-theory        71930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-48.           (((A -> (B and 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-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-71930.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-453, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71931
in-theory        71931
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
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-48.           (((A -> (B and 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-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-71931.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (C -> (C or D))))), M:tm-443, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71932
in-theory        71932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-48.           (((A -> (B and 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-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-71932.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-409, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71933
in-theory        71933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-48.           (((A -> (B and 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-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-71933.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-400, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71934
in-theory        71934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-48.           (((A -> (B and 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-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-71934.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-391, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71935
in-theory        71935
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-48.           (((A -> (B and 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-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-71935.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-382, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71936
in-theory        71936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-48.           (((A -> (B and 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-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-71936.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (G or H)))), M:tm-373, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71937
in-theory        71937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-71937.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-364, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71938
in-theory        71938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-6.            (A -> (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-71938.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-354, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71939
in-theory        71939
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> ((A or (B -> (A and B))) and C)) or D))
theorem-size     21
proof            (modus-ponens tm-349 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (or (-> B (and (or Am (-> Bm (and Am Bm))) B)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       167
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-48.           (((A -> (B and 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-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-71939.        ((A or (B -> (A and B))) -> ((C -> ((A or (B -> (A and B))) and C)) or D)), M:tm-349, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (or (-> B (and (or Am (-> Bm (and Am Bm))) B)) Dm)))
================================================================
tm-name          tm-71940
in-theory        71940
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (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-71940.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71941
in-theory        71941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71941.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (E or F)))), M:tm-338, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71942
in-theory        71942
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (C or D)))))
theorem-size     35
proof            (modus-ponens tm-328 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
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-328.          ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71942.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (C or D))))), M:tm-328, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71943
in-theory        71943
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (C -> (C or D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71943.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (C -> (C or D))))), M:tm-327, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71944
in-theory        71944
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71944.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (C -> (C or D))))), M:tm-326, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71945
in-theory        71945
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71945.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (C -> (C or D))))), M:tm-325, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71946
in-theory        71946
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (C -> (C or D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71946.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (C -> (C or D))))), M:tm-324, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71947
in-theory        71947
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (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-71947.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (C -> (C or D))))), M:tm-323, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71948
in-theory        71948
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-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-6.            (A -> (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-71948.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71949
in-theory        71949
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-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-6.            (A -> (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-71949.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71950
in-theory        71950
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-6.            (A -> (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-71950.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71951
in-theory        71951
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-316 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-6.            (A -> (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-71951.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71952
in-theory        71952
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-6.            (A -> (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-71952.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71953
in-theory        71953
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (((A or (B -> (A and B))) -> (not (C -> (C or D)))) -> (not (A or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-313 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71953.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (((A or (B -> (A and B))) -> (not (C -> (C or D)))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71954
in-theory        71954
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> (((A or (B -> (A and B))) or (C -> (C or D))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
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-48.           (((A -> (B and 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-71954.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> (((A or (B -> (A and B))) or (C -> (C or D))) -> E))), M:tm-312, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71955
in-theory        71955
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (E or ((A or (B -> (A and B))) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71955.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (E or ((A or (B -> (A and B))) -> (C -> (C or D))))), M:tm-311, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71956
in-theory        71956
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (((A or (B -> (A and B))) -> (C -> (C or D))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
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-48.           (((A -> (B and 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-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-71956.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (((A or (B -> (A and B))) -> (C -> (C or D))) or E)), M:tm-310, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71957
in-theory        71957
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (((A or (B -> (A and B))) -> (C -> (C or D))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71957.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> (((A or (B -> (A and B))) -> (C -> (C or D))) and E))), M:tm-309, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71958
in-theory        71958
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (C or D))))
theorem-size     35
proof            (modus-ponens tm-306 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (or Cm Dm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71958.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (C or D)))), M:tm-306, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-71959
in-theory        71959
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> ((A or (B -> (A and B))) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or 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-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-6.            (A -> (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-71959.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (E -> ((A or (B -> (A and B))) -> (C -> (C or D))))), M:tm-305, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71960
in-theory        71960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71960.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-303, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71961
in-theory        71961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71961.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-270, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71962
in-theory        71962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71962.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-239, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71963
in-theory        71963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71963.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (G or H)))), M:tm-210, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71964
in-theory        71964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-6.            (A -> (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-71964.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-183, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71965
in-theory        71965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-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-6.            (A -> (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-71965.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-157, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71966
in-theory        71966
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71966.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-147, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71967
in-theory        71967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-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-6.            (A -> (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-71967.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-134, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71968
in-theory        71968
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71968.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-125, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71969
in-theory        71969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-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-6.            (A -> (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-71969.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (G or H)))), M:tm-113, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71970
in-theory        71970
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71970.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-105, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71971
in-theory        71971
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) or C))
theorem-size     17
proof            (modus-ponens tm-99 tm-830 ((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (or (or Am (-> Bm (and Am Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-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-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-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-71971.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) or C)), M:tm-99, m:tm-830, u:((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (or (or Am (-> Bm (and Am Bm))) Dm)))
================================================================
tm-name          tm-71972
in-theory        71972
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (A or (B -> (A and B)))) or D))
theorem-size     19
proof            (modus-ponens tm-98 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (or (-> B (or Am (-> Bm (and Am Bm)))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-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-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-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-71972.        ((A or (B -> (A and B))) -> ((C -> (A or (B -> (A and B)))) or D)), M:tm-98, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (or (-> B (or Am (-> Bm (and Am Bm)))) Dm)))
================================================================
tm-name          tm-71973
in-theory        71973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-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-6.            (A -> (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-71973.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (E or F)))), M:tm-95, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71974
in-theory        71974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-6.            (A -> (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-71974.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-83, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71975
in-theory        71975
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71975.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (D or E)))), M:tm-76, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71976
in-theory        71976
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (C or D)))
theorem-size     23
proof            (modus-ponens tm-73 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 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-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-71976.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (C or D))), M:tm-73, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71977
in-theory        71977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71977.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (E or F)))), M:tm-69, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71978
in-theory        71978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-71978.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-54, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71979
in-theory        71979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-50 tm-830 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 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-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-71979.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (C or D))), M:tm-50, m:tm-830, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71980
in-theory        71980
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-49 tm-830 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       113
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-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-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-71980.        ((A or (A or (B -> (A and B)))) -> (C -> (C or D))), M:tm-49, m:tm-830, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71981
in-theory        71981
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-47 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 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-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-71981.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (D or E))), M:tm-47, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71982
in-theory        71982
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-46 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 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-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-71982.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (D or E))), M:tm-46, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71983
in-theory        71983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71983.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (E or F)))), M:tm-42, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71984
in-theory        71984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-1.            (A -> (B -> A)), 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-71984.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (E or F)))), M:tm-32, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71985
in-theory        71985
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (C or D))))
theorem-size     21
proof            (modus-ponens tm-24 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
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-48.           (((A -> (B and 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-71985.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (C or D)))), M:tm-24, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71986
in-theory        71986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71986.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (E or F)))), M:tm-23, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71987
in-theory        71987
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71987.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (E or F)))), M:tm-22, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71988
in-theory        71988
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71988.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (E or F)))), M:tm-21, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71989
in-theory        71989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-71989.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-20, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71990
in-theory        71990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-6.            (A -> (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-71990.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (E or F)))), M:tm-19, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71991
in-theory        71991
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (C -> (C or D)))) -> (not (A or (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-9 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-9 tm-8 tm-5 tm-1 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-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-71991.        (((A or (B -> (A and B))) -> (not (C -> (C or D)))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71992
in-theory        71992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (((D or (E -> (D and E))) or (A -> (A or B))) -> C))
theorem-size     23
proof            (modus-ponens tm-8 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-6.            (A -> (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-71992.        (((A -> (A or B)) -> C) -> (((D or (E -> (D and E))) or (A -> (A or B))) -> C)), M:tm-8, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-71993
in-theory        71993
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-8 tm-5 tm-1 tm-6)
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-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-71993.        (A or ((B or (C -> (B and C))) -> (D -> (D or E)))), M:tm-7, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71994
in-theory        71994
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-8 tm-5 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-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-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-71994.        (((A or (B -> (A and B))) -> (C -> (C or D))) or E), M:tm-6, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71995
in-theory        71995
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (D -> (D or E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-830 ((A (-> (or Am (-> Bm (and 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-48.           (((A -> (B and 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-71995.        (A -> (((B or (C -> (B and C))) -> (D -> (D or E))) and A)), M:tm-5, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71996
in-theory        71996
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (C or D)))
theorem-size     21
proof            (modus-ponens tm-2 tm-830 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-6)
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-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-71996.        (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (C or D))), M:tm-2, m:tm-830, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-71997
in-theory        71997
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-8 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (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-71997.        (A -> ((B or (C -> (B and C))) -> (D -> (D or E)))), M:tm-1, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-71998
in-theory        71998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71998.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-808, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-71999
in-theory        71999
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-798 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-71999.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B))))), M:tm-798, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72000
in-theory        72000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-72000.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-757, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72001
in-theory        72001
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-747 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-7.            (A -> (B or 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-72001.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B))))), M:tm-747, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72002
in-theory        72002
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-72002.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F))))), M:tm-708, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72003
in-theory        72003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-72003.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-665, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72004
in-theory        72004
times-derived    1
----------------------------------------------------------------
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-623 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-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-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-72004.        ((A or (B -> (A and B))) -> (C or ((D -> (E or D)) and (B -> (A and B))))), M:tm-623, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72005
in-theory        72005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-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-72005.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-622, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72006
in-theory        72006
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-72006.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (F or E))), M:tm-609, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72007
in-theory        72007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-72007.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-605, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72008
in-theory        72008
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-72008.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))))), M:tm-595, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72009
in-theory        72009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-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-72009.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-550, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72010
in-theory        72010
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-72010.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-540, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72011
in-theory        72011
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-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-72011.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-530, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72012
in-theory        72012
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-72012.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-520, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72013
in-theory        72013
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-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-72013.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-510, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72014
in-theory        72014
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-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-72014.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-500, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72015
in-theory        72015
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-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-72015.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F))))), M:tm-490, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72016
in-theory        72016
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-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-72016.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-480, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72017
in-theory        72017
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D or C)) and (B -> (A and B))) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or 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-72017.        ((A or (B -> (A and B))) -> (((C -> (D or C)) and (B -> (A and B))) or E)), M:tm-470, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72018
in-theory        72018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-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-7.            (A -> (B or 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-72018.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-469, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72019
in-theory        72019
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or 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-72019.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (E or F))), M:tm-456, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72020
in-theory        72020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-72020.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-453, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72021
in-theory        72021
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or 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-72021.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))))), M:tm-443, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72022
in-theory        72022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-72022.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-409, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72023
in-theory        72023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-72023.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-400, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72024
in-theory        72024
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-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-7.            (A -> (B or 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-72024.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-391, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72025
in-theory        72025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-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-7.            (A -> (B or 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-72025.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-382, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72026
in-theory        72026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-7.            (A -> (B or 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-72026.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F))))), M:tm-373, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72027
in-theory        72027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-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-7.            (A -> (B or 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-72027.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-364, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72028
in-theory        72028
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D -> (E or D)) and (B -> (A and B))) and C)))
theorem-size     23
proof            (modus-ponens tm-355 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-7.            (A -> (B or 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-72028.        ((A or (B -> (A and B))) -> (C -> (((D -> (E or D)) and (B -> (A and B))) and C))), M:tm-355, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72029
in-theory        72029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-7.            (A -> (B or 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-72029.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-354, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72030
in-theory        72030
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or 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-72030.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72031
in-theory        72031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-7.            (A -> (B or 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-72031.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D))))), M:tm-338, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72032
in-theory        72032
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-328 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-7.            (A -> (B or 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-72032.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D or C)) and (B -> (A and B)))))), M:tm-328, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72033
in-theory        72033
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or 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-72033.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))))), M:tm-327, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72034
in-theory        72034
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or 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-72034.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))))), M:tm-326, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72035
in-theory        72035
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or 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-72035.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))))), M:tm-325, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72036
in-theory        72036
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-7.            (A -> (B or 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-72036.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))))), M:tm-324, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72037
in-theory        72037
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or 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-72037.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))))), M:tm-323, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72038
in-theory        72038
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or 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-72038.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E and F) -> F)), M:tm-322, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72039
in-theory        72039
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or 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-72039.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E and F) -> E)), M:tm-320, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72040
in-theory        72040
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-7.            (A -> (B or 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-72040.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72041
in-theory        72041
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-7.            (A -> (B or 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-72041.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72042
in-theory        72042
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or 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-72042.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (F -> E))), M:tm-315, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72043
in-theory        72043
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not ((C -> (D or C)) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))))
theorem-size     49
proof            (modus-ponens tm-313 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-7.            (A -> (B or 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-72043.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> (not ((C -> (D or C)) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72044
in-theory        72044
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((((C -> (D or C)) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or ((C -> (D or C)) and (B -> (A and B)))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-7.            (A -> (B or 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-72044.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((((C -> (D or C)) and (B -> (A and B))) -> E) -> (((A or (B -> (A and B))) or ((C -> (D or C)) and (B -> (A and B)))) -> E))), M:tm-312, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72045
in-theory        72045
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
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-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-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-72045.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E or ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))))), M:tm-311, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72046
in-theory        72046
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-72046.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) or E)), M:tm-310, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72047
in-theory        72047
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 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-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-7.            (A -> (B or 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-72047.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and E))), M:tm-309, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72048
in-theory        72048
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-7.            (A -> (B or 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-72048.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (E -> ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))))), M:tm-305, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72049
in-theory        72049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-7.            (A -> (B or 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-72049.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-303, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72050
in-theory        72050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-7.            (A -> (B or 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-72050.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-270, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72051
in-theory        72051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-7.            (A -> (B or 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-72051.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-239, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72052
in-theory        72052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-7.            (A -> (B or 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-72052.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F))))), M:tm-210, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72053
in-theory        72053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-7.            (A -> (B or 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-72053.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-183, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72054
in-theory        72054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-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-7.            (A -> (B or 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-72054.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-157, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72055
in-theory        72055
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-7.            (A -> (B or 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-72055.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-147, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72056
in-theory        72056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-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-7.            (A -> (B or 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-72056.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-134, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72057
in-theory        72057
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-7.            (A -> (B or 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-72057.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-125, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72058
in-theory        72058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-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-7.            (A -> (B or 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-72058.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F))))), M:tm-113, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72059
in-theory        72059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-7.            (A -> (B or 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-72059.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-105, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72060
in-theory        72060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-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-7.            (A -> (B or 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-72060.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D))))), M:tm-95, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72061
in-theory        72061
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (E or D)) and (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-84 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or 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-72061.        ((A or (B -> (A and B))) -> (C -> ((D -> (E or D)) and (B -> (A and B))))), M:tm-84, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72062
in-theory        72062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-7.            (A -> (B or 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-72062.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-83, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72063
in-theory        72063
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (E or D)) and (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-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-7.            (A -> (B or 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-72063.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> ((D -> (E or D)) and (C -> (B and C))))), M:tm-76, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72064
in-theory        72064
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-73 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
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-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-72064.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B)))), M:tm-73, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72065
in-theory        72065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-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-7.            (A -> (B or 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-72065.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D))))), M:tm-69, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72066
in-theory        72066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-72066.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-54, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72067
in-theory        72067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (D or C)) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-50 tm-831 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-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-72067.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> ((C -> (D or C)) and (A -> (B and A)))), M:tm-50, m:tm-831, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72068
in-theory        72068
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-49 tm-831 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-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-72068.        ((A or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B)))), M:tm-49, m:tm-831, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72069
in-theory        72069
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (E or D)) and (C -> (B and C))))
theorem-size     29
proof            (modus-ponens tm-47 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-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-72069.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> ((D -> (E or D)) and (C -> (B and C)))), M:tm-47, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72070
in-theory        72070
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (E or D)) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-46 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
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-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-72070.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> ((D -> (E or D)) and (B -> (A and B)))), M:tm-46, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72071
in-theory        72071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
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-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-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-72071.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D))))), M:tm-42, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72072
in-theory        72072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-72072.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D))))), M:tm-32, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72073
in-theory        72073
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D or C)) and (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-24 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
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-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-7.            (A -> (B or 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-72073.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and ((C -> (D or C)) and (B -> (A and B))))), M:tm-24, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72074
in-theory        72074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-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-7.            (A -> (B or 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-72074.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D))))), M:tm-23, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72075
in-theory        72075
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-7.            (A -> (B or 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-72075.        (((A and B) -> B) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D))))), M:tm-22, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72076
in-theory        72076
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-7.            (A -> (B or 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-72076.        (((A and B) -> A) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D))))), M:tm-21, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72077
in-theory        72077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-7.            (A -> (B or 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-72077.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-20, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72078
in-theory        72078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-7.            (A -> (B or 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-72078.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> ((E -> (F or E)) and (D -> (C and D))))), M:tm-19, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72079
in-theory        72079
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not ((C -> (D or C)) and (B -> (A and B))))) -> (not (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-9 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-7)
proof-size       117
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-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-72079.        (((A or (B -> (A and B))) -> (not ((C -> (D or C)) and (B -> (A and B))))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72080
in-theory        72080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or ((A -> (B or A)) and (C -> (D and C)))) -> E))
theorem-size     35
proof            (modus-ponens tm-8 tm-831 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-5 tm-7)
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-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-72080.        ((((A -> (B or A)) and (C -> (D and C))) -> E) -> (((D or (C -> (D and C))) or ((A -> (B or A)) and (C -> (D and C)))) -> E)), M:tm-8, m:tm-831, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-72081
in-theory        72081
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> ((D -> (E or D)) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-72081.        (A or ((B or (C -> (B and C))) -> ((D -> (E or D)) and (C -> (B and C))))), M:tm-7, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72082
in-theory        72082
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or 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-72082.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) or E), M:tm-6, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72083
in-theory        72083
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> ((D -> (E or D)) and (C -> (B and C)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am 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-48.           (((A -> (B and 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-72083.        (A -> (((B or (C -> (B and C))) -> ((D -> (E or D)) and (C -> (B and C)))) and A)), M:tm-5, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72084
in-theory        72084
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> ((D -> (E or D)) and (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or 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-72084.        (A -> ((B or (C -> (B and C))) -> ((D -> (E or D)) and (C -> (B and C))))), M:tm-1, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72085
in-theory        72085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72085.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-808, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72086
in-theory        72086
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (D or C))))
theorem-size     37
proof            (modus-ponens tm-798 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72086.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (((E and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (C -> (D or C)))), M:tm-798, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72087
in-theory        72087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 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-48.           (((A -> (B and 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-72087.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-757, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72088
in-theory        72088
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (C -> (D or C))))
theorem-size     37
proof            (modus-ponens tm-747 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72088.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((((A or (B -> (A and B))) and E) or (A or (B -> (A and B)))) -> (C -> (D or C)))), M:tm-747, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72089
in-theory        72089
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-72089.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H or G)))), M:tm-708, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72090
in-theory        72090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or 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-48.           (((A -> (B and 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-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-72090.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-665, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72091
in-theory        72091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72091.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-622, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72092
in-theory        72092
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D or (A or (B -> (A and B))))))
theorem-size     19
proof            (modus-ponens tm-617 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (or Dm (or B (or Am (-> Bm (and Am Bm))))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (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-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-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-72092.        ((A or (B -> (A and B))) -> (C or (D or (A or (B -> (A and B)))))), M:tm-617, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or B (or Am (-> Bm (and Am Bm))))) (C (or Dm (or B (or Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-72093
in-theory        72093
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-72093.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72094
in-theory        72094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-48.           (((A -> (B and 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-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-72094.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-605, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72095
in-theory        72095
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
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-48.           (((A -> (B and 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-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-72095.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (F or E)) and ((A or (B -> (A and B))) -> (C -> (D or C))))), M:tm-595, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72096
in-theory        72096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-48.           (((A -> (B and 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-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-72096.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-550, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72097
in-theory        72097
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-48.           (((A -> (B and 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-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-72097.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-540, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72098
in-theory        72098
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-48.           (((A -> (B and 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-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-72098.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-530, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72099
in-theory        72099
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-48.           (((A -> (B and 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-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-72099.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-520, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72100
in-theory        72100
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-48.           (((A -> (B and 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-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-72100.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-510, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72101
in-theory        72101
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-48.           (((A -> (B and 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-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-72101.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-500, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72102
in-theory        72102
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-48.           (((A -> (B and 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-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-72102.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H or G)))), M:tm-490, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72103
in-theory        72103
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72103.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-480, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72104
in-theory        72104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-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-7.            (A -> (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-72104.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-469, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72105
in-theory        72105
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or ((A or (B -> (A and B))) or D)))
theorem-size     19
proof            (modus-ponens tm-464 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (or Dm (or (or Am (-> Bm (and Am Bm))) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-7)
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-6.            (A -> (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-48.           (((A -> (B and 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-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-72105.        ((A or (B -> (A and B))) -> (C or ((A or (B -> (A and B))) or D))), M:tm-464, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (or (or Am (-> Bm (and Am Bm))) B)) (C (or Dm (or (or Am (-> Bm (and Am Bm))) B))))
================================================================
tm-name          tm-72106
in-theory        72106
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-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-7.            (A -> (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-72106.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72107
in-theory        72107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72107.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-453, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72108
in-theory        72108
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72108.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (E or F)) and ((A or (B -> (A and B))) -> (C -> (D or C))))), M:tm-443, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72109
in-theory        72109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72109.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-409, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72110
in-theory        72110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72110.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-400, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72111
in-theory        72111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72111.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-391, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72112
in-theory        72112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72112.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-382, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72113
in-theory        72113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72113.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H or G)))), M:tm-373, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72114
in-theory        72114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-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-7.            (A -> (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-72114.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-364, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72115
in-theory        72115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-7.            (A -> (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-72115.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-354, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72116
in-theory        72116
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D -> ((A or (B -> (A and B))) and D))))
theorem-size     21
proof            (modus-ponens tm-349 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (or Dm (-> B (and (or Am (-> Bm (and Am Bm))) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       167
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-48.           (((A -> (B and 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-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-72116.        ((A or (B -> (A and B))) -> (C or (D -> ((A or (B -> (A and B))) and D)))), M:tm-349, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (and (or Am (-> Bm (and Am Bm))) B))) (C (or Dm (-> B (and (or Am (-> Bm (and Am Bm))) B)))))
================================================================
tm-name          tm-72117
in-theory        72117
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (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-72117.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72118
in-theory        72118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72118.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F or E)))), M:tm-338, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72119
in-theory        72119
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D or C)))))
theorem-size     35
proof            (modus-ponens tm-328 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
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-328.          ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72119.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D or C))))), M:tm-328, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72120
in-theory        72120
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (C -> (D or C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72120.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A or (B -> (A and B))) -> (C -> (D or C))))), M:tm-327, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72121
in-theory        72121
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72121.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (((E and F) -> F) and ((A or (B -> (A and B))) -> (C -> (D or C))))), M:tm-326, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72122
in-theory        72122
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72122.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (((E and F) -> E) and ((A or (B -> (A and B))) -> (C -> (D or C))))), M:tm-325, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72123
in-theory        72123
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (C -> (D or C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72123.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (A and B))) -> (C -> (D or C))))), M:tm-324, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72124
in-theory        72124
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (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-72124.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (F -> E)) and ((A or (B -> (A and B))) -> (C -> (D or C))))), M:tm-323, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72125
in-theory        72125
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-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-7.            (A -> (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-72125.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72126
in-theory        72126
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-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-7.            (A -> (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-72126.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72127
in-theory        72127
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-7.            (A -> (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-72127.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72128
in-theory        72128
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-316 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-7.            (A -> (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-72128.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72129
in-theory        72129
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-7.            (A -> (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-72129.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72130
in-theory        72130
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (((A or (B -> (A and B))) -> (not (C -> (D or C)))) -> (not (A or (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-313 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72130.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (((A or (B -> (A and B))) -> (not (C -> (D or C)))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72131
in-theory        72131
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> (((A or (B -> (A and B))) or (C -> (D or C))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm 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-48.           (((A -> (B and 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-72131.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> (((A or (B -> (A and B))) or (C -> (D or C))) -> E))), M:tm-312, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72132
in-theory        72132
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (E or ((A or (B -> (A and B))) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
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-48.           (((A -> (B and 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-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-72132.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (E or ((A or (B -> (A and B))) -> (C -> (D or C))))), M:tm-311, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72133
in-theory        72133
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (((A or (B -> (A and B))) -> (C -> (D or C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72133.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (((A or (B -> (A and B))) -> (C -> (D or C))) or E)), M:tm-310, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72134
in-theory        72134
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (((A or (B -> (A and B))) -> (C -> (D or C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72134.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> (((A or (B -> (A and B))) -> (C -> (D or C))) and E))), M:tm-309, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72135
in-theory        72135
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D or C))))
theorem-size     35
proof            (modus-ponens tm-306 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (or Dm 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72135.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D or C)))), M:tm-306, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-72136
in-theory        72136
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> ((A or (B -> (A and B))) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
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-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-7.            (A -> (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-72136.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (E -> ((A or (B -> (A and B))) -> (C -> (D or C))))), M:tm-305, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72137
in-theory        72137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72137.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-303, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72138
in-theory        72138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72138.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-270, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72139
in-theory        72139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72139.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-239, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72140
in-theory        72140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72140.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (G -> (H or G)))), M:tm-210, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72141
in-theory        72141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-7.            (A -> (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-72141.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-183, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72142
in-theory        72142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-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-7.            (A -> (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-72142.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-157, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72143
in-theory        72143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72143.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-147, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72144
in-theory        72144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-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-7.            (A -> (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-72144.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-134, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72145
in-theory        72145
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72145.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-125, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72146
in-theory        72146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-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-7.            (A -> (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-72146.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (G -> (H or G)))), M:tm-113, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72147
in-theory        72147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72147.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-105, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72148
in-theory        72148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (A or (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-99 tm-832 ((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (or Dm (or Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-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-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-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-72148.        ((A or (B -> (A and B))) -> (C or (A or (B -> (A and B))))), M:tm-99, m:tm-832, u:((Cm (or Am (-> Bm (and Am Bm)))) (A (or Am (-> Bm (and Am Bm)))) (B (or Dm (or Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-72149
in-theory        72149
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D -> (A or (B -> (A and B))))))
theorem-size     19
proof            (modus-ponens tm-98 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (or Dm (-> B (or Am (-> Bm (and Am Bm))))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-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-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-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-72149.        ((A or (B -> (A and B))) -> (C or (D -> (A or (B -> (A and B)))))), M:tm-98, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B (or Am (-> Bm (and Am Bm))))) (C (or Dm (-> B (or Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-72150
in-theory        72150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-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-7.            (A -> (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-72150.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (E -> (F or E)))), M:tm-95, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72151
in-theory        72151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 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-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-7.            (A -> (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-72151.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-83, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72152
in-theory        72152
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72152.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (D -> (E or D)))), M:tm-76, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72153
in-theory        72153
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (D or C)))
theorem-size     23
proof            (modus-ponens tm-73 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 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-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-72153.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (C -> (D or C))), M:tm-73, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72154
in-theory        72154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72154.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (E -> (F or E)))), M:tm-69, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72155
in-theory        72155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-72155.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-54, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72156
in-theory        72156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-50 tm-832 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
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-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-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-72156.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (C -> (D or C))), M:tm-50, m:tm-832, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72157
in-theory        72157
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-832 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-7)
proof-size       113
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-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-72157.        ((A or (A or (B -> (A and B)))) -> (C -> (D or C))), M:tm-49, m:tm-832, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72158
in-theory        72158
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-47 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 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-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-72158.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (D -> (E or D))), M:tm-47, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72159
in-theory        72159
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-46 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 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-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-72159.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (D -> (E or D))), M:tm-46, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72160
in-theory        72160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm 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-42.           (A -> ((B -> (C or B)) and A)), 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-1.            (A -> (B -> 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-72160.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (E -> (F or E)))), M:tm-42, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72161
in-theory        72161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm 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-32.           (A -> ((B -> (B or C)) and A)), 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72161.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (E -> (F or E)))), M:tm-32, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72162
in-theory        72162
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D or C))))
theorem-size     21
proof            (modus-ponens tm-24 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
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-48.           (((A -> (B and 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-72162.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (C -> (D or C)))), M:tm-24, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72163
in-theory        72163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72163.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (E -> (F or E)))), M:tm-23, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72164
in-theory        72164
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72164.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (E -> (F or E)))), M:tm-22, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72165
in-theory        72165
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72165.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (E -> (F or E)))), M:tm-21, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72166
in-theory        72166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-72166.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-20, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72167
in-theory        72167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm 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-19.           (A -> ((B -> (C -> B)) and 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-7.            (A -> (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-72167.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (E -> (F or E)))), M:tm-19, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72168
in-theory        72168
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (C -> (D or C)))) -> (not (A or (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-9 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-5 tm-1 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-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-72168.        (((A or (B -> (A and B))) -> (not (C -> (D or C)))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72169
in-theory        72169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (((D or (E -> (D and E))) or (A -> (B or A))) -> C))
theorem-size     23
proof            (modus-ponens tm-8 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
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-7.            (A -> (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-72169.        (((A -> (B or A)) -> C) -> (((D or (E -> (D and E))) or (A -> (B or A))) -> C)), M:tm-8, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-72170
in-theory        72170
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-8 tm-5 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-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-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-72170.        (A or ((B or (C -> (B and C))) -> (D -> (E or D)))), M:tm-7, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72171
in-theory        72171
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-5 tm-1 tm-7)
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-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-72171.        (((A or (B -> (A and B))) -> (C -> (D or C))) or E), M:tm-6, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72172
in-theory        72172
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (D -> (E or D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-832 ((A (-> (or Am (-> Bm (and 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-48.           (((A -> (B and 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-72172.        (A -> (((B or (C -> (B and C))) -> (D -> (E or D))) and A)), M:tm-5, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72173
in-theory        72173
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D or C)))
theorem-size     21
proof            (modus-ponens tm-2 tm-832 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-7)
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-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-72173.        (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> (D or C))), M:tm-2, m:tm-832, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-72174
in-theory        72174
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-8 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (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-72174.        (A -> ((B or (C -> (B and C))) -> (D -> (E or D)))), M:tm-1, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-72175
in-theory        72175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     35
proof            (modus-ponens tm-808 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72175.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-808, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72176
in-theory        72176
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((D and (A or ((B -> C) -> (A and (B -> C))))) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C)))))
theorem-size     61
proof            (modus-ponens tm-798 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72176.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((D and (A or ((B -> C) -> (A and (B -> C))))) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C))))), M:tm-798, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72177
in-theory        72177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     35
proof            (modus-ponens tm-757 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-1.            (A -> (B -> A)), 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-72177.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-757, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72178
in-theory        72178
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((((A or ((B -> C) -> (A and (B -> C)))) and D) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C)))))
theorem-size     61
proof            (modus-ponens tm-747 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
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-48.           (((A -> (B and 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-72178.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((((A or ((B -> C) -> (A and (B -> C)))) and D) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C))))), M:tm-747, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72179
in-theory        72179
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G)))))
theorem-size     49
proof            (modus-ponens tm-708 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72179.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G))))), M:tm-708, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72180
in-theory        72180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-665 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-72180.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-665, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72181
in-theory        72181
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> (D or ((C or (B -> C)) -> (A and (B -> C)))))
theorem-size     25
proof            (modus-ponens tm-623 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
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-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-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-72181.        ((A or ((B -> C) -> (A and (B -> C)))) -> (D or ((C or (B -> C)) -> (A and (B -> C))))), M:tm-623, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72182
in-theory        72182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-622 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 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-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-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-72182.        ((A -> (B -> (C or B))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-622, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72183
in-theory        72183
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72183.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (E or D))), M:tm-609, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72184
in-theory        72184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-605 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-1.            (A -> (B -> A)), 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-72184.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-605, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72185
in-theory        72185
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (E or D)) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72185.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (E or D)) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-595, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72186
in-theory        72186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-550 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-1.            (A -> (B -> A)), 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-72186.        (((A -> (B or A)) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-550, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72187
in-theory        72187
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-540 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-1.            (A -> (B -> A)), 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-72187.        ((A or (B -> (C or B))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-540, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72188
in-theory        72188
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-530 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-1.            (A -> (B -> A)), 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-72188.        ((A or (B -> (B or C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-530, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72189
in-theory        72189
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-520 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-1.            (A -> (B -> A)), 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-72189.        ((A or (B -> (C -> (B and C)))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-520, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72190
in-theory        72190
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-510 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-1.            (A -> (B -> A)), 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-72190.        ((A or ((B and C) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-510, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72191
in-theory        72191
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-500 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-1.            (A -> (B -> A)), 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-72191.        ((A or ((B and C) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-500, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72192
in-theory        72192
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G)))))
theorem-size     39
proof            (modus-ponens tm-490 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72192.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G))))), M:tm-490, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72193
in-theory        72193
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-480 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-72193.        ((A or (B -> (C -> B))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-480, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72194
in-theory        72194
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> (((C or (B -> C)) -> (A and (B -> C))) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
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-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-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-72194.        ((A or ((B -> C) -> (A and (B -> C)))) -> (((C or (B -> C)) -> (A and (B -> C))) or D)), M:tm-470, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72195
in-theory        72195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-469 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 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-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-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-72195.        ((A -> (B -> (B or C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-469, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72196
in-theory        72196
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72196.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (D or E))), M:tm-456, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72197
in-theory        72197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-453 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-1.            (A -> (B -> A)), 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-72197.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-453, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72198
in-theory        72198
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (D or E)) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72198.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (D or E)) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-443, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72199
in-theory        72199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-409 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-1.            (A -> (B -> A)), 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-72199.        (((A -> (A or B)) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-409, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72200
in-theory        72200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-400 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-1.            (A -> (B -> A)), 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-72200.        (((A -> (B -> (A and B))) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-400, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72201
in-theory        72201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-391 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-1.            (A -> (B -> A)), 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-72201.        ((((A and B) -> B) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-391, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72202
in-theory        72202
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-382 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-1.            (A -> (B -> A)), 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-72202.        ((((A and B) -> A) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-382, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72203
in-theory        72203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G)))))
theorem-size     39
proof            (modus-ponens tm-373 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72203.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G))))), M:tm-373, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72204
in-theory        72204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-364 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-72204.        (((A -> (B -> A)) or C) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-364, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72205
in-theory        72205
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> (D -> (((C or (B -> C)) -> (A and (B -> C))) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72205.        ((A or ((B -> C) -> (A and (B -> C)))) -> (D -> (((C or (B -> C)) -> (A and (B -> C))) and D))), M:tm-355, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72206
in-theory        72206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-354 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 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-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-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-72206.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-354, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72207
in-theory        72207
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-72207.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72208
in-theory        72208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E)))))
theorem-size     33
proof            (modus-ponens tm-338 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72208.        (((A -> B) -> (A -> (A and B))) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E))))), M:tm-338, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72209
in-theory        72209
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((A or ((B -> C) -> (A and (B -> C)))) and ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     59
proof            (modus-ponens tm-328 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm 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-328.          ((A -> 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-1.            (A -> (B -> A)), 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-72209.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((A or ((B -> C) -> (A and (B -> C)))) and ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-328, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72210
in-theory        72210
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (E -> (D and E))) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72210.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (E -> (D and E))) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-327, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72211
in-theory        72211
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((D and E) -> E) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72211.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((D and E) -> E) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-326, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72212
in-theory        72212
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((D and E) -> D) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72212.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((D and E) -> D) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-325, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72213
in-theory        72213
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> A)), 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-72213.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-324, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72214
in-theory        72214
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (E -> D)) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72214.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (E -> D)) and ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-323, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72215
in-theory        72215
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72215.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D and E) -> E)), M:tm-322, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72216
in-theory        72216
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72216.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D and E) -> D)), M:tm-320, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72217
in-theory        72217
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72217.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72218
in-theory        72218
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((A or ((B -> C) -> (A and (B -> C)))) -> (A or ((B -> C) -> (A and (B -> C))))))
theorem-size     47
proof            (modus-ponens tm-316 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-72218.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((A or ((B -> C) -> (A and (B -> C)))) -> (A or ((B -> C) -> (A and (B -> C)))))), M:tm-316, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72219
in-theory        72219
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-72219.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (E -> D))), M:tm-315, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72220
in-theory        72220
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((A or ((B -> C) -> (A and (B -> C)))) -> (not ((C or (B -> C)) -> (A and (B -> C))))) -> (not (A or ((B -> C) -> (A and (B -> C)))))))
theorem-size     61
proof            (modus-ponens tm-313 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
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-48.           (((A -> (B and 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-72220.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((A or ((B -> C) -> (A and (B -> C)))) -> (not ((C or (B -> C)) -> (A and (B -> C))))) -> (not (A or ((B -> C) -> (A and (B -> C))))))), M:tm-313, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72221
in-theory        72221
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((((C or (B -> C)) -> (A and (B -> C))) -> D) -> (((A or ((B -> C) -> (A and (B -> C)))) or ((C or (B -> C)) -> (A and (B -> C)))) -> D)))
theorem-size     63
proof            (modus-ponens tm-312 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
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-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), 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-72221.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((((C or (B -> C)) -> (A and (B -> C))) -> D) -> (((A or ((B -> C) -> (A and (B -> C)))) or ((C or (B -> C)) -> (A and (B -> C)))) -> D))), M:tm-312, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72222
in-theory        72222
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D or ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72222.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D or ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-311, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72223
in-theory        72223
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72223.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) or D)), M:tm-310, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72224
in-theory        72224
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm 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-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-1.            (A -> (B -> A)), 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-72224.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and D))), M:tm-309, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72225
in-theory        72225
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((A or ((B -> C) -> (A and (B -> C)))) -> (C or (B -> C))) -> ((A or ((B -> C) -> (A and (B -> C)))) -> (A and (B -> C)))))
theorem-size     59
proof            (modus-ponens tm-306 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (or Cm (-> Bm Cm))) (C (and Am (-> Bm 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), 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-72225.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (((A or ((B -> C) -> (A and (B -> C)))) -> (C or (B -> C))) -> ((A or ((B -> C) -> (A and (B -> C)))) -> (A and (B -> C))))), M:tm-306, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (or Cm (-> Bm Cm))) (C (and Am (-> Bm Cm))))
================================================================
tm-name          tm-72226
in-theory        72226
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72226.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and (D -> ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))))), M:tm-305, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72227
in-theory        72227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     35
proof            (modus-ponens tm-303 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-72227.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-303, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72228
in-theory        72228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-270 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-48.           (((A -> (B and 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-72228.        ((A -> (((B and C) -> C) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-270, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72229
in-theory        72229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-239 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-48.           (((A -> (B and 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-72229.        ((A -> (((B and C) -> B) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-239, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72230
in-theory        72230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G)))))
theorem-size     41
proof            (modus-ponens tm-210 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72230.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G))))), M:tm-210, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72231
in-theory        72231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-183 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 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-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-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-72231.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-183, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72232
in-theory        72232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-157 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 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-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-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-72232.        ((A -> ((B and C) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-157, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72233
in-theory        72233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-147 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72233.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-147, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72234
in-theory        72234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-134 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 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-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-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-72234.        ((A -> ((B and C) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-134, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72235
in-theory        72235
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-125 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and 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-72235.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-125, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72236
in-theory        72236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G)))))
theorem-size     39
proof            (modus-ponens tm-113 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72236.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G))))), M:tm-113, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72237
in-theory        72237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     43
proof            (modus-ponens tm-105 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-1.            (A -> (B -> A)), 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-72237.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-105, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72238
in-theory        72238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E)))))
theorem-size     31
proof            (modus-ponens tm-95 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72238.        (((A -> B) -> (A -> A)) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E))))), M:tm-95, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72239
in-theory        72239
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> (D -> ((C or (B -> C)) -> (A and (B -> C)))))
theorem-size     25
proof            (modus-ponens tm-84 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
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-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-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-72239.        ((A or ((B -> C) -> (A and (B -> C)))) -> (D -> ((C or (B -> C)) -> (A and (B -> C))))), M:tm-84, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72240
in-theory        72240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-83 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 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-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-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-72240.        ((A -> (B -> (C -> B))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-83, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72241
in-theory        72241
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C -> D) -> (B and (C -> D)))) -> ((D or (C -> D)) -> (B and (C -> D)))))
theorem-size     29
proof            (modus-ponens tm-76 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-48.           (((A -> (B and 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-72241.        (((not (not A)) -> A) and ((B or ((C -> D) -> (B and (C -> D)))) -> ((D or (C -> D)) -> (B and (C -> D))))), M:tm-76, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72242
in-theory        72242
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or ((B -> C) -> (A and (B -> C)))))) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C))))
theorem-size     37
proof            (modus-ponens tm-73 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
proof-size       157
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-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-72242.        (((not (not (A or ((B -> C) -> (A and (B -> C)))))) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C)))), M:tm-73, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72243
in-theory        72243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-69 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-48.           (((A -> (B and 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-72243.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E))))), M:tm-69, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72244
in-theory        72244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-54 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-72244.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-54, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72245
in-theory        72245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C and (A -> B))) or (C or ((A -> B) -> (C and (A -> B))))) -> ((B or (A -> B)) -> (C and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-50 tm-833 ((A Am) (B (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       155
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-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-72245.        ((((A -> B) -> (C and (A -> B))) or (C or ((A -> B) -> (C and (A -> B))))) -> ((B or (A -> B)) -> (C and (A -> B)))), M:tm-50, m:tm-833, u:((A Am) (B (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72246
in-theory        72246
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C))))
theorem-size     25
proof            (modus-ponens tm-49 tm-833 ((A Am) (B (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
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-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-72246.        ((A or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C)))), M:tm-49, m:tm-833, u:((A Am) (B (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72247
in-theory        72247
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or ((C -> D) -> (B and (C -> D))))) or (B or ((C -> D) -> (B and (C -> D))))) -> ((D or (C -> D)) -> (B and (C -> D))))
theorem-size     37
proof            (modus-ponens tm-47 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       157
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-48.           (((A -> (B and 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-72247.        (((A and (B or ((C -> D) -> (B and (C -> D))))) or (B or ((C -> D) -> (B and (C -> D))))) -> ((D or (C -> D)) -> (B and (C -> D)))), M:tm-47, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72248
in-theory        72248
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B -> C) -> (A and (B -> C)))) and D) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C))))
theorem-size     37
proof            (modus-ponens tm-46 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
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-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-72248.        ((((A or ((B -> C) -> (A and (B -> C)))) and D) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C)))), M:tm-46, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72249
in-theory        72249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E)))))
theorem-size     29
proof            (modus-ponens tm-42 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-1.            (A -> (B -> A)), 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-72249.        ((A -> (B or A)) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E))))), M:tm-42, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72250
in-theory        72250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E)))))
theorem-size     29
proof            (modus-ponens tm-32 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-1.            (A -> (B -> A)), 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-72250.        ((A -> (A or B)) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E))))), M:tm-32, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72251
in-theory        72251
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> ((A or ((B -> C) -> (A and (B -> C)))) and ((C or (B -> C)) -> (A and (B -> C)))))
theorem-size     35
proof            (modus-ponens tm-24 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm 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-48.           (((A -> (B and 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-72251.        ((A or ((B -> C) -> (A and (B -> C)))) -> ((A or ((B -> C) -> (A and (B -> C)))) and ((C or (B -> C)) -> (A and (B -> C))))), M:tm-24, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72252
in-theory        72252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E)))))
theorem-size     31
proof            (modus-ponens tm-23 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-72252.        ((A -> (B -> (A and B))) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E))))), M:tm-23, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72253
in-theory        72253
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E)))))
theorem-size     29
proof            (modus-ponens tm-22 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-48.           (((A -> (B and 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-72253.        (((A and B) -> B) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E))))), M:tm-22, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72254
in-theory        72254
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E)))))
theorem-size     29
proof            (modus-ponens tm-21 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-48.           (((A -> (B and 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-72254.        (((A and B) -> A) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E))))), M:tm-21, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72255
in-theory        72255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-20 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm 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-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-1.            (A -> (B -> A)), 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-72255.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-20, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72256
in-theory        72256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E)))))
theorem-size     29
proof            (modus-ponens tm-19 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 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-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-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-72256.        ((A -> (B -> A)) and ((C or ((D -> E) -> (C and (D -> E)))) -> ((E or (D -> E)) -> (C and (D -> E))))), M:tm-19, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72257
in-theory        72257
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> (A or ((B -> C) -> (A and (B -> C)))))
theorem-size     23
proof            (modus-ponens tm-12 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-72257.        ((A or ((B -> C) -> (A and (B -> C)))) -> (A or ((B -> C) -> (A and (B -> C))))), M:tm-12, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72258
in-theory        72258
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> (not ((C or (B -> C)) -> (A and (B -> C))))) -> (not (A or ((B -> C) -> (A and (B -> C))))))
theorem-size     37
proof            (modus-ponens tm-9 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-1)
proof-size       139
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-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-72258.        (((A or ((B -> C) -> (A and (B -> C)))) -> (not ((C or (B -> C)) -> (A and (B -> C))))) -> (not (A or ((B -> C) -> (A and (B -> C)))))), M:tm-9, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72259
in-theory        72259
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> (C and (B -> A))) -> D) -> (((C or ((B -> A) -> (C and (B -> A)))) or ((A or (B -> A)) -> (C and (B -> A)))) -> D))
theorem-size     39
proof            (modus-ponens tm-8 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
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-1.            (A -> (B -> A)), 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-72259.        ((((A or (B -> A)) -> (C and (B -> A))) -> D) -> (((C or ((B -> A) -> (C and (B -> A)))) or ((A or (B -> A)) -> (C and (B -> A)))) -> D)), M:tm-8, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-72260
in-theory        72260
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or ((C -> D) -> (B and (C -> D)))) -> ((D or (C -> D)) -> (B and (C -> D)))))
theorem-size     25
proof            (modus-ponens tm-7 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-1)
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-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-72260.        (A or ((B or ((C -> D) -> (B and (C -> D)))) -> ((D or (C -> D)) -> (B and (C -> D))))), M:tm-7, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72261
in-theory        72261
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-1)
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-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-72261.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) or D), M:tm-6, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72262
in-theory        72262
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C -> D) -> (B and (C -> D)))) -> ((D or (C -> D)) -> (B and (C -> D)))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm 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-48.           (((A -> (B and 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-72262.        (A -> (((B or ((C -> D) -> (B and (C -> D)))) -> ((D or (C -> D)) -> (B and (C -> D)))) and A)), M:tm-5, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72263
in-theory        72263
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> (C or (B -> C))) -> ((A or ((B -> C) -> (A and (B -> C)))) -> (A and (B -> C))))
theorem-size     35
proof            (modus-ponens tm-2 tm-833 ((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (or Cm (-> Bm Cm))) (C (and Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1)
proof-size       139
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-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-72263.        (((A or ((B -> C) -> (A and (B -> C)))) -> (C or (B -> C))) -> ((A or ((B -> C) -> (A and (B -> C)))) -> (A and (B -> C)))), M:tm-2, m:tm-833, u:((A (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm))))) (B (or Cm (-> Bm Cm))) (C (and Am (-> Bm Cm))))
================================================================
tm-name          tm-72264
in-theory        72264
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> D) -> (B and (C -> D)))) -> ((D or (C -> D)) -> (B and (C -> D)))))
theorem-size     25
proof            (modus-ponens tm-1 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-1 tm-8 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-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-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-72264.        (A -> ((B or ((C -> D) -> (B and (C -> D)))) -> ((D or (C -> D)) -> (B and (C -> D))))), M:tm-1, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-72265
in-theory        72265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     55
proof            (modus-ponens tm-808 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72265.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-808, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72266
in-theory        72266
times-derived    1
----------------------------------------------------------------
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))))) and (((E and (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))))) or (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     109
proof            (modus-ponens tm-798 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72266.        (((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))))) and (((E and (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))))) or (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-798, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72267
in-theory        72267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     55
proof            (modus-ponens tm-757 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72267.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-757, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72268
in-theory        72268
times-derived    1
----------------------------------------------------------------
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))))) and ((((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) and E) or (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     109
proof            (modus-ponens tm-747 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72268.        (((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))))) and ((((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) and E) or (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-747, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72269
in-theory        72269
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 and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H))))))
theorem-size     69
proof            (modus-ponens tm-708 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-72269.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H)))))), M:tm-708, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72270
in-theory        72270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     57
proof            (modus-ponens tm-665 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72270.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-665, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72271
in-theory        72271
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (E or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-623 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       215
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72271.        ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (E or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))))), M:tm-623, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72272
in-theory        72272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-622 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72272.        ((A -> (B -> (C or B))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-622, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72273
in-theory        72273
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (F or E)))
theorem-size     49
proof            (modus-ponens tm-609 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72273.        (((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))))) and (E -> (F or E))), M:tm-609, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72274
in-theory        72274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-605 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72274.        ((A -> ((B -> (C or B)) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-605, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72275
in-theory        72275
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (F or E)) and ((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     93
proof            (modus-ponens tm-595 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72275.        (((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))))) and ((E -> (F or E)) and ((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-595, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72276
in-theory        72276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-550 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72276.        (((A -> (B or A)) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-550, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72277
in-theory        72277
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-540 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72277.        ((A or (B -> (C or B))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-540, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72278
in-theory        72278
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-530 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72278.        ((A or (B -> (B or C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-530, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72279
in-theory        72279
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-520 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72279.        ((A or (B -> (C -> (B and C)))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-520, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72280
in-theory        72280
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-510 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72280.        ((A or ((B and C) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-510, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72281
in-theory        72281
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-500 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72281.        ((A or ((B and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-500, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72282
in-theory        72282
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H))))))
theorem-size     59
proof            (modus-ponens tm-490 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72282.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H)))))), M:tm-490, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72283
in-theory        72283
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-480 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72283.        ((A or (B -> (C -> B))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-480, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72284
in-theory        72284
times-derived    1
----------------------------------------------------------------
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)))) or E))
theorem-size     45
proof            (modus-ponens tm-470 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       215
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72284.        ((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)))) or E)), M:tm-470, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72285
in-theory        72285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-469 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72285.        ((A -> (B -> (B or C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-469, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72286
in-theory        72286
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (E or F)))
theorem-size     49
proof            (modus-ponens tm-456 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72286.        (((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))))) and (E -> (E or F))), M:tm-456, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72287
in-theory        72287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-453 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72287.        ((A -> ((B -> (B or C)) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-453, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72288
in-theory        72288
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (E or F)) and ((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     93
proof            (modus-ponens tm-443 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72288.        (((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))))) and ((E -> (E or F)) and ((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-443, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72289
in-theory        72289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-409 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72289.        (((A -> (A or B)) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-409, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72290
in-theory        72290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-400 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72290.        (((A -> (B -> (A and B))) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-400, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72291
in-theory        72291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-391 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72291.        ((((A and B) -> B) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-391, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72292
in-theory        72292
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-382 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72292.        ((((A and B) -> A) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-382, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72293
in-theory        72293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H))))))
theorem-size     59
proof            (modus-ponens tm-373 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72293.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H)))))), M:tm-373, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72294
in-theory        72294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-364 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72294.        (((A -> (B -> A)) or C) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-364, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72295
in-theory        72295
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (E -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))) and E)))
theorem-size     47
proof            (modus-ponens tm-355 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (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       223
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72295.        ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (E -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))) and E))), M:tm-355, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72296
in-theory        72296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-354 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72296.        ((A -> (B -> (C -> (B and C)))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-354, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72297
in-theory        72297
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (F -> (E and F))))
theorem-size     51
proof            (modus-ponens tm-341 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72297.        (((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))))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72298
in-theory        72298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F))))))
theorem-size     53
proof            (modus-ponens tm-338 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72298.        (((A -> B) -> (A -> (A and B))) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F)))))), M:tm-338, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72299
in-theory        72299
times-derived    1
----------------------------------------------------------------
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))))) and ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((A or (((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     107
proof            (modus-ponens tm-328 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       309
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72299.        (((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))))) and ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((A or (((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-328, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72300
in-theory        72300
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (F -> (E and F))) and ((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     95
proof            (modus-ponens tm-327 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72300.        (((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))))) and ((E -> (F -> (E and F))) and ((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-327, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72301
in-theory        72301
times-derived    1
----------------------------------------------------------------
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))))) and (((E and F) -> F) and ((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     93
proof            (modus-ponens tm-326 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72301.        (((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))))) and (((E and F) -> F) and ((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-326, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72302
in-theory        72302
times-derived    1
----------------------------------------------------------------
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))))) and (((E and F) -> E) and ((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     93
proof            (modus-ponens tm-325 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72302.        (((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))))) and (((E and F) -> E) and ((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-325, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72303
in-theory        72303
times-derived    1
----------------------------------------------------------------
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))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((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     101
proof            (modus-ponens tm-324 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       317
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72303.        (((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))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((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-324, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72304
in-theory        72304
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (F -> E)) and ((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     93
proof            (modus-ponens tm-323 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72304.        (((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))))) and ((E -> (F -> E)) and ((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-323, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72305
in-theory        72305
times-derived    1
----------------------------------------------------------------
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))))) and ((E and F) -> F))
theorem-size     49
proof            (modus-ponens tm-322 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72305.        (((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))))) and ((E and F) -> F)), M:tm-322, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72306
in-theory        72306
times-derived    1
----------------------------------------------------------------
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))))) and ((E and F) -> E))
theorem-size     49
proof            (modus-ponens tm-320 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72306.        (((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))))) and ((E and F) -> E)), M:tm-320, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72307
in-theory        72307
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     57
proof            (modus-ponens tm-318 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72307.        (((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))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72308
in-theory        72308
times-derived    1
----------------------------------------------------------------
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))))) and ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))))))
theorem-size     83
proof            (modus-ponens tm-316 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72308.        (((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))))) and ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))))), M:tm-316, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72309
in-theory        72309
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (F -> E)))
theorem-size     49
proof            (modus-ponens tm-315 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72309.        (((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))))) and (E -> (F -> E))), M:tm-315, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72310
in-theory        72310
times-derived    1
----------------------------------------------------------------
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))))) and (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))))) -> (not (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))))))
theorem-size     109
proof            (modus-ponens tm-313 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       295
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72310.        (((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))))) and (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))))) -> (not (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))))))), M:tm-313, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72311
in-theory        72311
times-derived    1
----------------------------------------------------------------
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))))) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))) -> E) -> (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D))))) -> E)))
theorem-size     115
proof            (modus-ponens tm-312 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       305
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72311.        (((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))))) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))) -> E) -> (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D))))) -> E))), M:tm-312, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72312
in-theory        72312
times-derived    1
----------------------------------------------------------------
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))))) and (E or ((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     89
proof            (modus-ponens tm-311 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72312.        (((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))))) and (E or ((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-311, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72313
in-theory        72313
times-derived    1
----------------------------------------------------------------
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))))) and (((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))))) or E))
theorem-size     89
proof            (modus-ponens tm-310 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72313.        (((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))))) and (((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))))) or E)), M:tm-310, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72314
in-theory        72314
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (((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))))) and E)))
theorem-size     91
proof            (modus-ponens tm-309 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72314.        (((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))))) and (E -> (((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))))) and E))), M:tm-309, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72315
in-theory        72315
times-derived    1
----------------------------------------------------------------
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))))) and (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (A and ((B -> C) -> (B -> D))))))
theorem-size     107
proof            (modus-ponens tm-306 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72315.        (((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))))) and (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (A and ((B -> C) -> (B -> D)))))), M:tm-306, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (and Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-72316
in-theory        72316
times-derived    1
----------------------------------------------------------------
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))))) and (E -> ((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     89
proof            (modus-ponens tm-305 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72316.        (((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))))) and (E -> ((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-305, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72317
in-theory        72317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     55
proof            (modus-ponens tm-303 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72317.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-303, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72318
in-theory        72318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-270 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72318.        ((A -> (((B and C) -> C) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-270, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72319
in-theory        72319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-239 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72319.        ((A -> (((B and C) -> B) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-239, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72320
in-theory        72320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H))))))
theorem-size     61
proof            (modus-ponens tm-210 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       257
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72320.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H)))))), M:tm-210, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72321
in-theory        72321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-183 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72321.        ((A -> ((B -> (C -> B)) and A)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-183, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72322
in-theory        72322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-157 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72322.        ((A -> ((B and C) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-157, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72323
in-theory        72323
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     59
proof            (modus-ponens tm-147 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72323.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-147, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72324
in-theory        72324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-134 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72324.        ((A -> ((B and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-134, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72325
in-theory        72325
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     59
proof            (modus-ponens tm-125 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72325.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-125, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72326
in-theory        72326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H))))))
theorem-size     59
proof            (modus-ponens tm-113 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72326.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H)))))), M:tm-113, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72327
in-theory        72327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     63
proof            (modus-ponens tm-105 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       269
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72327.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-105, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72328
in-theory        72328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F))))))
theorem-size     51
proof            (modus-ponens tm-95 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72328.        (((A -> B) -> (A -> A)) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F)))))), M:tm-95, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72329
in-theory        72329
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (E -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-84 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       215
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72329.        ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (E -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))))), M:tm-84, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72330
in-theory        72330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     51
proof            (modus-ponens tm-83 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72330.        ((A -> (B -> (C -> B))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-83, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72331
in-theory        72331
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-76 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72331.        (((not (not A)) -> A) and ((B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E)))))), M:tm-76, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72332
in-theory        72332
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))))) or (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     65
proof            (modus-ponens tm-73 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-10 tm-5 tm-2)
proof-size       225
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-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-72332.        (((not (not (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))))) or (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-73, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72333
in-theory        72333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F))))))
theorem-size     55
proof            (modus-ponens tm-69 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72333.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F)))))), M:tm-69, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72334
in-theory        72334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     57
proof            (modus-ponens tm-54 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72334.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-54, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72335
in-theory        72335
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) or (D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-50 tm-834 ((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       223
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-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-72335.        (((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) or (D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C))))), M:tm-50, m:tm-834, u:((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72336
in-theory        72336
times-derived    1
----------------------------------------------------------------
theorem          ((A or (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     45
proof            (modus-ponens tm-49 tm-834 ((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       207
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-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-72336.        ((A or (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-49, m:tm-834, u:((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72337
in-theory        72337
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E)))))) or (B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E)))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E)))))
theorem-size     65
proof            (modus-ponens tm-47 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       225
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-48.           (((A -> (B and 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-72337.        (((A and (B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E)))))) or (B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E)))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E))))), M:tm-47, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72338
in-theory        72338
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) and E) or (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     65
proof            (modus-ponens tm-46 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       225
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-48.           (((A -> (B and 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-72338.        ((((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) and E) or (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-46, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72339
in-theory        72339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F))))))
theorem-size     49
proof            (modus-ponens tm-42 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72339.        ((A -> (B or A)) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F)))))), M:tm-42, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72340
in-theory        72340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F))))))
theorem-size     49
proof            (modus-ponens tm-32 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72340.        ((A -> (A or B)) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F)))))), M:tm-32, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72341
in-theory        72341
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((A or (((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     63
proof            (modus-ponens tm-24 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72341.        ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((A or (((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-24, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72342
in-theory        72342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F))))))
theorem-size     51
proof            (modus-ponens tm-23 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72342.        ((A -> (B -> (A and B))) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F)))))), M:tm-23, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72343
in-theory        72343
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F))))))
theorem-size     49
proof            (modus-ponens tm-22 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72343.        (((A and B) -> B) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F)))))), M:tm-22, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72344
in-theory        72344
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F))))))
theorem-size     49
proof            (modus-ponens tm-21 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72344.        (((A and B) -> A) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F)))))), M:tm-21, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72345
in-theory        72345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     57
proof            (modus-ponens tm-20 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72345.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-20, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72346
in-theory        72346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F))))))
theorem-size     49
proof            (modus-ponens tm-19 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72346.        ((A -> (B -> A)) and ((C or (((D -> E) -> (D -> F)) -> (C and ((D -> E) -> (D -> F))))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (C and ((D -> E) -> (D -> F)))))), M:tm-19, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72347
in-theory        72347
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))))
theorem-size     39
proof            (modus-ponens tm-12 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       195
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72347.        ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))))), M:tm-12, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72348
in-theory        72348
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))))) -> (not (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))))))
theorem-size     65
proof            (modus-ponens tm-9 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-9 tm-8 tm-5 tm-2)
proof-size       207
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-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-72348.        (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))))) -> (not (A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))))), M:tm-9, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72349
in-theory        72349
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C)))) -> E) -> (((D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C))))) -> E))
theorem-size     71
proof            (modus-ponens tm-8 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       215
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-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-72349.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C)))) -> E) -> (((D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C))))) -> E)), M:tm-8, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-72350
in-theory        72350
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-7 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-7 tm-8 tm-5 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72350.        (A or ((B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E)))))), M:tm-7, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72351
in-theory        72351
times-derived    1
----------------------------------------------------------------
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))))) or E)
theorem-size     45
proof            (modus-ponens tm-6 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-6 tm-8 tm-5 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72351.        (((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))))) or E), M:tm-6, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72352
in-theory        72352
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E))))) and A))
theorem-size     47
proof            (modus-ponens tm-5 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm 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-48.           (((A -> (B and 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-72352.        (A -> (((B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E))))) and A)), M:tm-5, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72353
in-theory        72353
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (A and ((B -> C) -> (B -> D)))))
theorem-size     63
proof            (modus-ponens tm-2 tm-834 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       207
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72353.        (((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (A and ((B -> C) -> (B -> D))))), M:tm-2, m:tm-834, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (and Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-72354
in-theory        72354
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-1 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-1 tm-8 tm-5 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-72354.        (A -> ((B or (((C -> D) -> (C -> E)) -> (B and ((C -> D) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (B and ((C -> D) -> (C -> E)))))), M:tm-1, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-72355
in-theory        72355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-808 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72355.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-808, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72356
in-theory        72356
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B))))
theorem-size     45
proof            (modus-ponens tm-798 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72356.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B)))), M:tm-798, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72357
in-theory        72357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-757 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72357.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-757, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72358
in-theory        72358
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B))))
theorem-size     45
proof            (modus-ponens tm-747 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72358.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B)))), M:tm-747, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72359
in-theory        72359
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F))))
theorem-size     43
proof            (modus-ponens tm-708 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
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-48.           (((A -> (B and 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-72359.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F)))), M:tm-708, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72360
in-theory        72360
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-665 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
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-48.           (((A -> (B and 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-72360.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-665, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72361
in-theory        72361
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (((B and D) or B) -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-623 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> A), axiom
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-72361.        ((A or (B -> (A and B))) -> (C or (((B and D) or B) -> (A and B)))), M:tm-623, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72362
in-theory        72362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-622 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> A), axiom
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-72362.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-622, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72363
in-theory        72363
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72363.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (E or D))), M:tm-609, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72364
in-theory        72364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-605 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-3.            ((A and B) -> A), axiom
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-72364.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-605, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72365
in-theory        72365
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-3.            ((A and B) -> A), axiom
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-72365.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))))), M:tm-595, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72366
in-theory        72366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-550 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-3.            ((A and B) -> A), axiom
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-72366.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-550, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72367
in-theory        72367
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-540 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-3.            ((A and B) -> A), axiom
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-72367.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-540, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72368
in-theory        72368
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-530 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-3.            ((A and B) -> A), axiom
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-72368.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-530, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72369
in-theory        72369
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-520 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-3.            ((A and B) -> A), axiom
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-72369.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-520, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72370
in-theory        72370
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-510 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-3.            ((A and B) -> A), axiom
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-72370.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-510, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72371
in-theory        72371
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-500 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72371.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-500, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72372
in-theory        72372
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-490 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
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-48.           (((A -> (B and 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-72372.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F)))), M:tm-490, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72373
in-theory        72373
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-480 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and B) -> A), axiom
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-72373.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-480, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72374
in-theory        72374
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((B and C) or B) -> (A and B)) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> A), axiom
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-72374.        ((A or (B -> (A and B))) -> ((((B and C) or B) -> (A and B)) or D)), M:tm-470, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72375
in-theory        72375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-469 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> A), axiom
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-72375.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-469, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72376
in-theory        72376
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72376.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (D or E))), M:tm-456, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72377
in-theory        72377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-453 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-3.            ((A and B) -> A), axiom
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-72377.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-453, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72378
in-theory        72378
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-3.            ((A and B) -> A), axiom
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-72378.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))))), M:tm-443, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72379
in-theory        72379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-409 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-3.            ((A and B) -> A), axiom
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-72379.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-409, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72380
in-theory        72380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-400 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-3.            ((A and B) -> A), axiom
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-72380.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-400, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72381
in-theory        72381
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-391 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-3.            ((A and B) -> A), axiom
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-72381.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-391, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72382
in-theory        72382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-382 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72382.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-382, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72383
in-theory        72383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-373 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
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-48.           (((A -> (B and 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-72383.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F)))), M:tm-373, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72384
in-theory        72384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-364 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and B) -> A), axiom
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-72384.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-364, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72385
in-theory        72385
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((((B and D) or B) -> (A and B)) and C)))
theorem-size     21
proof            (modus-ponens tm-355 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-3.            ((A and B) -> A), axiom
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-72385.        ((A or (B -> (A and B))) -> (C -> ((((B and D) or B) -> (A and B)) and C))), M:tm-355, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72386
in-theory        72386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-354 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-3.            ((A and B) -> A), axiom
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-72386.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-354, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72387
in-theory        72387
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72387.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72388
in-theory        72388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D))))
theorem-size     27
proof            (modus-ponens tm-338 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-3.            ((A and B) -> A), axiom
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-72388.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D)))), M:tm-338, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72389
in-theory        72389
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((B and C) or B) -> (A and B)))))
theorem-size     43
proof            (modus-ponens tm-328 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-3.            ((A and B) -> A), axiom
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-72389.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((B and C) or B) -> (A and B))))), M:tm-328, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72390
in-theory        72390
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-3.            ((A and B) -> A), axiom
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-72390.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))))), M:tm-327, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72391
in-theory        72391
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-3.            ((A and B) -> A), axiom
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-72391.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))))), M:tm-326, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72392
in-theory        72392
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-72392.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))))), M:tm-325, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72393
in-theory        72393
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-3.            ((A and B) -> A), axiom
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-72393.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))))), M:tm-324, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72394
in-theory        72394
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A and B) -> A), axiom
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-72394.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))))), M:tm-323, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72395
in-theory        72395
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72395.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D and E) -> E)), M:tm-322, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72396
in-theory        72396
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72396.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D and E) -> D)), M:tm-320, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72397
in-theory        72397
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72397.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72398
in-theory        72398
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-316 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-3.            ((A and B) -> A), axiom
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-72398.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72399
in-theory        72399
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> A), axiom
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-72399.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (E -> D))), M:tm-315, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72400
in-theory        72400
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((A or (B -> (A and B))) -> (not (((B and C) or B) -> (A and B)))) -> (not (A or (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-313 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-3.            ((A and B) -> A), axiom
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-72400.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((A or (B -> (A and B))) -> (not (((B and C) or B) -> (A and B)))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72401
in-theory        72401
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((((B and C) or B) -> (A and B)) -> D) -> (((A or (B -> (A and B))) or (((B and C) or B) -> (A and B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-312 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-3.            ((A and B) -> A), axiom
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-72401.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((((B and C) or B) -> (A and B)) -> D) -> (((A or (B -> (A and B))) or (((B and C) or B) -> (A and B))) -> D))), M:tm-312, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72402
in-theory        72402
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D or ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-3.            ((A and B) -> A), axiom
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-72402.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D or ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))))), M:tm-311, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72403
in-theory        72403
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-3.            ((A and B) -> A), axiom
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-72403.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) or D)), M:tm-310, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72404
in-theory        72404
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-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-3.            ((A and B) -> A), axiom
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-72404.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and D))), M:tm-309, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72405
in-theory        72405
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((A or (B -> (A and B))) -> ((B and C) or B)) -> ((A or (B -> (A and B))) -> (A and B))))
theorem-size     43
proof            (modus-ponens tm-306 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (or (and Bm Cm) Bm)) (C (and Am 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-306.          ((A -> (B -> C)) -> ((A -> (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-3.            ((A and B) -> A), axiom
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-72405.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((A or (B -> (A and B))) -> ((B and C) or B)) -> ((A or (B -> (A and B))) -> (A and B)))), M:tm-306, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (and Bm Cm) Bm)) (C (and Am Bm)))
================================================================
tm-name          tm-72406
in-theory        72406
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-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-3.            ((A and B) -> A), axiom
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-72406.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (D -> ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))))), M:tm-305, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72407
in-theory        72407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-303 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-72407.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-303, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72408
in-theory        72408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-270 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
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-48.           (((A -> (B and 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-72408.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-270, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72409
in-theory        72409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-239 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72409.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-239, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72410
in-theory        72410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-210 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-3.            ((A and B) -> A), axiom
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-72410.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F)))), M:tm-210, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72411
in-theory        72411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-183 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-3.            ((A and B) -> A), axiom
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-72411.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-183, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72412
in-theory        72412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-157 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> A), axiom
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-72412.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-157, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72413
in-theory        72413
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-147 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-3.            ((A and B) -> A), axiom
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-72413.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-147, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72414
in-theory        72414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-134 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72414.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-134, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72415
in-theory        72415
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-125 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-72415.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-125, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72416
in-theory        72416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-113 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72416.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F)))), M:tm-113, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72417
in-theory        72417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     37
proof            (modus-ponens tm-105 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-3.            ((A and B) -> A), axiom
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-72417.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-105, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72418
in-theory        72418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-95 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72418.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D)))), M:tm-95, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72419
in-theory        72419
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((B and D) or B) -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-84 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> A), axiom
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-72419.        ((A or (B -> (A and B))) -> (C -> (((B and D) or B) -> (A and B)))), M:tm-84, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72420
in-theory        72420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-83 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> A), axiom
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-72420.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-83, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72421
in-theory        72421
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((C and D) or C) -> (B and C))))
theorem-size     23
proof            (modus-ponens tm-76 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
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-48.           (((A -> (B and 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-72421.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((C and D) or C) -> (B and C)))), M:tm-76, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72422
in-theory        72422
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B)))
theorem-size     27
proof            (modus-ponens tm-73 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-10 tm-5 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-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-72422.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B))), M:tm-73, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72423
in-theory        72423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D))))
theorem-size     29
proof            (modus-ponens tm-69 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
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-48.           (((A -> (B and 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-72423.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D)))), M:tm-69, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72424
in-theory        72424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-54 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-3.            ((A and B) -> A), axiom
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-72424.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-54, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72425
in-theory        72425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((A and C) or A) -> (B and A)))
theorem-size     23
proof            (modus-ponens tm-50 tm-835 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-7 tm-5 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-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-72425.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((A and C) or A) -> (B and A))), M:tm-50, m:tm-835, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72426
in-theory        72426
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-835 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
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-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-72426.        ((A or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B))), M:tm-49, m:tm-835, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72427
in-theory        72427
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((C and D) or C) -> (B and C)))
theorem-size     27
proof            (modus-ponens tm-47 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-4 tm-5 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-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-72427.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((C and D) or C) -> (B and C))), M:tm-47, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72428
in-theory        72428
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((B and D) or B) -> (A and B)))
theorem-size     27
proof            (modus-ponens tm-46 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-3 tm-5)
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-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-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-72428.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((B and D) or B) -> (A and B))), M:tm-46, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72429
in-theory        72429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-42 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-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-3.            ((A and B) -> A), axiom
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-72429.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D)))), M:tm-42, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72430
in-theory        72430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-32 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-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-3.            ((A and B) -> A), axiom
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-72430.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D)))), M:tm-32, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72431
in-theory        72431
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((B and C) or B) -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-24 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am 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-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-3.            ((A and B) -> A), axiom
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-72431.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((B and C) or B) -> (A and B)))), M:tm-24, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72432
in-theory        72432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-23 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 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-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-3.            ((A and B) -> A), axiom
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-72432.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D)))), M:tm-23, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72433
in-theory        72433
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-22 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-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-3.            ((A and B) -> A), axiom
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-72433.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D)))), M:tm-22, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72434
in-theory        72434
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-21 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-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-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-72434.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D)))), M:tm-21, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72435
in-theory        72435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-20 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-3.            ((A and B) -> A), axiom
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-72435.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-20, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72436
in-theory        72436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-19 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
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-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-3.            ((A and B) -> A), axiom
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-72436.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((D and E) or D) -> (C and D)))), M:tm-19, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72437
in-theory        72437
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (((B and C) or B) -> (A and B)))) -> (not (A or (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-9 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-9 tm-8 tm-5 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-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-72437.        (((A or (B -> (A and B))) -> (not (((B and C) or B) -> (A and B)))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72438
in-theory        72438
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> (C and A)) -> D) -> (((C or (A -> (C and A))) or (((A and B) or A) -> (C and A))) -> D))
theorem-size     31
proof            (modus-ponens tm-8 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm)))))
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-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-72438.        (((((A and B) or A) -> (C and A)) -> D) -> (((C or (A -> (C and A))) or (((A and B) or A) -> (C and A))) -> D)), M:tm-8, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72439
in-theory        72439
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (((C and D) or C) -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-7 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-7 tm-8 tm-5 tm-3)
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-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-72439.        (A or ((B or (C -> (B and C))) -> (((C and D) or C) -> (B and C)))), M:tm-7, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72440
in-theory        72440
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-6 tm-8 tm-5 tm-3)
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-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-72440.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) or D), M:tm-6, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72441
in-theory        72441
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (((C and D) or C) -> (B and C))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-72441.        (A -> (((B or (C -> (B and C))) -> (((C and D) or C) -> (B and C))) and A)), M:tm-5, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72442
in-theory        72442
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B and C) or B)) -> ((A or (B -> (A and B))) -> (A and B)))
theorem-size     25
proof            (modus-ponens tm-2 tm-835 ((A (or Am (-> Bm (and Am Bm)))) (B (or (and Bm Cm) Bm)) (C (and Am Bm))))
axioms-used      (tm-2 tm-8 tm-5 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-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-72442.        (((A or (B -> (A and B))) -> ((B and C) or B)) -> ((A or (B -> (A and B))) -> (A and B))), M:tm-2, m:tm-835, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (and Bm Cm) Bm)) (C (and Am Bm)))
================================================================
tm-name          tm-72443
in-theory        72443
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (((C and D) or C) -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-1 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-1 tm-8 tm-5 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-72443.        (A -> ((B or (C -> (B and C))) -> (((C and D) or C) -> (B and C)))), M:tm-1, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72444
in-theory        72444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-808 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am 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-72444.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-808, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72445
in-theory        72445
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B))))
theorem-size     45
proof            (modus-ponens tm-798 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am 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-72445.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((D and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B)))), M:tm-798, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72446
in-theory        72446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-757 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-48.           (((A -> (B and 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-72446.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-757, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72447
in-theory        72447
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B))))
theorem-size     45
proof            (modus-ponens tm-747 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-72447.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((((A or (B -> (A and B))) and D) or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B)))), M:tm-747, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72448
in-theory        72448
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F))))
theorem-size     43
proof            (modus-ponens tm-708 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-48.           (((A -> (B and 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-72448.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F)))), M:tm-708, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72449
in-theory        72449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-665 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-4.            ((A and B) -> B), axiom
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-72449.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-665, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72450
in-theory        72450
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (((D and B) or B) -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-623 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-72450.        ((A or (B -> (A and B))) -> (C or (((D and B) or B) -> (A and B)))), M:tm-623, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72451
in-theory        72451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-622 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-72451.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-622, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72452
in-theory        72452
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72452.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (E or D))), M:tm-609, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72453
in-theory        72453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-605 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-72453.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-605, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72454
in-theory        72454
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-72454.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (E or D)) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))))), M:tm-595, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72455
in-theory        72455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-550 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
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-48.           (((A -> (B and 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-72455.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-550, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72456
in-theory        72456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-540 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-48.           (((A -> (B and 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-72456.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-540, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72457
in-theory        72457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-530 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
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-48.           (((A -> (B and 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-72457.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-530, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72458
in-theory        72458
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-520 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-4.            ((A and B) -> B), axiom
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-72458.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-520, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72459
in-theory        72459
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-510 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72459.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-510, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72460
in-theory        72460
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-500 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
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-48.           (((A -> (B and 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-72460.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-500, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72461
in-theory        72461
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-490 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-48.           (((A -> (B and 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-72461.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F)))), M:tm-490, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72462
in-theory        72462
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-480 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
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-48.           (((A -> (B and 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-72462.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-480, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72463
in-theory        72463
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C and B) or B) -> (A and B)) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-72463.        ((A or (B -> (A and B))) -> ((((C and B) or B) -> (A and B)) or D)), M:tm-470, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72464
in-theory        72464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-469 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-72464.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-469, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72465
in-theory        72465
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72465.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (D or E))), M:tm-456, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72466
in-theory        72466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-453 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-72466.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-453, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72467
in-theory        72467
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-72467.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (D or E)) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))))), M:tm-443, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72468
in-theory        72468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-409 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-48.           (((A -> (B and 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-72468.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-409, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72469
in-theory        72469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-400 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-4.            ((A and B) -> B), axiom
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-72469.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-400, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72470
in-theory        72470
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-391 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72470.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-391, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72471
in-theory        72471
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-382 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
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-48.           (((A -> (B and 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-72471.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-382, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72472
in-theory        72472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-373 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-48.           (((A -> (B and 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-72472.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F)))), M:tm-373, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72473
in-theory        72473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-364 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
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-48.           (((A -> (B and 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-72473.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-364, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72474
in-theory        72474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((((D and B) or B) -> (A and B)) and C)))
theorem-size     21
proof            (modus-ponens tm-355 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-4.            ((A and B) -> B), axiom
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-72474.        ((A or (B -> (A and B))) -> (C -> ((((D and B) or B) -> (A and B)) and C))), M:tm-355, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72475
in-theory        72475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-354 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-4.            ((A and B) -> B), axiom
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-72475.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-354, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72476
in-theory        72476
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> B), axiom
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-72476.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72477
in-theory        72477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D))))
theorem-size     27
proof            (modus-ponens tm-338 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> B), axiom
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-72477.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D)))), M:tm-338, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72478
in-theory        72478
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and B) or B) -> (A and B)))))
theorem-size     43
proof            (modus-ponens tm-328 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-4.            ((A and B) -> B), axiom
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-72478.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and B) or B) -> (A and B))))), M:tm-328, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72479
in-theory        72479
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-72479.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (E -> (D and E))) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))))), M:tm-327, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72480
in-theory        72480
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-72480.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((D and E) -> E) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))))), M:tm-326, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72481
in-theory        72481
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-72481.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((D and E) -> D) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))))), M:tm-325, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72482
in-theory        72482
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-4.            ((A and B) -> B), axiom
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-72482.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))))), M:tm-324, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72483
in-theory        72483
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> B), axiom
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-72483.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (E -> D)) and ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))))), M:tm-323, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72484
in-theory        72484
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72484.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D and E) -> E)), M:tm-322, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72485
in-theory        72485
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72485.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D and E) -> D)), M:tm-320, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72486
in-theory        72486
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72486.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72487
in-theory        72487
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-316 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-4.            ((A and B) -> B), axiom
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-72487.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((A or (B -> (A and B))) -> (A or (B -> (A and B))))), M:tm-316, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72488
in-theory        72488
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-72488.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (E -> D))), M:tm-315, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72489
in-theory        72489
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((A or (B -> (A and B))) -> (not (((C and B) or B) -> (A and B)))) -> (not (A or (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-313 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-48.           (((A -> (B and 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-72489.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((A or (B -> (A and B))) -> (not (((C and B) or B) -> (A and B)))) -> (not (A or (B -> (A and B)))))), M:tm-313, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72490
in-theory        72490
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((((C and B) or B) -> (A and B)) -> D) -> (((A or (B -> (A and B))) or (((C and B) or B) -> (A and B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-312 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-4.            ((A and B) -> B), axiom
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-72490.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((((C and B) or B) -> (A and B)) -> D) -> (((A or (B -> (A and B))) or (((C and B) or B) -> (A and B))) -> D))), M:tm-312, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72491
in-theory        72491
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D or ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-72491.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D or ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))))), M:tm-311, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72492
in-theory        72492
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-72492.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) or D)), M:tm-310, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72493
in-theory        72493
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-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-4.            ((A and B) -> B), axiom
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-72493.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and D))), M:tm-309, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72494
in-theory        72494
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((A or (B -> (A and B))) -> ((C and B) or B)) -> ((A or (B -> (A and B))) -> (A and B))))
theorem-size     43
proof            (modus-ponens tm-306 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (or (and Cm Bm) Bm)) (C (and Am Bm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-4.            ((A and B) -> B), axiom
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-72494.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((A or (B -> (A and B))) -> ((C and B) or B)) -> ((A or (B -> (A and B))) -> (A and B)))), M:tm-306, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (and Cm Bm) Bm)) (C (and Am Bm)))
================================================================
tm-name          tm-72495
in-theory        72495
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-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-4.            ((A and B) -> B), axiom
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-72495.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (D -> ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))))), M:tm-305, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72496
in-theory        72496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-303 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-72496.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-303, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72497
in-theory        72497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-270 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72497.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-270, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72498
in-theory        72498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-239 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-48.           (((A -> (B and 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-72498.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-239, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72499
in-theory        72499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-210 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> B), axiom
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-72499.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F)))), M:tm-210, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72500
in-theory        72500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-183 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-4.            ((A and B) -> B), axiom
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-72500.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-183, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72501
in-theory        72501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-157 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72501.        ((A -> ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-157, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72502
in-theory        72502
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-147 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-72502.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-147, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72503
in-theory        72503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-134 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-72503.        ((A -> ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-134, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72504
in-theory        72504
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-125 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-72504.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-125, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72505
in-theory        72505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-113 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72505.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F)))), M:tm-113, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72506
in-theory        72506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     37
proof            (modus-ponens tm-105 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> B), axiom
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-72506.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-105, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72507
in-theory        72507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-95 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-48.           (((A -> (B and 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-72507.        (((A -> B) -> (A -> A)) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D)))), M:tm-95, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72508
in-theory        72508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D and B) or B) -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-84 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-72508.        ((A or (B -> (A and B))) -> (C -> (((D and B) or B) -> (A and B)))), M:tm-84, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72509
in-theory        72509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-83 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-72509.        ((A -> (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-83, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72510
in-theory        72510
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((D and C) or C) -> (B and C))))
theorem-size     23
proof            (modus-ponens tm-76 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
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-48.           (((A -> (B and 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-72510.        (((not (not A)) -> A) and ((B or (C -> (B and C))) -> (((D and C) or C) -> (B and C)))), M:tm-76, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72511
in-theory        72511
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B)))
theorem-size     27
proof            (modus-ponens tm-73 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-10 tm-5 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-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-72511.        (((not (not (A or (B -> (A and B))))) or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B))), M:tm-73, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72512
in-theory        72512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D))))
theorem-size     29
proof            (modus-ponens tm-69 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
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-48.           (((A -> (B and 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-72512.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D)))), M:tm-69, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72513
in-theory        72513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-54 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-72513.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-54, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72514
in-theory        72514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((C and A) or A) -> (B and A)))
theorem-size     23
proof            (modus-ponens tm-50 tm-836 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-7 tm-5 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-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-72514.        (((A -> (B and A)) or (B or (A -> (B and A)))) -> (((C and A) or A) -> (B and A))), M:tm-50, m:tm-836, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72515
in-theory        72515
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-836 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
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-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-72515.        ((A or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B))), M:tm-49, m:tm-836, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72516
in-theory        72516
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((D and C) or C) -> (B and C)))
theorem-size     27
proof            (modus-ponens tm-47 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-4 tm-5)
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-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-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-72516.        (((A and (B or (C -> (B and C)))) or (B or (C -> (B and C)))) -> (((D and C) or C) -> (B and C))), M:tm-47, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72517
in-theory        72517
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((D and B) or B) -> (A and B)))
theorem-size     27
proof            (modus-ponens tm-46 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-3 tm-5 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-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-72517.        ((((A or (B -> (A and B))) and C) or (A or (B -> (A and B)))) -> (((D and B) or B) -> (A and B))), M:tm-46, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72518
in-theory        72518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-42 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-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-4.            ((A and B) -> B), axiom
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-72518.        ((A -> (B or A)) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D)))), M:tm-42, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72519
in-theory        72519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-32 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-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-4.            ((A and B) -> B), axiom
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-72519.        ((A -> (A or B)) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D)))), M:tm-32, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72520
in-theory        72520
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and B) or B) -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-24 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
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-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-4.            ((A and B) -> B), axiom
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-72520.        ((A or (B -> (A and B))) -> ((A or (B -> (A and B))) and (((C and B) or B) -> (A and B)))), M:tm-24, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72521
in-theory        72521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-23 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-72521.        ((A -> (B -> (A and B))) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D)))), M:tm-23, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72522
in-theory        72522
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-22 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-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-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-72522.        (((A and B) -> B) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D)))), M:tm-22, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72523
in-theory        72523
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-21 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-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-4.            ((A and B) -> B), axiom
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-72523.        (((A and B) -> A) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D)))), M:tm-21, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72524
in-theory        72524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-20 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-4.            ((A and B) -> B), axiom
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-72524.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-20, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72525
in-theory        72525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-19 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
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-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-4.            ((A and B) -> B), axiom
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-72525.        ((A -> (B -> A)) and ((C or (D -> (C and D))) -> (((E and D) or D) -> (C and D)))), M:tm-19, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72526
in-theory        72526
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (not (((C and B) or B) -> (A and B)))) -> (not (A or (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-9 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-9 tm-8 tm-5 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-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-72526.        (((A or (B -> (A and B))) -> (not (((C and B) or B) -> (A and B)))) -> (not (A or (B -> (A and B))))), M:tm-9, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72527
in-theory        72527
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> (C and B)) -> D) -> (((C or (B -> (C and B))) or (((A and B) or B) -> (C and B))) -> D))
theorem-size     31
proof            (modus-ponens tm-8 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm)))))
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-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-72527.        (((((A and B) or B) -> (C and B)) -> D) -> (((C or (B -> (C and B))) or (((A and B) or B) -> (C and B))) -> D)), M:tm-8, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-72528
in-theory        72528
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> (B and C))) -> (((D and C) or C) -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-7 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-7 tm-8 tm-5 tm-4)
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-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-72528.        (A or ((B or (C -> (B and C))) -> (((D and C) or C) -> (B and C)))), M:tm-7, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72529
in-theory        72529
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-6 tm-8 tm-5 tm-4)
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-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-72529.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) or D), M:tm-6, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72530
in-theory        72530
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (B and C))) -> (((D and C) or C) -> (B and C))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-72530.        (A -> (((B or (C -> (B and C))) -> (((D and C) or C) -> (B and C))) and A)), M:tm-5, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72531
in-theory        72531
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and B) or B)) -> ((A or (B -> (A and B))) -> (A and B)))
theorem-size     25
proof            (modus-ponens tm-2 tm-836 ((A (or Am (-> Bm (and Am Bm)))) (B (or (and Cm Bm) Bm)) (C (and Am Bm))))
axioms-used      (tm-2 tm-8 tm-5 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-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-72531.        (((A or (B -> (A and B))) -> ((C and B) or B)) -> ((A or (B -> (A and B))) -> (A and B))), M:tm-2, m:tm-836, u:((A (or Am (-> Bm (and Am Bm)))) (B (or (and Cm Bm) Bm)) (C (and Am Bm)))
================================================================
tm-name          tm-72532
in-theory        72532
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (((D and C) or C) -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-1 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-1 tm-8 tm-5 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-72532.        (A -> ((B or (C -> (B and C))) -> (((D and C) or C) -> (B and C)))), M:tm-1, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-72533
in-theory        72533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     43
proof            (modus-ponens tm-808 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72533.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-808, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72534
in-theory        72534
times-derived    1
----------------------------------------------------------------
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))))) and (((D and (A or ((B -> (C and B)) -> (A and (B -> (C and B)))))) or (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     81
proof            (modus-ponens tm-798 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72534.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (((D and (A or ((B -> (C and B)) -> (A and (B -> (C and B)))))) or (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-798, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72535
in-theory        72535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     43
proof            (modus-ponens tm-757 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-72535.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-757, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72536
in-theory        72536
times-derived    1
----------------------------------------------------------------
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))))) and ((((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) and D) or (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     81
proof            (modus-ponens tm-747 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-72536.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) and D) or (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-747, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72537
in-theory        72537
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F))))))
theorem-size     57
proof            (modus-ponens tm-708 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72537.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F)))))), M:tm-708, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72538
in-theory        72538
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     45
proof            (modus-ponens tm-665 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-72538.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-665, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72539
in-theory        72539
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (D or ((C or (B -> (C and B))) -> (A and (B -> (C and B))))))
theorem-size     33
proof            (modus-ponens tm-623 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
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-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-72539.        ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (D or ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))), M:tm-623, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72540
in-theory        72540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-622 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-48.           (((A -> (B and 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-72540.        ((A -> (B -> (C or B))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-622, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72541
in-theory        72541
times-derived    1
----------------------------------------------------------------
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))))) and (D -> (E or D)))
theorem-size     37
proof            (modus-ponens tm-609 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72541.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (D -> (E or D))), M:tm-609, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72542
in-theory        72542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     41
proof            (modus-ponens tm-605 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-72542.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-605, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72543
in-theory        72543
times-derived    1
----------------------------------------------------------------
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))))) and ((D -> (E or D)) and ((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     69
proof            (modus-ponens tm-595 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-72543.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((D -> (E or D)) and ((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-595, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72544
in-theory        72544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-550 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-48.           (((A -> (B and 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-72544.        (((A -> (B or A)) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-550, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72545
in-theory        72545
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-540 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-72545.        ((A or (B -> (C or B))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-540, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72546
in-theory        72546
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-530 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-48.           (((A -> (B and 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-72546.        ((A or (B -> (B or C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-530, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72547
in-theory        72547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     41
proof            (modus-ponens tm-520 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-72547.        ((A or (B -> (C -> (B and C)))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-520, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72548
in-theory        72548
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-510 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-48.           (((A -> (B and 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-72548.        ((A or ((B and C) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-510, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72549
in-theory        72549
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-500 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-48.           (((A -> (B and 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-72549.        ((A or ((B and C) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-500, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72550
in-theory        72550
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F))))))
theorem-size     47
proof            (modus-ponens tm-490 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-48.           (((A -> (B and 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-72550.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F)))))), M:tm-490, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72551
in-theory        72551
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-480 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-48.           (((A -> (B and 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-72551.        ((A or (B -> (C -> B))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-480, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72552
in-theory        72552
times-derived    1
----------------------------------------------------------------
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)))) or D))
theorem-size     33
proof            (modus-ponens tm-470 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
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-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-72552.        ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (((C or (B -> (C and B))) -> (A and (B -> (C and B)))) or D)), M:tm-470, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72553
in-theory        72553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-469 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-48.           (((A -> (B and 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-72553.        ((A -> (B -> (B or C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-469, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72554
in-theory        72554
times-derived    1
----------------------------------------------------------------
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))))) and (D -> (D or E)))
theorem-size     37
proof            (modus-ponens tm-456 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72554.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (D -> (D or E))), M:tm-456, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72555
in-theory        72555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     41
proof            (modus-ponens tm-453 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-72555.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-453, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72556
in-theory        72556
times-derived    1
----------------------------------------------------------------
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))))) and ((D -> (D or E)) and ((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     69
proof            (modus-ponens tm-443 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-72556.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((D -> (D or E)) and ((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-443, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72557
in-theory        72557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-409 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-72557.        (((A -> (A or B)) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-409, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72558
in-theory        72558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     41
proof            (modus-ponens tm-400 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-72558.        (((A -> (B -> (A and B))) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-400, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72559
in-theory        72559
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-391 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-48.           (((A -> (B and 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-72559.        ((((A and B) -> B) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-391, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72560
in-theory        72560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-382 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-48.           (((A -> (B and 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-72560.        ((((A and B) -> A) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-382, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72561
in-theory        72561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F))))))
theorem-size     47
proof            (modus-ponens tm-373 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-48.           (((A -> (B and 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-72561.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F)))))), M:tm-373, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72562
in-theory        72562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-364 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-48.           (((A -> (B and 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-72562.        (((A -> (B -> A)) or C) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-364, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72563
in-theory        72563
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (D -> (((C or (B -> (C and B))) -> (A and (B -> (C and B)))) and D)))
theorem-size     35
proof            (modus-ponens tm-355 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
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-48.           (((A -> (B and 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-72563.        ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (D -> (((C or (B -> (C and B))) -> (A and (B -> (C and B)))) and D))), M:tm-355, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72564
in-theory        72564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     41
proof            (modus-ponens tm-354 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-72564.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-354, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72565
in-theory        72565
times-derived    1
----------------------------------------------------------------
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))))) and (D -> (E -> (D and E))))
theorem-size     39
proof            (modus-ponens tm-341 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72565.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72566
in-theory        72566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D))))))
theorem-size     41
proof            (modus-ponens tm-338 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-2 tm-8)
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-48.           (((A -> (B and 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-72566.        (((A -> B) -> (A -> (A and B))) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D)))))), M:tm-338, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72567
in-theory        72567
times-derived    1
----------------------------------------------------------------
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))))) and ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) and ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))))
theorem-size     79
proof            (modus-ponens tm-328 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
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-328.          ((A -> 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-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-72567.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) and ((C or (B -> (C and B))) -> (A and (B -> (C and B))))))), M:tm-328, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72568
in-theory        72568
times-derived    1
----------------------------------------------------------------
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))))) and ((D -> (E -> (D and E))) and ((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     71
proof            (modus-ponens tm-327 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-72568.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((D -> (E -> (D and E))) and ((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-327, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72569
in-theory        72569
times-derived    1
----------------------------------------------------------------
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))))) and (((D and E) -> E) and ((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     69
proof            (modus-ponens tm-326 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72569.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (((D and E) -> E) and ((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-326, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72570
in-theory        72570
times-derived    1
----------------------------------------------------------------
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))))) and (((D and E) -> D) and ((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     69
proof            (modus-ponens tm-325 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72570.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (((D and E) -> D) and ((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-325, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72571
in-theory        72571
times-derived    1
----------------------------------------------------------------
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))))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((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     77
proof            (modus-ponens tm-324 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-72571.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((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-324, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72572
in-theory        72572
times-derived    1
----------------------------------------------------------------
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))))) and ((D -> (E -> D)) and ((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     69
proof            (modus-ponens tm-323 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-72572.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((D -> (E -> D)) and ((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-323, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72573
in-theory        72573
times-derived    1
----------------------------------------------------------------
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))))) and ((D and E) -> E))
theorem-size     37
proof            (modus-ponens tm-322 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72573.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((D and E) -> E)), M:tm-322, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72574
in-theory        72574
times-derived    1
----------------------------------------------------------------
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))))) and ((D and E) -> D))
theorem-size     37
proof            (modus-ponens tm-320 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72574.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((D and E) -> D)), M:tm-320, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72575
in-theory        72575
times-derived    1
----------------------------------------------------------------
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))))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-318 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72575.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72576
in-theory        72576
times-derived    1
----------------------------------------------------------------
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))))) and ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (A or ((B -> (C and B)) -> (A and (B -> (C and B)))))))
theorem-size     63
proof            (modus-ponens tm-316 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-72576.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (A or ((B -> (C and B)) -> (A and (B -> (C and B))))))), M:tm-316, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72577
in-theory        72577
times-derived    1
----------------------------------------------------------------
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))))) and (D -> (E -> D)))
theorem-size     37
proof            (modus-ponens tm-315 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72577.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (D -> (E -> D))), M:tm-315, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72578
in-theory        72578
times-derived    1
----------------------------------------------------------------
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))))) and (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (not ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))) -> (not (A or ((B -> (C and B)) -> (A and (B -> (C and B))))))))
theorem-size     81
proof            (modus-ponens tm-313 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-72578.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (not ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))) -> (not (A or ((B -> (C and B)) -> (A and (B -> (C and B)))))))), M:tm-313, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72579
in-theory        72579
times-derived    1
----------------------------------------------------------------
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))))) and ((((C or (B -> (C and B))) -> (A and (B -> (C and B)))) -> D) -> (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) or ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) -> D)))
theorem-size     83
proof            (modus-ponens tm-312 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-72579.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((((C or (B -> (C and B))) -> (A and (B -> (C and B)))) -> D) -> (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) or ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) -> D))), M:tm-312, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72580
in-theory        72580
times-derived    1
----------------------------------------------------------------
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))))) and (D or ((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     65
proof            (modus-ponens tm-311 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-72580.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (D or ((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-311, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72581
in-theory        72581
times-derived    1
----------------------------------------------------------------
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))))) and (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) or D))
theorem-size     65
proof            (modus-ponens tm-310 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-72581.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) or D)), M:tm-310, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72582
in-theory        72582
times-derived    1
----------------------------------------------------------------
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))))) and (D -> (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and D)))
theorem-size     67
proof            (modus-ponens tm-309 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-2 tm-5 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-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-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-72582.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (D -> (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and D))), M:tm-309, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72583
in-theory        72583
times-derived    1
----------------------------------------------------------------
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))))) and (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (C or (B -> (C and B)))) -> ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (A and (B -> (C and B))))))
theorem-size     79
proof            (modus-ponens tm-306 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (and Am (-> Bm (and Cm Bm))))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-72583.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (C or (B -> (C and B)))) -> ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (A and (B -> (C and B)))))), M:tm-306, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (and Am (-> Bm (and Cm Bm)))))
================================================================
tm-name          tm-72584
in-theory        72584
times-derived    1
----------------------------------------------------------------
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))))) and (D -> ((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     65
proof            (modus-ponens tm-305 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-1.            (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-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-72584.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and (D -> ((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-305, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72585
in-theory        72585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     43
proof            (modus-ponens tm-303 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-72585.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-303, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72586
in-theory        72586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     41
proof            (modus-ponens tm-270 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-4 tm-8)
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-48.           (((A -> (B and 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-72586.        ((A -> (((B and C) -> C) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-270, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72587
in-theory        72587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     41
proof            (modus-ponens tm-239 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-3 tm-8)
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-48.           (((A -> (B and 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-72587.        ((A -> (((B and C) -> B) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-239, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72588
in-theory        72588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F))))))
theorem-size     49
proof            (modus-ponens tm-210 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-2 tm-8)
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-48.           (((A -> (B and 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-72588.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F)))))), M:tm-210, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72589
in-theory        72589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     41
proof            (modus-ponens tm-183 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-72589.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-183, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72590
in-theory        72590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-157 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-48.           (((A -> (B and 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-72590.        ((A -> ((B and C) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-157, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72591
in-theory        72591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     47
proof            (modus-ponens tm-147 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72591.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-147, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72592
in-theory        72592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-134 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-48.           (((A -> (B and 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-72592.        ((A -> ((B and C) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-134, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72593
in-theory        72593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     47
proof            (modus-ponens tm-125 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72593.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-125, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72594
in-theory        72594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F))))))
theorem-size     47
proof            (modus-ponens tm-113 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72594.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F)))))), M:tm-113, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72595
in-theory        72595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     51
proof            (modus-ponens tm-105 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-2 tm-8)
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-48.           (((A -> (B and 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-72595.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-105, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72596
in-theory        72596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D))))))
theorem-size     39
proof            (modus-ponens tm-95 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-48.           (((A -> (B and 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-72596.        (((A -> B) -> (A -> A)) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D)))))), M:tm-95, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72597
in-theory        72597
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (D -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))))
theorem-size     33
proof            (modus-ponens tm-84 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-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-72597.        ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (D -> ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))), M:tm-84, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72598
in-theory        72598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     39
proof            (modus-ponens tm-83 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-72598.        ((A -> (B -> (C -> B))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-83, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72599
in-theory        72599
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C -> (D and C)) -> (B and (C -> (D and C))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C))))))
theorem-size     37
proof            (modus-ponens tm-76 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-10 tm-8)
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-48.           (((A -> (B and 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-72599.        (((not (not A)) -> A) and ((B or ((C -> (D and C)) -> (B and (C -> (D and C))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C)))))), M:tm-76, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72600
in-theory        72600
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or ((B -> (C and B)) -> (A and (B -> (C and B))))))) or (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     49
proof            (modus-ponens tm-73 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-8 tm-10 tm-5)
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-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-72600.        (((not (not (A or ((B -> (C and B)) -> (A and (B -> (C and B))))))) or (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-73, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72601
in-theory        72601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D))))))
theorem-size     43
proof            (modus-ponens tm-69 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-9 tm-8)
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-48.           (((A -> (B and 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-72601.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D)))))), M:tm-69, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72602
in-theory        72602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     45
proof            (modus-ponens tm-54 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-72602.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-54, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72603
in-theory        72603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C and (A -> (B and A)))) or (C or ((A -> (B and A)) -> (C and (A -> (B and A)))))) -> ((B or (A -> (B and A))) -> (C and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-50 tm-837 ((A Am) (B (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       181
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-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-72603.        ((((A -> (B and A)) -> (C and (A -> (B and A)))) or (C or ((A -> (B and A)) -> (C and (A -> (B and A)))))) -> ((B or (A -> (B and A))) -> (C and (A -> (B and A))))), M:tm-50, m:tm-837, u:((A Am) (B (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72604
in-theory        72604
times-derived    1
----------------------------------------------------------------
theorem          ((A or (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     33
proof            (modus-ponens tm-49 tm-837 ((A Am) (B (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-72604.        ((A or (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-49, m:tm-837, u:((A Am) (B (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72605
in-theory        72605
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or ((C -> (D and C)) -> (B and (C -> (D and C)))))) or (B or ((C -> (D and C)) -> (B and (C -> (D and C)))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C)))))
theorem-size     49
proof            (modus-ponens tm-47 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-8 tm-4 tm-5)
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-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-72605.        (((A and (B or ((C -> (D and C)) -> (B and (C -> (D and C)))))) or (B or ((C -> (D and C)) -> (B and (C -> (D and C)))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C))))), M:tm-47, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72606
in-theory        72606
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) and D) or (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     49
proof            (modus-ponens tm-46 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-8 tm-3 tm-5)
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-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-72606.        ((((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) and D) or (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-46, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72607
in-theory        72607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D))))))
theorem-size     37
proof            (modus-ponens tm-42 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-72607.        ((A -> (B or A)) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D)))))), M:tm-42, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72608
in-theory        72608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D))))))
theorem-size     37
proof            (modus-ponens tm-32 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-72608.        ((A -> (A or B)) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D)))))), M:tm-32, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72609
in-theory        72609
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) and ((C or (B -> (C and B))) -> (A and (B -> (C and B))))))
theorem-size     47
proof            (modus-ponens tm-24 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
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-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-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-72609.        ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) and ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))), M:tm-24, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72610
in-theory        72610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D))))))
theorem-size     39
proof            (modus-ponens tm-23 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-72610.        ((A -> (B -> (A and B))) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D)))))), M:tm-23, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72611
in-theory        72611
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D))))))
theorem-size     37
proof            (modus-ponens tm-22 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-4 tm-8)
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-48.           (((A -> (B and 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-72611.        (((A and B) -> B) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D)))))), M:tm-22, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72612
in-theory        72612
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D))))))
theorem-size     37
proof            (modus-ponens tm-21 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-3 tm-8)
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-48.           (((A -> (B and 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-72612.        (((A and B) -> A) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D)))))), M:tm-21, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72613
in-theory        72613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     45
proof            (modus-ponens tm-20 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
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-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-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-72613.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-20, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72614
in-theory        72614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D))))))
theorem-size     37
proof            (modus-ponens tm-19 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-72614.        ((A -> (B -> A)) and ((C or ((D -> (E and D)) -> (C and (D -> (E and D))))) -> ((E or (D -> (E and D))) -> (C and (D -> (E and D)))))), M:tm-19, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72615
in-theory        72615
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (A or ((B -> (C and B)) -> (A and (B -> (C and B))))))
theorem-size     31
proof            (modus-ponens tm-12 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
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-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-72615.        ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (A or ((B -> (C and B)) -> (A and (B -> (C and B)))))), M:tm-12, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72616
in-theory        72616
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (not ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))) -> (not (A or ((B -> (C and B)) -> (A and (B -> (C and B)))))))
theorem-size     49
proof            (modus-ponens tm-9 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-9 tm-8 tm-5)
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-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-72616.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (not ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))) -> (not (A or ((B -> (C and B)) -> (A and (B -> (C and B))))))), M:tm-9, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72617
in-theory        72617
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> (C and (B -> (A and B)))) -> D) -> (((C or ((B -> (A and B)) -> (C and (B -> (A and B))))) or ((A or (B -> (A and B))) -> (C and (B -> (A and B))))) -> D))
theorem-size     51
proof            (modus-ponens tm-8 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-8 tm-5)
proof-size       169
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-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-72617.        ((((A or (B -> (A and B))) -> (C and (B -> (A and B)))) -> D) -> (((C or ((B -> (A and B)) -> (C and (B -> (A and B))))) or ((A or (B -> (A and B))) -> (C and (B -> (A and B))))) -> D)), M:tm-8, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-72618
in-theory        72618
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or ((C -> (D and C)) -> (B and (C -> (D and C))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C))))))
theorem-size     33
proof            (modus-ponens tm-7 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-7 tm-8 tm-5)
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-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-72618.        (A or ((B or ((C -> (D and C)) -> (B and (C -> (D and C))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C)))))), M:tm-7, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72619
in-theory        72619
times-derived    1
----------------------------------------------------------------
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))))) or D)
theorem-size     33
proof            (modus-ponens tm-6 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-6 tm-8 tm-5)
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-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-72619.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) or D), M:tm-6, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72620
in-theory        72620
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C -> (D and C)) -> (B and (C -> (D and C))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C))))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-72620.        (A -> (((B or ((C -> (D and C)) -> (B and (C -> (D and C))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C))))) and A)), M:tm-5, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72621
in-theory        72621
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (C or (B -> (C and B)))) -> ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (A and (B -> (C and B)))))
theorem-size     47
proof            (modus-ponens tm-2 tm-837 ((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (and Am (-> Bm (and Cm Bm))))))
axioms-used      (tm-2 tm-8 tm-5)
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-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-72621.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (C or (B -> (C and B)))) -> ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (A and (B -> (C and B))))), M:tm-2, m:tm-837, u:((A (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm)))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (and Am (-> Bm (and Cm Bm)))))
================================================================
tm-name          tm-72622
in-theory        72622
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> (D and C)) -> (B and (C -> (D and C))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C))))))
theorem-size     33
proof            (modus-ponens tm-1 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-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-72622.        (A -> ((B or ((C -> (D and C)) -> (B and (C -> (D and C))))) -> ((D or (C -> (D and C))) -> (B and (C -> (D and C)))))), M:tm-1, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-72623
in-theory        72623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-808 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72623.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-808, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72624
in-theory        72624
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((E and ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D)))
theorem-size     75
proof            (modus-ponens tm-798 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-72624.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((E and ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D))), M:tm-798, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72625
in-theory        72625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-757 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72625.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-757, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72626
in-theory        72626
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) and E) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D)))
theorem-size     75
proof            (modus-ponens tm-747 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-48.           (((A -> (B and 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-72626.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) and E) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D))), M:tm-747, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72627
in-theory        72627
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H)))
theorem-size     53
proof            (modus-ponens tm-708 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72627.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H))), M:tm-708, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72628
in-theory        72628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-665 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72628.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-665, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72629
in-theory        72629
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (E or ((C or (B -> (C and B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-623 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72629.        (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (E or ((C or (B -> (C and B))) -> D))), M:tm-623, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72630
in-theory        72630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-622 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72630.        ((A -> (B -> (C or B))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-622, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72631
in-theory        72631
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-609 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72631.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (F or E))), M:tm-609, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72632
in-theory        72632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-605 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72632.        ((A -> ((B -> (C or B)) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-605, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72633
in-theory        72633
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (F or E)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-595 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-72633.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (F or E)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))), M:tm-595, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72634
in-theory        72634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-550 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-48.           (((A -> (B and 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-72634.        (((A -> (B or A)) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-550, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72635
in-theory        72635
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-540 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-48.           (((A -> (B and 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-72635.        ((A or (B -> (C or B))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-540, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72636
in-theory        72636
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-530 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-48.           (((A -> (B and 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-72636.        ((A or (B -> (B or C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-530, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72637
in-theory        72637
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-520 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72637.        ((A or (B -> (C -> (B and C)))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-520, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72638
in-theory        72638
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-510 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-48.           (((A -> (B and 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-72638.        ((A or ((B and C) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-510, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72639
in-theory        72639
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-500 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-48.           (((A -> (B and 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-72639.        ((A or ((B and C) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-500, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72640
in-theory        72640
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H)))
theorem-size     43
proof            (modus-ponens tm-490 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72640.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H))), M:tm-490, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72641
in-theory        72641
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-480 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-72641.        ((A or (B -> (C -> B))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-480, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72642
in-theory        72642
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (((C or (B -> (C and B))) -> D) or E))
theorem-size     29
proof            (modus-ponens tm-470 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72642.        (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (((C or (B -> (C and B))) -> D) or E)), M:tm-470, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72643
in-theory        72643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-469 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72643.        ((A -> (B -> (B or C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-469, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72644
in-theory        72644
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-456 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72644.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (E or F))), M:tm-456, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72645
in-theory        72645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-453 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72645.        ((A -> ((B -> (B or C)) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-453, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72646
in-theory        72646
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (E or F)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-443 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-72646.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (E or F)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))), M:tm-443, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72647
in-theory        72647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-409 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-48.           (((A -> (B and 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-72647.        (((A -> (A or B)) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-409, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72648
in-theory        72648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-400 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72648.        (((A -> (B -> (A and B))) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-400, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72649
in-theory        72649
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-391 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-48.           (((A -> (B and 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-72649.        ((((A and B) -> B) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-391, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72650
in-theory        72650
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-382 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-48.           (((A -> (B and 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-72650.        ((((A and B) -> A) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-382, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72651
in-theory        72651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H)))
theorem-size     43
proof            (modus-ponens tm-373 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72651.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H))), M:tm-373, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72652
in-theory        72652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-364 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-72652.        (((A -> (B -> A)) or C) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-364, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72653
in-theory        72653
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (E -> (((C or (B -> (C and B))) -> D) and E)))
theorem-size     31
proof            (modus-ponens tm-355 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72653.        (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (E -> (((C or (B -> (C and B))) -> D) and E))), M:tm-355, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72654
in-theory        72654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-354 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72654.        ((A -> (B -> (C -> (B and C)))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-354, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72655
in-theory        72655
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-341 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-72655.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72656
in-theory        72656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-338 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-72656.        (((A -> B) -> (A -> (A and B))) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-338, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72657
in-theory        72657
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) and ((C or (B -> (C and B))) -> D))))
theorem-size     73
proof            (modus-ponens tm-328 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) 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-328.          ((A -> 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-48.           (((A -> (B and 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-72657.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) and ((C or (B -> (C and B))) -> D)))), M:tm-328, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72658
in-theory        72658
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))))
theorem-size     63
proof            (modus-ponens tm-327 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72658.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))), M:tm-327, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72659
in-theory        72659
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((E and F) -> F) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-326 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-72659.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((E and F) -> F) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))), M:tm-326, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72660
in-theory        72660
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((E and F) -> E) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-325 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-72660.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((E and F) -> E) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))), M:tm-325, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72661
in-theory        72661
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))))
theorem-size     69
proof            (modus-ponens tm-324 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72661.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))), M:tm-324, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72662
in-theory        72662
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (F -> E)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-323 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-72662.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (F -> E)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))), M:tm-323, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72663
in-theory        72663
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-322 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
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-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-48.           (((A -> (B and 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-72663.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72664
in-theory        72664
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-320 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-72664.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72665
in-theory        72665
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-318 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-72665.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72666
in-theory        72666
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))))
theorem-size     63
proof            (modus-ponens tm-316 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-48.           (((A -> (B and 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-72666.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)))), M:tm-316, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72667
in-theory        72667
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-315 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72667.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72668
in-theory        72668
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)))))
theorem-size     75
proof            (modus-ponens tm-313 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-48.           (((A -> (B and 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-72668.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))))), M:tm-313, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72669
in-theory        72669
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((C or (B -> (C and B))) -> D) -> E) -> ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) or ((C or (B -> (C and B))) -> D)) -> E)))
theorem-size     69
proof            (modus-ponens tm-312 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-312.          ((A -> B) -> ((A -> B) and ((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-48.           (((A -> (B and 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-72669.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((C or (B -> (C and B))) -> D) -> E) -> ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) or ((C or (B -> (C and B))) -> D)) -> E))), M:tm-312, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72670
in-theory        72670
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E or (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))))
theorem-size     57
proof            (modus-ponens tm-311 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-72670.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E or (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))), M:tm-311, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72671
in-theory        72671
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) or E))
theorem-size     57
proof            (modus-ponens tm-310 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-72671.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) or E)), M:tm-310, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72672
in-theory        72672
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and E)))
theorem-size     59
proof            (modus-ponens tm-309 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) 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-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-48.           (((A -> (B and 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-72672.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and E))), M:tm-309, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72673
in-theory        72673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (C or (B -> (C and B)))) -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> D)))
theorem-size     73
proof            (modus-ponens tm-306 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (or Cm (-> Bm (and Cm Bm)))) (C 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-306.          ((A -> (B -> C)) -> ((A -> (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-48.           (((A -> (B and 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-72673.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (C or (B -> (C and B)))) -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> D))), M:tm-306, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (or Cm (-> Bm (and Cm Bm)))) (C Dm))
================================================================
tm-name          tm-72674
in-theory        72674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))))
theorem-size     57
proof            (modus-ponens tm-305 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-48.           (((A -> (B and 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-72674.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (E -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))), M:tm-305, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72675
in-theory        72675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-303 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72675.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-303, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72676
in-theory        72676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-270 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-48.           (((A -> (B and 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-72676.        ((A -> (((B and C) -> C) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-270, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72677
in-theory        72677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-239 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72677.        ((A -> (((B and C) -> B) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-239, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72678
in-theory        72678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H)))
theorem-size     45
proof            (modus-ponens tm-210 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-72678.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H))), M:tm-210, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72679
in-theory        72679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-183 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72679.        ((A -> ((B -> (C -> B)) and A)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-183, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72680
in-theory        72680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-157 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-48.           (((A -> (B and 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-72680.        ((A -> ((B and C) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-157, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72681
in-theory        72681
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-147 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-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-48.           (((A -> (B and 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-72681.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-147, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72682
in-theory        72682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-134 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-72682.        ((A -> ((B and C) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-134, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72683
in-theory        72683
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-125 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-72683.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-125, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72684
in-theory        72684
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> (D -> E))) or ((B -> (C and B)) -> (D -> E))) -> (((C or (B -> (C and B))) -> D) -> ((C or (B -> (C and B))) -> E)))
theorem-size     41
proof            (modus-ponens tm-114 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) (-> C D))) (-> (-> Bm (and Cm Bm)) (-> C D)))) (B (or Cm (-> Bm (and Cm Bm)))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5)
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-4.            ((A and B) -> B), axiom
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-72684.        (((A and ((B -> (C and B)) -> (D -> E))) or ((B -> (C and B)) -> (D -> E))) -> (((C or (B -> (C and B))) -> D) -> ((C or (B -> (C and B))) -> E))), M:tm-114, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) (-> C D))) (-> (-> Bm (and Cm Bm)) (-> C D)))) (B (or Cm (-> Bm (and Cm Bm)))) (Dm (-> C D)))
================================================================
tm-name          tm-72685
in-theory        72685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H)))
theorem-size     43
proof            (modus-ponens tm-113 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72685.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H))), M:tm-113, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72686
in-theory        72686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     47
proof            (modus-ponens tm-105 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72686.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-105, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72687
in-theory        72687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-95 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-48.           (((A -> (B and 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-72687.        (((A -> B) -> (A -> A)) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-95, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72688
in-theory        72688
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (E -> ((C or (B -> (C and B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-84 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72688.        (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (E -> ((C or (B -> (C and B))) -> D))), M:tm-84, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72689
in-theory        72689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-83 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72689.        ((A -> (B -> (C -> B))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-83, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72690
in-theory        72690
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-76 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72690.        (((not (not A)) -> A) and (((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-76, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72691
in-theory        72691
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)))) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D))
theorem-size     47
proof            (modus-ponens tm-73 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-8 tm-10 tm-4 tm-5)
proof-size       169
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-48.           (((A -> (B and 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-72691.        (((not (not ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)))) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D)), M:tm-73, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72692
in-theory        72692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     39
proof            (modus-ponens tm-69 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72692.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-69, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72693
in-theory        72693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-54 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72693.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-54, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72694
in-theory        72694
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((D and ((A -> (B and A)) -> C)) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C))
theorem-size     35
proof            (modus-ponens tm-50 tm-838 ((A (and Am (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-8 tm-7 tm-4 tm-5)
proof-size       159
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-48.           (((A -> (B and 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-72694.        ((((A -> (B and A)) -> C) or ((D and ((A -> (B and A)) -> C)) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C)), M:tm-50, m:tm-838, u:((A (and Am (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72695
in-theory        72695
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D))
theorem-size     37
proof            (modus-ponens tm-49 tm-838 ((A (and Am (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-8 tm-6 tm-4 tm-5)
proof-size       161
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-48.           (((A -> (B and 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-72695.        (((A and ((B -> (C and B)) -> D)) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D)), M:tm-49, m:tm-838, u:((A (and Am (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72696
in-theory        72696
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E))) or ((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E))) -> ((D or (C -> (D and C))) -> E))
theorem-size     47
proof            (modus-ponens tm-47 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       169
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-48.           (((A -> (B and 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-72696.        (((A and ((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E))) or ((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E))) -> ((D or (C -> (D and C))) -> E)), M:tm-47, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72697
in-theory        72697
times-derived    1
----------------------------------------------------------------
theorem          (((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) and E) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D))
theorem-size     47
proof            (modus-ponens tm-46 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-8 tm-3 tm-4 tm-5)
proof-size       169
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-48.           (((A -> (B and 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-72697.        (((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) and E) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D)), M:tm-46, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72698
in-theory        72698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-42 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72698.        ((A -> (B or A)) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-42, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72699
in-theory        72699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-32 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72699.        ((A -> (A or B)) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-32, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72700
in-theory        72700
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) and ((C or (B -> (C and B))) -> D)))
theorem-size     45
proof            (modus-ponens tm-24 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72700.        (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) and ((C or (B -> (C and B))) -> D))), M:tm-24, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72701
in-theory        72701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-23 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72701.        ((A -> (B -> (A and B))) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-23, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72702
in-theory        72702
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-22 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-48.           (((A -> (B and 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-72702.        (((A and B) -> B) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-22, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72703
in-theory        72703
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-21 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72703.        (((A and B) -> A) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-21, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72704
in-theory        72704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-20 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-48.           (((A -> (B and 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-72704.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-20, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72705
in-theory        72705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-19 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72705.        ((A -> (B -> A)) and (((C and ((D -> (E and D)) -> F)) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-19, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72706
in-theory        72706
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)))
theorem-size     35
proof            (modus-ponens tm-12 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-72706.        (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))), M:tm-12, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72707
in-theory        72707
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))))
theorem-size     47
proof            (modus-ponens tm-9 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-9 tm-8 tm-4 tm-5)
proof-size       151
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-48.           (((A -> (B and 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-72707.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)))), M:tm-9, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72708
in-theory        72708
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> ((((E and ((B -> (A and B)) -> C)) or ((B -> (A and B)) -> C)) or ((A or (B -> (A and B))) -> C)) -> D))
theorem-size     41
proof            (modus-ponens tm-8 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-8 tm-4 tm-5)
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-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-72708.        ((((A or (B -> (A and B))) -> C) -> D) -> ((((E and ((B -> (A and B)) -> C)) or ((B -> (A and B)) -> C)) or ((A or (B -> (A and B))) -> C)) -> D)), M:tm-8, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-72709
in-theory        72709
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-7 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-5)
proof-size       127
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-48.           (((A -> (B and 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-72709.        (A or (((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-7, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72710
in-theory        72710
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) or E)
theorem-size     29
proof            (modus-ponens tm-6 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-5)
proof-size       127
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-48.           (((A -> (B and 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-72710.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) or E), M:tm-6, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72711
in-theory        72711
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-72711.        (A -> ((((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)) and A)), M:tm-5, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72712
in-theory        72712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (C or (B -> (C and B)))) -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> D))
theorem-size     45
proof            (modus-ponens tm-2 tm-838 ((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (or Cm (-> Bm (and Cm Bm)))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-4 tm-5)
proof-size       151
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-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-72712.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (C or (B -> (C and B)))) -> (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> D)), M:tm-2, m:tm-838, u:((A (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm))) (B (or Cm (-> Bm (and Cm Bm)))) (C Dm))
================================================================
tm-name          tm-72713
in-theory        72713
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-1 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-5)
proof-size       127
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-48.           (((A -> (B and 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-72713.        (A -> (((B and ((C -> (D and C)) -> E)) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-1, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-72714
in-theory        72714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     39
proof            (modus-ponens tm-808 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72714.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-808, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72715
in-theory        72715
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (((E and ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C)))
theorem-size     75
proof            (modus-ponens tm-798 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72715.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (((E and ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C))), M:tm-798, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72716
in-theory        72716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     39
proof            (modus-ponens tm-757 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-72716.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-757, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72717
in-theory        72717
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((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)) and E) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C)))
theorem-size     75
proof            (modus-ponens tm-747 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> 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       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-48.           (((A -> (B and 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-72717.        ((((((A -> (B and A)) -> C) and D) or ((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)) and E) or ((((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-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72718
in-theory        72718
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     53
proof            (modus-ponens tm-708 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72718.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-708, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72719
in-theory        72719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     41
proof            (modus-ponens tm-665 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72719.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-665, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72720
in-theory        72720
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (E or ((B or (A -> (B and A))) -> C)))
theorem-size     29
proof            (modus-ponens tm-623 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72720.        (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (E or ((B or (A -> (B and A))) -> C))), M:tm-623, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72721
in-theory        72721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-622 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72721.        ((A -> (B -> (C or B))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-622, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72722
in-theory        72722
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-609 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72722.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (F or E))), M:tm-609, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72723
in-theory        72723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-605 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72723.        ((A -> ((B -> (C or B)) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-605, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72724
in-theory        72724
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (F or E)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))))
theorem-size     61
proof            (modus-ponens tm-595 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-72724.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (F or E)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))), M:tm-595, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72725
in-theory        72725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-550 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-48.           (((A -> (B and 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-72725.        (((A -> (B or A)) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-550, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72726
in-theory        72726
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-540 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-48.           (((A -> (B and 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-72726.        ((A or (B -> (C or B))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-540, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72727
in-theory        72727
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-530 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-48.           (((A -> (B and 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-72727.        ((A or (B -> (B or C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-530, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72728
in-theory        72728
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-520 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72728.        ((A or (B -> (C -> (B and C)))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-520, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72729
in-theory        72729
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-510 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-48.           (((A -> (B and 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-72729.        ((A or ((B and C) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-510, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72730
in-theory        72730
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-500 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72730.        ((A or ((B and C) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-500, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72731
in-theory        72731
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-490 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72731.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-490, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72732
in-theory        72732
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-480 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-72732.        ((A or (B -> (C -> B))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-480, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72733
in-theory        72733
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (((B or (A -> (B and A))) -> C) or E))
theorem-size     29
proof            (modus-ponens tm-470 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72733.        (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (((B or (A -> (B and A))) -> C) or E)), M:tm-470, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72734
in-theory        72734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-469 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72734.        ((A -> (B -> (B or C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-469, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72735
in-theory        72735
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-456 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72735.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (E or F))), M:tm-456, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72736
in-theory        72736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-453 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72736.        ((A -> ((B -> (B or C)) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-453, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72737
in-theory        72737
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (E or F)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))))
theorem-size     61
proof            (modus-ponens tm-443 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-72737.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (E or F)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))), M:tm-443, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72738
in-theory        72738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-409 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-48.           (((A -> (B and 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-72738.        (((A -> (A or B)) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-409, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72739
in-theory        72739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-400 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72739.        (((A -> (B -> (A and B))) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-400, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72740
in-theory        72740
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-391 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-48.           (((A -> (B and 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-72740.        ((((A and B) -> B) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-391, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72741
in-theory        72741
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-382 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72741.        ((((A and B) -> A) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-382, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72742
in-theory        72742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-373 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72742.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-373, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72743
in-theory        72743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-364 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-72743.        (((A -> (B -> A)) or C) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-364, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72744
in-theory        72744
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (E -> (((B or (A -> (B and A))) -> C) and E)))
theorem-size     31
proof            (modus-ponens tm-355 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72744.        (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (E -> (((B or (A -> (B and A))) -> C) and E))), M:tm-355, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72745
in-theory        72745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-354 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72745.        ((A -> (B -> (C -> (B and C)))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-354, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72746
in-theory        72746
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-341 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-72746.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72747
in-theory        72747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     37
proof            (modus-ponens tm-338 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-72747.        (((A -> B) -> (A -> (A and B))) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-338, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72748
in-theory        72748
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((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)) -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) and ((B or (A -> (B and A))) -> C))))
theorem-size     73
proof            (modus-ponens tm-328 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> 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       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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72748.        ((((((A -> (B and A)) -> C) and D) or ((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)) -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) and ((B or (A -> (B and A))) -> C)))), M:tm-328, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72749
in-theory        72749
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (F -> (E and F))) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))))
theorem-size     63
proof            (modus-ponens tm-327 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-72749.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (F -> (E and F))) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))), M:tm-327, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72750
in-theory        72750
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (((E and F) -> F) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))))
theorem-size     61
proof            (modus-ponens tm-326 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-72750.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (((E and F) -> F) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))), M:tm-326, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72751
in-theory        72751
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (((E and F) -> E) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))))
theorem-size     61
proof            (modus-ponens tm-325 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-72751.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (((E and F) -> E) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))), M:tm-325, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72752
in-theory        72752
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))))
theorem-size     69
proof            (modus-ponens tm-324 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-72752.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))), M:tm-324, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72753
in-theory        72753
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (F -> E)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))))
theorem-size     61
proof            (modus-ponens tm-323 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-72753.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (F -> E)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))), M:tm-323, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72754
in-theory        72754
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-322 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-72754.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72755
in-theory        72755
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-320 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> 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       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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72755.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72756
in-theory        72756
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-318 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-72756.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72757
in-theory        72757
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((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)) -> ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))))
theorem-size     63
proof            (modus-ponens tm-316 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-48.           (((A -> (B and 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-72757.        ((((((A -> (B and A)) -> C) and D) or ((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)) -> ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)))), M:tm-316, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72758
in-theory        72758
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-315 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72758.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72759
in-theory        72759
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((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)) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)))))
theorem-size     75
proof            (modus-ponens tm-313 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-48.           (((A -> (B and 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-72759.        ((((((A -> (B and A)) -> C) and D) or ((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)) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))))), M:tm-313, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72760
in-theory        72760
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((((B or (A -> (B and A))) -> C) -> E) -> ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) or ((B or (A -> (B and A))) -> C)) -> E)))
theorem-size     69
proof            (modus-ponens tm-312 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> 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       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-312.          ((A -> B) -> ((A -> B) and ((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-48.           (((A -> (B and 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-72760.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((((B or (A -> (B and A))) -> C) -> E) -> ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) or ((B or (A -> (B and A))) -> C)) -> E))), M:tm-312, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72761
in-theory        72761
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E or (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))))
theorem-size     57
proof            (modus-ponens tm-311 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-72761.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E 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-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72762
in-theory        72762
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((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)) or E))
theorem-size     57
proof            (modus-ponens tm-310 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-72762.        ((((((A -> (B and A)) -> C) and D) or ((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)) or E)), M:tm-310, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72763
in-theory        72763
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and E)))
theorem-size     59
proof            (modus-ponens tm-309 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-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-48.           (((A -> (B and 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-72763.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and E))), M:tm-309, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72764
in-theory        72764
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((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)))) -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> C)))
theorem-size     73
proof            (modus-ponens tm-306 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (or Bm (-> Am (and Bm Am)))) (C Cm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-48.           (((A -> (B and 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-72764.        ((((((A -> (B and A)) -> C) and D) or ((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)))) -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> C))), M:tm-306, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (or Bm (-> Am (and Bm Am)))) (C Cm))
================================================================
tm-name          tm-72765
in-theory        72765
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))))
theorem-size     57
proof            (modus-ponens tm-305 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-48.           (((A -> (B and 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-72765.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and (E -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))), M:tm-305, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72766
in-theory        72766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     39
proof            (modus-ponens tm-303 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72766.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-303, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72767
in-theory        72767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-270 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72767.        ((A -> (((B and C) -> C) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-270, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72768
in-theory        72768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-239 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72768.        ((A -> (((B and C) -> B) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-239, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72769
in-theory        72769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     45
proof            (modus-ponens tm-210 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-72769.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-210, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72770
in-theory        72770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-183 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72770.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-183, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72771
in-theory        72771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-157 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-72771.        ((A -> ((B and C) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-157, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72772
in-theory        72772
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     43
proof            (modus-ponens tm-147 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-72772.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-147, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72773
in-theory        72773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-134 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72773.        ((A -> ((B and C) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-134, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72774
in-theory        72774
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     43
proof            (modus-ponens tm-125 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72774.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-125, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72775
in-theory        72775
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> (C -> D)) and E) or ((A -> (B and A)) -> (C -> D))) -> (((B or (A -> (B and A))) -> C) -> ((B or (A -> (B and A))) -> D)))
theorem-size     41
proof            (modus-ponens tm-114 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) (-> C D)) Dm) (-> (-> 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-3 tm-5)
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-3.            ((A and B) -> A), axiom
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-72775.        (((((A -> (B and A)) -> (C -> D)) and E) or ((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-839, u:((A (or (and (-> (-> Am (and Bm Am)) (-> C D)) Dm) (-> (-> Am (and Bm Am)) (-> C D)))) (B (or Bm (-> Am (and Bm Am)))) (Cm (-> C D)))
================================================================
tm-name          tm-72776
in-theory        72776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-113 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72776.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-113, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72777
in-theory        72777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     47
proof            (modus-ponens tm-105 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72777.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-105, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72778
in-theory        72778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     35
proof            (modus-ponens tm-95 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-48.           (((A -> (B and 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-72778.        (((A -> B) -> (A -> A)) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-95, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72779
in-theory        72779
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (E -> ((B or (A -> (B and A))) -> C)))
theorem-size     29
proof            (modus-ponens tm-84 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72779.        (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (E -> ((B or (A -> (B and A))) -> C))), M:tm-84, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72780
in-theory        72780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-83 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72780.        ((A -> (B -> (C -> B))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-83, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72781
in-theory        72781
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))
theorem-size     33
proof            (modus-ponens tm-76 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72781.        (((not (not A)) -> A) and (((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))), M:tm-76, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72782
in-theory        72782
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)))) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C))
theorem-size     47
proof            (modus-ponens tm-73 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-10 tm-3 tm-5)
proof-size       169
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-48.           (((A -> (B and 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-72782.        (((not (not ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)))) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C)), M:tm-73, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72783
in-theory        72783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     39
proof            (modus-ponens tm-69 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72783.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-69, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72784
in-theory        72784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     41
proof            (modus-ponens tm-54 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72784.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-54, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72785
in-theory        72785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C))
theorem-size     35
proof            (modus-ponens tm-50 tm-839 ((A (and (-> (-> Am (and Bm Am)) Cm) Dm)) (B (-> (-> Am (and Bm Am)) Cm)) (C (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-7 tm-3 tm-5)
proof-size       159
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-48.           (((A -> (B and 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-72785.        ((((A -> (B and A)) -> C) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C)), M:tm-50, m:tm-839, u:((A (and (-> (-> Am (and Bm Am)) Cm) Dm)) (B (-> (-> Am (and Bm Am)) Cm)) (C (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72786
in-theory        72786
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) 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-49 tm-839 ((A (and (-> (-> Am (and Bm Am)) Cm) Dm)) (B (-> (-> Am (and Bm Am)) Cm)) (C (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-6 tm-3 tm-5)
proof-size       161
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-48.           (((A -> (B and 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-72786.        (((((A -> (B and A)) -> C) and D) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C)), M:tm-49, m:tm-839, u:((A (and (-> (-> Am (and Bm Am)) Cm) Dm)) (B (-> (-> Am (and Bm Am)) Cm)) (C (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72787
in-theory        72787
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D))) or ((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D))
theorem-size     47
proof            (modus-ponens tm-47 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-4 tm-3 tm-5)
proof-size       169
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-48.           (((A -> (B and 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-72787.        (((A and ((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D))) or ((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D)), M:tm-47, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72788
in-theory        72788
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) and E) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C))
theorem-size     47
proof            (modus-ponens tm-46 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       169
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-48.           (((A -> (B and 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-72788.        (((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) and E) or ((((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-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72789
in-theory        72789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-42 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-48.           (((A -> (B and 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-72789.        ((A -> (B or A)) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-42, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72790
in-theory        72790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-32 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-48.           (((A -> (B and 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-72790.        ((A -> (A or B)) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-32, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72791
in-theory        72791
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) and ((B or (A -> (B and A))) -> C)))
theorem-size     45
proof            (modus-ponens tm-24 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> 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       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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72791.        (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) and ((B or (A -> (B and A))) -> C))), M:tm-24, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72792
in-theory        72792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     35
proof            (modus-ponens tm-23 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72792.        ((A -> (B -> (A and B))) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-23, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72793
in-theory        72793
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-22 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72793.        (((A and B) -> B) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-22, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72794
in-theory        72794
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-21 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72794.        (((A and B) -> A) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-21, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72795
in-theory        72795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     41
proof            (modus-ponens tm-20 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72795.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-20, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72796
in-theory        72796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-19 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and 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-48.           (((A -> (B and 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-72796.        ((A -> (B -> A)) and (((((C -> (D and C)) -> E) and F) or ((C -> (D and C)) -> E)) -> ((D or (C -> (D and C))) -> E))), M:tm-19, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72797
in-theory        72797
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)))
theorem-size     35
proof            (modus-ponens tm-12 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
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-72797.        (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))), M:tm-12, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72798
in-theory        72798
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))))
theorem-size     47
proof            (modus-ponens tm-9 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-9 tm-8 tm-3 tm-5)
proof-size       151
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-48.           (((A -> (B and 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-72798.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)))), M:tm-9, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72799
in-theory        72799
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> ((((((B -> (A and B)) -> C) and E) or ((B -> (A and B)) -> C)) or ((A or (B -> (A and B))) -> C)) -> D))
theorem-size     41
proof            (modus-ponens tm-8 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-3 tm-5)
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-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-72799.        ((((A or (B -> (A and B))) -> C) -> D) -> ((((((B -> (A and B)) -> C) and E) or ((B -> (A and B)) -> C)) or ((A or (B -> (A and B))) -> C)) -> D)), M:tm-8, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-72800
in-theory        72800
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-7 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-5)
proof-size       127
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-48.           (((A -> (B and 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-72800.        (A or (((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))), M:tm-7, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72801
in-theory        72801
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) or E)
theorem-size     29
proof            (modus-ponens tm-6 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-6 tm-8 tm-3 tm-5)
proof-size       127
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-48.           (((A -> (B and 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-72801.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) or E), M:tm-6, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72802
in-theory        72802
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-72802.        (A -> ((((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and A)), M:tm-5, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72803
in-theory        72803
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (B or (A -> (B and A)))) -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> C))
theorem-size     45
proof            (modus-ponens tm-2 tm-839 ((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (or Bm (-> Am (and Bm Am)))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-3 tm-5)
proof-size       151
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-48.           (((A -> (B and 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-72803.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (B or (A -> (B and A)))) -> (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> C)), M:tm-2, m:tm-839, u:((A (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm))) (B (or Bm (-> Am (and Bm Am)))) (C Cm))
================================================================
tm-name          tm-72804
in-theory        72804
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-1 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-1 tm-8 tm-3 tm-5)
proof-size       127
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-48.           (((A -> (B and 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-72804.        (A -> (((((B -> (C and B)) -> D) and E) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))), M:tm-1, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-72805
in-theory        72805
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (B -> (A and B))))
theorem-size     15
proof            (modus-ponens tm-840 tm-34 ((Am (-> Cm (-> (and B Cm) (-> Cm (and B Cm))))) (Bm (-> Cm (and B Cm))) (A Cm) (C (-> Cm (and B Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-72805.        ((A or (B -> (A and B))) -> (B -> (B -> (A and B)))), M:tm-840, m:tm-34, u:((Am (-> Cm (-> (and B Cm) (-> Cm (and B Cm))))) (Bm (-> Cm (and B Cm))) (A Cm) (C (-> Cm (and B Cm))))
================================================================
tm-name          tm-72806
in-theory        72806
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> ((B -> (A and B)) and B)))
theorem-size     17
proof            (modus-ponens tm-840 tm-38 ((Am (-> Cm (-> (and B Cm) (and (-> Cm (and B Cm)) Cm)))) (Bm (-> Cm (and B Cm))) (A Cm) (C (and (-> Cm (and B Cm)) Cm))))
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-72806.        ((A or (B -> (A and B))) -> (B -> ((B -> (A and B)) and B))), M:tm-840, m:tm-38, u:((Am (-> Cm (-> (and B Cm) (and (-> Cm (and B Cm)) Cm)))) (Bm (-> Cm (and B Cm))) (A Cm) (C (and (-> Cm (and B Cm)) Cm)))
================================================================
tm-name          tm-72807
in-theory        72807
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (C -> B)))
theorem-size     13
proof            (modus-ponens tm-840 tm-81 ((Am (-> Cm (-> (and B Cm) (-> Dm Cm)))) (Bm (-> Cm (and B Cm))) (A Cm) (C (-> Dm Cm))))
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-48.           (((A -> (B and 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-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-72807.        ((A or (B -> (A and B))) -> (B -> (C -> B))), M:tm-840, m:tm-81, u:((Am (-> Cm (-> (and B Cm) (-> Dm Cm)))) (Bm (-> Cm (and B Cm))) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-72808
in-theory        72808
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> (A and (B -> (C -> D))))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-840 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> (and B (-> Cm (-> Dm Em))) (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) (and B (-> Cm (-> Dm Em))))) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-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-72808.        ((A or ((B -> (C -> D)) -> (A and (B -> (C -> D))))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-840, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> (and B (-> Cm (-> Dm Em))) (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) (and B (-> Cm (-> Dm Em))))) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-72809
in-theory        72809
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> (A and (B and C)))) -> ((B and C) -> B))
theorem-size     17
proof            (modus-ponens tm-840 tm-132 ((Am (-> (and Cm Dm) (-> (and B (and Cm Dm)) Cm))) (Bm (-> (and Cm Dm) (and B (and Cm Dm)))) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-3)
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-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-72809.        ((A or ((B and C) -> (A and (B and C)))) -> ((B and C) -> B)), M:tm-840, m:tm-132, u:((Am (-> (and Cm Dm) (-> (and B (and Cm Dm)) Cm))) (Bm (-> (and Cm Dm) (and B (and Cm Dm)))) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-72810
in-theory        72810
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> (A and (B and C)))) -> ((B and C) -> C))
theorem-size     17
proof            (modus-ponens tm-840 tm-155 ((Am (-> (and Cm Dm) (-> (and B (and Cm Dm)) Dm))) (Bm (-> (and Cm Dm) (and B (and Cm Dm)))) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-4)
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-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-72810.        ((A or ((B and C) -> (A and (B and C)))) -> ((B and C) -> C)), M:tm-840, m:tm-155, u:((Am (-> (and Cm Dm) (-> (and B (and Cm Dm)) Dm))) (Bm (-> (and Cm Dm) (and B (and Cm Dm)))) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-72811
in-theory        72811
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (C -> (B and C))))
theorem-size     15
proof            (modus-ponens tm-840 tm-352 ((Am (-> Cm (-> (and B Cm) (-> Dm (and Cm Dm))))) (Bm (-> Cm (and B Cm))) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-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-72811.        ((A or (B -> (A and B))) -> (B -> (C -> (B and C)))), M:tm-840, m:tm-352, u:((Am (-> Cm (-> (and B Cm) (-> Dm (and Cm Dm))))) (Bm (-> Cm (and B Cm))) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-72812
in-theory        72812
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (B or C)))
theorem-size     13
proof            (modus-ponens tm-840 tm-467 ((Am (-> Cm (-> (and B Cm) (or Cm Dm)))) (Bm (-> Cm (and B Cm))) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-6)
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-48.           (((A -> (B and 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-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-72812.        ((A or (B -> (A and B))) -> (B -> (B or C))), M:tm-840, m:tm-467, u:((Am (-> Cm (-> (and B Cm) (or Cm Dm)))) (Bm (-> Cm (and B Cm))) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-72813
in-theory        72813
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (C or B)))
theorem-size     13
proof            (modus-ponens tm-840 tm-620 ((Am (-> Cm (-> (and B Cm) (or Dm Cm)))) (Bm (-> Cm (and B Cm))) (A Cm) (C (or Dm Cm))))
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-48.           (((A -> (B and 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-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-72813.        ((A or (B -> (A and B))) -> (B -> (C or B))), M:tm-840, m:tm-620, u:((Am (-> Cm (-> (and B Cm) (or Dm Cm)))) (Bm (-> Cm (and B Cm))) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-72814
in-theory        72814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-808 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72814.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-808, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72815
in-theory        72815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (((D and ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     79
proof            (modus-ponens tm-798 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72815.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (((D and ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C)))), M:tm-798, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72816
in-theory        72816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-757 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-48.           (((A -> (B and 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-72816.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-757, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72817
in-theory        72817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((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))) and D) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     79
proof            (modus-ponens tm-747 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-48.           (((A -> (B and 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-72817.        ((((A -> ((B and A) -> C)) or ((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))) and D) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C)))), M:tm-747, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72818
in-theory        72818
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G))))
theorem-size     55
proof            (modus-ponens tm-708 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       259
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-72818.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G)))), M:tm-708, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72819
in-theory        72819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-665 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-48.           (((A -> (B and 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-72819.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-665, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72820
in-theory        72820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (D or ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-623 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72820.        (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (D or ((B or (A -> (B and A))) -> (A -> C)))), M:tm-623, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72821
in-theory        72821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-622 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72821.        ((A -> (B -> (C or B))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-622, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72822
in-theory        72822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (E or D)))
theorem-size     35
proof            (modus-ponens tm-609 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72822.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (E or D))), M:tm-609, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72823
in-theory        72823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-605 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-48.           (((A -> (B and 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-72823.        ((A -> ((B -> (C or B)) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-605, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72824
in-theory        72824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (E or D)) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72824.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (E or D)) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))), M:tm-595, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72825
in-theory        72825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-550 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-48.           (((A -> (B and 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-72825.        (((A -> (B or A)) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-550, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72826
in-theory        72826
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-540 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-48.           (((A -> (B and 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-72826.        ((A or (B -> (C or B))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-540, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72827
in-theory        72827
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-530 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-48.           (((A -> (B and 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-72827.        ((A or (B -> (B or C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-530, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72828
in-theory        72828
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-520 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-48.           (((A -> (B and 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-72828.        ((A or (B -> (C -> (B and C)))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-520, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72829
in-theory        72829
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-510 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-48.           (((A -> (B and 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-72829.        ((A or ((B and C) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-510, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72830
in-theory        72830
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-500 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-48.           (((A -> (B and 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-72830.        ((A or ((B and C) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-500, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72831
in-theory        72831
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-490 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-48.           (((A -> (B and 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-72831.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G)))), M:tm-490, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72832
in-theory        72832
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-480 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-72832.        ((A or (B -> (C -> B))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-480, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72833
in-theory        72833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((B or (A -> (B and A))) -> (A -> C)) or D))
theorem-size     31
proof            (modus-ponens tm-470 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72833.        (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((B or (A -> (B and A))) -> (A -> C)) or D)), M:tm-470, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72834
in-theory        72834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-469 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72834.        ((A -> (B -> (B or C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-469, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72835
in-theory        72835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (D or E)))
theorem-size     35
proof            (modus-ponens tm-456 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72835.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (D or E))), M:tm-456, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72836
in-theory        72836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-453 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-48.           (((A -> (B and 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-72836.        ((A -> ((B -> (B or C)) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-453, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72837
in-theory        72837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (D or E)) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72837.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (D or E)) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))), M:tm-443, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72838
in-theory        72838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-409 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-48.           (((A -> (B and 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-72838.        (((A -> (A or B)) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-409, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72839
in-theory        72839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-400 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-48.           (((A -> (B and 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-72839.        (((A -> (B -> (A and B))) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-400, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72840
in-theory        72840
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-391 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-48.           (((A -> (B and 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-72840.        ((((A and B) -> B) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-391, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72841
in-theory        72841
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-382 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-48.           (((A -> (B and 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-72841.        ((((A and B) -> A) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-382, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72842
in-theory        72842
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-373 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-72842.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G)))), M:tm-373, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72843
in-theory        72843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-364 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-72843.        (((A -> (B -> A)) or C) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-364, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72844
in-theory        72844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (D -> (((B or (A -> (B and A))) -> (A -> C)) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       195
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-48.           (((A -> (B and 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-72844.        (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (D -> (((B or (A -> (B and A))) -> (A -> C)) and D))), M:tm-355, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72845
in-theory        72845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-354 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-48.           (((A -> (B and 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-72845.        ((A -> (B -> (C -> (B and C)))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-354, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72846
in-theory        72846
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (E -> (D and E))))
theorem-size     37
proof            (modus-ponens tm-341 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-72846.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72847
in-theory        72847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E))))
theorem-size     39
proof            (modus-ponens tm-338 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-72847.        (((A -> B) -> (A -> (A and B))) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E)))), M:tm-338, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72848
in-theory        72848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((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))) -> (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) and ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     77
proof            (modus-ponens tm-328 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-48.           (((A -> (B and 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-72848.        ((((A -> ((B and A) -> C)) or ((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))) -> (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) and ((B or (A -> (B and A))) -> (A -> C))))), M:tm-328, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72849
in-theory        72849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-48.           (((A -> (B and 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-72849.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))), M:tm-327, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72850
in-theory        72850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (((D and E) -> E) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72850.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (((D and E) -> E) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))), M:tm-326, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72851
in-theory        72851
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (((D and E) -> D) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72851.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (((D and E) -> D) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))), M:tm-325, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72852
in-theory        72852
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72852.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))), M:tm-324, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72853
in-theory        72853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (E -> D)) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-72853.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (E -> D)) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))), M:tm-323, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72854
in-theory        72854
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D and E) -> E))
theorem-size     35
proof            (modus-ponens tm-322 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-72854.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D and E) -> E)), M:tm-322, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72855
in-theory        72855
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D and E) -> D))
theorem-size     35
proof            (modus-ponens tm-320 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-72855.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D and E) -> D)), M:tm-320, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72856
in-theory        72856
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-318 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-72856.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72857
in-theory        72857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((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))) -> ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-316 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-48.           (((A -> (B and 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-72857.        ((((A -> ((B and A) -> C)) or ((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))) -> ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))))), M:tm-316, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72858
in-theory        72858
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (E -> D)))
theorem-size     35
proof            (modus-ponens tm-315 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72858.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (E -> D))), M:tm-315, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72859
in-theory        72859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((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))) -> (not ((B or (A -> (B and A))) -> (A -> C)))) -> (not ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))))))
theorem-size     79
proof            (modus-ponens tm-313 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-48.           (((A -> (B and 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-72859.        ((((A -> ((B and A) -> C)) or ((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))) -> (not ((B or (A -> (B and A))) -> (A -> C)))) -> (not ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))))), M:tm-313, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72860
in-theory        72860
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((((B or (A -> (B and A))) -> (A -> C)) -> D) -> ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) or ((B or (A -> (B and A))) -> (A -> C))) -> D)))
theorem-size     75
proof            (modus-ponens tm-312 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> 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-48.           (((A -> (B and 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-72860.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((((B or (A -> (B and A))) -> (A -> C)) -> D) -> ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) or ((B or (A -> (B and A))) -> (A -> C))) -> D))), M:tm-312, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72861
in-theory        72861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D or (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72861.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D or (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))), M:tm-311, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72862
in-theory        72862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((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))) or D))
theorem-size     61
proof            (modus-ponens tm-310 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72862.        ((((A -> ((B and A) -> C)) or ((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))) or D)), M:tm-310, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72863
in-theory        72863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and D)))
theorem-size     63
proof            (modus-ponens tm-309 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am 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-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-48.           (((A -> (B and 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-72863.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and D))), M:tm-309, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72864
in-theory        72864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((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 -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (A -> C))))
theorem-size     77
proof            (modus-ponens tm-306 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (or Bm (-> Am (and Bm Am)))) (C (-> Am Cm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-48.           (((A -> (B and 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-72864.        ((((A -> ((B and A) -> C)) or ((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 -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (A -> C)))), M:tm-306, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (or Bm (-> Am (and Bm Am)))) (C (-> Am Cm)))
================================================================
tm-name          tm-72865
in-theory        72865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72865.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and (D -> (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))), M:tm-305, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72866
in-theory        72866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-303 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-48.           (((A -> (B and 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-72866.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-303, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72867
in-theory        72867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-270 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-48.           (((A -> (B and 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-72867.        ((A -> (((B and C) -> C) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-270, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72868
in-theory        72868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-239 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-48.           (((A -> (B and 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-72868.        ((A -> (((B and C) -> B) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-239, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72869
in-theory        72869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-210 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-72869.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G)))), M:tm-210, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72870
in-theory        72870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-183 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-48.           (((A -> (B and 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-72870.        ((A -> ((B -> (C -> B)) and A)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-183, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72871
in-theory        72871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-157 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-72871.        ((A -> ((B and C) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-157, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72872
in-theory        72872
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-147 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-72872.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-147, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72873
in-theory        72873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-134 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-72873.        ((A -> ((B and C) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-134, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72874
in-theory        72874
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-125 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-72874.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-125, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72875
in-theory        72875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((B or (A -> (B and A))) -> A) -> ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-114 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (or Bm (-> Am (and Bm Am)))) (C Am) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       217
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-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-72875.        (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((B or (A -> (B and A))) -> A) -> ((B or (A -> (B and A))) -> C))), M:tm-114, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (or Bm (-> Am (and Bm Am)))) (C Am) (D Cm))
================================================================
tm-name          tm-72876
in-theory        72876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-113 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-48.           (((A -> (B and 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-72876.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G)))), M:tm-113, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72877
in-theory        72877
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     49
proof            (modus-ponens tm-105 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-48.           (((A -> (B and 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-72877.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-105, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72878
in-theory        72878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-95 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-48.           (((A -> (B and 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-72878.        (((A -> B) -> (A -> A)) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E)))), M:tm-95, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72879
in-theory        72879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (D -> ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-84 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72879.        (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (D -> ((B or (A -> (B and A))) -> (A -> C)))), M:tm-84, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72880
in-theory        72880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-83 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72880.        ((A -> (B -> (C -> B))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-83, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72881
in-theory        72881
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D))) -> ((C or (B -> (C and B))) -> (B -> D))))
theorem-size     35
proof            (modus-ponens tm-76 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-48.           (((A -> (B and 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-72881.        (((not (not A)) -> A) and (((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D))) -> ((C or (B -> (C and B))) -> (B -> D)))), M:tm-76, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72882
in-theory        72882
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))))) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C)))
theorem-size     49
proof            (modus-ponens tm-73 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       195
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-48.           (((A -> (B and 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-72882.        (((not (not ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))))) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C))), M:tm-73, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72883
in-theory        72883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E))))
theorem-size     41
proof            (modus-ponens tm-69 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-48.           (((A -> (B and 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-72883.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E)))), M:tm-69, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72884
in-theory        72884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-54 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-48.           (((A -> (B and 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-72884.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-54, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72885
in-theory        72885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (A -> C)) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C)))
theorem-size     39
proof            (modus-ponens tm-50 tm-840 ((A (-> Am (-> (and Bm Am) Cm))) (B (-> (-> Am (and Bm Am)) (-> Am Cm))) (C (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       187
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-48.           (((A -> (B and 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-72885.        ((((A -> (B and A)) -> (A -> C)) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C))), M:tm-50, m:tm-840, u:((A (-> Am (-> (and Bm Am) Cm))) (B (-> (-> Am (and Bm Am)) (-> Am Cm))) (C (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72886
in-theory        72886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C)))
theorem-size     37
proof            (modus-ponens tm-49 tm-840 ((A (-> Am (-> (and Bm Am) Cm))) (B (-> (-> Am (and Bm Am)) (-> Am Cm))) (C (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       185
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-48.           (((A -> (B and 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-72886.        (((A -> ((B and A) -> C)) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C))), M:tm-49, m:tm-840, u:((A (-> Am (-> (and Bm Am) Cm))) (B (-> (-> Am (and Bm Am)) (-> Am Cm))) (C (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72887
in-theory        72887
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D)))) or ((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D)))) -> ((C or (B -> (C and B))) -> (B -> D)))
theorem-size     49
proof            (modus-ponens tm-47 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       195
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-48.           (((A -> (B and 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-72887.        (((A and ((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D)))) or ((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D)))) -> ((C or (B -> (C and B))) -> (B -> D))), M:tm-47, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72888
in-theory        72888
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) and D) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C)))
theorem-size     49
proof            (modus-ponens tm-46 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       195
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-48.           (((A -> (B and 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-72888.        (((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) and D) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C))), M:tm-46, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72889
in-theory        72889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-42 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72889.        ((A -> (B or A)) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E)))), M:tm-42, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72890
in-theory        72890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-32 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72890.        ((A -> (A or B)) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E)))), M:tm-32, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72891
in-theory        72891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) and ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-24 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
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-48.           (((A -> (B and 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-72891.        (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) and ((B or (A -> (B and A))) -> (A -> C)))), M:tm-24, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72892
in-theory        72892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-23 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-48.           (((A -> (B and 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-72892.        ((A -> (B -> (A and B))) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E)))), M:tm-23, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72893
in-theory        72893
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-22 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72893.        (((A and B) -> B) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E)))), M:tm-22, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72894
in-theory        72894
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-21 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72894.        (((A and B) -> A) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E)))), M:tm-21, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72895
in-theory        72895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-20 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72895.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-20, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72896
in-theory        72896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-19 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-72896.        ((A -> (B -> A)) and (((C -> ((D and C) -> E)) or ((C -> (D and C)) -> (C -> E))) -> ((D or (C -> (D and C))) -> (C -> E)))), M:tm-19, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72897
in-theory        72897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-12 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       177
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-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-72897.        (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))), M:tm-12, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72898
in-theory        72898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (not ((B or (A -> (B and A))) -> (A -> C)))) -> (not ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-9 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-9 tm-8 tm-2 tm-5)
proof-size       177
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-48.           (((A -> (B and 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-72898.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (not ((B or (A -> (B and A))) -> (A -> C)))) -> (not ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))))), M:tm-9, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72899
in-theory        72899
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> (B -> C)) -> D) -> ((((B -> ((A and B) -> C)) or ((B -> (A and B)) -> (B -> C))) or ((A or (B -> (A and B))) -> (B -> C))) -> D))
theorem-size     45
proof            (modus-ponens tm-8 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-8 tm-2 tm-5)
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-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-72899.        ((((A or (B -> (A and B))) -> (B -> C)) -> D) -> ((((B -> ((A and B) -> C)) or ((B -> (A and B)) -> (B -> C))) or ((A or (B -> (A and B))) -> (B -> C))) -> D)), M:tm-8, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-72900
in-theory        72900
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D))) -> ((C or (B -> (C and B))) -> (B -> D))))
theorem-size     31
proof            (modus-ponens tm-7 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5)
proof-size       153
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-48.           (((A -> (B and 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-72900.        (A or (((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D))) -> ((C or (B -> (C and B))) -> (B -> D)))), M:tm-7, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72901
in-theory        72901
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) or D)
theorem-size     31
proof            (modus-ponens tm-6 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5)
proof-size       153
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-48.           (((A -> (B and 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-72901.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) or D), M:tm-6, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72902
in-theory        72902
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D))) -> ((C or (B -> (C and B))) -> (B -> D))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
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-48.           (((A -> (B and 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-72902.        (A -> ((((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D))) -> ((C or (B -> (C and B))) -> (B -> D))) and A)), M:tm-5, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72903
in-theory        72903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (B or (A -> (B and A)))) -> (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (A -> C)))
theorem-size     47
proof            (modus-ponens tm-2 tm-840 ((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (or Bm (-> Am (and Bm Am)))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       177
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-48.           (((A -> (B and 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-72903.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (B or (A -> (B and A)))) -> (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (A -> C))), M:tm-2, m:tm-840, u:((A (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm)))) (B (or Bm (-> Am (and Bm Am)))) (C (-> Am Cm)))
================================================================
tm-name          tm-72904
in-theory        72904
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D))) -> ((C or (B -> (C and B))) -> (B -> D))))
theorem-size     31
proof            (modus-ponens tm-1 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       153
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-48.           (((A -> (B and 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-72904.        (A -> (((B -> ((C and B) -> D)) or ((B -> (C and B)) -> (B -> D))) -> ((C or (B -> (C and B))) -> (B -> D)))), M:tm-1, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-72905
in-theory        72905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     31
proof            (modus-ponens tm-808 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72905.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-808, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72906
in-theory        72906
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((D and (A or ((B -> (C and B)) -> A))) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A)))
theorem-size     51
proof            (modus-ponens tm-798 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72906.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((D and (A or ((B -> (C and B)) -> A))) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A))), M:tm-798, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72907
in-theory        72907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     31
proof            (modus-ponens tm-757 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72907.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-757, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72908
in-theory        72908
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((((A or ((B -> (C and B)) -> A)) and D) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A)))
theorem-size     51
proof            (modus-ponens tm-747 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-48.           (((A -> (B and 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-72908.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((((A or ((B -> (C and B)) -> A)) and D) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A))), M:tm-747, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72909
in-theory        72909
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E)))
theorem-size     45
proof            (modus-ponens tm-708 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72909.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E))), M:tm-708, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72910
in-theory        72910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     33
proof            (modus-ponens tm-665 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-72910.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-665, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72911
in-theory        72911
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> A)) -> (D or ((C or (B -> (C and B))) -> A)))
theorem-size     21
proof            (modus-ponens tm-623 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-72911.        ((A or ((B -> (C and B)) -> A)) -> (D or ((C or (B -> (C and B))) -> A))), M:tm-623, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72912
in-theory        72912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-622 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72912.        ((A -> (B -> (C or B))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-622, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72913
in-theory        72913
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72913.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (E or D))), M:tm-609, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72914
in-theory        72914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     29
proof            (modus-ponens tm-605 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-48.           (((A -> (B and 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-72914.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-605, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72915
in-theory        72915
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (E or D)) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))))
theorem-size     45
proof            (modus-ponens tm-595 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72915.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (E or D)) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)))), M:tm-595, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72916
in-theory        72916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-550 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-48.           (((A -> (B and 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-72916.        (((A -> (B or A)) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-550, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72917
in-theory        72917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-540 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-48.           (((A -> (B and 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-72917.        ((A or (B -> (C or B))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-540, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72918
in-theory        72918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-530 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-48.           (((A -> (B and 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-72918.        ((A or (B -> (B or C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-530, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72919
in-theory        72919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     29
proof            (modus-ponens tm-520 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-48.           (((A -> (B and 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-72919.        ((A or (B -> (C -> (B and C)))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-520, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72920
in-theory        72920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-510 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-48.           (((A -> (B and 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-72920.        ((A or ((B and C) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-510, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72921
in-theory        72921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-500 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-48.           (((A -> (B and 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-72921.        ((A or ((B and C) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-500, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72922
in-theory        72922
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E)))
theorem-size     35
proof            (modus-ponens tm-490 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72922.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E))), M:tm-490, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72923
in-theory        72923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-480 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72923.        ((A or (B -> (C -> B))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-480, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72924
in-theory        72924
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> A)) -> (((C or (B -> (C and B))) -> A) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-72924.        ((A or ((B -> (C and B)) -> A)) -> (((C or (B -> (C and B))) -> A) or D)), M:tm-470, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72925
in-theory        72925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-469 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72925.        ((A -> (B -> (B or C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-469, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72926
in-theory        72926
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72926.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (D or E))), M:tm-456, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72927
in-theory        72927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     29
proof            (modus-ponens tm-453 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-48.           (((A -> (B and 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-72927.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-453, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72928
in-theory        72928
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (D or E)) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))))
theorem-size     45
proof            (modus-ponens tm-443 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72928.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (D or E)) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)))), M:tm-443, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72929
in-theory        72929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-409 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-48.           (((A -> (B and 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-72929.        (((A -> (A or B)) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-409, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72930
in-theory        72930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     29
proof            (modus-ponens tm-400 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-48.           (((A -> (B and 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-72930.        (((A -> (B -> (A and B))) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-400, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72931
in-theory        72931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-391 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-48.           (((A -> (B and 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-72931.        ((((A and B) -> B) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-391, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72932
in-theory        72932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-382 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-48.           (((A -> (B and 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-72932.        ((((A and B) -> A) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-382, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72933
in-theory        72933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E)))
theorem-size     35
proof            (modus-ponens tm-373 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72933.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E))), M:tm-373, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72934
in-theory        72934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-364 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72934.        (((A -> (B -> A)) or C) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-364, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72935
in-theory        72935
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> A)) -> (D -> (((C or (B -> (C and B))) -> A) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) 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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-48.           (((A -> (B and 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-72935.        ((A or ((B -> (C and B)) -> A)) -> (D -> (((C or (B -> (C and B))) -> A) and D))), M:tm-355, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72936
in-theory        72936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     29
proof            (modus-ponens tm-354 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72936.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-354, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72937
in-theory        72937
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-72937.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72938
in-theory        72938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C)))
theorem-size     29
proof            (modus-ponens tm-338 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-72938.        (((A -> B) -> (A -> (A and B))) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C))), M:tm-338, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72939
in-theory        72939
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((A or ((B -> (C and B)) -> A)) -> ((A or ((B -> (C and B)) -> A)) and ((C or (B -> (C and B))) -> A))))
theorem-size     49
proof            (modus-ponens tm-328 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm 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-328.          ((A -> 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-48.           (((A -> (B and 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-72939.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((A or ((B -> (C and B)) -> A)) -> ((A or ((B -> (C and B)) -> A)) and ((C or (B -> (C and B))) -> A)))), M:tm-328, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72940
in-theory        72940
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (E -> (D and E))) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))))
theorem-size     47
proof            (modus-ponens tm-327 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72940.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (E -> (D and E))) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)))), M:tm-327, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72941
in-theory        72941
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((D and E) -> E) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))))
theorem-size     45
proof            (modus-ponens tm-326 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72941.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((D and E) -> E) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)))), M:tm-326, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72942
in-theory        72942
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((D and E) -> D) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))))
theorem-size     45
proof            (modus-ponens tm-325 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72942.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((D and E) -> D) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)))), M:tm-325, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72943
in-theory        72943
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))))
theorem-size     53
proof            (modus-ponens tm-324 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72943.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)))), M:tm-324, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72944
in-theory        72944
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (E -> D)) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))))
theorem-size     45
proof            (modus-ponens tm-323 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72944.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (E -> D)) and ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)))), M:tm-323, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72945
in-theory        72945
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72945.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D and E) -> E)), M:tm-322, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72946
in-theory        72946
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72946.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D and E) -> D)), M:tm-320, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72947
in-theory        72947
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72947.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72948
in-theory        72948
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((A or ((B -> (C and B)) -> A)) -> (A or ((B -> (C and B)) -> A))))
theorem-size     39
proof            (modus-ponens tm-316 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm 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-48.           (((A -> (B and 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-72948.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((A or ((B -> (C and B)) -> A)) -> (A or ((B -> (C and B)) -> A)))), M:tm-316, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72949
in-theory        72949
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72949.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (E -> D))), M:tm-315, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72950
in-theory        72950
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((A or ((B -> (C and B)) -> A)) -> (not ((C or (B -> (C and B))) -> A))) -> (not (A or ((B -> (C and B)) -> A)))))
theorem-size     51
proof            (modus-ponens tm-313 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-48.           (((A -> (B and 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-72950.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((A or ((B -> (C and B)) -> A)) -> (not ((C or (B -> (C and B))) -> A))) -> (not (A or ((B -> (C and B)) -> A))))), M:tm-313, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72951
in-theory        72951
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((((C or (B -> (C and B))) -> A) -> D) -> (((A or ((B -> (C and B)) -> A)) or ((C or (B -> (C and B))) -> A)) -> D)))
theorem-size     53
proof            (modus-ponens tm-312 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
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-48.           (((A -> (B and 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-72951.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((((C or (B -> (C and B))) -> A) -> D) -> (((A or ((B -> (C and B)) -> A)) or ((C or (B -> (C and B))) -> A)) -> D))), M:tm-312, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72952
in-theory        72952
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D or ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))))
theorem-size     41
proof            (modus-ponens tm-311 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72952.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D or ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)))), M:tm-311, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72953
in-theory        72953
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72953.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) or D)), M:tm-310, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72954
in-theory        72954
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72954.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and D))), M:tm-309, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72955
in-theory        72955
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((A or ((B -> (C and B)) -> A)) -> (C or (B -> (C and B)))) -> ((A or ((B -> (C and B)) -> A)) -> A)))
theorem-size     49
proof            (modus-ponens tm-306 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (or Cm (-> Bm (and Cm Bm)))) (C Am)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-48.           (((A -> (B and 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-72955.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (((A or ((B -> (C and B)) -> A)) -> (C or (B -> (C and B)))) -> ((A or ((B -> (C and B)) -> A)) -> A))), M:tm-306, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (or Cm (-> Bm (and Cm Bm)))) (C Am))
================================================================
tm-name          tm-72956
in-theory        72956
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))))
theorem-size     41
proof            (modus-ponens tm-305 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72956.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and (D -> ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)))), M:tm-305, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72957
in-theory        72957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     31
proof            (modus-ponens tm-303 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72957.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-303, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72958
in-theory        72958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     29
proof            (modus-ponens tm-270 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72958.        ((A -> (((B and C) -> C) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-270, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72959
in-theory        72959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     29
proof            (modus-ponens tm-239 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72959.        ((A -> (((B and C) -> B) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-239, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72960
in-theory        72960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E)))
theorem-size     37
proof            (modus-ponens tm-210 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72960.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E))), M:tm-210, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72961
in-theory        72961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     29
proof            (modus-ponens tm-183 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72961.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-183, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72962
in-theory        72962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-157 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72962.        ((A -> ((B and C) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-157, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72963
in-theory        72963
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     35
proof            (modus-ponens tm-147 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72963.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-147, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72964
in-theory        72964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-134 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72964.        ((A -> ((B and C) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-134, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72965
in-theory        72965
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     35
proof            (modus-ponens tm-125 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72965.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-125, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72966
in-theory        72966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C -> (D and C)) -> (A -> B))) -> (((D or (C -> (D and C))) -> A) -> ((D or (C -> (D and C))) -> B)))
theorem-size     33
proof            (modus-ponens tm-114 tm-841 ((A (or (-> C D) (-> (-> Bm (and Cm Bm)) (-> C D)))) (B (or Cm (-> Bm (and Cm Bm)))) (Am (-> C D))))
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-14.           (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-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-72966.        (((A -> B) or ((C -> (D and C)) -> (A -> B))) -> (((D or (C -> (D and C))) -> A) -> ((D or (C -> (D and C))) -> B))), M:tm-114, m:tm-841, u:((A (or (-> C D) (-> (-> Bm (and Cm Bm)) (-> C D)))) (B (or Cm (-> Bm (and Cm Bm)))) (Am (-> C D)))
================================================================
tm-name          tm-72967
in-theory        72967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E)))
theorem-size     35
proof            (modus-ponens tm-113 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72967.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E))), M:tm-113, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72968
in-theory        72968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     39
proof            (modus-ponens tm-105 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72968.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-105, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72969
in-theory        72969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C)))
theorem-size     27
proof            (modus-ponens tm-95 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72969.        (((A -> B) -> (A -> A)) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C))), M:tm-95, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72970
in-theory        72970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> A)) -> (D -> ((C or (B -> (C and B))) -> A)))
theorem-size     21
proof            (modus-ponens tm-84 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-2 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72970.        ((A or ((B -> (C and B)) -> A)) -> (D -> ((C or (B -> (C and B))) -> A))), M:tm-84, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72971
in-theory        72971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     27
proof            (modus-ponens tm-83 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-72971.        ((A -> (B -> (C -> B))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-83, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72972
in-theory        72972
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C -> (D and C)) -> B)) -> ((D or (C -> (D and C))) -> B)))
theorem-size     25
proof            (modus-ponens tm-76 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-10 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72972.        (((not (not A)) -> A) and ((B or ((C -> (D and C)) -> B)) -> ((D or (C -> (D and C))) -> B))), M:tm-76, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72973
in-theory        72973
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or ((B -> (C and B)) -> A)))) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A))
theorem-size     31
proof            (modus-ponens tm-73 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
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-1.            (A -> (B -> A)), 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-72973.        (((not (not (A or ((B -> (C and B)) -> A)))) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A)), M:tm-73, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72974
in-theory        72974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C)))
theorem-size     31
proof            (modus-ponens tm-69 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-9 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72974.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C))), M:tm-69, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72975
in-theory        72975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     33
proof            (modus-ponens tm-54 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-48.           (((A -> (B and 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-72975.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-54, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72976
in-theory        72976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or (C or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C))
theorem-size     27
proof            (modus-ponens tm-50 tm-841 ((A Am) (B (-> (-> Bm (and Cm Bm)) Am)) (C (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
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-1.            (A -> (B -> A)), 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-72976.        ((((A -> (B and A)) -> C) or (C or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C)), M:tm-50, m:tm-841, u:((A Am) (B (-> (-> Bm (and Cm Bm)) Am)) (C (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72977
in-theory        72977
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A))
theorem-size     21
proof            (modus-ponens tm-49 tm-841 ((A Am) (B (-> (-> Bm (and Cm Bm)) Am)) (C (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       139
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-48.           (((A -> (B and 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-72977.        ((A or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A)), M:tm-49, m:tm-841, u:((A Am) (B (-> (-> Bm (and Cm Bm)) Am)) (C (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72978
in-theory        72978
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or ((C -> (D and C)) -> B))) or (B or ((C -> (D and C)) -> B))) -> ((D or (C -> (D and C))) -> B))
theorem-size     31
proof            (modus-ponens tm-47 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-8 tm-4 tm-1 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-1.            (A -> (B -> A)), 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-72978.        (((A and (B or ((C -> (D and C)) -> B))) or (B or ((C -> (D and C)) -> B))) -> ((D or (C -> (D and C))) -> B)), M:tm-47, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72979
in-theory        72979
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B -> (C and B)) -> A)) and D) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A))
theorem-size     31
proof            (modus-ponens tm-46 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-8 tm-3 tm-1 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-1.            (A -> (B -> A)), 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-72979.        ((((A or ((B -> (C and B)) -> A)) and D) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A)), M:tm-46, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72980
in-theory        72980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C)))
theorem-size     25
proof            (modus-ponens tm-42 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72980.        ((A -> (B or A)) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C))), M:tm-42, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72981
in-theory        72981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C)))
theorem-size     25
proof            (modus-ponens tm-32 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72981.        ((A -> (A or B)) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C))), M:tm-32, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72982
in-theory        72982
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> A)) -> ((A or ((B -> (C and B)) -> A)) and ((C or (B -> (C and B))) -> A)))
theorem-size     29
proof            (modus-ponens tm-24 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72982.        ((A or ((B -> (C and B)) -> A)) -> ((A or ((B -> (C and B)) -> A)) and ((C or (B -> (C and B))) -> A))), M:tm-24, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72983
in-theory        72983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C)))
theorem-size     27
proof            (modus-ponens tm-23 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72983.        ((A -> (B -> (A and B))) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C))), M:tm-23, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72984
in-theory        72984
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C)))
theorem-size     25
proof            (modus-ponens tm-22 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72984.        (((A and B) -> B) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C))), M:tm-22, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72985
in-theory        72985
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C)))
theorem-size     25
proof            (modus-ponens tm-21 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72985.        (((A and B) -> A) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C))), M:tm-21, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72986
in-theory        72986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     33
proof            (modus-ponens tm-20 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72986.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-20, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72987
in-theory        72987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C)))
theorem-size     25
proof            (modus-ponens tm-19 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-72987.        ((A -> (B -> A)) and ((C or ((D -> (E and D)) -> C)) -> ((E or (D -> (E and D))) -> C))), M:tm-19, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72988
in-theory        72988
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> A)) -> (A or ((B -> (C and B)) -> A)))
theorem-size     19
proof            (modus-ponens tm-12 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
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-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-72988.        ((A or ((B -> (C and B)) -> A)) -> (A or ((B -> (C and B)) -> A))), M:tm-12, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72989
in-theory        72989
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> (not ((C or (B -> (C and B))) -> A))) -> (not (A or ((B -> (C and B)) -> A))))
theorem-size     31
proof            (modus-ponens tm-9 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-9 tm-8 tm-1 tm-5)
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-1.            (A -> (B -> A)), 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-72989.        (((A or ((B -> (C and B)) -> A)) -> (not ((C or (B -> (C and B))) -> A))) -> (not (A or ((B -> (C and B)) -> A)))), M:tm-9, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72990
in-theory        72990
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> (((C or ((B -> (A and B)) -> C)) or ((A or (B -> (A and B))) -> C)) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-8 tm-1 tm-5)
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-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-72990.        ((((A or (B -> (A and B))) -> C) -> D) -> (((C or ((B -> (A and B)) -> C)) or ((A or (B -> (A and B))) -> C)) -> D)), M:tm-8, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-72991
in-theory        72991
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or ((C -> (D and C)) -> B)) -> ((D or (C -> (D and C))) -> B)))
theorem-size     21
proof            (modus-ponens tm-7 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-7 tm-8 tm-1 tm-5)
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-1.            (A -> (B -> A)), 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-72991.        (A or ((B or ((C -> (D and C)) -> B)) -> ((D or (C -> (D and C))) -> B))), M:tm-7, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72992
in-theory        72992
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-6 tm-8 tm-1 tm-5)
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-1.            (A -> (B -> A)), 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-72992.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) or D), M:tm-6, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72993
in-theory        72993
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C -> (D and C)) -> B)) -> ((D or (C -> (D and C))) -> B)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
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-48.           (((A -> (B and 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-72993.        (A -> (((B or ((C -> (D and C)) -> B)) -> ((D or (C -> (D and C))) -> B)) and A)), M:tm-5, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72994
in-theory        72994
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> (C or (B -> (C and B)))) -> ((A or ((B -> (C and B)) -> A)) -> A))
theorem-size     29
proof            (modus-ponens tm-2 tm-841 ((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (or Cm (-> Bm (and Cm Bm)))) (C Am)))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
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-1.            (A -> (B -> A)), 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-72994.        (((A or ((B -> (C and B)) -> A)) -> (C or (B -> (C and B)))) -> ((A or ((B -> (C and B)) -> A)) -> A)), M:tm-2, m:tm-841, u:((A (or Am (-> (-> Bm (and Cm Bm)) Am))) (B (or Cm (-> Bm (and Cm Bm)))) (C Am))
================================================================
tm-name          tm-72995
in-theory        72995
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> (D and C)) -> B)) -> ((D or (C -> (D and C))) -> B)))
theorem-size     21
proof            (modus-ponens tm-1 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       113
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-48.           (((A -> (B and 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-72995.        (A -> ((B or ((C -> (D and C)) -> B)) -> ((D or (C -> (D and C))) -> B))), M:tm-1, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-72996
in-theory        72996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-808 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48.           (((A -> (B and 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-72996.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-808, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-72997
in-theory        72997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-757 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48.           (((A -> (B and 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-72997.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-757, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-72998
in-theory        72998
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 G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-708 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-48.           (((A -> (B and 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-72998.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-708, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-72999
in-theory        72999
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-665 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48.           (((A -> (B and 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-72999.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-665, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73000
in-theory        73000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-622 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-73000.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-622, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73001
in-theory        73001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-73001.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73002
in-theory        73002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-605 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-73002.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-605, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73003
in-theory        73003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-73003.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-595, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73004
in-theory        73004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-550 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-73004.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-550, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73005
in-theory        73005
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-540 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-73005.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-540, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73006
in-theory        73006
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-530 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-73006.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-530, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73007
in-theory        73007
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-520 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-73007.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-520, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73008
in-theory        73008
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-510 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-73008.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-510, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73009
in-theory        73009
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-500 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-73009.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-500, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73010
in-theory        73010
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-490 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-73010.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-490, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73011
in-theory        73011
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-480 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-73011.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-480, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73012
in-theory        73012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-469 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-73012.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-469, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73013
in-theory        73013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-73013.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73014
in-theory        73014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-453 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-73014.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-453, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73015
in-theory        73015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-73015.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-443, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73016
in-theory        73016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-409 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-73016.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-409, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73017
in-theory        73017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-400 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-73017.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-400, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73018
in-theory        73018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-391 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-73018.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-391, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73019
in-theory        73019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-382 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-73019.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-382, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73020
in-theory        73020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-373 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-73020.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-373, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73021
in-theory        73021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-364 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-73021.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-364, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73022
in-theory        73022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-354 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-73022.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-354, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73023
in-theory        73023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-73023.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73024
in-theory        73024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-338 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-73024.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-338, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73025
in-theory        73025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73025.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-327, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73026
in-theory        73026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-73026.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-326, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73027
in-theory        73027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-73027.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-325, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73028
in-theory        73028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-73028.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-324, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73029
in-theory        73029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-73029.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-323, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73030
in-theory        73030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-73030.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73031
in-theory        73031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-73031.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73032
in-theory        73032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73032.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73033
in-theory        73033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-73033.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73034
in-theory        73034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-73034.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-311, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73035
in-theory        73035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-73035.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)), M:tm-310, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73036
in-theory        73036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-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-48.           (((A -> (B and 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-73036.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F))), M:tm-309, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73037
in-theory        73037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     41
proof            (modus-ponens tm-308 tm-842 ((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-73037.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-308, m:tm-842, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73038
in-theory        73038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (A -> (B or A)))
theorem-size     29
proof            (modus-ponens tm-307 tm-842 ((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-48.           (((A -> (B and 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-73038.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (A -> (B or A))), M:tm-307, m:tm-842, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73039
in-theory        73039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-48.           (((A -> (B and 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-73039.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-305, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73040
in-theory        73040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-303 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-73040.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-303, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73041
in-theory        73041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-270 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-73041.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-270, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73042
in-theory        73042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-239 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-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-73042.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-239, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73043
in-theory        73043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-210 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-73043.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-210, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73044
in-theory        73044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-183 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-73044.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-183, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73045
in-theory        73045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-157 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-73045.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-157, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73046
in-theory        73046
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-147 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-73046.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-147, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73047
in-theory        73047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-134 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-73047.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-134, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73048
in-theory        73048
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-125 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-73048.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-125, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73049
in-theory        73049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-113 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
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-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-73049.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-113, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73050
in-theory        73050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-105 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-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-73050.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-105, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73051
in-theory        73051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-95 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
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-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-73051.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-95, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73052
in-theory        73052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-83 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-73052.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-83, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73053
in-theory        73053
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     29
proof            (modus-ponens tm-76 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8)
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-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-73053.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-76, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73054
in-theory        73054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-69 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8)
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-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-73054.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-69, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73055
in-theory        73055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-54 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48.           (((A -> (B and 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-73055.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-54, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73056
in-theory        73056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-42 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-73056.        ((A -> (B or A)) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-42, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73057
in-theory        73057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-32 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-32.           (A -> ((B -> (B 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-48.           (((A -> (B and 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-73057.        ((A -> (A or B)) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-32, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73058
in-theory        73058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-23 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-73058.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-23, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73059
in-theory        73059
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-22 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-73059.        (((A and B) -> B) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-22, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73060
in-theory        73060
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-21 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-73060.        (((A and B) -> A) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-21, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73061
in-theory        73061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-20 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-73061.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-20, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73062
in-theory        73062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-19 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-19.           (A -> ((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-48.           (((A -> (B and 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-73062.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-19, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73063
in-theory        73063
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-7 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-7 tm-5 tm-8)
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-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-73063.        (A or ((B -> (C or B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-7, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73064
in-theory        73064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8)
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-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-73064.        (((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F), M:tm-6, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73065
in-theory        73065
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-48.           (((A -> (B and 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-73065.        (A -> (((B -> (C or B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A)), M:tm-5, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73066
in-theory        73066
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-1 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8)
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-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-73066.        (A -> ((B -> (C or B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-1, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73067
in-theory        73067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-808 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-73067.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-808, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73068
in-theory        73068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-757 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-73068.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-757, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73069
in-theory        73069
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 G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-708 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-48.           (((A -> (B and 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-73069.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-708, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73070
in-theory        73070
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-665 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-73070.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-665, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73071
in-theory        73071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-622 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-73071.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-622, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73072
in-theory        73072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-73072.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73073
in-theory        73073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-605 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-73073.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-605, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73074
in-theory        73074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-73074.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-595, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73075
in-theory        73075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-550 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-73075.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-550, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73076
in-theory        73076
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-540 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-73076.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-540, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73077
in-theory        73077
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-530 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-73077.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-530, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73078
in-theory        73078
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-520 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-73078.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-520, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73079
in-theory        73079
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-510 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-73079.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-510, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73080
in-theory        73080
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-500 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-73080.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-500, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73081
in-theory        73081
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-490 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-73081.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-490, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73082
in-theory        73082
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-480 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-73082.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-480, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73083
in-theory        73083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-469 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-73083.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-469, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73084
in-theory        73084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-73084.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73085
in-theory        73085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-453 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-73085.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-453, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73086
in-theory        73086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-73086.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-443, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73087
in-theory        73087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-409 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-73087.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-409, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73088
in-theory        73088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-400 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-73088.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-400, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73089
in-theory        73089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-391 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-73089.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-391, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73090
in-theory        73090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-382 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-73090.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-382, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73091
in-theory        73091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-373 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-73091.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-373, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73092
in-theory        73092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-364 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-73092.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-364, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73093
in-theory        73093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-354 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-73093.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-354, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73094
in-theory        73094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-73094.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73095
in-theory        73095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-338 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-6 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-73095.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-338, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73096
in-theory        73096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73096.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-327, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73097
in-theory        73097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-73097.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-326, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73098
in-theory        73098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-73098.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-325, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73099
in-theory        73099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-73099.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-324, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73100
in-theory        73100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-73100.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-323, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73101
in-theory        73101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-73101.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73102
in-theory        73102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-73102.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73103
in-theory        73103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73103.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73104
in-theory        73104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-73104.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73105
in-theory        73105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-73105.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-311, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73106
in-theory        73106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-73106.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)), M:tm-310, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73107
in-theory        73107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-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-48.           (((A -> (B and 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-73107.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F))), M:tm-309, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73108
in-theory        73108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     41
proof            (modus-ponens tm-308 tm-843 ((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-73108.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-308, m:tm-843, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73109
in-theory        73109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (A -> (A or B)))
theorem-size     29
proof            (modus-ponens tm-307 tm-843 ((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-48.           (((A -> (B and 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-73109.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (A -> (A or B))), M:tm-307, m:tm-843, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73110
in-theory        73110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-48.           (((A -> (B and 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-73110.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-305, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73111
in-theory        73111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-303 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-73111.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-303, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73112
in-theory        73112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-270 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-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-73112.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-270, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73113
in-theory        73113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-239 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
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-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-73113.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-239, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73114
in-theory        73114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-210 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-73114.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-210, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73115
in-theory        73115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-183 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-73115.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-183, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73116
in-theory        73116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-157 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-73116.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-157, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73117
in-theory        73117
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-147 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-73117.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-147, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73118
in-theory        73118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-134 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-73118.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-134, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73119
in-theory        73119
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-125 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-73119.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-125, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73120
in-theory        73120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-113 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
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-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-73120.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-113, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73121
in-theory        73121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-105 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
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-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-73121.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-105, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73122
in-theory        73122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-95 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
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-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-73122.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-95, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73123
in-theory        73123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-83 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-73123.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-83, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73124
in-theory        73124
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     29
proof            (modus-ponens tm-76 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-10 tm-6 tm-8)
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-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-73124.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-76, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73125
in-theory        73125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-69 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-9 tm-6 tm-8)
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-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-73125.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-69, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73126
in-theory        73126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-54 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-73126.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-54, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73127
in-theory        73127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-42 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-42.           (A -> ((B -> (C 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-48.           (((A -> (B and 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-73127.        ((A -> (B or A)) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-42, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73128
in-theory        73128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-32 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-73128.        ((A -> (A or B)) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-32, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73129
in-theory        73129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-23 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-73129.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-23, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73130
in-theory        73130
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-22 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-73130.        (((A and B) -> B) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-22, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73131
in-theory        73131
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-21 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-73131.        (((A and B) -> A) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-21, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73132
in-theory        73132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-20 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-73132.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-20, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73133
in-theory        73133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-19 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-19.           (A -> ((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-48.           (((A -> (B and 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-73133.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-19, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73134
in-theory        73134
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-7 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8)
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-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-73134.        (A or ((B -> (B or C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-7, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73135
in-theory        73135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-6 tm-5 tm-8)
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-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-73135.        (((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F), M:tm-6, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73136
in-theory        73136
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-48.           (((A -> (B and 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-73136.        (A -> (((B -> (B or C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A)), M:tm-5, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73137
in-theory        73137
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-1 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-1 tm-5 tm-6 tm-8)
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-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-73137.        (A -> ((B -> (B or C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-1, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73138
in-theory        73138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C -> (A -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-1 ((Am (-> A (and B A))) (C (-> Bm (-> A (and B A))))))
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-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-1.            (A -> (B -> A)), axiom
tm-73138.        (((A -> (B and A)) -> (C -> (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C -> (A -> (B and A))))), M:tm-844, m:tm-1, u:((Am (-> A (and B A))) (C (-> Bm (-> A (and B A)))))
================================================================
tm-name          tm-73139
in-theory        73139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> ((A -> (B and A)) and C))) and ((B or (A -> (B and A))) -> (C -> ((A -> (B and A)) and C))))
theorem-size     33
proof            (modus-ponens tm-844 tm-5 ((Am (-> A (and B A))) (C (-> Bm (and (-> A (and B A)) Bm)))))
axioms-used      (tm-2 tm-5 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-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-73139.        (((A -> (B and A)) -> (C -> ((A -> (B and A)) and C))) and ((B or (A -> (B and A))) -> (C -> ((A -> (B and A)) and C)))), M:tm-844, m:tm-5, u:((Am (-> A (and B A))) (C (-> Bm (and (-> A (and B A)) Bm))))
================================================================
tm-name          tm-73140
in-theory        73140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) or C)) and ((B or (A -> (B and A))) -> ((A -> (B and A)) or C)))
theorem-size     29
proof            (modus-ponens tm-844 tm-6 ((Am (-> A (and B A))) (C (or (-> A (and B A)) Bm))))
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-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-6.            (A -> (A or B)), axiom
tm-73140.        (((A -> (B and A)) -> ((A -> (B and A)) or C)) and ((B or (A -> (B and A))) -> ((A -> (B and A)) or C))), M:tm-844, m:tm-6, u:((Am (-> A (and B A))) (C (or (-> A (and B A)) Bm)))
================================================================
tm-name          tm-73141
in-theory        73141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C or (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C or (A -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-7 ((Am (-> A (and B A))) (C (or Bm (-> A (and B A))))))
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-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-7.            (A -> (B or A)), axiom
tm-73141.        (((A -> (B and A)) -> (C or (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C or (A -> (B and A))))), M:tm-844, m:tm-7, u:((Am (-> A (and B A))) (C (or Bm (-> A (and B A)))))
================================================================
tm-name          tm-73142
in-theory        73142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((B and A) -> C) -> ((A or (B and A)) -> C))) and ((B or (A -> (B and A))) -> (((B and A) -> C) -> ((A or (B and A)) -> C))))
theorem-size     41
proof            (modus-ponens tm-844 tm-8 ((A Am) (Bm (and B Am)) (C (-> (-> (and B Am) Cm) (-> (or Am (and B 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-48.           (((A -> (B and 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-73142.        (((A -> (B and A)) -> (((B and A) -> C) -> ((A or (B and A)) -> C))) and ((B or (A -> (B and A))) -> (((B and A) -> C) -> ((A or (B and A)) -> C)))), M:tm-844, m:tm-8, u:((A Am) (Bm (and B Am)) (C (-> (-> (and B Am) Cm) (-> (or Am (and B Am)) Cm))))
================================================================
tm-name          tm-73143
in-theory        73143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (not (B and A))) -> (not A))) and ((B or (A -> (B and A))) -> ((A -> (not (B and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-844 tm-9 ((A Am) (Bm (and B Am)) (C (-> (-> Am (not (and B Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
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-48.           (((A -> (B and 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-73143.        (((A -> (B and A)) -> ((A -> (not (B and A))) -> (not A))) and ((B or (A -> (B and A))) -> ((A -> (not (B and A))) -> (not A)))), M:tm-844, m:tm-9, u:((A Am) (Bm (and B Am)) (C (-> (-> Am (not (and B Am))) (not Am))))
================================================================
tm-name          tm-73144
in-theory        73144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (D -> C))) and ((B or (A -> (B and A))) -> (C -> (D -> C))))
theorem-size     25
proof            (modus-ponens tm-844 tm-11 ((Am (-> A (and B A))) (C (-> Bm (-> 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-73144.        (((A -> (B and A)) -> (C -> (D -> C))) and ((B or (A -> (B and A))) -> (C -> (D -> C)))), M:tm-844, m:tm-11, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-73145
in-theory        73145
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> A)) and ((B or (A -> (B and A))) -> (A -> A)))
theorem-size     21
proof            (modus-ponens tm-844 tm-12 ((A Am) (Bm (and B Am)) (C (-> Am 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-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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-73145.        (((A -> (B and A)) -> (A -> A)) and ((B or (A -> (B and A))) -> (A -> A))), M:tm-844, m:tm-12, u:((A Am) (Bm (and B Am)) (C (-> Am Am)))
================================================================
tm-name          tm-73146
in-theory        73146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((B or (A -> (B and A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-14 ((Am (-> A (and B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-73146.        (((A -> (B and A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((B or (A -> (B and A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-844, m:tm-14, u:((Am (-> A (and B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-73147
in-theory        73147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C and D) -> C)) and ((B or (A -> (B and A))) -> ((C and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-844 tm-16 ((Am (-> A (and B A))) (C (-> (and Bm 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-73147.        (((A -> (B and A)) -> ((C and D) -> C)) and ((B or (A -> (B and A))) -> ((C and D) -> C))), M:tm-844, m:tm-16, u:((Am (-> A (and B A))) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-73148
in-theory        73148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C and D) -> D)) and ((B or (A -> (B and A))) -> ((C and D) -> D)))
theorem-size     25
proof            (modus-ponens tm-844 tm-18 ((Am (-> A (and B A))) (C (-> (and Bm Cm) Cm))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-73148.        (((A -> (B and A)) -> ((C and D) -> D)) and ((B or (A -> (B and A))) -> ((C and D) -> D))), M:tm-844, m:tm-18, u:((Am (-> A (and B A))) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-73149
in-theory        73149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D -> C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> C)) and (A -> (B and A)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-19 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (and B A))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-73149.        (((A -> (B and A)) -> ((C -> (D -> C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> C)) and (A -> (B and A))))), M:tm-844, m:tm-19, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-73150
in-theory        73150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A)))))
theorem-size     53
proof            (modus-ponens tm-844 tm-20 ((Am (-> A (and B A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and B A))))))
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-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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-73150.        (((A -> (B and A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A))))), M:tm-844, 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-73151
in-theory        73151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C and D) -> C) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C and D) -> C) and (A -> (B and A)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-21 ((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Bm) (-> A (and B A))))))
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-73151.        (((A -> (B and A)) -> (((C and D) -> C) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C and D) -> C) and (A -> (B and A))))), M:tm-844, m:tm-21, u:((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Bm) (-> A (and B A)))))
================================================================
tm-name          tm-73152
in-theory        73152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C and D) -> D) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C and D) -> D) and (A -> (B and A)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-22 ((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Cm) (-> A (and B A))))))
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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-73152.        (((A -> (B and A)) -> (((C and D) -> D) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C and D) -> D) and (A -> (B and A))))), M:tm-844, m:tm-22, u:((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Cm) (-> A (and B A)))))
================================================================
tm-name          tm-73153
in-theory        73153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D -> (C and D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (C and D))) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-23 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and B A))))))
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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-73153.        (((A -> (B and A)) -> ((C -> (D -> (C and D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (C and D))) and (A -> (B and A))))), M:tm-844, m:tm-23, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73154
in-theory        73154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> (A and (B and A)))) and ((B or (A -> (B and A))) -> (A -> (A and (B and A)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-24 ((A Am) (Bm (and B Am)) (C (-> Am (and Am (and B Am))))))
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-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-73154.        (((A -> (B and A)) -> (A -> (A and (B and A)))) and ((B or (A -> (B and A))) -> (A -> (A and (B and A))))), M:tm-844, m:tm-24, u:((A Am) (Bm (and B Am)) (C (-> Am (and Am (and B Am)))))
================================================================
tm-name          tm-73155
in-theory        73155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (D -> (C and D)))) and ((B or (A -> (B and A))) -> (C -> (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-25 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-73155.        (((A -> (B and A)) -> (C -> (D -> (C and D)))) and ((B or (A -> (B and A))) -> (C -> (D -> (C and D))))), M:tm-844, m:tm-25, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-73156
in-theory        73156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (C or D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (C or D)) and (A -> (B and A)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-32 ((Am (-> A (and B A))) (C (and (-> Bm (or Bm Cm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-73156.        (((A -> (B and A)) -> ((C -> (C or D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (C or D)) and (A -> (B and A))))), M:tm-844, m:tm-32, u:((Am (-> A (and B A))) (C (and (-> Bm (or Bm Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-73157
in-theory        73157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (C or D))) and ((B or (A -> (B and A))) -> (C -> (C or D))))
theorem-size     25
proof            (modus-ponens tm-844 tm-33 ((Am (-> A (and B A))) (C (-> Bm (or Bm Cm)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-73157.        (((A -> (B and A)) -> (C -> (C or D))) and ((B or (A -> (B and A))) -> (C -> (C or D)))), M:tm-844, m:tm-33, u:((Am (-> A (and B A))) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-73158
in-theory        73158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D or C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D or C)) and (A -> (B and A)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-42 ((Am (-> A (and B A))) (C (and (-> Bm (or Cm Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-73158.        (((A -> (B and A)) -> ((C -> (D or C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D or C)) and (A -> (B and A))))), M:tm-844, m:tm-42, u:((Am (-> A (and B A))) (C (and (-> Bm (or Cm Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-73159
in-theory        73159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (D or C))) and ((B or (A -> (B and A))) -> (C -> (D or C))))
theorem-size     25
proof            (modus-ponens tm-844 tm-43 ((Am (-> A (and B A))) (C (-> Bm (or 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-73159.        (((A -> (B and A)) -> (C -> (D or C))) and ((B or (A -> (B and A))) -> (C -> (D or C)))), M:tm-844, m:tm-43, u:((Am (-> A (and B A))) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-73160
in-theory        73160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C and (A -> B))) -> ((B or (A -> B)) -> (C and (A -> B)))) and ((C or ((A -> B) -> (C and (A -> B)))) -> ((B or (A -> B)) -> (C and (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-44 ((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (and B (-> Am 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-73160.        ((((A -> B) -> (C and (A -> B))) -> ((B or (A -> B)) -> (C and (A -> B)))) and ((C or ((A -> B) -> (C and (A -> B)))) -> ((B or (A -> B)) -> (C and (A -> B))))), M:tm-844, m:tm-44, u:((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (and B (-> Am Bm)))))
================================================================
tm-name          tm-73161
in-theory        73161
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C))))) and ((D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C))))))
theorem-size     85
proof            (modus-ponens tm-844 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-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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-73161.        (((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C))))) and ((D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C)))))), M:tm-844, 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-73162
in-theory        73162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((A and C) or A) -> (B and A))) and ((B or (A -> (B and A))) -> (((A and C) or A) -> (B and A))))
theorem-size     33
proof            (modus-ponens tm-844 tm-46 ((A Am) (Bm (and B Am)) (C (-> (or (and Am Cm) Am) (and B Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-73162.        (((A -> (B and A)) -> (((A and C) or A) -> (B and A))) and ((B or (A -> (B and A))) -> (((A and C) or A) -> (B and A)))), M:tm-844, m:tm-46, u:((A Am) (Bm (and B Am)) (C (-> (or (and Am Cm) Am) (and B Am))))
================================================================
tm-name          tm-73163
in-theory        73163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C and A) or A) -> (B and A))) and ((B or (A -> (B and A))) -> (((C and A) or A) -> (B and A))))
theorem-size     33
proof            (modus-ponens tm-844 tm-47 ((A Am) (Bm (and B Am)) (C (-> (or (and Cm Am) Am) (and B Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-73163.        (((A -> (B and A)) -> (((C and A) or A) -> (B and A))) and ((B or (A -> (B and A))) -> (((C and A) or A) -> (B and A)))), M:tm-844, m:tm-47, u:((A Am) (Bm (and B Am)) (C (-> (or (and Cm Am) Am) (and B Am))))
================================================================
tm-name          tm-73164
in-theory        73164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C and (A -> (B and A)))) -> ((B or (A -> (B and A))) -> (C and (A -> (B and A))))) and ((C or ((A -> (B and A)) -> (C and (A -> (B and A))))) -> ((B or (A -> (B and A))) -> (C and (A -> (B and A))))))
theorem-size     61
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-73164.        ((((A -> (B and A)) -> (C and (A -> (B and A)))) -> ((B or (A -> (B and A))) -> (C and (A -> (B and A))))) and ((C or ((A -> (B and A)) -> (C and (A -> (B and A))))) -> ((B or (A -> (B and A))) -> (C and (A -> (B and A)))))), M:tm-844, 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-73165
in-theory        73165
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and (A or B))) -> ((A or (A or B)) -> (C and (A or B)))) and ((C or ((A or B) -> (C and (A or B)))) -> ((A or (A or B)) -> (C and (A or B)))))
theorem-size     45
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-73165.        ((((A or B) -> (C and (A or B))) -> ((A or (A or B)) -> (C and (A or B)))) and ((C or ((A or B) -> (C and (A or B)))) -> ((A or (A or B)) -> (C and (A or B))))), M:tm-844, 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-73166
in-theory        73166
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and (A or B))) -> ((B or (A or B)) -> (C and (A or B)))) and ((C or ((A or B) -> (C and (A or B)))) -> ((B or (A or B)) -> (C and (A or B)))))
theorem-size     45
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-73166.        ((((A or B) -> (C and (A or B))) -> ((B or (A or B)) -> (C and (A or B)))) and ((C or ((A or B) -> (C and (A or B)))) -> ((B or (A or B)) -> (C and (A or B))))), M:tm-844, 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-73167
in-theory        73167
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B))))) and ((D or (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B))))))
theorem-size     97
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-73167.        (((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B))))) and ((D or (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B)))))), M:tm-844, 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-73168
in-theory        73168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> (B and A)))))
theorem-size     53
proof            (modus-ponens tm-844 tm-54 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (and B A))))))
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-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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-73168.        (((A -> (B and A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> (B and A))))), M:tm-844, 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-73169
in-theory        73169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((B or (A -> (B and A))) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-56 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
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-48.           (((A -> (B and 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-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-73169.        (((A -> (B and A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((B or (A -> (B and A))) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-844, m:tm-56, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-73170
in-theory        73170
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> (C and ((A -> (not B)) -> (not A)))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (C and ((A -> (not B)) -> (not A))))) and ((C or (((A -> (not B)) -> (not A)) -> (C and ((A -> (not B)) -> (not A))))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (C and ((A -> (not B)) -> (not A))))))
theorem-size     81
proof            (modus-ponens tm-844 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-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-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-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-73170.        (((((A -> (not B)) -> (not A)) -> (C and ((A -> (not B)) -> (not A)))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (C and ((A -> (not B)) -> (not A))))) and ((C or (((A -> (not B)) -> (not A)) -> (C and ((A -> (not B)) -> (not A))))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (C and ((A -> (not B)) -> (not A)))))), M:tm-844, 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-73171
in-theory        73171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> (B and A)))))
theorem-size     49
proof            (modus-ponens tm-844 tm-69 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-73171.        (((A -> (B and A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> (B and A))))), M:tm-844, 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-73172
in-theory        73172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((B or (A -> (B and A))) -> ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-71 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
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-48.           (((A -> (B and 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-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-73172.        (((A -> (B and A)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((B or (A -> (B and A))) -> ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-844, m:tm-71, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-73173
in-theory        73173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((not (not A)) or A) -> (B and A))) and ((B or (A -> (B and A))) -> (((not (not A)) or A) -> (B and A))))
theorem-size     33
proof            (modus-ponens tm-844 tm-73 ((A Am) (Bm (and B Am)) (C (-> (or (not (not Am)) Am) (and B Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
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-48.           (((A -> (B and 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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-73173.        (((A -> (B and A)) -> (((not (not A)) or A) -> (B and A))) and ((B or (A -> (B and A))) -> (((not (not A)) or A) -> (B and A)))), M:tm-844, m:tm-73, u:((A Am) (Bm (and B Am)) (C (-> (or (not (not Am)) Am) (and B Am))))
================================================================
tm-name          tm-73174
in-theory        73174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((not (not C)) -> C) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((not (not C)) -> C) and (A -> (B and A)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-76 ((Am (-> A (and B A))) (C (and (-> (not (not Bm)) Bm) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-73174.        (((A -> (B and A)) -> (((not (not C)) -> C) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((not (not C)) -> C) and (A -> (B and A))))), M:tm-844, m:tm-76, u:((Am (-> A (and B A))) (C (and (-> (not (not Bm)) Bm) (-> A (and B A)))))
================================================================
tm-name          tm-73175
in-theory        73175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((not (not C)) -> C)) and ((B or (A -> (B and A))) -> ((not (not C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-844 tm-78 ((Am (-> A (and B A))) (C (-> (not (not Bm)) 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-48.           (((A -> (B and 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-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-73175.        (((A -> (B and A)) -> ((not (not C)) -> C)) and ((B or (A -> (B and A))) -> ((not (not C)) -> C))), M:tm-844, m:tm-78, u:((Am (-> A (and B A))) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-73176
in-theory        73176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (C and (A -> (B -> A)))) -> ((D or (A -> (B -> A))) -> (C and (A -> (B -> A))))) and ((C or ((A -> (B -> A)) -> (C and (A -> (B -> A))))) -> ((D or (A -> (B -> A))) -> (C and (A -> (B -> A))))))
theorem-size     61
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-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-73176.        ((((A -> (B -> A)) -> (C and (A -> (B -> A)))) -> ((D or (A -> (B -> A))) -> (C and (A -> (B -> A))))) and ((C or ((A -> (B -> A)) -> (C and (A -> (B -> A))))) -> ((D or (A -> (B -> A))) -> (C and (A -> (B -> A)))))), M:tm-844, 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-73177
in-theory        73177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D -> (E -> D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (E -> D))) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-83 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (and B A))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-73177.        (((A -> (B and A)) -> ((C -> (D -> (E -> D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (E -> D))) and (A -> (B and A))))), M:tm-844, m:tm-83, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73178
in-theory        73178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> (C -> (B and A)))) and ((B or (A -> (B and A))) -> (A -> (C -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-84 ((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and B 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-73178.        (((A -> (B and A)) -> (A -> (C -> (B and A)))) and ((B or (A -> (B and A))) -> (A -> (C -> (B and A))))), M:tm-844, m:tm-84, u:((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and B Am)))))
================================================================
tm-name          tm-73179
in-theory        73179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (D -> (E -> D)))) and ((B or (A -> (B and A))) -> (C -> (D -> (E -> D)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-85 ((Am (-> A (and B A))) (C (-> Bm (-> 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-48.           (((A -> (B and 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-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-73179.        (((A -> (B and A)) -> (C -> (D -> (E -> D)))) and ((B or (A -> (B and A))) -> (C -> (D -> (E -> D))))), M:tm-844, m:tm-85, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-73180
in-theory        73180
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> (B and A))) and ((B or (A -> (B and A))) -> (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-844 tm-86 ((Am (-> A (and B A))) (C (-> A (and B A)))))
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-48.           (((A -> (B and 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-1.            (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-73180.        (((A -> (B and A)) -> (A -> (B and A))) and ((B or (A -> (B and A))) -> (A -> (B and A)))), M:tm-844, m:tm-86, u:((Am (-> A (and B A))) (C (-> A (and B A))))
================================================================
tm-name          tm-73181
in-theory        73181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> (B and (A -> A))) -> (((A -> C) or (A -> A)) -> (B and (A -> A)))) and ((B or ((A -> A) -> (B and (A -> A)))) -> (((A -> C) or (A -> A)) -> (B and (A -> A)))))
theorem-size     49
proof            (modus-ponens tm-844 tm-92 ((A (-> Am Am)) (Bm (and B (-> Am Am))) (C (-> (or (-> Am Cm) (-> Am Am)) (and B (-> Am Am))))))
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-48.           (((A -> (B and 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-1.            (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-73181.        ((((A -> A) -> (B and (A -> A))) -> (((A -> C) or (A -> A)) -> (B and (A -> A)))) and ((B or ((A -> A) -> (B and (A -> A)))) -> (((A -> C) or (A -> A)) -> (B and (A -> A))))), M:tm-844, 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-73182
in-theory        73182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> D) -> (C -> C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> (C -> C)) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-95 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (and B A))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-73182.        (((A -> (B and A)) -> (((C -> D) -> (C -> C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> (C -> C)) and (A -> (B and A))))), M:tm-844, m:tm-95, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-73183
in-theory        73183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> D) -> (C -> C))) and ((B or (A -> (B and A))) -> ((C -> D) -> (C -> C))))
theorem-size     29
proof            (modus-ponens tm-844 tm-97 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm 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-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-1.            (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-73183.        (((A -> (B and A)) -> ((C -> D) -> (C -> C))) and ((B or (A -> (B and A))) -> ((C -> D) -> (C -> C)))), M:tm-844, m:tm-97, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-73184
in-theory        73184
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> (D and ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D and ((A -> (B -> C)) -> (A -> C))))) and ((D or (((A -> (B -> C)) -> (A -> C)) -> (D and ((A -> (B -> C)) -> (A -> C))))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     109
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-73184.        (((((A -> (B -> C)) -> (A -> C)) -> (D and ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D and ((A -> (B -> C)) -> (A -> C))))) and ((D or (((A -> (B -> C)) -> (A -> C)) -> (D and ((A -> (B -> C)) -> (A -> C))))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D and ((A -> (B -> C)) -> (A -> C)))))), M:tm-844, 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-73185
in-theory        73185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> (B and A)))))
theorem-size     65
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-73185.        (((A -> (B and A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> (B and A))))), M:tm-844, 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-73186
in-theory        73186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((B or (A -> (B and A))) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     53
proof            (modus-ponens tm-844 tm-107 ((Am (-> A (and B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm 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-48.           (((A -> (B and 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-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-73186.        (((A -> (B and A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((B or (A -> (B and A))) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-844, m:tm-107, u:((Am (-> A (and B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-73187
in-theory        73187
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) and ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     125
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 tm-1)
proof-size       295
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-73187.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) and ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-844, 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-73188
in-theory        73188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A)))))
theorem-size     57
proof            (modus-ponens tm-844 tm-113 ((Am (-> A (and B A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and B A))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-73188.        (((A -> (B and A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A))))), M:tm-844, 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-73189
in-theory        73189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A -> (B and A))) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     45
proof            (modus-ponens tm-844 tm-115 ((Am (-> A (and B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-73189.        (((A -> (B and A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A -> (B and A))) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-844, m:tm-115, u:((Am (-> A (and B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-73190
in-theory        73190
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> (D and (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D and (((A -> B) and C) -> B)))) and ((D or ((((A -> B) and C) -> B) -> (D and (((A -> B) and C) -> B)))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D and (((A -> B) and C) -> B)))))
theorem-size     89
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-73190.        ((((((A -> B) and C) -> B) -> (D and (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D and (((A -> B) and C) -> B)))) and ((D or ((((A -> B) and C) -> B) -> (D and (((A -> B) and C) -> B)))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D and (((A -> B) and C) -> B))))), M:tm-844, 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-73191
in-theory        73191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> (B and A)))))
theorem-size     57
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-73191.        (((A -> (B and A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> (B and A))))), M:tm-844, 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-73192
in-theory        73192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((B or (A -> (B and A))) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-844 tm-127 ((Am (-> A (and B A))) (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       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-48.           (((A -> (B and 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-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-73192.        (((A -> (B and A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((B or (A -> (B and A))) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-844, m:tm-127, u:((Am (-> A (and B A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-73193
in-theory        73193
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> (C and ((A and B) -> A))) -> ((D or ((A and B) -> A)) -> (C and ((A and B) -> A)))) and ((C or (((A and B) -> A) -> (C and ((A and B) -> A)))) -> ((D or ((A and B) -> A)) -> (C and ((A and B) -> A)))))
theorem-size     61
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-73193.        (((((A and B) -> A) -> (C and ((A and B) -> A))) -> ((D or ((A and B) -> A)) -> (C and ((A and B) -> A)))) and ((C or (((A and B) -> A) -> (C and ((A and B) -> A)))) -> ((D or ((A and B) -> A)) -> (C and ((A and B) -> A))))), M:tm-844, 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-73194
in-theory        73194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> ((D and E) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D and E) -> D)) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-134 ((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (and B A))))))
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-73194.        (((A -> (B and A)) -> ((C -> ((D and E) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D and E) -> D)) and (A -> (B and A))))), M:tm-844, m:tm-134, u:((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-73195
in-theory        73195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> B)) and ((B or (A -> (B and A))) -> (A -> B)))
theorem-size     21
proof            (modus-ponens tm-844 tm-135 ((Cm Am) (B Bm) (A Am) (C (-> Am Bm))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-73195.        (((A -> (B and A)) -> (A -> B)) and ((B or (A -> (B and A))) -> (A -> B))), M:tm-844, m:tm-135, u:((Cm Am) (B Bm) (A Am) (C (-> Am Bm)))
================================================================
tm-name          tm-73196
in-theory        73196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> ((D and E) -> D))) and ((B or (A -> (B and A))) -> (C -> ((D and E) -> D))))
theorem-size     29
proof            (modus-ponens tm-844 tm-136 ((Am (-> A (and B A))) (C (-> Bm (-> (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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-73196.        (((A -> (B and A)) -> (C -> ((D and E) -> D))) and ((B or (A -> (B and A))) -> (C -> ((D and E) -> D)))), M:tm-844, m:tm-136, u:((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-73197
in-theory        73197
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> (D and ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D and ((A and (B -> C)) -> C)))) and ((D or (((A and (B -> C)) -> C) -> (D and ((A and (B -> C)) -> C)))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D and ((A and (B -> C)) -> C)))))
theorem-size     89
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-73197.        (((((A and (B -> C)) -> C) -> (D and ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D and ((A and (B -> C)) -> C)))) and ((D or (((A and (B -> C)) -> C) -> (D and ((A and (B -> C)) -> C)))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D and ((A and (B -> C)) -> C))))), M:tm-844, 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-73198
in-theory        73198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> (B and A)))))
theorem-size     57
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-73198.        (((A -> (B and A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> (B and A))))), M:tm-844, 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-73199
in-theory        73199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((B or (A -> (B and A))) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     45
proof            (modus-ponens tm-844 tm-149 ((Am (-> A (and B A))) (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       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-48.           (((A -> (B and 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-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-73199.        (((A -> (B and A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((B or (A -> (B and A))) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-844, m:tm-149, u:((Am (-> A (and B A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-73200
in-theory        73200
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> (C and ((A and B) -> B))) -> ((D or ((A and B) -> B)) -> (C and ((A and B) -> B)))) and ((C or (((A and B) -> B) -> (C and ((A and B) -> B)))) -> ((D or ((A and B) -> B)) -> (C and ((A and B) -> B)))))
theorem-size     61
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-73200.        (((((A and B) -> B) -> (C and ((A and B) -> B))) -> ((D or ((A and B) -> B)) -> (C and ((A and B) -> B)))) and ((C or (((A and B) -> B) -> (C and ((A and B) -> B)))) -> ((D or ((A and B) -> B)) -> (C and ((A and B) -> B))))), M:tm-844, 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-73201
in-theory        73201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> ((D and E) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D and E) -> E)) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-157 ((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-73201.        (((A -> (B and A)) -> ((C -> ((D and E) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D and E) -> E)) and (A -> (B and A))))), M:tm-844, m:tm-157, u:((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-73202
in-theory        73202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> ((D and E) -> E))) and ((B or (A -> (B and A))) -> (C -> ((D and E) -> E))))
theorem-size     29
proof            (modus-ponens tm-844 tm-159 ((Am (-> A (and B A))) (C (-> Bm (-> (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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-73202.        (((A -> (B and A)) -> (C -> ((D and E) -> E))) and ((B or (A -> (B and A))) -> (C -> ((D and E) -> E)))), M:tm-844, m:tm-159, u:((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-73203
in-theory        73203
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> (D and ((A -> (B -> A)) and C))) -> ((C or ((A -> (B -> A)) and C)) -> (D and ((A -> (B -> A)) and C)))) and ((D or (((A -> (B -> A)) and C) -> (D and ((A -> (B -> A)) and C)))) -> ((C or ((A -> (B -> A)) and C)) -> (D and ((A -> (B -> A)) and C)))))
theorem-size     77
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-1.            (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-73203.        (((((A -> (B -> A)) and C) -> (D and ((A -> (B -> A)) and C))) -> ((C or ((A -> (B -> A)) and C)) -> (D and ((A -> (B -> A)) and C)))) and ((D or (((A -> (B -> A)) and C) -> (D and ((A -> (B -> A)) and C)))) -> ((C or ((A -> (B -> A)) and C)) -> (D and ((A -> (B -> A)) and C))))), M:tm-844, 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-73204
in-theory        73204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> ((D -> (E -> D)) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (E -> D)) and C)) and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-183 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (and B A))))))
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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-73204.        (((A -> (B and A)) -> ((C -> ((D -> (E -> D)) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (E -> D)) and C)) and (A -> (B and A))))), M:tm-844, m:tm-183, u:((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-73205
in-theory        73205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> ((D -> (E -> D)) and C))) and ((B or (A -> (B and A))) -> (C -> ((D -> (E -> D)) and C))))
theorem-size     33
proof            (modus-ponens tm-844 tm-184 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) 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-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-1.            (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-73205.        (((A -> (B and A)) -> (C -> ((D -> (E -> D)) and C))) and ((B or (A -> (B and A))) -> (C -> ((D -> (E -> D)) and C)))), M:tm-844, m:tm-184, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-73206
in-theory        73206
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))) and ((E or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))))
theorem-size     141
proof            (modus-ponens tm-844 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-2 tm-5 tm-8)
proof-size       319
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-20.           (A -> (((B -> (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-73206.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))) and ((E or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))))), M:tm-844, 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-73207
in-theory        73207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> (B and A)))))
theorem-size     61
proof            (modus-ponens tm-844 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-2 tm-5 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-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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-73207.        (((A -> (B and A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> (B and A))))), M:tm-844, 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-73208
in-theory        73208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((B or (A -> (B and A))) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     49
proof            (modus-ponens tm-844 tm-211 ((Am (-> A (and B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) 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-48.           (((A -> (B and 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-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-73208.        (((A -> (B and A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((B or (A -> (B and A))) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-844, m:tm-211, u:((Am (-> A (and B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-73209
in-theory        73209
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> (D and (((A and B) -> A) and C))) -> ((C or (((A and B) -> A) and C)) -> (D and (((A and B) -> A) and C)))) and ((D or ((((A and B) -> A) and C) -> (D and (((A and B) -> A) and C)))) -> ((C or (((A and B) -> A) and C)) -> (D and (((A and B) -> A) and C)))))
theorem-size     77
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-3.            ((A and B) -> 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-73209.        ((((((A and B) -> A) and C) -> (D and (((A and B) -> A) and C))) -> ((C or (((A and B) -> A) and C)) -> (D and (((A and B) -> A) and C)))) and ((D or ((((A and B) -> A) and C) -> (D and (((A and B) -> A) and C)))) -> ((C or (((A and B) -> A) and C)) -> (D and (((A and B) -> A) and C))))), M:tm-844, 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-73210
in-theory        73210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (((D and E) -> D) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (((D and E) -> D) and C)) and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-239 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-73210.        (((A -> (B and A)) -> ((C -> (((D and E) -> D) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (((D and E) -> D) and C)) and (A -> (B and A))))), M:tm-844, 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-73211
in-theory        73211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (((D and E) -> D) and C))) and ((B or (A -> (B and A))) -> (C -> (((D and E) -> D) and C))))
theorem-size     33
proof            (modus-ponens tm-844 tm-240 ((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
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-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-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-73211.        (((A -> (B and A)) -> (C -> (((D and E) -> D) and C))) and ((B or (A -> (B and A))) -> (C -> (((D and E) -> D) and C)))), M:tm-844, m:tm-240, u:((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-73212
in-theory        73212
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> (D and (((A and B) -> B) and C))) -> ((C or (((A and B) -> B) and C)) -> (D and (((A and B) -> B) and C)))) and ((D or ((((A and B) -> B) and C) -> (D and (((A and B) -> B) and C)))) -> ((C or (((A and B) -> B) and C)) -> (D and (((A and B) -> B) and C)))))
theorem-size     77
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> 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-73212.        ((((((A and B) -> B) and C) -> (D and (((A and B) -> B) and C))) -> ((C or (((A and B) -> B) and C)) -> (D and (((A and B) -> B) and C)))) and ((D or ((((A and B) -> B) and C) -> (D and (((A and B) -> B) and C)))) -> ((C or (((A and B) -> B) and C)) -> (D and (((A and B) -> B) and C))))), M:tm-844, 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-73213
in-theory        73213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (((D and E) -> E) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (((D and E) -> E) and C)) and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-270 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-73213.        (((A -> (B and A)) -> ((C -> (((D and E) -> E) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (((D and E) -> E) and C)) and (A -> (B and A))))), M:tm-844, 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-73214
in-theory        73214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (((D and E) -> E) and C))) and ((B or (A -> (B and A))) -> (C -> (((D and E) -> E) and C))))
theorem-size     33
proof            (modus-ponens tm-844 tm-271 ((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
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-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-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-73214.        (((A -> (B and A)) -> (C -> (((D and E) -> E) and C))) and ((B or (A -> (B and A))) -> (C -> (((D and E) -> E) and C)))), M:tm-844, m:tm-271, u:((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-73215
in-theory        73215
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> (D and ((A -> (B -> (A and B))) and C))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (D and ((A -> (B -> (A and B))) and C)))) and ((D or (((A -> (B -> (A and B))) and C) -> (D and ((A -> (B -> (A and B))) and C)))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (D and ((A -> (B -> (A and B))) and C)))))
theorem-size     93
proof            (modus-ponens tm-844 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-2 tm-5 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-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-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-73215.        (((((A -> (B -> (A and B))) and C) -> (D and ((A -> (B -> (A and B))) and C))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (D and ((A -> (B -> (A and B))) and C)))) and ((D or (((A -> (B -> (A and B))) and C) -> (D and ((A -> (B -> (A and B))) and C)))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (D and ((A -> (B -> (A and B))) and C))))), M:tm-844, 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-73216
in-theory        73216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> (B and A)))))
theorem-size     49
proof            (modus-ponens tm-844 tm-303 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-73216.        (((A -> (B and A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> (B and A))))), M:tm-844, 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-73217
in-theory        73217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> ((D -> (E -> (D and E))) and C))) and ((B or (A -> (B and A))) -> (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     37
proof            (modus-ponens tm-844 tm-304 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) 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-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-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-73217.        (((A -> (B and A)) -> (C -> ((D -> (E -> (D and E))) and C))) and ((B or (A -> (B and A))) -> (C -> ((D -> (E -> (D and E))) and C)))), M:tm-844, m:tm-304, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-73218
in-theory        73218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (A -> (B and A))))))
theorem-size     41
proof            (modus-ponens tm-844 tm-305 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> A (and B A)))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-73218.        (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (A -> (B and A)))))), M:tm-844, m:tm-305, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> A (and B A))))))
================================================================
tm-name          tm-73219
in-theory        73219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (C -> ((A -> (B and A)) and C)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> ((A -> (B and A)) and C)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-309 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (and (-> A (and B A)) Bm))))))
axioms-used      (tm-2 tm-5 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-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-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-73219.        (((A -> (B and A)) -> ((A -> (B and A)) and (C -> ((A -> (B and A)) and C)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> ((A -> (B and A)) and C))))), M:tm-844, 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-73220
in-theory        73220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and ((A -> (B and A)) or C))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((A -> (B and A)) or C))))
theorem-size     41
proof            (modus-ponens tm-844 tm-310 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (or (-> A (and B A)) Bm)))))
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-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-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-73220.        (((A -> (B and A)) -> ((A -> (B and A)) and ((A -> (B and A)) or C))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((A -> (B and A)) or C)))), M:tm-844, m:tm-310, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (or (-> A (and B A)) Bm))))
================================================================
tm-name          tm-73221
in-theory        73221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (C or (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C or (A -> (B and A))))))
theorem-size     41
proof            (modus-ponens tm-844 tm-311 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (or Bm (-> A (and B A)))))))
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-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-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-73221.        (((A -> (B and A)) -> ((A -> (B and A)) and (C or (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C or (A -> (B and A)))))), M:tm-844, m:tm-311, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (or Bm (-> A (and B A))))))
================================================================
tm-name          tm-73222
in-theory        73222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (((B and A) -> C) -> ((A or (B and A)) -> C)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((B and A) -> C) -> ((A or (B and A)) -> C)))))
theorem-size     53
proof            (modus-ponens tm-844 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-2 tm-5 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-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-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-73222.        (((A -> (B and A)) -> ((A -> (B and A)) and (((B and A) -> C) -> ((A or (B and A)) -> C)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((B and A) -> C) -> ((A or (B and A)) -> C))))), M:tm-844, 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-73223
in-theory        73223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and ((A -> (not (B and A))) -> (not A)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((A -> (not (B and A))) -> (not A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-313 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (-> Am (not (and B Am))) (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-73223.        (((A -> (B and A)) -> ((A -> (B and A)) and ((A -> (not (B and A))) -> (not A)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((A -> (not (B and A))) -> (not A))))), M:tm-844, 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-73224
in-theory        73224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D -> C)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-315 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm 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-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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-73224.        (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D -> C)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (D -> C))))), M:tm-844, m:tm-315, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-73225
in-theory        73225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (A -> A))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (A -> A))))
theorem-size     33
proof            (modus-ponens tm-844 tm-316 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 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-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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-73225.        (((A -> (B and A)) -> ((A -> (B and A)) and (A -> A))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (A -> A)))), M:tm-844, m:tm-316, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am Am))))
================================================================
tm-name          tm-73226
in-theory        73226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-844 tm-318 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-73226.        (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-844, 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-73227
in-theory        73227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and ((C and D) -> C))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-844 tm-320 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-73227.        (((A -> (B and A)) -> ((A -> (B and A)) and ((C and D) -> C))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C and D) -> C)))), M:tm-844, m:tm-320, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-73228
in-theory        73228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and ((C and D) -> D))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-844 tm-322 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-73228.        (((A -> (B and A)) -> ((A -> (B and A)) and ((C and D) -> D))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C and D) -> D)))), M:tm-844, m:tm-322, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-73229
in-theory        73229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> C)) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (D -> C)) and (A -> (B and A))))))
theorem-size     49
proof            (modus-ponens tm-844 tm-323 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (-> Cm Bm)) (-> A (and B A)))))))
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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-73229.        (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> C)) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (D -> C)) and (A -> (B and A)))))), M:tm-844, 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-73230
in-theory        73230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A))))))
theorem-size     65
proof            (modus-ponens tm-844 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-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-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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-73230.        (((A -> (B and A)) -> ((A -> (B and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A)))))), M:tm-844, 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-73231
in-theory        73231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (((C and D) -> C) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((C and D) -> C) and (A -> (B and A))))))
theorem-size     49
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-73231.        (((A -> (B and A)) -> ((A -> (B and A)) and (((C and D) -> C) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((C and D) -> C) and (A -> (B and A)))))), M:tm-844, 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-73232
in-theory        73232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (((C and D) -> D) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((C and D) -> D) and (A -> (B and A))))))
theorem-size     49
proof            (modus-ponens tm-844 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-2 tm-5 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-73232.        (((A -> (B and A)) -> ((A -> (B and A)) and (((C and D) -> D) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((C and D) -> D) and (A -> (B and A)))))), M:tm-844, 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-73233
in-theory        73233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> (C and D))) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (D -> (C and D))) and (A -> (B and A))))))
theorem-size     53
proof            (modus-ponens tm-844 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-2 tm-5 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-73233.        (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> (C and D))) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (D -> (C and D))) and (A -> (B and A)))))), M:tm-844, 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-73234
in-theory        73234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (A -> (A and (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (A -> (A and (B and A))))))
theorem-size     41
proof            (modus-ponens tm-844 tm-328 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am (and Am (and B Am)))))))
axioms-used      (tm-2 tm-5 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-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-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-73234.        (((A -> (B and A)) -> ((A -> (B and A)) and (A -> (A and (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (A -> (A and (B and A)))))), M:tm-844, 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-73235
in-theory        73235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> (C and (A -> (A and B)))) -> (((A -> B) or (A -> (A and B))) -> (C and (A -> (A and B))))) and ((C or ((A -> (A and B)) -> (C and (A -> (A and B))))) -> (((A -> B) or (A -> (A and B))) -> (C and (A -> (A and B))))))
theorem-size     65
proof            (modus-ponens tm-844 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-2 tm-5 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-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-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-73235.        ((((A -> (A and B)) -> (C and (A -> (A and B)))) -> (((A -> B) or (A -> (A and B))) -> (C and (A -> (A and B))))) and ((C or ((A -> (A and B)) -> (C and (A -> (A and B))))) -> (((A -> B) or (A -> (A and B))) -> (C and (A -> (A and B)))))), M:tm-844, 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-73236
in-theory        73236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> D) -> (C -> (C and D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> (C -> (C and D))) and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-338 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 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-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-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-73236.        (((A -> (B and A)) -> (((C -> D) -> (C -> (C and D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> (C -> (C and D))) and (A -> (B and A))))), M:tm-844, m:tm-338, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73237
in-theory        73237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> D) -> (C -> (C and D)))) and ((B or (A -> (B and A))) -> ((C -> D) -> (C -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-844 tm-340 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
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-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-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-73237.        (((A -> (B and A)) -> ((C -> D) -> (C -> (C and D)))) and ((B or (A -> (B and A))) -> ((C -> D) -> (C -> (C and D))))), M:tm-844, m:tm-340, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-73238
in-theory        73238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D -> (C and D))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-844 tm-341 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm (and 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-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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-73238.        (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D -> (C and D))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (D -> (C and D)))))), M:tm-844, m:tm-341, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-73239
in-theory        73239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (C and (A -> (B -> (A and B))))) -> ((D or (A -> (B -> (A and B)))) -> (C and (A -> (B -> (A and B)))))) and ((C or ((A -> (B -> (A and B))) -> (C and (A -> (B -> (A and B)))))) -> ((D or (A -> (B -> (A and B)))) -> (C and (A -> (B -> (A and B)))))))
theorem-size     77
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-1.            (A -> (B -> 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-73239.        ((((A -> (B -> (A and B))) -> (C and (A -> (B -> (A and B))))) -> ((D or (A -> (B -> (A and B)))) -> (C and (A -> (B -> (A and B)))))) and ((C or ((A -> (B -> (A and B))) -> (C and (A -> (B -> (A and B)))))) -> ((D or (A -> (B -> (A and B)))) -> (C and (A -> (B -> (A and B))))))), M:tm-844, 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-73240
in-theory        73240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D -> (E -> (D and E)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (E -> (D and E)))) and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-354 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A))))))
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-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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-73240.        (((A -> (B and A)) -> ((C -> (D -> (E -> (D and E)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (E -> (D and E)))) and (A -> (B and A))))), M:tm-844, m:tm-354, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A)))))
================================================================
tm-name          tm-73241
in-theory        73241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> (C -> ((B and A) and C)))) and ((B or (A -> (B and A))) -> (A -> (C -> ((B and A) and C)))))
theorem-size     33
proof            (modus-ponens tm-844 tm-355 ((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and (and B Am) Cm))))))
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-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-1.            (A -> (B -> 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-73241.        (((A -> (B and A)) -> (A -> (C -> ((B and A) and C)))) and ((B or (A -> (B and A))) -> (A -> (C -> ((B and A) and C))))), M:tm-844, m:tm-355, u:((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and (and B Am) Cm)))))
================================================================
tm-name          tm-73242
in-theory        73242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (D -> (E -> (D and E))))) and ((B or (A -> (B and A))) -> (C -> (D -> (E -> (D and E))))))
theorem-size     33
proof            (modus-ponens tm-844 tm-356 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
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-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-1.            (A -> (B -> 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-73242.        (((A -> (B and A)) -> (C -> (D -> (E -> (D and E))))) and ((B or (A -> (B and A))) -> (C -> (D -> (E -> (D and E)))))), M:tm-844, m:tm-356, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-73243
in-theory        73243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> (D -> C)) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (D -> C)) or E) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-364 ((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-73243.        (((A -> (B and A)) -> (((C -> (D -> C)) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (D -> C)) or E) and (A -> (B and A))))), M:tm-844, m:tm-364, u:((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73244
in-theory        73244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D -> C)) or E)) and ((B or (A -> (B and A))) -> ((C -> (D -> C)) or E)))
theorem-size     29
proof            (modus-ponens tm-844 tm-365 ((Am (-> A (and B A))) (C (or (-> Bm (-> Cm Bm)) 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-48.           (((A -> (B and 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-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-73244.        (((A -> (B and A)) -> ((C -> (D -> C)) or E)) and ((B or (A -> (B and A))) -> ((C -> (D -> C)) or E))), M:tm-844, m:tm-365, u:((Am (-> A (and B A))) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-73245
in-theory        73245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> (B and A)))))
theorem-size     57
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-73245.        (((A -> (B and A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> (B and A))))), M:tm-844, 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-73246
in-theory        73246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((B or (A -> (B and A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     45
proof            (modus-ponens tm-844 tm-374 ((Am (-> A (and B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-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-73246.        (((A -> (B and A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((B or (A -> (B and A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-844, m:tm-374, u:((Am (-> A (and B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-73247
in-theory        73247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C and D) -> C) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C and D) -> C) or E) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-382 ((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-73247.        (((A -> (B and A)) -> ((((C and D) -> C) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C and D) -> C) or E) and (A -> (B and A))))), M:tm-844, m:tm-382, u:((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73248
in-theory        73248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C and D) -> C) or E)) and ((B or (A -> (B and A))) -> (((C and D) -> C) or E)))
theorem-size     29
proof            (modus-ponens tm-844 tm-383 ((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 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-48.           (((A -> (B and 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-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-73248.        (((A -> (B and A)) -> (((C and D) -> C) or E)) and ((B or (A -> (B and A))) -> (((C and D) -> C) or E))), M:tm-844, m:tm-383, u:((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-73249
in-theory        73249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C and D) -> D) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C and D) -> D) or E) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-391 ((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-73249.        (((A -> (B and A)) -> ((((C and D) -> D) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C and D) -> D) or E) and (A -> (B and A))))), M:tm-844, m:tm-391, u:((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73250
in-theory        73250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C and D) -> D) or E)) and ((B or (A -> (B and A))) -> (((C and D) -> D) or E)))
theorem-size     29
proof            (modus-ponens tm-844 tm-392 ((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 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-48.           (((A -> (B and 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-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-73250.        (((A -> (B and A)) -> (((C and D) -> D) or E)) and ((B or (A -> (B and A))) -> (((C and D) -> D) or E))), M:tm-844, m:tm-392, u:((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-73251
in-theory        73251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> (D -> (C and D))) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (D -> (C and D))) or E) and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-400 ((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-73251.        (((A -> (B and A)) -> (((C -> (D -> (C and D))) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (D -> (C and D))) or E) and (A -> (B and A))))), M:tm-844, 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-73252
in-theory        73252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D -> (C and D))) or E)) and ((B or (A -> (B and A))) -> ((C -> (D -> (C and D))) or E)))
theorem-size     33
proof            (modus-ponens tm-844 tm-401 ((Am (-> A (and B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
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-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-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-73252.        (((A -> (B and A)) -> ((C -> (D -> (C and D))) or E)) and ((B or (A -> (B and A))) -> ((C -> (D -> (C and D))) or E))), M:tm-844, m:tm-401, u:((Am (-> A (and B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-73253
in-theory        73253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> (C or D)) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (C or D)) or E) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-409 ((Am (-> A (and B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-73253.        (((A -> (B and A)) -> (((C -> (C or D)) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (C or D)) or E) and (A -> (B and A))))), M:tm-844, m:tm-409, u:((Am (-> A (and B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73254
in-theory        73254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (C or D)) or E)) and ((B or (A -> (B and A))) -> ((C -> (C or D)) or E)))
theorem-size     29
proof            (modus-ponens tm-844 tm-410 ((Am (-> A (and B A))) (C (or (-> Bm (or Bm 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-48.           (((A -> (B and 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-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-73254.        (((A -> (B and A)) -> ((C -> (C or D)) or E)) and ((B or (A -> (B and A))) -> ((C -> (C or D)) or E))), M:tm-844, m:tm-410, u:((Am (-> A (and B A))) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-73255
in-theory        73255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (C or D)) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (C or D)) and (A -> (B and A))))))
theorem-size     49
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-73255.        (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (C or D)) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (C or D)) and (A -> (B and A)))))), M:tm-844, 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-73256
in-theory        73256
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> (D and ((A -> (A or B)) and C))) -> ((C or ((A -> (A or B)) and C)) -> (D and ((A -> (A or B)) and C)))) and ((D or (((A -> (A or B)) and C) -> (D and ((A -> (A or B)) and C)))) -> ((C or ((A -> (A or B)) and C)) -> (D and ((A -> (A or B)) and C)))))
theorem-size     77
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or 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-73256.        (((((A -> (A or B)) and C) -> (D and ((A -> (A or B)) and C))) -> ((C or ((A -> (A or B)) and C)) -> (D and ((A -> (A or B)) and C)))) and ((D or (((A -> (A or B)) and C) -> (D and ((A -> (A or B)) and C)))) -> ((C or ((A -> (A or B)) and C)) -> (D and ((A -> (A or B)) and C))))), M:tm-844, 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-73257
in-theory        73257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> ((D -> (D or E)) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (D or E)) and C)) and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-453 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-73257.        (((A -> (B and A)) -> ((C -> ((D -> (D or E)) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (D or E)) and C)) and (A -> (B and A))))), M:tm-844, 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-73258
in-theory        73258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> ((D -> (D or E)) and C))) and ((B or (A -> (B and A))) -> (C -> ((D -> (D or E)) and C))))
theorem-size     33
proof            (modus-ponens tm-844 tm-454 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
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-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-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-73258.        (((A -> (B and A)) -> (C -> ((D -> (D or E)) and C))) and ((B or (A -> (B and A))) -> (C -> ((D -> (D or E)) and C)))), M:tm-844, m:tm-454, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-73259
in-theory        73259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (C or D)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-456 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-73259.        (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (C or D)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (C or D))))), M:tm-844, m:tm-456, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-73260
in-theory        73260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> (C and (A -> (A or B)))) -> ((D or (A -> (A or B))) -> (C and (A -> (A or B))))) and ((C or ((A -> (A or B)) -> (C and (A -> (A or B))))) -> ((D or (A -> (A or B))) -> (C and (A -> (A or B))))))
theorem-size     61
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-73260.        ((((A -> (A or B)) -> (C and (A -> (A or B)))) -> ((D or (A -> (A or B))) -> (C and (A -> (A or B))))) and ((C or ((A -> (A or B)) -> (C and (A -> (A or B))))) -> ((D or (A -> (A or B))) -> (C and (A -> (A or B)))))), M:tm-844, 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-73261
in-theory        73261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D -> (D or E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (D or E))) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-469 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-73261.        (((A -> (B and A)) -> ((C -> (D -> (D or E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (D or E))) and (A -> (B and A))))), M:tm-844, m:tm-469, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (and B A)))))
================================================================
tm-name          tm-73262
in-theory        73262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> ((B and A) or C))) and ((B or (A -> (B and A))) -> (A -> ((B and A) or C))))
theorem-size     29
proof            (modus-ponens tm-844 tm-470 ((A Am) (Bm (and B Am)) (C (-> Am (or (and B Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-73262.        (((A -> (B and A)) -> (A -> ((B and A) or C))) and ((B or (A -> (B and A))) -> (A -> ((B and A) or C)))), M:tm-844, m:tm-470, u:((A Am) (Bm (and B Am)) (C (-> Am (or (and B Am) Cm))))
================================================================
tm-name          tm-73263
in-theory        73263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (D -> (D or E)))) and ((B or (A -> (B and A))) -> (C -> (D -> (D or E)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-471 ((Am (-> A (and B A))) (C (-> Bm (-> 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-73263.        (((A -> (B and A)) -> (C -> (D -> (D or E)))) and ((B or (A -> (B and A))) -> (C -> (D -> (D or E))))), M:tm-844, m:tm-471, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-73264
in-theory        73264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or (D -> (E -> D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or (D -> (E -> D))) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-480 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-73264.        (((A -> (B and A)) -> ((C or (D -> (E -> D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or (D -> (E -> D))) and (A -> (B and A))))), M:tm-844, m:tm-480, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73265
in-theory        73265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C or (D -> (E -> D)))) and ((B or (A -> (B and A))) -> (C or (D -> (E -> D)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-481 ((Am (-> A (and B A))) (C (or Bm (-> Cm (-> 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-48.           (((A -> (B and 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-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-73265.        (((A -> (B and A)) -> (C or (D -> (E -> D)))) and ((B or (A -> (B and A))) -> (C or (D -> (E -> D))))), M:tm-844, m:tm-481, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-73266
in-theory        73266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A)))))
theorem-size     57
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-73266.        (((A -> (B and A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A))))), M:tm-844, 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-73267
in-theory        73267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A -> (B and A))) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     45
proof            (modus-ponens tm-844 tm-491 ((Am (-> A (and B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-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-73267.        (((A -> (B and A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A -> (B and A))) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-844, m:tm-491, u:((Am (-> A (and B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-73268
in-theory        73268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or ((D and E) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or ((D and E) -> D)) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-500 ((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-73268.        (((A -> (B and A)) -> ((C or ((D and E) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or ((D and E) -> D)) and (A -> (B and A))))), M:tm-844, m:tm-500, u:((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-73269
in-theory        73269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C or ((D and E) -> D))) and ((B or (A -> (B and A))) -> (C or ((D and E) -> D))))
theorem-size     29
proof            (modus-ponens tm-844 tm-501 ((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 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-48.           (((A -> (B and 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-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-73269.        (((A -> (B and A)) -> (C or ((D and E) -> D))) and ((B or (A -> (B and A))) -> (C or ((D and E) -> D)))), M:tm-844, m:tm-501, u:((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-73270
in-theory        73270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or ((D and E) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or ((D and E) -> E)) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-510 ((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-73270.        (((A -> (B and A)) -> ((C or ((D and E) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or ((D and E) -> E)) and (A -> (B and A))))), M:tm-844, m:tm-510, u:((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-73271
in-theory        73271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C or ((D and E) -> E))) and ((B or (A -> (B and A))) -> (C or ((D and E) -> E))))
theorem-size     29
proof            (modus-ponens tm-844 tm-511 ((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 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-48.           (((A -> (B and 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-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-73271.        (((A -> (B and A)) -> (C or ((D and E) -> E))) and ((B or (A -> (B and A))) -> (C or ((D and E) -> E)))), M:tm-844, m:tm-511, u:((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-73272
in-theory        73272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or (D -> (E -> (D and E)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or (D -> (E -> (D and E)))) and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-520 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-73272.        (((A -> (B and A)) -> ((C or (D -> (E -> (D and E)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or (D -> (E -> (D and E)))) and (A -> (B and A))))), M:tm-844, 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-73273
in-theory        73273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C or (D -> (E -> (D and E))))) and ((B or (A -> (B and A))) -> (C or (D -> (E -> (D and E))))))
theorem-size     33
proof            (modus-ponens tm-844 tm-521 ((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
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-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-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-73273.        (((A -> (B and A)) -> (C or (D -> (E -> (D and E))))) and ((B or (A -> (B and A))) -> (C or (D -> (E -> (D and E)))))), M:tm-844, m:tm-521, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-73274
in-theory        73274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or (D -> (D or E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or (D -> (D or E))) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-530 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-73274.        (((A -> (B and A)) -> ((C or (D -> (D or E))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or (D -> (D or E))) and (A -> (B and A))))), M:tm-844, m:tm-530, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (and B A)))))
================================================================
tm-name          tm-73275
in-theory        73275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C or (D -> (D or E)))) and ((B or (A -> (B and A))) -> (C or (D -> (D or E)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-531 ((Am (-> A (and B A))) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 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-48.           (((A -> (B and 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-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-73275.        (((A -> (B and A)) -> (C or (D -> (D or E)))) and ((B or (A -> (B and A))) -> (C or (D -> (D or E))))), M:tm-844, m:tm-531, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-73276
in-theory        73276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or (D -> (E or D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or (D -> (E or D))) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-540 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-73276.        (((A -> (B and A)) -> ((C or (D -> (E or D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or (D -> (E or D))) and (A -> (B and A))))), M:tm-844, m:tm-540, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73277
in-theory        73277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C or (D -> (E or D)))) and ((B or (A -> (B and A))) -> (C or (D -> (E or D)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-541 ((Am (-> A (and B A))) (C (or Bm (-> 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-48.           (((A -> (B and 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-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-73277.        (((A -> (B and A)) -> (C or (D -> (E or D)))) and ((B or (A -> (B and A))) -> (C or (D -> (E or D))))), M:tm-844, m:tm-541, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-73278
in-theory        73278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> (D or C)) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (D or C)) or E) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-550 ((Am (-> A (and B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-73278.        (((A -> (B and A)) -> (((C -> (D or C)) or E) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> (D or C)) or E) and (A -> (B and A))))), M:tm-844, m:tm-550, u:((Am (-> A (and B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73279
in-theory        73279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D or C)) or E)) and ((B or (A -> (B and A))) -> ((C -> (D or C)) or E)))
theorem-size     29
proof            (modus-ponens tm-844 tm-551 ((Am (-> A (and B A))) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 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-48.           (((A -> (B and 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-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-73279.        (((A -> (B and A)) -> ((C -> (D or C)) or E)) and ((B or (A -> (B and A))) -> ((C -> (D or C)) or E))), M:tm-844, m:tm-551, u:((Am (-> A (and B A))) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-73280
in-theory        73280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D or C)) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (D or C)) and (A -> (B and A))))))
theorem-size     49
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-73280.        (((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D or C)) and (A -> (B and A))))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and ((C -> (D or C)) and (A -> (B and A)))))), M:tm-844, 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-73281
in-theory        73281
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> (D and ((A -> (B or A)) and C))) -> ((C or ((A -> (B or A)) and C)) -> (D and ((A -> (B or A)) and C)))) and ((D or (((A -> (B or A)) and C) -> (D and ((A -> (B or A)) and C)))) -> ((C or ((A -> (B or A)) and C)) -> (D and ((A -> (B or A)) and C)))))
theorem-size     77
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or 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-73281.        (((((A -> (B or A)) and C) -> (D and ((A -> (B or A)) and C))) -> ((C or ((A -> (B or A)) and C)) -> (D and ((A -> (B or A)) and C)))) and ((D or (((A -> (B or A)) and C) -> (D and ((A -> (B or A)) and C)))) -> ((C or ((A -> (B or A)) and C)) -> (D and ((A -> (B or A)) and C))))), M:tm-844, 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-73282
in-theory        73282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> ((D -> (E or D)) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (E or D)) and C)) and (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-605 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-73282.        (((A -> (B and A)) -> ((C -> ((D -> (E or D)) and C)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> ((D -> (E or D)) and C)) and (A -> (B and A))))), M:tm-844, 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-73283
in-theory        73283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> ((D -> (E or D)) and C))) and ((B or (A -> (B and A))) -> (C -> ((D -> (E or D)) and C))))
theorem-size     33
proof            (modus-ponens tm-844 tm-606 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
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-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-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-73283.        (((A -> (B and A)) -> (C -> ((D -> (E or D)) and C))) and ((B or (A -> (B and A))) -> (C -> ((D -> (E or D)) and C)))), M:tm-844, m:tm-606, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-73284
in-theory        73284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D or C)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-844 tm-609 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-73284.        (((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D or C)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (C -> (D or C))))), M:tm-844, m:tm-609, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-73285
in-theory        73285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> (C and (A -> (B or A)))) -> ((D or (A -> (B or A))) -> (C and (A -> (B or A))))) and ((C or ((A -> (B or A)) -> (C and (A -> (B or A))))) -> ((D or (A -> (B or A))) -> (C and (A -> (B or A))))))
theorem-size     61
proof            (modus-ponens tm-844 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-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-73285.        ((((A -> (B or A)) -> (C and (A -> (B or A)))) -> ((D or (A -> (B or A))) -> (C and (A -> (B or A))))) and ((C or ((A -> (B or A)) -> (C and (A -> (B or A))))) -> ((D or (A -> (B or A))) -> (C and (A -> (B or A)))))), M:tm-844, 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-73286
in-theory        73286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> (D -> (E or D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (E or D))) and (A -> (B and A)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-622 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-73286.        (((A -> (B and A)) -> ((C -> (D -> (E or D))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C -> (D -> (E or D))) and (A -> (B and A))))), M:tm-844, m:tm-622, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73287
in-theory        73287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> (C or (B and A)))) and ((B or (A -> (B and A))) -> (A -> (C or (B and A)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-623 ((A Am) (Bm (and B Am)) (C (-> Am (or Cm (and B Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-73287.        (((A -> (B and A)) -> (A -> (C or (B and A)))) and ((B or (A -> (B and A))) -> (A -> (C or (B and A))))), M:tm-844, m:tm-623, u:((A Am) (Bm (and B Am)) (C (-> Am (or Cm (and B Am)))))
================================================================
tm-name          tm-73288
in-theory        73288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> (D -> (E or D)))) and ((B or (A -> (B and A))) -> (C -> (D -> (E or D)))))
theorem-size     29
proof            (modus-ponens tm-844 tm-624 ((Am (-> A (and B A))) (C (-> Bm (-> 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-73288.        (((A -> (B and A)) -> (C -> (D -> (E or D)))) and ((B or (A -> (B and A))) -> (C -> (D -> (E or D))))), M:tm-844, m:tm-624, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-73289
in-theory        73289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C and (A -> B))) -> (((A -> B) -> (C and (A -> B))) and ((B or (A -> B)) -> (C and (A -> B))))) and ((C or ((A -> B) -> (C and (A -> B)))) -> (((A -> B) -> (C and (A -> B))) and ((B or (A -> B)) -> (C and (A -> B))))))
theorem-size     65
proof            (modus-ponens tm-844 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-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-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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-73289.        ((((A -> B) -> (C and (A -> B))) -> (((A -> B) -> (C and (A -> B))) and ((B or (A -> B)) -> (C and (A -> B))))) and ((C or ((A -> B) -> (C and (A -> B)))) -> (((A -> B) -> (C and (A -> B))) and ((B or (A -> B)) -> (C and (A -> B)))))), M:tm-844, 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-73290
in-theory        73290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C and (A -> B))) -> ((A -> B) -> (C and (A -> B)))) and ((C or ((A -> B) -> (C and (A -> B)))) -> ((A -> B) -> (C and (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-660 ((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (-> Am Bm) (and B (-> Am Bm))))))
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-48.           (((A -> (B and 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-1.            (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-73290.        ((((A -> B) -> (C and (A -> B))) -> ((A -> B) -> (C and (A -> B)))) and ((C or ((A -> B) -> (C and (A -> B)))) -> ((A -> B) -> (C and (A -> B))))), M:tm-844, m:tm-660, u:((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (-> Am Bm) (and B (-> Am Bm)))))
================================================================
tm-name          tm-73291
in-theory        73291
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> (D and ((A or (B -> A)) -> C))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> (D and ((A or (B -> A)) -> C)))) and ((D or (((A or (B -> A)) -> C) -> (D and ((A or (B -> A)) -> C)))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> (D and ((A or (B -> A)) -> C)))))
theorem-size     85
proof            (modus-ponens tm-844 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-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-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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-73291.        (((((A or (B -> A)) -> C) -> (D and ((A or (B -> A)) -> C))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> (D and ((A or (B -> A)) -> C)))) and ((D or (((A or (B -> A)) -> C) -> (D and ((A or (B -> A)) -> C)))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> (D and ((A or (B -> A)) -> C))))), M:tm-844, 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-73292
in-theory        73292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> (B and A)))))
theorem-size     53
proof            (modus-ponens tm-844 tm-665 ((Am (-> A (and B A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (and B A))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-73292.        (((A -> (B and A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> (B and A))))), M:tm-844, 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-73293
in-theory        73293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((B or (A -> (B and A))) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     41
proof            (modus-ponens tm-844 tm-667 ((Am (-> A (and B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-73293.        (((A -> (B and A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((B or (A -> (B and A))) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-844, m:tm-667, u:((Am (-> A (and B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-73294
in-theory        73294
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C)))))) and ((D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C)))))))
theorem-size     121
proof            (modus-ponens tm-844 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-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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-73294.        (((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C)))))) and ((D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C))))))), M:tm-844, 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-73295
in-theory        73295
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) and ((D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) -> (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))))
theorem-size     73
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-1.            (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-73295.        (((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) and ((D or (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))) -> (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))))), M:tm-844, 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-73296
in-theory        73296
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (E and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((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)))) and ((E or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (E and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (((((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)))))
theorem-size     157
proof            (modus-ponens tm-844 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-2 tm-5 tm-8)
proof-size       357
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-73296.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (E and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((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)))) and ((E or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (E and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (((((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))))), M:tm-844, 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-73297
in-theory        73297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> (B and A)))))
theorem-size     77
proof            (modus-ponens tm-844 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-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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-73297.        (((A -> (B and A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> (B and A))))), M:tm-844, 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-73298
in-theory        73298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((B or (A -> (B and A))) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     65
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-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-73298.        (((A -> (B and A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((B or (A -> (B and A))) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-844, 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-73299
in-theory        73299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (((A and C) or A) -> (B and A)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((A and C) or A) -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 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-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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-73299.        (((A -> (B and A)) -> ((A -> (B and A)) and (((A and C) or A) -> (B and A)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((A and C) or A) -> (B and A))))), M:tm-844, 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-73300
in-theory        73300
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> (D and (((A and B) or A) -> C))) -> (((A -> C) or (((A and B) or A) -> C)) -> (D and (((A and B) or A) -> C)))) and ((D or ((((A and B) or A) -> C) -> (D and (((A and B) or A) -> C)))) -> (((A -> C) or (((A and B) or A) -> C)) -> (D and (((A and B) or A) -> C)))))
theorem-size     81
proof            (modus-ponens tm-844 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-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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-73300.        ((((((A and B) or A) -> C) -> (D and (((A and B) or A) -> C))) -> (((A -> C) or (((A and B) or A) -> C)) -> (D and (((A and B) or A) -> C)))) and ((D or ((((A and B) or A) -> C) -> (D and (((A and B) or A) -> C)))) -> (((A -> C) or (((A and B) or A) -> C)) -> (D and (((A and B) or A) -> C))))), M:tm-844, 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-73301
in-theory        73301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> (B and A)))))
theorem-size     49
proof            (modus-ponens tm-844 tm-757 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (and B A))))))
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-73301.        (((A -> (B and A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> (B and A))))), M:tm-844, 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-73302
in-theory        73302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> D) -> (((C and E) or C) -> D))) and ((B or (A -> (B and A))) -> ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     37
proof            (modus-ponens tm-844 tm-759 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) 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-48.           (((A -> (B and 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-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-73302.        (((A -> (B and A)) -> ((C -> D) -> (((C and E) or C) -> D))) and ((B or (A -> (B and A))) -> ((C -> D) -> (((C and E) or C) -> D)))), M:tm-844, m:tm-759, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-73303
in-theory        73303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((A -> (B and A)) and (((C and A) or A) -> (B and A)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((C and A) or A) -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-844 tm-798 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (or (and Cm Am) Am) (and B Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-4.            ((A and B) -> B), axiom
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-73303.        (((A -> (B and A)) -> ((A -> (B and A)) and (((C and A) or A) -> (B and A)))) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and (((C and A) or A) -> (B and A))))), M:tm-844, m:tm-798, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (or (and Cm Am) Am) (and B Am)))))
================================================================
tm-name          tm-73304
in-theory        73304
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> (D and (((A and B) or B) -> C))) -> (((B -> C) or (((A and B) or B) -> C)) -> (D and (((A and B) or B) -> C)))) and ((D or ((((A and B) or B) -> C) -> (D and (((A and B) or B) -> C)))) -> (((B -> C) or (((A and B) or B) -> C)) -> (D and (((A and B) or B) -> C)))))
theorem-size     81
proof            (modus-ponens tm-844 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (Dm (and B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (and B (-> (or (and Am Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-73304.        ((((((A and B) or B) -> C) -> (D and (((A and B) or B) -> C))) -> (((B -> C) or (((A and B) or B) -> C)) -> (D and (((A and B) or B) -> C)))) and ((D or ((((A and B) or B) -> C) -> (D and (((A and B) or B) -> C)))) -> (((B -> C) or (((A and B) or B) -> C)) -> (D and (((A and B) or B) -> C))))), M:tm-844, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (Dm (and B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (and B (-> (or (and Am Bm) Bm) Cm)))))
================================================================
tm-name          tm-73305
in-theory        73305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> (B and A)))))
theorem-size     49
proof            (modus-ponens tm-844 tm-808 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (and B A))))))
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-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-4.            ((A and B) -> B), axiom
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-73305.        (((A -> (B and A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> (B and A))))), M:tm-844, m:tm-808, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-73306
in-theory        73306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C -> D) -> (((E and C) or C) -> D))) and ((B or (A -> (B and A))) -> ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     37
proof            (modus-ponens tm-844 tm-810 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-73306.        (((A -> (B and A)) -> ((C -> D) -> (((E and C) or C) -> D))) and ((B or (A -> (B and A))) -> ((C -> D) -> (((E and C) or C) -> D)))), M:tm-844, m:tm-810, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-73307
in-theory        73307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C and (A -> (B and A)))) -> (((A -> (B and A)) -> (C and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C and (A -> (B and A)))))) and ((C or ((A -> (B and A)) -> (C and (A -> (B and A))))) -> (((A -> (B and A)) -> (C and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C and (A -> (B and A)))))))
theorem-size     89
proof            (modus-ponens tm-844 tm-844 ((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (and B (-> Am (and Bm Am))))))))
axioms-used      (tm-2 tm-5 tm-8)
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-48.           (((A -> (B and 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-73307.        ((((A -> (B and A)) -> (C and (A -> (B and A)))) -> (((A -> (B and A)) -> (C and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C and (A -> (B and A)))))) and ((C or ((A -> (B and A)) -> (C and (A -> (B and A))))) -> (((A -> (B and A)) -> (C and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C and (A -> (B and A))))))), M:tm-844, m:tm-844, u:((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (and B (-> Am (and Bm Am)))))))
================================================================
tm-name          tm-73308
in-theory        73308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     37
proof            (modus-ponens tm-808 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-73308.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-808, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73309
in-theory        73309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((D and ((A -> (B and A)) -> C)) or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))
theorem-size     61
proof            (modus-ponens tm-798 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-73309.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((D and ((A -> (B and A)) -> C)) or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))), M:tm-798, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73310
in-theory        73310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     37
proof            (modus-ponens tm-757 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-73310.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-757, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73311
in-theory        73311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))
theorem-size     61
proof            (modus-ponens tm-747 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-73311.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))), M:tm-747, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73312
in-theory        73312
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G))))
theorem-size     51
proof            (modus-ponens tm-708 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-48.           (((A -> (B and 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-73312.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G)))), M:tm-708, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73313
in-theory        73313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> C)) -> (((A -> (B and A)) -> (A -> C)) and ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-703 tm-844 ((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (and (-> (-> Am (and Bm Am)) (-> Am C)) (-> (or Bm (-> Am (and Bm Am))) (-> Am 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-48.           (((A -> (B and 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-73313.        (((A -> (B and A)) -> (A -> C)) -> (((A -> (B and A)) -> (A -> C)) and ((B or (A -> (B and A))) -> (A -> C)))), M:tm-703, m:tm-844, u:((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (and (-> (-> Am (and Bm Am)) (-> Am C)) (-> (or Bm (-> Am (and Bm Am))) (-> Am C)))))
================================================================
tm-name          tm-73314
in-theory        73314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (A -> C)) -> (((A -> (B and A)) -> (A -> C)) and ((B or (A -> (B and A))) -> (A -> C)))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((A -> (B and A)) -> (A -> C)) and ((B or (A -> (B and A))) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-697 tm-844 ((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (and (-> (-> Am (and Bm Am)) (-> Am C)) (-> (or Bm (-> Am (and Bm Am))) (-> Am C))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-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-73314.        ((((A -> (B and A)) -> (A -> C)) -> (((A -> (B and A)) -> (A -> C)) and ((B or (A -> (B and A))) -> (A -> C)))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((A -> (B and A)) -> (A -> C)) and ((B or (A -> (B and A))) -> (A -> C))))), M:tm-697, m:tm-844, u:((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (and (-> (-> Am (and Bm Am)) (-> Am C)) (-> (or Bm (-> Am (and Bm Am))) (-> Am C)))))
================================================================
tm-name          tm-73315
in-theory        73315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     39
proof            (modus-ponens tm-665 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-73315.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-665, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73316
in-theory        73316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((C or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))
theorem-size     53
proof            (modus-ponens tm-654 tm-844 ((A (-> Am (and Bm Am))) (B Cm) (C (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-73316.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((C or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))), M:tm-654, m:tm-844, u:((A (-> Am (and Bm Am))) (B Cm) (C (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73317
in-theory        73317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (D or (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))
theorem-size     27
proof            (modus-ponens tm-623 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8)
proof-size       157
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-48.           (((A -> (B and 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-73317.        (((A -> (B and A)) -> C) -> (D or (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))), M:tm-623, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73318
in-theory        73318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-622 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-73318.        ((A -> (B -> (C or B))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-622, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73319
in-theory        73319
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (D or (B -> (C and B))))) -> (((B -> (C and B)) -> (D or (B -> (C and B)))) and ((C or (B -> (C and B))) -> (D or (B -> (C and B))))))
theorem-size     45
proof            (modus-ponens tm-619 tm-844 ((A (-> Am (and Bm Am))) (Cm (or B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (or B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (or B (-> Am (and Bm Am))))))))
axioms-used      (tm-8 tm-1 tm-7 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-7.            (A -> (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-48.           (((A -> (B and 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-73319.        ((A or ((B -> (C and B)) -> (D or (B -> (C and B))))) -> (((B -> (C and B)) -> (D or (B -> (C and B)))) and ((C or (B -> (C and B))) -> (D or (B -> (C and B)))))), M:tm-619, m:tm-844, u:((A (-> Am (and Bm Am))) (Cm (or B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (or B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (or B (-> Am (and Bm Am)))))))
================================================================
tm-name          tm-73320
in-theory        73320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (E or D)))
theorem-size     31
proof            (modus-ponens tm-609 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> 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       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-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-73320.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (E or D))), M:tm-609, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73321
in-theory        73321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-605 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73321.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-605, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73322
in-theory        73322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (E or D)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-73322.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (E or D)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-595, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73323
in-theory        73323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-550 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-48.           (((A -> (B and 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-73323.        (((A -> (B or A)) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-550, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73324
in-theory        73324
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-540 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-48.           (((A -> (B and 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-73324.        ((A or (B -> (C or B))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-540, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73325
in-theory        73325
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-530 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-48.           (((A -> (B and 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-73325.        ((A or (B -> (B or C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-530, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73326
in-theory        73326
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-520 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73326.        ((A or (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-520, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73327
in-theory        73327
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-510 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-48.           (((A -> (B and 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-73327.        ((A or ((B and C) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-510, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73328
in-theory        73328
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-500 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73328.        ((A or ((B and C) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-500, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73329
in-theory        73329
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G))))
theorem-size     41
proof            (modus-ponens tm-490 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73329.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G)))), M:tm-490, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73330
in-theory        73330
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-480 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-73330.        ((A or (B -> (C -> B))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-480, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73331
in-theory        73331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> ((((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)) or D))
theorem-size     27
proof            (modus-ponens tm-470 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8)
proof-size       157
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-48.           (((A -> (B and 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-73331.        (((A -> (B and A)) -> C) -> ((((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)) or D)), M:tm-470, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73332
in-theory        73332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-469 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-73332.        ((A -> (B -> (B or C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-469, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73333
in-theory        73333
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> ((B -> (C and B)) or D))) -> (((B -> (C and B)) -> ((B -> (C and B)) or D)) and ((C or (B -> (C and B))) -> ((B -> (C and B)) or D))))
theorem-size     45
proof            (modus-ponens tm-466 tm-844 ((A (-> Am (and Bm Am))) (Cm (or (-> Am (and Bm Am)) B)) (C (and (-> (-> Am (and Bm Am)) (or (-> Am (and Bm Am)) B)) (-> (or Bm (-> Am (and Bm Am))) (or (-> Am (and Bm Am)) B))))))
axioms-used      (tm-8 tm-1 tm-6 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-6.            (A -> (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-48.           (((A -> (B and 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-73333.        ((A or ((B -> (C and B)) -> ((B -> (C and B)) or D))) -> (((B -> (C and B)) -> ((B -> (C and B)) or D)) and ((C or (B -> (C and B))) -> ((B -> (C and B)) or D)))), M:tm-466, m:tm-844, u:((A (-> Am (and Bm Am))) (Cm (or (-> Am (and Bm Am)) B)) (C (and (-> (-> Am (and Bm Am)) (or (-> Am (and Bm Am)) B)) (-> (or Bm (-> Am (and Bm Am))) (or (-> Am (and Bm Am)) B)))))
================================================================
tm-name          tm-73334
in-theory        73334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (D or E)))
theorem-size     31
proof            (modus-ponens tm-456 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> 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       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-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-73334.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (D or E))), M:tm-456, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73335
in-theory        73335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-453 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73335.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-453, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73336
in-theory        73336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (D or E)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-73336.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (D or E)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-443, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73337
in-theory        73337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-409 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-48.           (((A -> (B and 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-73337.        (((A -> (A or B)) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-409, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73338
in-theory        73338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-400 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73338.        (((A -> (B -> (A and B))) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-400, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73339
in-theory        73339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-391 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-48.           (((A -> (B and 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-73339.        ((((A and B) -> B) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-391, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73340
in-theory        73340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-382 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73340.        ((((A and B) -> A) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-382, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73341
in-theory        73341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G))))
theorem-size     41
proof            (modus-ponens tm-373 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73341.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G)))), M:tm-373, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73342
in-theory        73342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-364 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-73342.        (((A -> (B -> A)) or C) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-364, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73343
in-theory        73343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (D -> ((((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       165
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-48.           (((A -> (B and 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-73343.        (((A -> (B and A)) -> C) -> (D -> ((((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)) and D))), M:tm-355, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73344
in-theory        73344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-354 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-48.           (((A -> (B and 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-73344.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-354, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73345
in-theory        73345
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (D -> ((B -> (C and B)) and D)))) -> (((B -> (C and B)) -> (D -> ((B -> (C and B)) and D))) and ((C or (B -> (C and B))) -> (D -> ((B -> (C and B)) and D)))))
theorem-size     51
proof            (modus-ponens tm-351 tm-844 ((A (-> Am (and Bm Am))) (Cm (-> B (and (-> Am (and Bm Am)) B))) (C (and (-> (-> Am (and Bm Am)) (-> B (and (-> Am (and Bm Am)) B))) (-> (or Bm (-> Am (and Bm Am))) (-> B (and (-> Am (and Bm Am)) B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       197
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-48.           (((A -> (B and 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-73345.        ((A or ((B -> (C and B)) -> (D -> ((B -> (C and B)) and D)))) -> (((B -> (C and B)) -> (D -> ((B -> (C and B)) and D))) and ((C or (B -> (C and B))) -> (D -> ((B -> (C and B)) and D))))), M:tm-351, m:tm-844, u:((A (-> Am (and Bm Am))) (Cm (-> B (and (-> Am (and Bm Am)) B))) (C (and (-> (-> Am (and Bm Am)) (-> B (and (-> Am (and Bm Am)) B))) (-> (or Bm (-> Am (and Bm Am))) (-> B (and (-> Am (and Bm Am)) B))))))
================================================================
tm-name          tm-73346
in-theory        73346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (E -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-341 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-73346.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73347
in-theory        73347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E))))
theorem-size     35
proof            (modus-ponens tm-338 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-73347.        (((A -> B) -> (A -> (A and B))) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E)))), M:tm-338, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73348
in-theory        73348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> ((A -> (B and A)) and C))) -> (((A -> (B and A)) -> ((A -> (B and A)) and C)) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and C))))
theorem-size     51
proof            (modus-ponens tm-335 tm-844 ((A (-> Am (and Bm Am))) (Cm (and (-> Am (and Bm Am)) B)) (C (and (-> (-> Am (and Bm Am)) (and (-> Am (and Bm Am)) B)) (-> (or Bm (-> Am (and Bm Am))) (and (-> Am (and Bm Am)) B))))))
axioms-used      (tm-8 tm-2 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-5.            (A -> (B -> (A and B))), axiom
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-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-73348.        ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> ((A -> (B and A)) and C))) -> (((A -> (B and A)) -> ((A -> (B and A)) and C)) and ((B or (A -> (B and A))) -> ((A -> (B and A)) and C)))), M:tm-335, m:tm-844, u:((A (-> Am (and Bm Am))) (Cm (and (-> Am (and Bm Am)) B)) (C (and (-> (-> Am (and Bm Am)) (and (-> Am (and Bm Am)) B)) (-> (or Bm (-> Am (and Bm Am))) (and (-> Am (and Bm Am)) B)))))
================================================================
tm-name          tm-73349
in-theory        73349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     59
proof            (modus-ponens tm-328 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-73349.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-328, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73350
in-theory        73350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (E -> (D and E))) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-73350.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (E -> (D and E))) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-327, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73351
in-theory        73351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((D and E) -> E) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-73351.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((D and E) -> E) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-326, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73352
in-theory        73352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((D and E) -> D) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-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-73352.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((D and E) -> D) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-325, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73353
in-theory        73353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-73353.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-324, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73354
in-theory        73354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (E -> D)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-73354.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (E -> D)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-323, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73355
in-theory        73355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D and E) -> E))
theorem-size     31
proof            (modus-ponens tm-322 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> 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       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-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-73355.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73356
in-theory        73356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D and E) -> D))
theorem-size     31
proof            (modus-ponens tm-320 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> 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       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-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-73356.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73357
in-theory        73357
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-318 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-73357.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73358
in-theory        73358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))
theorem-size     41
proof            (modus-ponens tm-316 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73358.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))), M:tm-316, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73359
in-theory        73359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (E -> D)))
theorem-size     31
proof            (modus-ponens tm-315 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-73359.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73360
in-theory        73360
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((((A -> (B and A)) -> C) -> (not (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C))))
theorem-size     61
proof            (modus-ponens tm-313 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-73360.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and ((((A -> (B and A)) -> C) -> (not (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C)))), M:tm-313, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73361
in-theory        73361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)) -> D) -> ((((A -> (B and A)) -> C) or (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) -> D)))
theorem-size     73
proof            (modus-ponens tm-312 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-312.          ((A -> B) -> ((A -> B) and ((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-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-73361.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (((((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)) -> D) -> ((((A -> (B and A)) -> C) or (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) -> D))), M:tm-312, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73362
in-theory        73362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D or (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-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-73362.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D or (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-311, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73363
in-theory        73363
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((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))) or D))
theorem-size     53
proof            (modus-ponens tm-310 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-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-73363.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((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))) or D)), M:tm-310, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73364
in-theory        73364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and D)))
theorem-size     55
proof            (modus-ponens tm-309 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-2 tm-5 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-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-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-73364.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and D))), M:tm-309, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73365
in-theory        73365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-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-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-73365.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) and (D -> (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))), M:tm-305, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73366
in-theory        73366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     37
proof            (modus-ponens tm-303 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73366.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-303, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73367
in-theory        73367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-270 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73367.        ((A -> (((B and C) -> C) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-270, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73368
in-theory        73368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-239 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73368.        ((A -> (((B and C) -> B) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-239, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73369
in-theory        73369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G))))
theorem-size     43
proof            (modus-ponens tm-210 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73369.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G)))), M:tm-210, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73370
in-theory        73370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-183 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-48.           (((A -> (B and 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-73370.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-183, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73371
in-theory        73371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-157 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-73371.        ((A -> ((B and C) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-157, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73372
in-theory        73372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     41
proof            (modus-ponens tm-147 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-73372.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-147, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73373
in-theory        73373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-134 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73373.        ((A -> ((B and C) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-134, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73374
in-theory        73374
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     41
proof            (modus-ponens tm-125 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73374.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-125, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73375
in-theory        73375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G))))
theorem-size     41
proof            (modus-ponens tm-113 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73375.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G)))), M:tm-113, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73376
in-theory        73376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     45
proof            (modus-ponens tm-105 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-48.           (((A -> (B and 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-73376.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-105, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73377
in-theory        73377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E))))
theorem-size     33
proof            (modus-ponens tm-95 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-48.           (((A -> (B and 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-73377.        (((A -> B) -> (A -> A)) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E)))), M:tm-95, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73378
in-theory        73378
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> (A -> (B and A)))) -> (((A -> (B and A)) -> (A -> (B and A))) and ((B or (A -> (B and A))) -> (A -> (B and A)))))
theorem-size     45
proof            (modus-ponens tm-92 tm-844 ((Cm (-> Am (and Bm Am))) (A (-> Am (and Bm Am))) (B (and (-> (-> Am (and Bm Am)) (-> Am (and Bm Am))) (-> (or Bm (-> Am (and Bm Am))) (-> Am (and Bm Am)))))))
axioms-used      (tm-8 tm-2 tm-1 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-1.            (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-48.           (((A -> (B and 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-73378.        ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> (A -> (B and A)))) -> (((A -> (B and A)) -> (A -> (B and A))) and ((B or (A -> (B and A))) -> (A -> (B and A))))), M:tm-92, m:tm-844, u:((Cm (-> Am (and Bm Am))) (A (-> Am (and Bm Am))) (B (and (-> (-> Am (and Bm Am)) (-> Am (and Bm Am))) (-> (or Bm (-> Am (and Bm Am))) (-> Am (and Bm Am))))))
================================================================
tm-name          tm-73379
in-theory        73379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (D -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))
theorem-size     27
proof            (modus-ponens tm-84 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       157
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-48.           (((A -> (B and 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-73379.        (((A -> (B and A)) -> C) -> (D -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))), M:tm-84, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73380
in-theory        73380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     33
proof            (modus-ponens tm-83 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-73380.        ((A -> (B -> (C -> B))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-83, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73381
in-theory        73381
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (D -> (B -> (C and B))))) -> (((B -> (C and B)) -> (D -> (B -> (C and B)))) and ((C or (B -> (C and B))) -> (D -> (B -> (C and B))))))
theorem-size     45
proof            (modus-ponens tm-80 tm-844 ((A (-> Am (and Bm Am))) (Cm (-> B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (-> B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (-> B (-> Am (and Bm Am))))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-48.           (((A -> (B and 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-73381.        ((A or ((B -> (C and B)) -> (D -> (B -> (C and B))))) -> (((B -> (C and B)) -> (D -> (B -> (C and B)))) and ((C or (B -> (C and B))) -> (D -> (B -> (C and B)))))), M:tm-80, m:tm-844, u:((A (-> Am (and Bm Am))) (Cm (-> B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (-> B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (-> B (-> Am (and Bm Am)))))))
================================================================
tm-name          tm-73382
in-theory        73382
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C and B)) -> D) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D))))
theorem-size     31
proof            (modus-ponens tm-76 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73382.        (((not (not A)) -> A) and (((B -> (C and B)) -> D) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D)))), M:tm-76, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73383
in-theory        73383
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B and A)) -> C))) or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-73 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-73383.        (((not (not ((A -> (B and A)) -> C))) or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))), M:tm-73, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73384
in-theory        73384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E))))
theorem-size     37
proof            (modus-ponens tm-69 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73384.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E)))), M:tm-69, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73385
in-theory        73385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     39
proof            (modus-ponens tm-54 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> 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      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-48.           (((A -> (B and 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-73385.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-54, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73386
in-theory        73386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (((B -> (C and B)) -> ((A or B) -> (C and B))) and ((C or (B -> (C and B))) -> ((A or B) -> (C and B)))))
theorem-size     47
proof            (modus-ponens tm-51 tm-844 ((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (and (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am))) (-> (or Bm (-> Am (and Bm Am))) (-> (or C Am) (and Bm Am)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-73386.        (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (((B -> (C and B)) -> ((A or B) -> (C and B))) and ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))), M:tm-51, m:tm-844, u:((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (and (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am))) (-> (or Bm (-> Am (and Bm Am))) (-> (or C Am) (and Bm Am))))))
================================================================
tm-name          tm-73387
in-theory        73387
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (((B -> (C and B)) -> (A and (B -> (C and B)))) and ((C or (B -> (C and B))) -> (A and (B -> (C and B))))))
theorem-size     45
proof            (modus-ponens tm-48 tm-844 ((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (and B (-> Am (and Bm Am))))))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-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-73387.        ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> (((B -> (C and B)) -> (A and (B -> (C and B)))) and ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))), M:tm-48, m:tm-844, u:((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (and B (-> Am (and Bm Am)))))))
================================================================
tm-name          tm-73388
in-theory        73388
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D)))
theorem-size     35
proof            (modus-ponens tm-47 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-73388.        (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D))), M:tm-47, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73389
in-theory        73389
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-46 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-73389.        (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))), M:tm-46, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73390
in-theory        73390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((A -> (B and A)) -> (A -> C)) and ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-45 tm-844 ((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (and (-> (-> Am (and Bm Am)) (-> Am C)) (-> (or Bm (-> Am (and Bm Am))) (-> Am C))))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-48.           (((A -> (B and 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-73390.        (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> (((A -> (B and A)) -> (A -> C)) and ((B or (A -> (B and A))) -> (A -> C)))), M:tm-45, m:tm-844, u:((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (and (-> (-> Am (and Bm Am)) (-> Am C)) (-> (or Bm (-> Am (and Bm Am))) (-> Am C)))))
================================================================
tm-name          tm-73391
in-theory        73391
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> A)) -> (((B -> (C and B)) -> A) and ((C or (B -> (C and B))) -> A)))
theorem-size     27
proof            (modus-ponens tm-44 tm-844 ((A (-> Am (and Bm Am))) (B Cm) (C (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-48.           (((A -> (B and 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-73391.        ((A or ((B -> (C and B)) -> A)) -> (((B -> (C and B)) -> A) and ((C or (B -> (C and B))) -> A))), M:tm-44, m:tm-844, u:((A (-> Am (and Bm Am))) (B Cm) (C (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73392
in-theory        73392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E))))
theorem-size     31
proof            (modus-ponens tm-42 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73392.        ((A -> (B or A)) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E)))), M:tm-42, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73393
in-theory        73393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E))))
theorem-size     31
proof            (modus-ponens tm-32 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73393.        ((A -> (A or B)) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E)))), M:tm-32, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73394
in-theory        73394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))
theorem-size     33
proof            (modus-ponens tm-24 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-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-73394.        (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))), M:tm-24, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73395
in-theory        73395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E))))
theorem-size     33
proof            (modus-ponens tm-23 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> 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      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-48.           (((A -> (B and 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-73395.        ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E)))), M:tm-23, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73396
in-theory        73396
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E))))
theorem-size     31
proof            (modus-ponens tm-22 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73396.        (((A and B) -> B) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E)))), M:tm-22, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73397
in-theory        73397
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E))))
theorem-size     31
proof            (modus-ponens tm-21 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73397.        (((A and B) -> A) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E)))), M:tm-21, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73398
in-theory        73398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     39
proof            (modus-ponens tm-20 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-20.           (A -> (((B -> (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-48.           (((A -> (B and 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-73398.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-20, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73399
in-theory        73399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E))))
theorem-size     31
proof            (modus-ponens tm-19 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-19.           (A -> ((B -> (C -> B)) 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-48.           (((A -> (B and 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-73399.        ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> (((C -> (D and C)) -> E) and ((D or (C -> (D and C))) -> E)))), M:tm-19, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73400
in-theory        73400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (not (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C)))
theorem-size     35
proof            (modus-ponens tm-9 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-9 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73400.        ((((A -> (B and A)) -> C) -> (not (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C))), M:tm-9, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73401
in-theory        73401
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)) -> D) -> ((((A -> (B and A)) -> C) or (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) -> D))
theorem-size     47
proof            (modus-ponens tm-8 tm-844 ((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-73401.        (((((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)) -> D) -> ((((A -> (B and A)) -> C) or (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) -> D)), M:tm-8, m:tm-844, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-73402
in-theory        73402
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C and B)) -> D) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D))))
theorem-size     27
proof            (modus-ponens tm-7 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-8)
proof-size       123
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-48.           (((A -> (B and 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-73402.        (A or (((B -> (C and B)) -> D) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D)))), M:tm-7, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73403
in-theory        73403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) or D)
theorem-size     27
proof            (modus-ponens tm-6 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-8)
proof-size       123
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-48.           (((A -> (B and 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-73403.        ((((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))) or D), M:tm-6, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73404
in-theory        73404
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C and B)) -> D) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-73404.        (A -> ((((B -> (C and B)) -> D) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D))) and A)), M:tm-5, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73405
in-theory        73405
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C and B)) -> D) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D))))
theorem-size     27
proof            (modus-ponens tm-1 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-8)
proof-size       123
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-48.           (((A -> (B and 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-73405.        (A -> (((B -> (C and B)) -> D) -> (((B -> (C and B)) -> D) and ((C or (B -> (C and B))) -> D)))), M:tm-1, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-73406
in-theory        73406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-808 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (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-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-73406.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-808, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73407
in-theory        73407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-757 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-48.           (((A -> (B and 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-73407.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-757, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73408
in-theory        73408
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 G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-708 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (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-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-73408.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-708, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73409
in-theory        73409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-665 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-48.           (((A -> (B and 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-73409.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-665, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73410
in-theory        73410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-622 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-73410.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-622, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73411
in-theory        73411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F)))
theorem-size     31
proof            (modus-ponens tm-609 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-73411.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73412
in-theory        73412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-605 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-73412.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-605, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73413
in-theory        73413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-73413.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-595, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73414
in-theory        73414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-550 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-73414.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-550, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73415
in-theory        73415
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-540 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-73415.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-540, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73416
in-theory        73416
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-530 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-73416.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-530, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73417
in-theory        73417
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-520 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-73417.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-520, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73418
in-theory        73418
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-510 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-73418.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-510, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73419
in-theory        73419
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-500 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-73419.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-500, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73420
in-theory        73420
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-490 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-73420.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-490, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73421
in-theory        73421
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-480 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-73421.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-480, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73422
in-theory        73422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-469 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-73422.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-469, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73423
in-theory        73423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G)))
theorem-size     31
proof            (modus-ponens tm-456 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-73423.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73424
in-theory        73424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-453 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-73424.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-453, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73425
in-theory        73425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-73425.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-443, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73426
in-theory        73426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-409 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-73426.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-409, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73427
in-theory        73427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-400 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-73427.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-400, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73428
in-theory        73428
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-391 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-73428.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-391, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73429
in-theory        73429
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-382 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-73429.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-382, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73430
in-theory        73430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-373 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-73430.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-373, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73431
in-theory        73431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-364 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-73431.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-364, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73432
in-theory        73432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-354 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-73432.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-354, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73433
in-theory        73433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G))))
theorem-size     33
proof            (modus-ponens tm-341 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
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-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-73433.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73434
in-theory        73434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-338 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-73434.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-338, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73435
in-theory        73435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-73435.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-327, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73436
in-theory        73436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73436.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-326, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73437
in-theory        73437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73437.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-325, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73438
in-theory        73438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-8)
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-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-73438.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-324, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73439
in-theory        73439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73439.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-323, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73440
in-theory        73440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G))
theorem-size     31
proof            (modus-ponens tm-322 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73440.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73441
in-theory        73441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F))
theorem-size     31
proof            (modus-ponens tm-320 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73441.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73442
in-theory        73442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     39
proof            (modus-ponens tm-318 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73442.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73443
in-theory        73443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F)))
theorem-size     31
proof            (modus-ponens tm-315 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-73443.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73444
in-theory        73444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-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-48.           (((A -> (B and 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-73444.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-311, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73445
in-theory        73445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F))
theorem-size     53
proof            (modus-ponens tm-310 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-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-48.           (((A -> (B and 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-73445.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)), M:tm-310, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73446
in-theory        73446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F)))
theorem-size     55
proof            (modus-ponens tm-309 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-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-48.           (((A -> (B and 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-73446.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F))), M:tm-309, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73447
in-theory        73447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     43
proof            (modus-ponens tm-308 tm-845 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
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-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-48.           (((A -> (B and 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-73447.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-308, m:tm-845, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73448
in-theory        73448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (A -> (B -> (A and B))))
theorem-size     33
proof            (modus-ponens tm-307 tm-845 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
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-48.           (((A -> (B and 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-73448.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-845, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73449
in-theory        73449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73449.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-305, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73450
in-theory        73450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-303 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-73450.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-303, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73451
in-theory        73451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-270 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-73451.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-270, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73452
in-theory        73452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-239 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-73452.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-239, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73453
in-theory        73453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-210 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-73453.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-210, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73454
in-theory        73454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-183 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-73454.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-183, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73455
in-theory        73455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-157 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-73455.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-157, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73456
in-theory        73456
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-147 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73456.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-147, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73457
in-theory        73457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-134 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-73457.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-134, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73458
in-theory        73458
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-125 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73458.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-125, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73459
in-theory        73459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-113 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-73459.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-113, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73460
in-theory        73460
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     45
proof            (modus-ponens tm-105 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-73460.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-105, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73461
in-theory        73461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-95 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-48.           (((A -> (B and 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-73461.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-95, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73462
in-theory        73462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-83 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-73462.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-83, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73463
in-theory        73463
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     31
proof            (modus-ponens tm-76 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-10 tm-8)
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-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-73463.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-76, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73464
in-theory        73464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     37
proof            (modus-ponens tm-69 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-9 tm-8)
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-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-73464.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-69, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73465
in-theory        73465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-54 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-73465.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-54, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73466
in-theory        73466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-42 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73466.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-42, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73467
in-theory        73467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-32 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73467.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-32, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73468
in-theory        73468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-23 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-73468.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-23, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73469
in-theory        73469
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-22 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73469.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-22, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73470
in-theory        73470
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-21 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73470.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-21, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73471
in-theory        73471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-20 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73471.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-20, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73472
in-theory        73472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-19 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-73472.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-19, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73473
in-theory        73473
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-7 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-7 tm-5 tm-8)
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-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-73473.        (A or ((B -> (C -> (B and C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-7, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73474
in-theory        73474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)
theorem-size     27
proof            (modus-ponens tm-6 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-6 tm-5 tm-8)
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-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-73474.        (((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F), M:tm-6, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73475
in-theory        73475
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8)
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-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-73475.        (A -> (((B -> (C -> (B and C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A)), M:tm-5, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73476
in-theory        73476
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-1 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-1 tm-5 tm-8)
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-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-73476.        (A -> ((B -> (C -> (B and C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-1, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73477
in-theory        73477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-808 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-73477.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-808, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73478
in-theory        73478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-757 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-73478.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-757, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73479
in-theory        73479
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 G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-708 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-73479.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-708, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73480
in-theory        73480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-665 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-73480.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-665, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73481
in-theory        73481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-622 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-8)
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-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-73481.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-622, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73482
in-theory        73482
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-73482.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73483
in-theory        73483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-605 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-73483.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-605, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73484
in-theory        73484
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-73484.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-595, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73485
in-theory        73485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-550 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-8)
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-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-73485.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-550, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73486
in-theory        73486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-540 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-73486.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-540, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73487
in-theory        73487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-530 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-8)
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-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-73487.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-530, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73488
in-theory        73488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-520 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-73488.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-520, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73489
in-theory        73489
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-510 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-73489.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-510, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73490
in-theory        73490
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-500 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-8)
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-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-73490.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-500, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73491
in-theory        73491
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-490 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-8)
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-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-73491.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-490, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73492
in-theory        73492
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-480 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-8)
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-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-73492.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-480, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73493
in-theory        73493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-469 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-8)
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-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-73493.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-469, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73494
in-theory        73494
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-73494.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73495
in-theory        73495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-453 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-73495.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-453, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73496
in-theory        73496
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-73496.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-443, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73497
in-theory        73497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-409 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-73497.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-409, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73498
in-theory        73498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-400 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-73498.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-400, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73499
in-theory        73499
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-391 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-73499.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-391, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73500
in-theory        73500
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-382 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-8)
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-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-73500.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-382, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73501
in-theory        73501
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-373 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-8)
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-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-73501.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-373, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73502
in-theory        73502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-364 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-8)
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-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-73502.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-364, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73503
in-theory        73503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-354 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-73503.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-354, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73504
in-theory        73504
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-73504.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73505
in-theory        73505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-338 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-73505.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-338, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73506
in-theory        73506
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73506.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-327, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73507
in-theory        73507
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-73507.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-326, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73508
in-theory        73508
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-73508.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-325, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73509
in-theory        73509
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-73509.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-324, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73510
in-theory        73510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-73510.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-323, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73511
in-theory        73511
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-73511.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73512
in-theory        73512
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-73512.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73513
in-theory        73513
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73513.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73514
in-theory        73514
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-73514.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73515
in-theory        73515
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-73515.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-311, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73516
in-theory        73516
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-73516.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)), M:tm-310, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73517
in-theory        73517
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-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-48.           (((A -> (B and 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-73517.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F))), M:tm-309, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73518
in-theory        73518
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     41
proof            (modus-ponens tm-308 tm-846 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
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-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-48.           (((A -> (B and 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-73518.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-308, m:tm-846, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73519
in-theory        73519
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((A and B) -> B))
theorem-size     29
proof            (modus-ponens tm-307 tm-846 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-48.           (((A -> (B and 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-73519.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((A and B) -> B)), M:tm-307, m:tm-846, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73520
in-theory        73520
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-48.           (((A -> (B and 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-73520.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-305, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73521
in-theory        73521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-303 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-73521.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-303, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73522
in-theory        73522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-270 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-73522.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-270, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73523
in-theory        73523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-239 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8)
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-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-73523.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-239, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73524
in-theory        73524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-210 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-73524.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-210, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73525
in-theory        73525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-183 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-73525.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-183, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73526
in-theory        73526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-157 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-73526.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-157, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73527
in-theory        73527
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-147 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-73527.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-147, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73528
in-theory        73528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-134 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-8)
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-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-73528.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-134, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73529
in-theory        73529
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-125 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-73529.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-125, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73530
in-theory        73530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-113 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-8)
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-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-73530.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-113, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73531
in-theory        73531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-105 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-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-73531.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-105, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73532
in-theory        73532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-95 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-8)
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-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-73532.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-95, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73533
in-theory        73533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-83 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-73533.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-83, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73534
in-theory        73534
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     29
proof            (modus-ponens tm-76 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-10 tm-4 tm-8)
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-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-73534.        (((not (not A)) -> A) and (((B and C) -> C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-76, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73535
in-theory        73535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-69 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-9 tm-4 tm-8)
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-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-73535.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-69, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73536
in-theory        73536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-54 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-73536.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-54, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73537
in-theory        73537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-42 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-42.           (A -> ((B -> (C 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-48.           (((A -> (B and 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-73537.        ((A -> (B or A)) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-42, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73538
in-theory        73538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-32 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-32.           (A -> ((B -> (B 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-48.           (((A -> (B and 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-73538.        ((A -> (A or B)) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-32, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73539
in-theory        73539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-23 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-73539.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-23, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73540
in-theory        73540
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-22 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-73540.        (((A and B) -> B) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-22, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73541
in-theory        73541
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-21 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-73541.        (((A and B) -> A) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-21, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73542
in-theory        73542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-20 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-73542.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-20, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73543
in-theory        73543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-19 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-19.           (A -> ((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-48.           (((A -> (B and 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-73543.        ((A -> (B -> A)) and (((C and D) -> D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-19, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73544
in-theory        73544
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-7 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8)
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-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-73544.        (A or (((B and C) -> C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-7, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73545
in-theory        73545
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-6 tm-5 tm-4 tm-8)
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-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-73545.        ((((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F), M:tm-6, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73546
in-theory        73546
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-48.           (((A -> (B and 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-73546.        (A -> ((((B and C) -> C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A)), M:tm-5, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73547
in-theory        73547
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-1 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-1 tm-5 tm-4 tm-8)
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-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-73547.        (A -> (((B and C) -> C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-1, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73548
in-theory        73548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-808 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48.           (((A -> (B and 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-73548.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-808, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73549
in-theory        73549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-757 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-48.           (((A -> (B and 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-73549.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-757, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73550
in-theory        73550
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 G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-708 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-48.           (((A -> (B and 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-73550.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-708, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73551
in-theory        73551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-665 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48.           (((A -> (B and 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-73551.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-665, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73552
in-theory        73552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-622 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-8)
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-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-73552.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-622, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73553
in-theory        73553
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-73553.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73554
in-theory        73554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-605 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-73554.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-605, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73555
in-theory        73555
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-73555.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-595, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73556
in-theory        73556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-550 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-8)
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-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-73556.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-550, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73557
in-theory        73557
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-540 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-73557.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-540, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73558
in-theory        73558
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-530 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-8)
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-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-73558.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-530, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73559
in-theory        73559
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-520 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-73559.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-520, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73560
in-theory        73560
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-510 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-8)
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-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-73560.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-510, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73561
in-theory        73561
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-500 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-73561.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-500, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73562
in-theory        73562
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-490 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-8)
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-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-73562.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-490, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73563
in-theory        73563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-480 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-8)
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-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-73563.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-480, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73564
in-theory        73564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-469 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-8)
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-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-73564.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-469, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73565
in-theory        73565
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-73565.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73566
in-theory        73566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-453 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-73566.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-453, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73567
in-theory        73567
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-73567.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-443, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73568
in-theory        73568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-409 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-73568.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-409, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73569
in-theory        73569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-400 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-73569.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-400, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73570
in-theory        73570
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-391 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-8)
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-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-73570.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-391, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73571
in-theory        73571
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-382 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-73571.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-382, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73572
in-theory        73572
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-373 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-8)
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-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-73572.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-373, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73573
in-theory        73573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-364 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-8)
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-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-73573.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-364, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73574
in-theory        73574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-354 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-73574.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-354, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73575
in-theory        73575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-73575.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73576
in-theory        73576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-338 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-73576.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-338, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73577
in-theory        73577
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73577.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-327, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73578
in-theory        73578
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-73578.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-326, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73579
in-theory        73579
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-73579.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-325, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73580
in-theory        73580
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-73580.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-324, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73581
in-theory        73581
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-73581.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-323, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73582
in-theory        73582
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-73582.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73583
in-theory        73583
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-73583.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73584
in-theory        73584
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73584.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73585
in-theory        73585
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-73585.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73586
in-theory        73586
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-73586.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-311, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73587
in-theory        73587
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-73587.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)), M:tm-310, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73588
in-theory        73588
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 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-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-48.           (((A -> (B and 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-73588.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F))), M:tm-309, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73589
in-theory        73589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     41
proof            (modus-ponens tm-308 tm-847 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-73589.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-308, m:tm-847, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73590
in-theory        73590
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((A and B) -> A))
theorem-size     29
proof            (modus-ponens tm-307 tm-847 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
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-48.           (((A -> (B and 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-73590.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((A and B) -> A)), M:tm-307, m:tm-847, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73591
in-theory        73591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-48.           (((A -> (B and 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-73591.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-305, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73592
in-theory        73592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-303 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-73592.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-303, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73593
in-theory        73593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-270 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8)
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-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-73593.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-270, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73594
in-theory        73594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-239 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-73594.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-239, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73595
in-theory        73595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-210 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-73595.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-210, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73596
in-theory        73596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-183 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-73596.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-183, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73597
in-theory        73597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-157 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-8)
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-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-73597.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-157, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73598
in-theory        73598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-147 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-73598.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-147, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73599
in-theory        73599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-134 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-73599.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-134, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73600
in-theory        73600
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-125 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-73600.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-125, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73601
in-theory        73601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-113 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-8)
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-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-73601.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-113, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73602
in-theory        73602
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-105 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-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-73602.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-105, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73603
in-theory        73603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-95 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-8)
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-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-73603.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-95, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73604
in-theory        73604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-83 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-73604.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-83, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73605
in-theory        73605
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     29
proof            (modus-ponens tm-76 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-10 tm-3 tm-8)
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-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-73605.        (((not (not A)) -> A) and (((B and C) -> B) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-76, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73606
in-theory        73606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-69 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-9 tm-3 tm-8)
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-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-73606.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-69, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73607
in-theory        73607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-54 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48.           (((A -> (B and 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-73607.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-54, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73608
in-theory        73608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-42 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-42.           (A -> ((B -> (C 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-48.           (((A -> (B and 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-73608.        ((A -> (B or A)) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-42, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73609
in-theory        73609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-32 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-32.           (A -> ((B -> (B 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-48.           (((A -> (B and 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-73609.        ((A -> (A or B)) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-32, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73610
in-theory        73610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-23 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-73610.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-23, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73611
in-theory        73611
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-22 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-73611.        (((A and B) -> B) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-22, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73612
in-theory        73612
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-21 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-73612.        (((A and B) -> A) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-21, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73613
in-theory        73613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-20 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-73613.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-20, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73614
in-theory        73614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-19 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-19.           (A -> ((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-48.           (((A -> (B and 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-73614.        ((A -> (B -> A)) and (((C and D) -> C) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-19, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73615
in-theory        73615
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-7 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8)
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-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-73615.        (A or (((B and C) -> B) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-7, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73616
in-theory        73616
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-6 tm-5 tm-3 tm-8)
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-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-73616.        ((((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F), M:tm-6, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73617
in-theory        73617
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-48.           (((A -> (B and 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-73617.        (A -> ((((B and C) -> B) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A)), M:tm-5, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73618
in-theory        73618
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-1 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-1 tm-5 tm-3 tm-8)
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-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-73618.        (A -> (((B and C) -> B) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-1, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73619
in-theory        73619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-808 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-73619.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-808, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73620
in-theory        73620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-757 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-48.           (((A -> (B and 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-73620.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-757, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73621
in-theory        73621
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 H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     57
proof            (modus-ponens tm-708 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-48.           (((A -> (B and 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-73621.        (((((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 H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-708, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73622
in-theory        73622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-665 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-48.           (((A -> (B and 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-73622.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-665, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73623
in-theory        73623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-622 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
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-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-73623.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-622, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73624
in-theory        73624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H or G)))
theorem-size     37
proof            (modus-ponens tm-609 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73624.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73625
in-theory        73625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-605 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-73625.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-605, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73626
in-theory        73626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-73626.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-595, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73627
in-theory        73627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-550 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
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-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-73627.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-550, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73628
in-theory        73628
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-540 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-73628.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-540, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73629
in-theory        73629
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-530 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
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-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-73629.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-530, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73630
in-theory        73630
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-520 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-73630.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-520, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73631
in-theory        73631
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-510 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
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-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-73631.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-510, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73632
in-theory        73632
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-500 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
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-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-73632.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-500, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73633
in-theory        73633
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 H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-490 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-73633.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-490, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73634
in-theory        73634
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-480 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
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-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-73634.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-480, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73635
in-theory        73635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-469 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
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-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-73635.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-469, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73636
in-theory        73636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (G or H)))
theorem-size     37
proof            (modus-ponens tm-456 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73636.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73637
in-theory        73637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-453 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-73637.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-453, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73638
in-theory        73638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-73638.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-443, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73639
in-theory        73639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-409 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-73639.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-409, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73640
in-theory        73640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-400 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-73640.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-400, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73641
in-theory        73641
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-391 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
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-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-73641.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-391, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73642
in-theory        73642
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-382 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
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-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-73642.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-382, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73643
in-theory        73643
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 H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-373 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-73643.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-373, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73644
in-theory        73644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-364 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
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-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-73644.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-364, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73645
in-theory        73645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-354 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-73645.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-354, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73646
in-theory        73646
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H -> (G and H))))
theorem-size     39
proof            (modus-ponens tm-341 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73646.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73647
in-theory        73647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-338 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-73647.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-338, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73648
in-theory        73648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73648.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-327, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73649
in-theory        73649
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73649.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-326, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73650
in-theory        73650
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73650.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-325, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73651
in-theory        73651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-73651.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-324, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73652
in-theory        73652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-73652.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-323, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73653
in-theory        73653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G and H) -> H))
theorem-size     37
proof            (modus-ponens tm-322 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73653.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73654
in-theory        73654
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G and H) -> G))
theorem-size     37
proof            (modus-ponens tm-320 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73654.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73655
in-theory        73655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     45
proof            (modus-ponens tm-318 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73655.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73656
in-theory        73656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H -> G)))
theorem-size     37
proof            (modus-ponens tm-315 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73656.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73657
in-theory        73657
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-73657.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-311, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73658
in-theory        73658
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) or G))
theorem-size     65
proof            (modus-ponens tm-310 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-73658.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) or G)), M:tm-310, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73659
in-theory        73659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and G)))
theorem-size     67
proof            (modus-ponens tm-309 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 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-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-48.           (((A -> (B and 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-73659.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and G))), M:tm-309, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73660
in-theory        73660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     49
proof            (modus-ponens tm-308 tm-848 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-73660.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-308, m:tm-848, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))
================================================================
tm-name          tm-73661
in-theory        73661
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-307 tm-848 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73661.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-848, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))
================================================================
tm-name          tm-73662
in-theory        73662
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-1.            (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-48.           (((A -> (B and 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-73662.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-305, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73663
in-theory        73663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-303 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-73663.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-303, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73664
in-theory        73664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-270 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-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-73664.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-270, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73665
in-theory        73665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-239 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
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-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-73665.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-239, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73666
in-theory        73666
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 H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-210 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-48.           (((A -> (B and 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-73666.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-210, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73667
in-theory        73667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-183 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-73667.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-183, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73668
in-theory        73668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-157 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
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-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-73668.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-157, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73669
in-theory        73669
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 G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-147 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73669.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-147, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73670
in-theory        73670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-134 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
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-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-73670.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-134, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73671
in-theory        73671
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 G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-125 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73671.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-125, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73672
in-theory        73672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-113 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73672.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-113, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73673
in-theory        73673
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 G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-105 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-73673.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-105, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73674
in-theory        73674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-95 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-73674.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-95, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73675
in-theory        73675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-83 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-73675.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-83, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73676
in-theory        73676
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     37
proof            (modus-ponens tm-76 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
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-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-73676.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-76, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73677
in-theory        73677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-69 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
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-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-73677.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-69, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73678
in-theory        73678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-54 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-48.           (((A -> (B and 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-73678.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-54, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73679
in-theory        73679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-42 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-42.           (A -> ((B -> (C or B)) and 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-48.           (((A -> (B and 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-73679.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-42, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73680
in-theory        73680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-32 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-32.           (A -> ((B -> (B or C)) and 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-48.           (((A -> (B and 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-73680.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-32, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73681
in-theory        73681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-23 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-73681.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-23, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73682
in-theory        73682
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-22 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-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-73682.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-22, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73683
in-theory        73683
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-21 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
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-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-73683.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-21, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73684
in-theory        73684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-20 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) 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-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-73684.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-20, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73685
in-theory        73685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-19 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-19.           (A -> ((B -> (C -> B)) 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-48.           (((A -> (B and 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-73685.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-19, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73686
in-theory        73686
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-7 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8)
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-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-73686.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-7, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73687
in-theory        73687
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) or G)
theorem-size     33
proof            (modus-ponens tm-6 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-8)
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-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-73687.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) or G), M:tm-6, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73688
in-theory        73688
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))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-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-73688.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))) and A)), M:tm-5, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73689
in-theory        73689
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-1 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-8)
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-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-73689.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-1, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-73690
in-theory        73690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-808 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48.           (((A -> (B and 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-73690.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-808, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73691
in-theory        73691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-757 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48.           (((A -> (B and 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-73691.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-757, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73692
in-theory        73692
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 G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-708 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-48.           (((A -> (B and 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-73692.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-708, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73693
in-theory        73693
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-665 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-73693.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-665, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73694
in-theory        73694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-622 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-73694.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-622, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73695
in-theory        73695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-73695.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73696
in-theory        73696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-605 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-73696.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-605, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73697
in-theory        73697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-73697.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-595, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73698
in-theory        73698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-550 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8)
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-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-73698.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-550, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73699
in-theory        73699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-540 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-73699.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-540, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73700
in-theory        73700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-530 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8)
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-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-73700.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-530, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73701
in-theory        73701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-520 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-73701.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-520, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73702
in-theory        73702
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-510 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8)
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-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-73702.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-510, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73703
in-theory        73703
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-500 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
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-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-73703.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-500, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73704
in-theory        73704
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-490 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-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-73704.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-490, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73705
in-theory        73705
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-480 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-73705.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-480, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73706
in-theory        73706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-469 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-73706.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-469, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73707
in-theory        73707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-73707.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73708
in-theory        73708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-453 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-73708.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-453, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73709
in-theory        73709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-73709.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-443, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73710
in-theory        73710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-409 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-73710.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-409, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73711
in-theory        73711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-400 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-73711.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-400, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73712
in-theory        73712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-391 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8)
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-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-73712.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-391, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73713
in-theory        73713
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-382 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
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-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-73713.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-382, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73714
in-theory        73714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-373 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-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-73714.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-373, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73715
in-theory        73715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-364 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-73715.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-364, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73716
in-theory        73716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-354 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-73716.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-354, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73717
in-theory        73717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-73717.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73718
in-theory        73718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-338 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-73718.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-338, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73719
in-theory        73719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73719.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-327, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73720
in-theory        73720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-73720.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-326, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73721
in-theory        73721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-73721.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-325, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73722
in-theory        73722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-73722.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-324, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73723
in-theory        73723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-73723.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-323, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73724
in-theory        73724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-73724.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73725
in-theory        73725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-73725.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73726
in-theory        73726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73726.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73727
in-theory        73727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-73727.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73728
in-theory        73728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-73728.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F or ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-311, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73729
in-theory        73729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-73729.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)), M:tm-310, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73730
in-theory        73730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-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-48.           (((A -> (B and 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-73730.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and F))), M:tm-309, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73731
in-theory        73731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     41
proof            (modus-ponens tm-308 tm-849 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-73731.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-308, m:tm-849, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73732
in-theory        73732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (A -> (B -> A)))
theorem-size     29
proof            (modus-ponens tm-307 tm-849 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-48.           (((A -> (B and 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-73732.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (A -> (B -> A))), M:tm-307, m:tm-849, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))
================================================================
tm-name          tm-73733
in-theory        73733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-48.           (((A -> (B and 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-73733.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and (F -> ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))), M:tm-305, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73734
in-theory        73734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-303 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-73734.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-303, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73735
in-theory        73735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-270 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
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-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-73735.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-270, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73736
in-theory        73736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-239 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
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-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-73736.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-239, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73737
in-theory        73737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-210 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-73737.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-210, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73738
in-theory        73738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     33
proof            (modus-ponens tm-183 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-73738.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-183, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73739
in-theory        73739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-157 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-73739.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-157, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73740
in-theory        73740
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-147 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-73740.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-147, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73741
in-theory        73741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-134 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-73741.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-134, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73742
in-theory        73742
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-125 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-73742.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-125, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73743
in-theory        73743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-113 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-73743.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-113, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73744
in-theory        73744
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-105 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-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-73744.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-105, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73745
in-theory        73745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-95 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-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-73745.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-95, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73746
in-theory        73746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     31
proof            (modus-ponens tm-83 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-73746.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-83, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73747
in-theory        73747
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     29
proof            (modus-ponens tm-76 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8)
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-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-73747.        (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-76, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73748
in-theory        73748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-69 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8)
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-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-73748.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-69, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73749
in-theory        73749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-54 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48.           (((A -> (B and 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-73749.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-54, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73750
in-theory        73750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-42 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-42.           (A -> ((B -> (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-48.           (((A -> (B and 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-73750.        ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-42, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73751
in-theory        73751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-32 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-32.           (A -> ((B -> (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-48.           (((A -> (B and 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-73751.        ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-32, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73752
in-theory        73752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-23 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-73752.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-23, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73753
in-theory        73753
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-22 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-73753.        (((A and B) -> B) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-22, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73754
in-theory        73754
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-21 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-73754.        (((A and B) -> A) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-21, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73755
in-theory        73755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-20 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-73755.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-20, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73756
in-theory        73756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-19 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) 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-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-73756.        ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-19, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73757
in-theory        73757
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-7 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-7 tm-5 tm-1 tm-8)
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-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-73757.        (A or ((B -> (C -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-7, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73758
in-theory        73758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-6 tm-5 tm-1 tm-8)
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-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-73758.        (((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) or F), M:tm-6, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73759
in-theory        73759
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
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-48.           (((A -> (B and 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-73759.        (A -> (((B -> (C -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and A)), M:tm-5, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73760
in-theory        73760
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-1 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-1 tm-5 tm-8)
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-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-73760.        (A -> ((B -> (C -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-1, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-73761
in-theory        73761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (A -> (B and A))))
theorem-size     13
proof            (modus-ponens tm-850 tm-1 ((Am (-> A (and B A))) (C (-> Bm (-> A (and B A))))))
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-12.           ((A -> B) -> (A -> A)), M: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-73761.        ((A -> (B and A)) -> (C -> (A -> (B and A)))), M:tm-850, m:tm-1, u:((Am (-> A (and B A))) (C (-> Bm (-> A (and B A)))))
================================================================
tm-name          tm-73762
in-theory        73762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> ((A -> (B and A)) and C)))
theorem-size     15
proof            (modus-ponens tm-850 tm-5 ((Am (-> A (and B A))) (C (-> Bm (and (-> A (and B A)) Bm)))))
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-48.           (((A -> (B and 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-73762.        ((A -> (B and A)) -> (C -> ((A -> (B and A)) and C))), M:tm-850, m:tm-5, u:((Am (-> A (and B A))) (C (-> Bm (and (-> A (and B A)) Bm))))
================================================================
tm-name          tm-73763
in-theory        73763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) or C))
theorem-size     13
proof            (modus-ponens tm-850 tm-6 ((Am (-> A (and B A))) (C (or (-> A (and B A)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       95
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-73763.        ((A -> (B and A)) -> ((A -> (B and A)) or C)), M:tm-850, m:tm-6, u:((Am (-> A (and B A))) (C (or (-> A (and B A)) Bm)))
================================================================
tm-name          tm-73764
in-theory        73764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C or (A -> (B and A))))
theorem-size     13
proof            (modus-ponens tm-850 tm-7 ((Am (-> A (and B A))) (C (or Bm (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       95
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-73764.        ((A -> (B and A)) -> (C or (A -> (B and A)))), M:tm-850, m:tm-7, u:((Am (-> A (and B A))) (C (or Bm (-> A (and B A)))))
================================================================
tm-name          tm-73765
in-theory        73765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((B and A) -> C) -> ((A or (B and A)) -> C)))
theorem-size     19
proof            (modus-ponens tm-850 tm-8 ((A Am) (Bm (and B Am)) (C (-> (-> (and B Am) Cm) (-> (or Am (and B Am)) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-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-73765.        ((A -> (B and A)) -> (((B and A) -> C) -> ((A or (B and A)) -> C))), M:tm-850, m:tm-8, u:((A Am) (Bm (and B Am)) (C (-> (-> (and B Am) Cm) (-> (or Am (and B Am)) Cm))))
================================================================
tm-name          tm-73766
in-theory        73766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (not (B and A))) -> (not A)))
theorem-size     15
proof            (modus-ponens tm-850 tm-9 ((A Am) (Bm (and B Am)) (C (-> (-> Am (not (and B Am))) (not Am)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-73766.        ((A -> (B and A)) -> ((A -> (not (B and A))) -> (not A))), M:tm-850, m:tm-9, u:((A Am) (Bm (and B Am)) (C (-> (-> Am (not (and B Am))) (not Am))))
================================================================
tm-name          tm-73767
in-theory        73767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-850 tm-11 ((Am (-> A (and B A))) (C (-> Bm (-> Cm Bm)))))
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-12.           ((A -> B) -> (A -> A)), M: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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-73767.        ((A -> (B and A)) -> (C -> (D -> C))), M:tm-850, m:tm-11, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-73768
in-theory        73768
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (A -> A))
theorem-size     9
proof            (modus-ponens tm-850 tm-12 ((A Am) (Bm (and B Am)) (C (-> Am Am))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-73768.        ((A -> (B and A)) -> (A -> A)), M:tm-850, m:tm-12, u:((A Am) (Bm (and B Am)) (C (-> Am Am)))
================================================================
tm-name          tm-73769
in-theory        73769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-850 tm-14 ((Am (-> A (and B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm 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-12.           ((A -> B) -> (A -> A)), M: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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-73769.        ((A -> (B and A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-850, m:tm-14, u:((Am (-> A (and B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-73770
in-theory        73770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-850 tm-16 ((Am (-> A (and B A))) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-73770.        ((A -> (B and A)) -> ((C and D) -> C)), M:tm-850, m:tm-16, u:((Am (-> A (and B A))) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-73771
in-theory        73771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-850 tm-18 ((Am (-> A (and B A))) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-73771.        ((A -> (B and A)) -> ((C and D) -> D)), M:tm-850, m:tm-18, u:((Am (-> A (and B A))) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-73772
in-theory        73772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D -> C)) and (A -> (B and A))))
theorem-size     17
proof            (modus-ponens tm-850 tm-19 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 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-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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-73772.        ((A -> (B and A)) -> ((C -> (D -> C)) and (A -> (B and A)))), M:tm-850, m:tm-19, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-73773
in-theory        73773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-850 tm-20 ((Am (-> A (and B A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-73773.        ((A -> (B and A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A)))), M:tm-850, 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-73774
in-theory        73774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C and D) -> C) and (A -> (B and A))))
theorem-size     17
proof            (modus-ponens tm-850 tm-21 ((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Bm) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-73774.        ((A -> (B and A)) -> (((C and D) -> C) and (A -> (B and A)))), M:tm-850, m:tm-21, u:((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Bm) (-> A (and B A)))))
================================================================
tm-name          tm-73775
in-theory        73775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C and D) -> D) and (A -> (B and A))))
theorem-size     17
proof            (modus-ponens tm-850 tm-22 ((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Cm) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-73775.        ((A -> (B and A)) -> (((C and D) -> D) and (A -> (B and A)))), M:tm-850, m:tm-22, u:((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Cm) (-> A (and B A)))))
================================================================
tm-name          tm-73776
in-theory        73776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D -> (C and D))) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-23 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and B A))))))
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-12.           ((A -> B) -> (A -> A)), M: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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-73776.        ((A -> (B and A)) -> ((C -> (D -> (C and D))) and (A -> (B and A)))), M:tm-850, m:tm-23, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73777
in-theory        73777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (A -> (A and (B and A))))
theorem-size     13
proof            (modus-ponens tm-850 tm-24 ((A Am) (Bm (and B Am)) (C (-> Am (and Am (and B Am))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-73777.        ((A -> (B and A)) -> (A -> (A and (B and A)))), M:tm-850, m:tm-24, u:((A Am) (Bm (and B Am)) (C (-> Am (and Am (and B Am)))))
================================================================
tm-name          tm-73778
in-theory        73778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-850 tm-25 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-73778.        ((A -> (B and A)) -> (C -> (D -> (C and D)))), M:tm-850, m:tm-25, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-73779
in-theory        73779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (C or D)) and (A -> (B and A))))
theorem-size     17
proof            (modus-ponens tm-850 tm-32 ((Am (-> A (and B A))) (C (and (-> Bm (or Bm Cm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-73779.        ((A -> (B and A)) -> ((C -> (C or D)) and (A -> (B and A)))), M:tm-850, m:tm-32, u:((Am (-> A (and B A))) (C (and (-> Bm (or Bm Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-73780
in-theory        73780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-850 tm-33 ((Am (-> A (and B A))) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-73780.        ((A -> (B and A)) -> (C -> (C or D))), M:tm-850, m:tm-33, u:((Am (-> A (and B A))) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-73781
in-theory        73781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D or C)) and (A -> (B and A))))
theorem-size     17
proof            (modus-ponens tm-850 tm-42 ((Am (-> A (and B A))) (C (and (-> Bm (or Cm Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-73781.        ((A -> (B and A)) -> ((C -> (D or C)) and (A -> (B and A)))), M:tm-850, m:tm-42, u:((Am (-> A (and B A))) (C (and (-> Bm (or Cm Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-73782
in-theory        73782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-850 tm-43 ((Am (-> A (and B A))) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-73782.        ((A -> (B and A)) -> (C -> (D or C))), M:tm-850, m:tm-43, u:((Am (-> A (and B A))) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-73783
in-theory        73783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C and (A -> B))) -> ((B or (A -> B)) -> (C and (A -> B))))
theorem-size     21
proof            (modus-ponens tm-850 tm-44 ((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (and B (-> Am Bm))))))
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-12.           ((A -> B) -> (A -> A)), M: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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-73783.        (((A -> B) -> (C and (A -> B))) -> ((B or (A -> B)) -> (C and (A -> B)))), M:tm-850, m:tm-44, u:((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (and B (-> Am Bm)))))
================================================================
tm-name          tm-73784
in-theory        73784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       169
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-73784.        ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C))))), M:tm-850, 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-73785
in-theory        73785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((A and C) or A) -> (B and A)))
theorem-size     15
proof            (modus-ponens tm-850 tm-46 ((A Am) (Bm (and B Am)) (C (-> (or (and Am Cm) Am) (and B Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-73785.        ((A -> (B and A)) -> (((A and C) or A) -> (B and A))), M:tm-850, m:tm-46, u:((A Am) (Bm (and B Am)) (C (-> (or (and Am Cm) Am) (and B Am))))
================================================================
tm-name          tm-73786
in-theory        73786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C and A) or A) -> (B and A)))
theorem-size     15
proof            (modus-ponens tm-850 tm-47 ((A Am) (Bm (and B Am)) (C (-> (or (and Cm Am) Am) (and B Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-73786.        ((A -> (B and A)) -> (((C and A) or A) -> (B and A))), M:tm-850, m:tm-47, u:((A Am) (Bm (and B Am)) (C (-> (or (and Cm Am) Am) (and B Am))))
================================================================
tm-name          tm-73787
in-theory        73787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C and (A -> (B and A)))) -> ((B or (A -> (B and A))) -> (C and (A -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-850 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-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-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-73787.        (((A -> (B and A)) -> (C and (A -> (B and A)))) -> ((B or (A -> (B and A))) -> (C and (A -> (B and A))))), M:tm-850, 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-73788
in-theory        73788
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C and (A or B))) -> ((A or (A or B)) -> (C and (A or B))))
theorem-size     21
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-6)
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-73788.        (((A or B) -> (C and (A or B))) -> ((A or (A or B)) -> (C and (A or B)))), M:tm-850, 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-73789
in-theory        73789
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C and (A or B))) -> ((B or (A or B)) -> (C and (A or B))))
theorem-size     21
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-7)
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-73789.        (((A or B) -> (C and (A or B))) -> ((B or (A or B)) -> (C and (A or B)))), M:tm-850, 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-73790
in-theory        73790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B)))))
theorem-size     47
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       177
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-73790.        ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B))))), M:tm-850, 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-73791
in-theory        73791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-850 tm-54 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-73791.        ((A -> (B and A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> (B and A)))), M:tm-850, 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-73792
in-theory        73792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-850 tm-56 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or 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-12.           ((A -> B) -> (A -> A)), M: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-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-73792.        ((A -> (B and A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-850, m:tm-56, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-73793
in-theory        73793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> (C and ((A -> (not B)) -> (not A)))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (C and ((A -> (not B)) -> (not A)))))
theorem-size     39
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-9)
proof-size       163
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-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-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-73793.        ((((A -> (not B)) -> (not A)) -> (C and ((A -> (not B)) -> (not A)))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (C and ((A -> (not B)) -> (not A))))), M:tm-850, 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-73794
in-theory        73794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> (B and A))))
theorem-size     23
proof            (modus-ponens tm-850 tm-69 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-9)
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-73794.        ((A -> (B and A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> (B and A)))), M:tm-850, 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-73795
in-theory        73795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-850 tm-71 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-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-73795.        ((A -> (B and A)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-850, m:tm-71, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-73796
in-theory        73796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((not (not A)) or A) -> (B and A)))
theorem-size     15
proof            (modus-ponens tm-850 tm-73 ((A Am) (Bm (and B Am)) (C (-> (or (not (not Am)) Am) (and B Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-10)
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-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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-73796.        ((A -> (B and A)) -> (((not (not A)) or A) -> (B and A))), M:tm-850, m:tm-73, u:((A Am) (Bm (and B Am)) (C (-> (or (not (not Am)) Am) (and B Am))))
================================================================
tm-name          tm-73797
in-theory        73797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((not (not C)) -> C) and (A -> (B and A))))
theorem-size     17
proof            (modus-ponens tm-850 tm-76 ((Am (-> A (and B A))) (C (and (-> (not (not Bm)) Bm) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-10)
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-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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-73797.        ((A -> (B and A)) -> (((not (not C)) -> C) and (A -> (B and A)))), M:tm-850, m:tm-76, u:((Am (-> A (and B A))) (C (and (-> (not (not Bm)) Bm) (-> A (and B A)))))
================================================================
tm-name          tm-73798
in-theory        73798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-850 tm-78 ((Am (-> A (and B A))) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-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-73798.        ((A -> (B and A)) -> ((not (not C)) -> C)), M:tm-850, m:tm-78, u:((Am (-> A (and B A))) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-73799
in-theory        73799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> (C and (A -> (B -> A)))) -> ((D or (A -> (B -> A))) -> (C and (A -> (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-850 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-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-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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-73799.        (((A -> (B -> A)) -> (C and (A -> (B -> A)))) -> ((D or (A -> (B -> A))) -> (C and (A -> (B -> A))))), M:tm-850, 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-73800
in-theory        73800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D -> (E -> D))) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-83 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (and B A))))))
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-12.           ((A -> B) -> (A -> A)), M: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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-73800.        ((A -> (B and A)) -> ((C -> (D -> (E -> D))) and (A -> (B and A)))), M:tm-850, m:tm-83, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73801
in-theory        73801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (A -> (C -> (B and A))))
theorem-size     13
proof            (modus-ponens tm-850 tm-84 ((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and B Am))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-73801.        ((A -> (B and A)) -> (A -> (C -> (B and A)))), M:tm-850, m:tm-84, u:((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and B Am)))))
================================================================
tm-name          tm-73802
in-theory        73802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-850 tm-85 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm Cm))))))
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-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-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-73802.        ((A -> (B and A)) -> (C -> (D -> (E -> D)))), M:tm-850, m:tm-85, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-73803
in-theory        73803
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (A -> (B and A)))
theorem-size     11
proof            (modus-ponens tm-850 tm-86 ((Am (-> A (and B A))) (C (-> A (and B A)))))
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-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-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-73803.        ((A -> (B and A)) -> (A -> (B and A))), M:tm-850, m:tm-86, u:((Am (-> A (and B A))) (C (-> A (and B A))))
================================================================
tm-name          tm-73804
in-theory        73804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> (B and (A -> A))) -> (((A -> C) or (A -> A)) -> (B and (A -> A))))
theorem-size     23
proof            (modus-ponens tm-850 tm-92 ((A (-> Am Am)) (Bm (and B (-> Am Am))) (C (-> (or (-> Am Cm) (-> Am Am)) (and B (-> Am Am))))))
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-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-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-73804.        (((A -> A) -> (B and (A -> A))) -> (((A -> C) or (A -> A)) -> (B and (A -> A)))), M:tm-850, 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-73805
in-theory        73805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> D) -> (C -> C)) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-95 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-73805.        ((A -> (B and A)) -> (((C -> D) -> (C -> C)) and (A -> (B and A)))), M:tm-850, m:tm-95, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-73806
in-theory        73806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-850 tm-97 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-73806.        ((A -> (B and A)) -> ((C -> D) -> (C -> C))), M:tm-850, m:tm-97, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-73807
in-theory        73807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> (D and ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-73807.        ((((A -> (B -> C)) -> (A -> C)) -> (D and ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D and ((A -> (B -> C)) -> (A -> C))))), M:tm-850, 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-73808
in-theory        73808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> (B and A))))
theorem-size     31
proof            (modus-ponens tm-850 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-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-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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-73808.        ((A -> (B and A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> (B and A)))), M:tm-850, 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-73809
in-theory        73809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-850 tm-107 ((Am (-> A (and B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 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-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-13.           (((A -> (B -> C)) -> (A -> 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-73809.        ((A -> (B and A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-850, m:tm-107, u:((Am (-> A (and B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-73810
in-theory        73810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-14.           (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-73810.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (D and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))), M:tm-850, 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-73811
in-theory        73811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-850 tm-113 ((Am (-> A (and B A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-73811.        ((A -> (B and A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A)))), M:tm-850, 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-73812
in-theory        73812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-850 tm-115 ((Am (-> A (and B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-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-14.           (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-73812.        ((A -> (B and A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-850, m:tm-115, u:((Am (-> A (and B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-73813
in-theory        73813
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> (D and (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D and (((A -> B) and C) -> B))))
theorem-size     43
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-3)
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-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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-73813.        (((((A -> B) and C) -> B) -> (D and (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D and (((A -> B) and C) -> B)))), M:tm-850, 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-73814
in-theory        73814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 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-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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-73814.        ((A -> (B and A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> (B and A)))), M:tm-850, 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-73815
in-theory        73815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-850 tm-127 ((Am (-> A (and B A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
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-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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-73815.        ((A -> (B and A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-850, m:tm-127, u:((Am (-> A (and B A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-73816
in-theory        73816
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> (C and ((A and B) -> A))) -> ((D or ((A and B) -> A)) -> (C and ((A and B) -> A))))
theorem-size     29
proof            (modus-ponens tm-850 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-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-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-3.            ((A 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-73816.        ((((A and B) -> A) -> (C and ((A and B) -> A))) -> ((D or ((A and B) -> A)) -> (C and ((A and B) -> A)))), M:tm-850, 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-73817
in-theory        73817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> ((D and E) -> D)) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-134 ((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-73817.        ((A -> (B and A)) -> ((C -> ((D and E) -> D)) and (A -> (B and A)))), M:tm-850, m:tm-134, u:((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-73818
in-theory        73818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (A -> B))
theorem-size     9
proof            (modus-ponens tm-850 tm-135 ((Cm Am) (B Bm) (A Am) (C (-> Am Bm))))
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-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-3.            ((A 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-73818.        ((A -> (B and A)) -> (A -> B)), M:tm-850, m:tm-135, u:((Cm Am) (B Bm) (A Am) (C (-> Am Bm)))
================================================================
tm-name          tm-73819
in-theory        73819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-850 tm-136 ((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A 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-73819.        ((A -> (B and A)) -> (C -> ((D and E) -> D))), M:tm-850, m:tm-136, u:((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-73820
in-theory        73820
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> (D and ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D and ((A and (B -> C)) -> C))))
theorem-size     43
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-4)
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-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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-73820.        ((((A and (B -> C)) -> C) -> (D and ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D and ((A and (B -> C)) -> C)))), M:tm-850, 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-73821
in-theory        73821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 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-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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-73821.        ((A -> (B and A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> (B and A)))), M:tm-850, 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-73822
in-theory        73822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-850 tm-149 ((Am (-> A (and B A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
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-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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-73822.        ((A -> (B and A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-850, m:tm-149, u:((Am (-> A (and B A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-73823
in-theory        73823
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> (C and ((A and B) -> B))) -> ((D or ((A and B) -> B)) -> (C and ((A and B) -> B))))
theorem-size     29
proof            (modus-ponens tm-850 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-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-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-4.            ((A 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-73823.        ((((A and B) -> B) -> (C and ((A and B) -> B))) -> ((D or ((A and B) -> B)) -> (C and ((A and B) -> B)))), M:tm-850, 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-73824
in-theory        73824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> ((D and E) -> E)) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-157 ((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-73824.        ((A -> (B and A)) -> ((C -> ((D and E) -> E)) and (A -> (B and A)))), M:tm-850, m:tm-157, u:((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-73825
in-theory        73825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-850 tm-159 ((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A 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-73825.        ((A -> (B and A)) -> (C -> ((D and E) -> E))), M:tm-850, m:tm-159, u:((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-73826
in-theory        73826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> (D and ((A -> (B -> A)) and C))) -> ((C or ((A -> (B -> A)) and C)) -> (D and ((A -> (B -> A)) and C))))
theorem-size     37
proof            (modus-ponens tm-850 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-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-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-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-73826.        ((((A -> (B -> A)) and C) -> (D and ((A -> (B -> A)) and C))) -> ((C or ((A -> (B -> A)) and C)) -> (D and ((A -> (B -> A)) and C)))), M:tm-850, 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-73827
in-theory        73827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> ((D -> (E -> D)) and C)) and (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-183 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-73827.        ((A -> (B and A)) -> ((C -> ((D -> (E -> D)) and C)) and (A -> (B and A)))), M:tm-850, m:tm-183, u:((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-73828
in-theory        73828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-850 tm-184 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-73828.        ((A -> (B and A)) -> (C -> ((D -> (E -> D)) and C))), M:tm-850, m:tm-184, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-73829
in-theory        73829
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))))
theorem-size     69
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-20.           (A -> (((B -> (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-73829.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> (E and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))), M:tm-850, 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-73830
in-theory        73830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> (B and A))))
theorem-size     29
proof            (modus-ponens tm-850 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-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-12.           ((A -> B) -> (A -> A)), M: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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-73830.        ((A -> (B and A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> (B and A)))), M:tm-850, 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-73831
in-theory        73831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-850 tm-211 ((Am (-> A (and B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
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-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-20.           (A -> (((B -> (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-73831.        ((A -> (B and A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-850, m:tm-211, u:((Am (-> A (and B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-73832
in-theory        73832
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> (D and (((A and B) -> A) and C))) -> ((C or (((A and B) -> A) and C)) -> (D and (((A and B) -> A) and C))))
theorem-size     37
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A and B) -> 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-73832.        (((((A and B) -> A) and C) -> (D and (((A and B) -> A) and C))) -> ((C or (((A and B) -> A) and C)) -> (D and (((A and B) -> A) and C)))), M:tm-850, 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-73833
in-theory        73833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (((D and E) -> D) and C)) and (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-239 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-73833.        ((A -> (B and A)) -> ((C -> (((D and E) -> D) and C)) and (A -> (B and A)))), M:tm-850, 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-73834
in-theory        73834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-850 tm-240 ((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A and B) -> 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-73834.        ((A -> (B and A)) -> (C -> (((D and E) -> D) and C))), M:tm-850, m:tm-240, u:((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-73835
in-theory        73835
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> (D and (((A and B) -> B) and C))) -> ((C or (((A and B) -> B) and C)) -> (D and (((A and B) -> B) and C))))
theorem-size     37
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A and B) -> 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-73835.        (((((A and B) -> B) and C) -> (D and (((A and B) -> B) and C))) -> ((C or (((A and B) -> B) and C)) -> (D and (((A and B) -> B) and C)))), M:tm-850, 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-73836
in-theory        73836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (((D and E) -> E) and C)) and (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-270 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-73836.        ((A -> (B and A)) -> ((C -> (((D and E) -> E) and C)) and (A -> (B and A)))), M:tm-850, 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-73837
in-theory        73837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-850 tm-271 ((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A and B) -> 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-73837.        ((A -> (B and A)) -> (C -> (((D and E) -> E) and C))), M:tm-850, m:tm-271, u:((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-73838
in-theory        73838
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> (D and ((A -> (B -> (A and B))) and C))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (D and ((A -> (B -> (A and B))) and C))))
theorem-size     45
proof            (modus-ponens tm-850 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-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-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-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-73838.        ((((A -> (B -> (A and B))) and C) -> (D and ((A -> (B -> (A and B))) and C))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (D and ((A -> (B -> (A and B))) and C)))), M:tm-850, 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-73839
in-theory        73839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> (B and A))))
theorem-size     23
proof            (modus-ponens tm-850 tm-303 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-73839.        ((A -> (B and A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> (B and A)))), M:tm-850, 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-73840
in-theory        73840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-850 tm-304 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-73840.        ((A -> (B and A)) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-850, m:tm-304, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-73841
in-theory        73841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (A -> (B and A)))))
theorem-size     19
proof            (modus-ponens tm-850 tm-305 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> A (and B A)))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-73841.        ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (A -> (B and A))))), M:tm-850, m:tm-305, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> A (and B A))))))
================================================================
tm-name          tm-73842
in-theory        73842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (C -> ((A -> (B and A)) and C))))
theorem-size     21
proof            (modus-ponens tm-850 tm-309 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (and (-> A (and B A)) Bm))))))
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-73842.        ((A -> (B and A)) -> ((A -> (B and A)) and (C -> ((A -> (B and A)) and C)))), M:tm-850, 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-73843
in-theory        73843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and ((A -> (B and A)) or C)))
theorem-size     19
proof            (modus-ponens tm-850 tm-310 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (or (-> A (and B A)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-73843.        ((A -> (B and A)) -> ((A -> (B and A)) and ((A -> (B and A)) or C))), M:tm-850, m:tm-310, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (or (-> A (and B A)) Bm))))
================================================================
tm-name          tm-73844
in-theory        73844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (C or (A -> (B and A)))))
theorem-size     19
proof            (modus-ponens tm-850 tm-311 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (or Bm (-> A (and B A)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-73844.        ((A -> (B and A)) -> ((A -> (B and A)) and (C or (A -> (B and A))))), M:tm-850, m:tm-311, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (or Bm (-> A (and B A))))))
================================================================
tm-name          tm-73845
in-theory        73845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (((B and A) -> C) -> ((A or (B and A)) -> C))))
theorem-size     25
proof            (modus-ponens tm-850 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-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-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-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-73845.        ((A -> (B and A)) -> ((A -> (B and A)) and (((B and A) -> C) -> ((A or (B and A)) -> C)))), M:tm-850, 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-73846
in-theory        73846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and ((A -> (not (B and A))) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-313 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (-> Am (not (and B Am))) (not Am))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-9)
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-73846.        ((A -> (B and A)) -> ((A -> (B and A)) and ((A -> (not (B and A))) -> (not A)))), M:tm-850, 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-73847
in-theory        73847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-850 tm-315 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       149
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-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-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-73847.        ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D -> C)))), M:tm-850, m:tm-315, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-73848
in-theory        73848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (A -> A)))
theorem-size     15
proof            (modus-ponens tm-850 tm-316 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       157
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-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-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-73848.        ((A -> (B and A)) -> ((A -> (B and A)) and (A -> A))), M:tm-850, m:tm-316, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am Am))))
================================================================
tm-name          tm-73849
in-theory        73849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-850 tm-318 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       181
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-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-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-73849.        ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-850, 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-73850
in-theory        73850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-850 tm-320 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       149
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-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-24.           ((A -> B) -> (A -> (A and 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-73850.        ((A -> (B and A)) -> ((A -> (B and A)) and ((C and D) -> C))), M:tm-850, m:tm-320, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-73851
in-theory        73851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-850 tm-322 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       149
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-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-24.           ((A -> B) -> (A -> (A and 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-73851.        ((A -> (B and A)) -> ((A -> (B and A)) and ((C and D) -> D))), M:tm-850, m:tm-322, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-73852
in-theory        73852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> C)) and (A -> (B and A)))))
theorem-size     23
proof            (modus-ponens tm-850 tm-323 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (-> Cm Bm)) (-> A (and B A)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       161
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-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-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-73852.        ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> C)) and (A -> (B and A))))), M:tm-850, 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-73853
in-theory        73853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A)))))
theorem-size     31
proof            (modus-ponens tm-850 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-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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-73853.        ((A -> (B and A)) -> ((A -> (B and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B and A))))), M:tm-850, 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-73854
in-theory        73854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (((C and D) -> C) and (A -> (B and A)))))
theorem-size     23
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-3)
proof-size       161
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-73854.        ((A -> (B and A)) -> ((A -> (B and A)) and (((C and D) -> C) and (A -> (B and A))))), M:tm-850, 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-73855
in-theory        73855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (((C and D) -> D) and (A -> (B and A)))))
theorem-size     23
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-4)
proof-size       161
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-73855.        ((A -> (B and A)) -> ((A -> (B and A)) and (((C and D) -> D) and (A -> (B and A))))), M:tm-850, 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-73856
in-theory        73856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> (C and D))) and (A -> (B and A)))))
theorem-size     25
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       169
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-73856.        ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D -> (C and D))) and (A -> (B and A))))), M:tm-850, 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-73857
in-theory        73857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (A -> (A and (B and A)))))
theorem-size     19
proof            (modus-ponens tm-850 tm-328 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am (and Am (and B Am)))))))
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-73857.        ((A -> (B and A)) -> ((A -> (B and A)) and (A -> (A and (B and A))))), M:tm-850, 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-73858
in-theory        73858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> (C and (A -> (A and B)))) -> (((A -> B) or (A -> (A and B))) -> (C and (A -> (A and B)))))
theorem-size     31
proof            (modus-ponens tm-850 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-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-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-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-73858.        (((A -> (A and B)) -> (C and (A -> (A and B)))) -> (((A -> B) or (A -> (A and B))) -> (C and (A -> (A and B))))), M:tm-850, 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-73859
in-theory        73859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> D) -> (C -> (C and D))) and (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-338 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-73859.        ((A -> (B and A)) -> (((C -> D) -> (C -> (C and D))) and (A -> (B and A)))), M:tm-850, m:tm-338, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73860
in-theory        73860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-850 tm-340 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-73860.        ((A -> (B and A)) -> ((C -> D) -> (C -> (C and D)))), M:tm-850, m:tm-340, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-73861
in-theory        73861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-850 tm-341 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       157
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-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-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-73861.        ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D -> (C and D))))), M:tm-850, m:tm-341, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-73862
in-theory        73862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> (C and (A -> (B -> (A and B))))) -> ((D or (A -> (B -> (A and B)))) -> (C and (A -> (B -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-850 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-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-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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-73862.        (((A -> (B -> (A and B))) -> (C and (A -> (B -> (A and B))))) -> ((D or (A -> (B -> (A and B)))) -> (C and (A -> (B -> (A and B)))))), M:tm-850, 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-73863
in-theory        73863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D -> (E -> (D and E)))) and (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-354 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-73863.        ((A -> (B and A)) -> ((C -> (D -> (E -> (D and E)))) and (A -> (B and A)))), M:tm-850, m:tm-354, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A)))))
================================================================
tm-name          tm-73864
in-theory        73864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (A -> (C -> ((B and A) and C))))
theorem-size     15
proof            (modus-ponens tm-850 tm-355 ((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and (and B Am) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-73864.        ((A -> (B and A)) -> (A -> (C -> ((B and A) and C)))), M:tm-850, m:tm-355, u:((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and (and B Am) Cm)))))
================================================================
tm-name          tm-73865
in-theory        73865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-850 tm-356 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-73865.        ((A -> (B and A)) -> (C -> (D -> (E -> (D and E))))), M:tm-850, m:tm-356, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-73866
in-theory        73866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> (D -> C)) or E) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-364 ((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (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-73866.        ((A -> (B and A)) -> (((C -> (D -> C)) or E) and (A -> (B and A)))), M:tm-850, m:tm-364, u:((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73867
in-theory        73867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-850 tm-365 ((Am (-> A (and B A))) (C (or (-> Bm (-> Cm Bm)) Dm))))
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-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-6.            (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-73867.        ((A -> (B and A)) -> ((C -> (D -> C)) or E)), M:tm-850, m:tm-365, u:((Am (-> A (and B A))) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-73868
in-theory        73868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 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-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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-73868.        ((A -> (B and A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> (B and A)))), M:tm-850, 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-73869
in-theory        73869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-850 tm-374 ((Am (-> A (and B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
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-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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (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-73869.        ((A -> (B and A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-850, m:tm-374, u:((Am (-> A (and B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-73870
in-theory        73870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C and D) -> C) or E) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-382 ((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 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-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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-73870.        ((A -> (B and A)) -> ((((C and D) -> C) or E) and (A -> (B and A)))), M:tm-850, m:tm-382, u:((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73871
in-theory        73871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-850 tm-383 ((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-73871.        ((A -> (B and A)) -> (((C and D) -> C) or E)), M:tm-850, m:tm-383, u:((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-73872
in-theory        73872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C and D) -> D) or E) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-391 ((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 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-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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-73872.        ((A -> (B and A)) -> ((((C and D) -> D) or E) and (A -> (B and A)))), M:tm-850, m:tm-391, u:((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73873
in-theory        73873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-850 tm-392 ((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-73873.        ((A -> (B and A)) -> (((C and D) -> D) or E)), M:tm-850, m:tm-392, u:((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-73874
in-theory        73874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> (D -> (C and D))) or E) and (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-400 ((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-73874.        ((A -> (B and A)) -> (((C -> (D -> (C and D))) or E) and (A -> (B and A)))), M:tm-850, 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-73875
in-theory        73875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-850 tm-401 ((Am (-> A (and B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), 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-73875.        ((A -> (B and A)) -> ((C -> (D -> (C and D))) or E)), M:tm-850, m:tm-401, u:((Am (-> A (and B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-73876
in-theory        73876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> (C or D)) or E) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-409 ((Am (-> A (and B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-73876.        ((A -> (B and A)) -> (((C -> (C or D)) or E) and (A -> (B and A)))), M:tm-850, m:tm-409, u:((Am (-> A (and B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73877
in-theory        73877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-850 tm-410 ((Am (-> A (and B A))) (C (or (-> Bm (or Bm Cm)) Dm))))
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-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-6.            (A -> (A 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-73877.        ((A -> (B and A)) -> ((C -> (C or D)) or E)), M:tm-850, m:tm-410, u:((Am (-> A (and B A))) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-73878
in-theory        73878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (C or D)) and (A -> (B and A)))))
theorem-size     23
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-6)
proof-size       161
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-73878.        ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (C or D)) and (A -> (B and A))))), M:tm-850, 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-73879
in-theory        73879
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> (D and ((A -> (A or B)) and C))) -> ((C or ((A -> (A or B)) and C)) -> (D and ((A -> (A or B)) and C))))
theorem-size     37
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-6)
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-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-6.            (A -> (A or 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-73879.        ((((A -> (A or B)) and C) -> (D and ((A -> (A or B)) and C))) -> ((C or ((A -> (A or B)) and C)) -> (D and ((A -> (A or B)) and C)))), M:tm-850, 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-73880
in-theory        73880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> ((D -> (D or E)) and C)) and (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-453 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-73880.        ((A -> (B and A)) -> ((C -> ((D -> (D or E)) and C)) and (A -> (B and A)))), M:tm-850, 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-73881
in-theory        73881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-850 tm-454 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or 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-73881.        ((A -> (B and A)) -> (C -> ((D -> (D or E)) and C))), M:tm-850, m:tm-454, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-73882
in-theory        73882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-850 tm-456 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       149
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-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-24.           ((A -> B) -> (A -> (A and 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-73882.        ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (C or D)))), M:tm-850, m:tm-456, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-73883
in-theory        73883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> (C and (A -> (A or B)))) -> ((D or (A -> (A or B))) -> (C and (A -> (A or B)))))
theorem-size     29
proof            (modus-ponens tm-850 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-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-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-6.            (A -> (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-73883.        (((A -> (A or B)) -> (C and (A -> (A or B)))) -> ((D or (A -> (A or B))) -> (C and (A -> (A or B))))), M:tm-850, 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-73884
in-theory        73884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D -> (D or E))) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-469 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-73884.        ((A -> (B and A)) -> ((C -> (D -> (D or E))) and (A -> (B and A)))), M:tm-850, m:tm-469, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (and B A)))))
================================================================
tm-name          tm-73885
in-theory        73885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (A -> ((B and A) or C)))
theorem-size     13
proof            (modus-ponens tm-850 tm-470 ((A Am) (Bm (and B Am)) (C (-> Am (or (and B Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-73885.        ((A -> (B and A)) -> (A -> ((B and A) or C))), M:tm-850, m:tm-470, u:((A Am) (Bm (and B Am)) (C (-> Am (or (and B Am) Cm))))
================================================================
tm-name          tm-73886
in-theory        73886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-850 tm-471 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Cm Dm))))))
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-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-6.            (A -> (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-73886.        ((A -> (B and A)) -> (C -> (D -> (D or E)))), M:tm-850, m:tm-471, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-73887
in-theory        73887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C or (D -> (E -> D))) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-480 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (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-73887.        ((A -> (B and A)) -> ((C or (D -> (E -> D))) and (A -> (B and A)))), M:tm-850, m:tm-480, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73888
in-theory        73888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-850 tm-481 ((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm Cm))))))
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-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-7.            (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-73888.        ((A -> (B and A)) -> (C or (D -> (E -> D)))), M:tm-850, m:tm-481, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-73889
in-theory        73889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 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-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-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-73889.        ((A -> (B and A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (B and A)))), M:tm-850, 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-73890
in-theory        73890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-850 tm-491 ((Am (-> A (and B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-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-7.            (A -> (B or A)), axiom
tm-35.           (A 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-73890.        ((A -> (B and A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-850, m:tm-491, u:((Am (-> A (and B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-73891
in-theory        73891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C or ((D and E) -> D)) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-500 ((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 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-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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-73891.        ((A -> (B and A)) -> ((C or ((D and E) -> D)) and (A -> (B and A)))), M:tm-850, m:tm-500, u:((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-73892
in-theory        73892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-850 tm-501 ((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-73892.        ((A -> (B and A)) -> (C or ((D and E) -> D))), M:tm-850, m:tm-501, u:((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-73893
in-theory        73893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C or ((D and E) -> E)) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-510 ((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 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-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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-73893.        ((A -> (B and A)) -> ((C or ((D and E) -> E)) and (A -> (B and A)))), M:tm-850, m:tm-510, u:((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-73894
in-theory        73894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-850 tm-511 ((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-73894.        ((A -> (B and A)) -> (C or ((D and E) -> E))), M:tm-850, m:tm-511, u:((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-73895
in-theory        73895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C or (D -> (E -> (D and E)))) and (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-520 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-73895.        ((A -> (B and A)) -> ((C or (D -> (E -> (D and E)))) and (A -> (B and A)))), M:tm-850, 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-73896
in-theory        73896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-850 tm-521 ((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), 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-73896.        ((A -> (B and A)) -> (C or (D -> (E -> (D and E))))), M:tm-850, m:tm-521, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-73897
in-theory        73897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C or (D -> (D or E))) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-530 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-73897.        ((A -> (B and A)) -> ((C or (D -> (D or E))) and (A -> (B and A)))), M:tm-850, m:tm-530, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (and B A)))))
================================================================
tm-name          tm-73898
in-theory        73898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-850 tm-531 ((Am (-> A (and B A))) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 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-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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A 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-73898.        ((A -> (B and A)) -> (C or (D -> (D or E)))), M:tm-850, m:tm-531, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-73899
in-theory        73899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C or (D -> (E or D))) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-540 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-73899.        ((A -> (B and A)) -> ((C or (D -> (E or D))) and (A -> (B and A)))), M:tm-850, m:tm-540, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73900
in-theory        73900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-850 tm-541 ((Am (-> A (and B A))) (C (or Bm (-> Cm (or Dm Cm))))))
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-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-7.            (A -> (B 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-73900.        ((A -> (B and A)) -> (C or (D -> (E or D)))), M:tm-850, m:tm-541, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-73901
in-theory        73901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> (D or C)) or E) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-550 ((Am (-> A (and B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-73901.        ((A -> (B and A)) -> (((C -> (D or C)) or E) and (A -> (B and A)))), M:tm-850, m:tm-550, u:((Am (-> A (and B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-73902
in-theory        73902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-850 tm-551 ((Am (-> A (and B A))) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 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-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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B 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-73902.        ((A -> (B and A)) -> ((C -> (D or C)) or E)), M:tm-850, m:tm-551, u:((Am (-> A (and B A))) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-73903
in-theory        73903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D or C)) and (A -> (B and A)))))
theorem-size     23
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-7)
proof-size       161
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-73903.        ((A -> (B and A)) -> ((A -> (B and A)) and ((C -> (D or C)) and (A -> (B and A))))), M:tm-850, 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-73904
in-theory        73904
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> (D and ((A -> (B or A)) and C))) -> ((C or ((A -> (B or A)) and C)) -> (D and ((A -> (B or A)) and C))))
theorem-size     37
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-7)
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-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-7.            (A -> (B or 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-73904.        ((((A -> (B or A)) and C) -> (D and ((A -> (B or A)) and C))) -> ((C or ((A -> (B or A)) and C)) -> (D and ((A -> (B or A)) and C)))), M:tm-850, 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-73905
in-theory        73905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> ((D -> (E or D)) and C)) and (A -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-605 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-73905.        ((A -> (B and A)) -> ((C -> ((D -> (E or D)) and C)) and (A -> (B and A)))), M:tm-850, 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-73906
in-theory        73906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-850 tm-606 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or 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-73906.        ((A -> (B and A)) -> (C -> ((D -> (E or D)) and C))), M:tm-850, m:tm-606, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-73907
in-theory        73907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-850 tm-609 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       149
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-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-24.           ((A -> B) -> (A -> (A and 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-73907.        ((A -> (B and A)) -> ((A -> (B and A)) and (C -> (D or C)))), M:tm-850, m:tm-609, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-73908
in-theory        73908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> (C and (A -> (B or A)))) -> ((D or (A -> (B or A))) -> (C and (A -> (B or A)))))
theorem-size     29
proof            (modus-ponens tm-850 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-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-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-7.            (A -> (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-73908.        (((A -> (B or A)) -> (C and (A -> (B or A)))) -> ((D or (A -> (B or A))) -> (C and (A -> (B or A))))), M:tm-850, 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-73909
in-theory        73909
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> (D -> (E or D))) and (A -> (B and A))))
theorem-size     19
proof            (modus-ponens tm-850 tm-622 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-73909.        ((A -> (B and A)) -> ((C -> (D -> (E or D))) and (A -> (B and A)))), M:tm-850, m:tm-622, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-73910
in-theory        73910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (A -> (C or (B and A))))
theorem-size     13
proof            (modus-ponens tm-850 tm-623 ((A Am) (Bm (and B Am)) (C (-> Am (or Cm (and B Am))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-73910.        ((A -> (B and A)) -> (A -> (C or (B and A)))), M:tm-850, m:tm-623, u:((A Am) (Bm (and B Am)) (C (-> Am (or Cm (and B Am)))))
================================================================
tm-name          tm-73911
in-theory        73911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-850 tm-624 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Dm Cm))))))
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-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-7.            (A -> (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-73911.        ((A -> (B and A)) -> (C -> (D -> (E or D)))), M:tm-850, m:tm-624, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-73912
in-theory        73912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C and (A -> B))) -> (((A -> B) -> (C and (A -> B))) and ((B or (A -> B)) -> (C and (A -> B)))))
theorem-size     31
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       187
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-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-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-73912.        (((A -> B) -> (C and (A -> B))) -> (((A -> B) -> (C and (A -> B))) and ((B or (A -> B)) -> (C and (A -> B))))), M:tm-850, 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-73913
in-theory        73913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C and (A -> B))) -> ((A -> B) -> (C and (A -> B))))
theorem-size     19
proof            (modus-ponens tm-850 tm-660 ((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (-> Am Bm) (and B (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       163
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-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-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-73913.        (((A -> B) -> (C and (A -> B))) -> ((A -> B) -> (C and (A -> B)))), M:tm-850, m:tm-660, u:((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (-> Am Bm) (and B (-> Am Bm)))))
================================================================
tm-name          tm-73914
in-theory        73914
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> (D and ((A or (B -> A)) -> C))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> (D and ((A or (B -> A)) -> C))))
theorem-size     41
proof            (modus-ponens tm-850 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-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-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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-73914.        ((((A or (B -> A)) -> C) -> (D and ((A or (B -> A)) -> C))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> (D and ((A or (B -> A)) -> C)))), M:tm-850, 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-73915
in-theory        73915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-850 tm-665 ((Am (-> A (and B A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (and B A))))))
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-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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-73915.        ((A -> (B and A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> (B and A)))), M:tm-850, 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-73916
in-theory        73916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-850 tm-667 ((Am (-> A (and B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 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-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-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-73916.        ((A -> (B and A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-850, m:tm-667, u:((Am (-> A (and B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-73917
in-theory        73917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C))))))
theorem-size     59
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       251
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-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-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-73917.        ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and ((A -> B) -> (A -> C)))))), M:tm-850, 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-73918
in-theory        73918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       207
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-73918.        ((((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> (D and ((A -> B) -> (A -> C))))), M:tm-850, 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-73919
in-theory        73919
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (E and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((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))))
theorem-size     77
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-73919.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (E and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((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)))), M:tm-850, 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-73920
in-theory        73920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> (B and A))))
theorem-size     37
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
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-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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-73920.        ((A -> (B and A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> (B and A)))), M:tm-850, 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-73921
in-theory        73921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-73921.        ((A -> (B and A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-850, 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-73922
in-theory        73922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (((A and C) or A) -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 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-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-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-24.           ((A -> B) -> (A -> (A and 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-73922.        ((A -> (B and A)) -> ((A -> (B and A)) and (((A and C) or A) -> (B and A)))), M:tm-850, 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-73923
in-theory        73923
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> (D and (((A and B) or A) -> C))) -> (((A -> C) or (((A and B) or A) -> C)) -> (D and (((A and B) or A) -> C))))
theorem-size     39
proof            (modus-ponens tm-850 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-2 tm-1 tm-8 tm-5 tm-3)
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-73923.        (((((A and B) or A) -> C) -> (D and (((A and B) or A) -> C))) -> (((A -> C) or (((A and B) or A) -> C)) -> (D and (((A and B) or A) -> C)))), M:tm-850, 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-73924
in-theory        73924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> (B and A))))
theorem-size     23
proof            (modus-ponens tm-850 tm-757 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-73924.        ((A -> (B and A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> (B and A)))), M:tm-850, 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-73925
in-theory        73925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-850 tm-759 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-3.            ((A and B) -> A), axiom
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-73925.        ((A -> (B and A)) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-850, m:tm-759, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-73926
in-theory        73926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((A -> (B and A)) and (((C and A) or A) -> (B and A))))
theorem-size     21
proof            (modus-ponens tm-850 tm-798 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (or (and Cm Am) Am) (and B Am))))))
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-73926.        ((A -> (B and A)) -> ((A -> (B and A)) and (((C and A) or A) -> (B and A)))), M:tm-850, m:tm-798, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (or (and Cm Am) Am) (and B Am)))))
================================================================
tm-name          tm-73927
in-theory        73927
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> (D and (((A and B) or B) -> C))) -> (((B -> C) or (((A and B) or B) -> C)) -> (D and (((A and B) or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-850 tm-805 ((A (-> (or (and Am Bm) Bm) Cm)) (Dm (and B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (and B (-> (or (and Am Bm) Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
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-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-4.            ((A and B) -> B), axiom
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-73927.        (((((A and B) or B) -> C) -> (D and (((A and B) or B) -> C))) -> (((B -> C) or (((A and B) or B) -> C)) -> (D and (((A and B) or B) -> C)))), M:tm-850, m:tm-805, u:((A (-> (or (and Am Bm) Bm) Cm)) (Dm (and B (-> (or (and Am Bm) Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (and B (-> (or (and Am Bm) Bm) Cm)))))
================================================================
tm-name          tm-73928
in-theory        73928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> (B and A))))
theorem-size     23
proof            (modus-ponens tm-850 tm-808 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
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-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-4.            ((A and B) -> B), axiom
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-73928.        ((A -> (B and A)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A -> (B and A)))), M:tm-850, m:tm-808, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-73929
in-theory        73929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-850 tm-810 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-4.            ((A and B) -> B), axiom
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-73929.        ((A -> (B and A)) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-850, m:tm-810, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-73930
in-theory        73930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C and (A -> (B and A)))) -> (((A -> (B and A)) -> (C and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C and (A -> (B and A))))))
theorem-size     43
proof            (modus-ponens tm-850 tm-844 ((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (and B (-> Am (and Bm Am))))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       211
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-73930.        (((A -> (B and A)) -> (C and (A -> (B and A)))) -> (((A -> (B and A)) -> (C and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (C and (A -> (B and A)))))), M:tm-850, m:tm-844, u:((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (and (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am)))) (-> (or Bm (-> Am (and Bm Am))) (and B (-> Am (and Bm Am)))))))
================================================================
tm-name          tm-73931
in-theory        73931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C and (A -> (B and A)))) -> ((A -> (B and A)) -> (C and (A -> (B and A)))))
theorem-size     27
proof            (modus-ponens tm-850 tm-850 ((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       181
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-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-73931.        (((A -> (B and A)) -> (C and (A -> (B and A)))) -> ((A -> (B and A)) -> (C and (A -> (B and A))))), M:tm-850, m:tm-850, u:((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am))))))
================================================================
tm-name          tm-73932
in-theory        73932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C and (A -> (B and A)))) -> ((A -> (B and A)) -> (C and (A -> (B and A))))) and ((C or ((A -> (B and A)) -> (C and (A -> (B and A))))) -> ((A -> (B and A)) -> (C and (A -> (B and A))))))
theorem-size     57
proof            (modus-ponens tm-844 tm-850 ((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am)))))))
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-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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
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-73932.        ((((A -> (B and A)) -> (C and (A -> (B and A)))) -> ((A -> (B and A)) -> (C and (A -> (B and A))))) and ((C or ((A -> (B and A)) -> (C and (A -> (B and A))))) -> ((A -> (B and A)) -> (C and (A -> (B and A)))))), M:tm-844, m:tm-850, u:((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am))))))
================================================================
tm-name          tm-73933
in-theory        73933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-808 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-73933.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-808, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73934
in-theory        73934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((D and ((A -> (B and A)) -> C)) or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C)))
theorem-size     41
proof            (modus-ponens tm-798 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-73934.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((D and ((A -> (B and A)) -> C)) or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C))), M:tm-798, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73935
in-theory        73935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-757 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-73935.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-757, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73936
in-theory        73936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C)))
theorem-size     41
proof            (modus-ponens tm-747 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-73936.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C))), M:tm-747, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73937
in-theory        73937
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G)))
theorem-size     41
proof            (modus-ponens tm-708 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-73937.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G))), M:tm-708, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73938
in-theory        73938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> C)) -> ((A -> (B and A)) -> (A -> C)))
theorem-size     19
proof            (modus-ponens tm-703 tm-850 ((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (-> Am (and Bm Am)) (-> Am C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       191
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-48.           (((A -> (B and 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-73938.        (((A -> (B and A)) -> (A -> C)) -> ((A -> (B and A)) -> (A -> C))), M:tm-703, m:tm-850, u:((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (-> Am (and Bm Am)) (-> Am C))))
================================================================
tm-name          tm-73939
in-theory        73939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (A -> C)) -> ((A -> (B and A)) -> (A -> C))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((A -> (B and A)) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-697 tm-850 ((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (-> Am (and Bm Am)) (-> Am C)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-48.           (((A -> (B and 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-73939.        ((((A -> (B and A)) -> (A -> C)) -> ((A -> (B and A)) -> (A -> C))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((A -> (B and A)) -> (A -> C)))), M:tm-697, m:tm-850, u:((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (-> Am (and Bm Am)) (-> Am C))))
================================================================
tm-name          tm-73940
in-theory        73940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-665 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-73940.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-665, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73941
in-theory        73941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((C or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C)))
theorem-size     33
proof            (modus-ponens tm-654 tm-850 ((A (-> Am (and Bm Am))) (B Cm) (C (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-48.           (((A -> (B and 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-73941.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((C or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C))), M:tm-654, m:tm-850, u:((A (-> Am (and Bm Am))) (B Cm) (C (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73942
in-theory        73942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (D or ((A -> (B and A)) -> C)))
theorem-size     17
proof            (modus-ponens tm-623 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-73942.        (((A -> (B and A)) -> C) -> (D or ((A -> (B and A)) -> C))), M:tm-623, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73943
in-theory        73943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-622 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> 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-48.           (((A -> (B and 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-73943.        ((A -> (B -> (C or B))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-622, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73944
in-theory        73944
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (D or (B -> (C and B))))) -> ((B -> (C and B)) -> (D or (B -> (C and B)))))
theorem-size     29
proof            (modus-ponens tm-619 tm-850 ((A (-> Am (and Bm Am))) (Cm (or B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (or B (-> Am (and Bm Am)))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73944.        ((A or ((B -> (C and B)) -> (D or (B -> (C and B))))) -> ((B -> (C and B)) -> (D or (B -> (C and B))))), M:tm-619, m:tm-850, u:((A (-> Am (and Bm Am))) (Cm (or B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (or B (-> Am (and Bm Am))))))
================================================================
tm-name          tm-73945
in-theory        73945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73945.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73946
in-theory        73946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-605 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73946.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-605, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73947
in-theory        73947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (E or D)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))))
theorem-size     37
proof            (modus-ponens tm-595 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-73947.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (E or D)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))), M:tm-595, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73948
in-theory        73948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-550 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-48.           (((A -> (B and 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-73948.        (((A -> (B or A)) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-550, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73949
in-theory        73949
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-540 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-48.           (((A -> (B and 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-73949.        ((A or (B -> (C or B))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-540, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73950
in-theory        73950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-530 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-48.           (((A -> (B and 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-73950.        ((A or (B -> (B or C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-530, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73951
in-theory        73951
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-520 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73951.        ((A or (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-520, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73952
in-theory        73952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-510 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-48.           (((A -> (B and 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-73952.        ((A or ((B and C) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-510, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73953
in-theory        73953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-500 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-48.           (((A -> (B and 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-73953.        ((A or ((B and C) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-500, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73954
in-theory        73954
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-490 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73954.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G))), M:tm-490, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73955
in-theory        73955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-480 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> 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-48.           (((A -> (B and 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-73955.        ((A or (B -> (C -> B))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-480, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73956
in-theory        73956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-73956.        (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) or D)), M:tm-470, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73957
in-theory        73957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-469 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> 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-48.           (((A -> (B and 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-73957.        ((A -> (B -> (B or C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-469, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73958
in-theory        73958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> ((B -> (C and B)) or D))) -> ((B -> (C and B)) -> ((B -> (C and B)) or D)))
theorem-size     29
proof            (modus-ponens tm-466 tm-850 ((A (-> Am (and Bm Am))) (Cm (or (-> Am (and Bm Am)) B)) (C (-> (-> Am (and Bm Am)) (or (-> Am (and Bm Am)) B)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73958.        ((A or ((B -> (C and B)) -> ((B -> (C and B)) or D))) -> ((B -> (C and B)) -> ((B -> (C and B)) or D))), M:tm-466, m:tm-850, u:((A (-> Am (and Bm Am))) (Cm (or (-> Am (and Bm Am)) B)) (C (-> (-> Am (and Bm Am)) (or (-> Am (and Bm Am)) B))))
================================================================
tm-name          tm-73959
in-theory        73959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73959.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73960
in-theory        73960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-453 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73960.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-453, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73961
in-theory        73961
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (D or E)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))))
theorem-size     37
proof            (modus-ponens tm-443 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-73961.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (D or E)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))), M:tm-443, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73962
in-theory        73962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-409 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-48.           (((A -> (B and 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-73962.        (((A -> (A or B)) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-409, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73963
in-theory        73963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-400 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73963.        (((A -> (B -> (A and B))) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-400, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73964
in-theory        73964
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-391 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-48.           (((A -> (B and 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-73964.        ((((A and B) -> B) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-391, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73965
in-theory        73965
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-382 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-48.           (((A -> (B and 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-73965.        ((((A and B) -> A) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-382, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73966
in-theory        73966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-373 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73966.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G))), M:tm-373, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73967
in-theory        73967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-364 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> 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-48.           (((A -> (B and 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-73967.        (((A -> (B -> A)) or C) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-364, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73968
in-theory        73968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (D -> (((A -> (B and A)) -> C) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73968.        (((A -> (B and A)) -> C) -> (D -> (((A -> (B and A)) -> C) and D))), M:tm-355, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73969
in-theory        73969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-354 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> 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-48.           (((A -> (B and 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-73969.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-354, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73970
in-theory        73970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (D -> ((B -> (C and B)) and D)))) -> ((B -> (C and B)) -> (D -> ((B -> (C and B)) and D))))
theorem-size     33
proof            (modus-ponens tm-351 tm-850 ((A (-> Am (and Bm Am))) (Cm (-> B (and (-> Am (and Bm Am)) B))) (C (-> (-> Am (and Bm Am)) (-> B (and (-> Am (and Bm Am)) B))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-73970.        ((A or ((B -> (C and B)) -> (D -> ((B -> (C and B)) and D)))) -> ((B -> (C and B)) -> (D -> ((B -> (C and B)) and D)))), M:tm-351, m:tm-850, u:((A (-> Am (and Bm Am))) (Cm (-> B (and (-> Am (and Bm Am)) B))) (C (-> (-> Am (and Bm Am)) (-> B (and (-> Am (and Bm Am)) B)))))
================================================================
tm-name          tm-73971
in-theory        73971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73971.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73972
in-theory        73972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E)))
theorem-size     25
proof            (modus-ponens tm-338 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-73972.        (((A -> B) -> (A -> (A and B))) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E))), M:tm-338, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73973
in-theory        73973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> ((A -> (B and A)) and C))) -> ((A -> (B and A)) -> ((A -> (B and A)) and C)))
theorem-size     35
proof            (modus-ponens tm-335 tm-850 ((A (-> Am (and Bm Am))) (Cm (and (-> Am (and Bm Am)) B)) (C (-> (-> Am (and Bm Am)) (and (-> Am (and Bm Am)) B)))))
axioms-used      (tm-8 tm-2 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-5.            (A -> (B -> (A and B))), axiom
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-48.           (((A -> (B and 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-73973.        ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> ((A -> (B and A)) and C))) -> ((A -> (B and A)) -> ((A -> (B and A)) and C))), M:tm-335, m:tm-850, u:((A (-> Am (and Bm Am))) (Cm (and (-> Am (and Bm Am)) B)) (C (-> (-> Am (and Bm Am)) (and (-> Am (and Bm Am)) B))))
================================================================
tm-name          tm-73974
in-theory        73974
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((A -> (B and A)) -> C))))
theorem-size     39
proof            (modus-ponens tm-328 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and 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-328.          ((A -> 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-48.           (((A -> (B and 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-73974.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((A -> (B and A)) -> C)))), M:tm-328, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73975
in-theory        73975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (E -> (D and E))) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))))
theorem-size     39
proof            (modus-ponens tm-327 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73975.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (E -> (D and E))) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))), M:tm-327, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73976
in-theory        73976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((D and E) -> E) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))))
theorem-size     37
proof            (modus-ponens tm-326 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-73976.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((D and E) -> E) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))), M:tm-326, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73977
in-theory        73977
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((D and E) -> D) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))))
theorem-size     37
proof            (modus-ponens tm-325 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-73977.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((D and E) -> D) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))), M:tm-325, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73978
in-theory        73978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))))
theorem-size     45
proof            (modus-ponens tm-324 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-73978.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))), M:tm-324, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73979
in-theory        73979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (E -> D)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))))
theorem-size     37
proof            (modus-ponens tm-323 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-73979.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (E -> D)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))), M:tm-323, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73980
in-theory        73980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73980.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73981
in-theory        73981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73981.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73982
in-theory        73982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-73982.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73983
in-theory        73983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))
theorem-size     31
proof            (modus-ponens tm-316 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
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-48.           (((A -> (B and 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-73983.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))), M:tm-316, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73984
in-theory        73984
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73984.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73985
in-theory        73985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((((A -> (B and A)) -> C) -> (not ((A -> (B and A)) -> C))) -> (not ((A -> (B and A)) -> C))))
theorem-size     41
proof            (modus-ponens tm-313 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-48.           (((A -> (B and 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-73985.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((((A -> (B and A)) -> C) -> (not ((A -> (B and A)) -> C))) -> (not ((A -> (B and A)) -> C)))), M:tm-313, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73986
in-theory        73986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((((A -> (B and A)) -> C) -> D) -> ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> C)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) 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-312.          ((A -> B) -> ((A -> B) and ((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-48.           (((A -> (B and 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-73986.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((((A -> (B and A)) -> C) -> D) -> ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> C)) -> D))), M:tm-312, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-73987
in-theory        73987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D or (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))))
theorem-size     33
proof            (modus-ponens tm-311 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-73987.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D or (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))), M:tm-311, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73988
in-theory        73988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-73988.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) or D)), M:tm-310, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73989
in-theory        73989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (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-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-48.           (((A -> (B and 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-73989.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and D))), M:tm-309, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73990
in-theory        73990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((((A -> (B and A)) -> C) -> (A -> (B and A))) -> (((A -> (B and A)) -> C) -> C)))
theorem-size     39
proof            (modus-ponens tm-306 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> Am (and Bm Am))) (C Cm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-48.           (((A -> (B and 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-73990.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and ((((A -> (B and A)) -> C) -> (A -> (B and A))) -> (((A -> (B and A)) -> C) -> C))), M:tm-306, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> Am (and Bm Am))) (C Cm))
================================================================
tm-name          tm-73991
in-theory        73991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))))
theorem-size     33
proof            (modus-ponens tm-305 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and 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-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-48.           (((A -> (B and 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-73991.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) and (D -> (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))), M:tm-305, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73992
in-theory        73992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-303 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73992.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-303, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73993
in-theory        73993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-270 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73993.        ((A -> (((B and C) -> C) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-270, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73994
in-theory        73994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-239 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73994.        ((A -> (((B and C) -> B) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-239, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73995
in-theory        73995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-210 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-73995.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G))), M:tm-210, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73996
in-theory        73996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-183 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> 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-48.           (((A -> (B and 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-73996.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-183, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73997
in-theory        73997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-157 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> 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-48.           (((A -> (B and 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-73997.        ((A -> ((B and C) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-157, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73998
in-theory        73998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     31
proof            (modus-ponens tm-147 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-73998.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-147, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-73999
in-theory        73999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-134 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> 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-48.           (((A -> (B and 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-73999.        ((A -> ((B and C) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-134, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74000
in-theory        74000
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     31
proof            (modus-ponens tm-125 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74000.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-125, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74001
in-theory        74001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> D)) -> (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> D)))
theorem-size     25
proof            (modus-ponens tm-114 tm-850 ((A (-> (-> Am (and Bm Am)) (-> C D))) (B (-> Am (and Bm Am))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       165
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-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-74001.        (((A -> (B and A)) -> (C -> D)) -> (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> D))), M:tm-114, m:tm-850, u:((A (-> (-> Am (and Bm Am)) (-> C D))) (B (-> Am (and Bm Am))) (Cm (-> C D)))
================================================================
tm-name          tm-74002
in-theory        74002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-113 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74002.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G))), M:tm-113, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74003
in-theory        74003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     35
proof            (modus-ponens tm-105 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-48.           (((A -> (B and 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-74003.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-105, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74004
in-theory        74004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E)))
theorem-size     23
proof            (modus-ponens tm-95 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-48.           (((A -> (B and 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-74004.        (((A -> B) -> (A -> A)) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E))), M:tm-95, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74005
in-theory        74005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> (A -> (B and A)))) -> ((A -> (B and A)) -> (A -> (B and A))))
theorem-size     31
proof            (modus-ponens tm-92 tm-850 ((Cm (-> Am (and Bm Am))) (A (-> Am (and Bm Am))) (B (-> (-> Am (and Bm Am)) (-> Am (and Bm Am))))))
axioms-used      (tm-8 tm-2 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-1.            (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-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-74005.        ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> (A -> (B and A)))) -> ((A -> (B and A)) -> (A -> (B and A)))), M:tm-92, m:tm-850, u:((Cm (-> Am (and Bm Am))) (A (-> Am (and Bm Am))) (B (-> (-> Am (and Bm Am)) (-> Am (and Bm Am)))))
================================================================
tm-name          tm-74006
in-theory        74006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (D -> ((A -> (B and A)) -> C)))
theorem-size     17
proof            (modus-ponens tm-84 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-74006.        (((A -> (B and A)) -> C) -> (D -> ((A -> (B and A)) -> C))), M:tm-84, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-74007
in-theory        74007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     23
proof            (modus-ponens tm-83 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> 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-48.           (((A -> (B and 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-74007.        ((A -> (B -> (C -> B))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-83, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74008
in-theory        74008
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (D -> (B -> (C and B))))) -> ((B -> (C and B)) -> (D -> (B -> (C and B)))))
theorem-size     29
proof            (modus-ponens tm-80 tm-850 ((A (-> Am (and Bm Am))) (Cm (-> B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (-> B (-> Am (and Bm Am)))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74008.        ((A or ((B -> (C and B)) -> (D -> (B -> (C and B))))) -> ((B -> (C and B)) -> (D -> (B -> (C and B))))), M:tm-80, m:tm-850, u:((A (-> Am (and Bm Am))) (Cm (-> B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (-> B (-> Am (and Bm Am))))))
================================================================
tm-name          tm-74009
in-theory        74009
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C and B)) -> D) -> ((B -> (C and B)) -> D)))
theorem-size     21
proof            (modus-ponens tm-76 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74009.        (((not (not A)) -> A) and (((B -> (C and B)) -> D) -> ((B -> (C and B)) -> D))), M:tm-76, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74010
in-theory        74010
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B and A)) -> C))) or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C))
theorem-size     25
proof            (modus-ponens tm-73 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-5)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74010.        (((not (not ((A -> (B and A)) -> C))) or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C)), M:tm-73, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-74011
in-theory        74011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E)))
theorem-size     27
proof            (modus-ponens tm-69 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74011.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E))), M:tm-69, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74012
in-theory        74012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> (B and A))) -> (((A -> (B and A)) or (A -> (B and A))) -> (A -> (B and A))))
theorem-size     29
proof            (modus-ponens tm-55 tm-850 ((A (-> Am (and Bm Am))) (Cm (-> Am (and Bm Am))) (B (-> Am (and Bm Am))) (C (-> Am (and Bm Am)))))
axioms-used      (tm-2 tm-8 tm-1 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-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-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-74012.        (((A -> (B and A)) -> (A -> (B and A))) -> (((A -> (B and A)) or (A -> (B and A))) -> (A -> (B and A)))), M:tm-55, m:tm-850, u:((A (-> Am (and Bm Am))) (Cm (-> Am (and Bm Am))) (B (-> Am (and Bm Am))) (C (-> Am (and Bm Am))))
================================================================
tm-name          tm-74013
in-theory        74013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-54 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-74013.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-54, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74014
in-theory        74014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((B -> (C and B)) -> ((A or B) -> (C and B))))
theorem-size     31
proof            (modus-ponens tm-51 tm-850 ((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am))))))
axioms-used      (tm-8 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74014.        (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((B -> (C and B)) -> ((A or B) -> (C and B)))), M:tm-51, m:tm-850, u:((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am)))))
================================================================
tm-name          tm-74015
in-theory        74015
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((B -> (C and B)) -> (A and (B -> (C and B)))))
theorem-size     29
proof            (modus-ponens tm-48 tm-850 ((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am)))))))
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
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-74015.        ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((B -> (C and B)) -> (A and (B -> (C and B))))), M:tm-48, m:tm-850, u:((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (-> (-> Am (and Bm Am)) (and B (-> Am (and Bm Am))))))
================================================================
tm-name          tm-74016
in-theory        74016
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((B -> (C and B)) -> D))
theorem-size     25
proof            (modus-ponens tm-47 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-5)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74016.        (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((B -> (C and B)) -> D)), M:tm-47, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-74017
in-theory        74017
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C))
theorem-size     25
proof            (modus-ponens tm-46 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-8 tm-3 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74017.        (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((A -> (B and A)) -> C)), M:tm-46, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-74018
in-theory        74018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((A -> (B and A)) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-45 tm-850 ((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (-> Am (and Bm Am)) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74018.        (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((A -> (B and A)) -> (A -> C))), M:tm-45, m:tm-850, u:((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (-> Am (and Bm Am)) (-> Am C))))
================================================================
tm-name          tm-74019
in-theory        74019
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> A)) -> ((B -> (C and B)) -> A))
theorem-size     17
proof            (modus-ponens tm-44 tm-850 ((A (-> Am (and Bm Am))) (B Cm) (C (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-8 tm-1 tm-2 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-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-74019.        ((A or ((B -> (C and B)) -> A)) -> ((B -> (C and B)) -> A)), M:tm-44, m:tm-850, u:((A (-> Am (and Bm Am))) (B Cm) (C (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-74020
in-theory        74020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E)))
theorem-size     21
proof            (modus-ponens tm-42 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 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-42.           (A -> ((B -> (C or B)) and 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-48.           (((A -> (B and 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-74020.        ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E))), M:tm-42, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74021
in-theory        74021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E)))
theorem-size     21
proof            (modus-ponens tm-32 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 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-32.           (A -> ((B -> (B or C)) and 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-48.           (((A -> (B and 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-74021.        ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E))), M:tm-32, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74022
in-theory        74022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((A -> (B and A)) -> C)))
theorem-size     23
proof            (modus-ponens tm-24 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74022.        (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((A -> (B and A)) -> C))), M:tm-24, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-74023
in-theory        74023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E)))
theorem-size     23
proof            (modus-ponens tm-23 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-48.           (((A -> (B and 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-74023.        ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E))), M:tm-23, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74024
in-theory        74024
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E)))
theorem-size     21
proof            (modus-ponens tm-22 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74024.        (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E))), M:tm-22, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74025
in-theory        74025
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E)))
theorem-size     21
proof            (modus-ponens tm-21 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74025.        (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E))), M:tm-21, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74026
in-theory        74026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-20 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74026.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-20, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74027
in-theory        74027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E)))
theorem-size     21
proof            (modus-ponens tm-19 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) 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-19.           (A -> ((B -> (C -> B)) 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-48.           (((A -> (B and 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-74027.        ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((C -> (D and C)) -> E))), M:tm-19, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74028
in-theory        74028
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (not ((A -> (B and A)) -> C))) -> (not ((A -> (B and A)) -> C)))
theorem-size     25
proof            (modus-ponens tm-9 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-9 tm-2 tm-1 tm-8 tm-5)
proof-size       113
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-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-74028.        ((((A -> (B and A)) -> C) -> (not ((A -> (B and A)) -> C))) -> (not ((A -> (B and A)) -> C))), M:tm-9, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-74029
in-theory        74029
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> D) -> ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> C)) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm))))
axioms-used      (tm-8 tm-2 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74029.        ((((A -> (B and A)) -> C) -> D) -> ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> C)) -> D)), M:tm-8, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (-> Am (and Bm Am)) Cm)))
================================================================
tm-name          tm-74030
in-theory        74030
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C and B)) -> D) -> ((B -> (C and B)) -> D)))
theorem-size     17
proof            (modus-ponens tm-7 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-74030.        (A or (((B -> (C and B)) -> D) -> ((B -> (C and B)) -> D))), M:tm-7, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74031
in-theory        74031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-74031.        ((((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)) or D), M:tm-6, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74032
in-theory        74032
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C and B)) -> D) -> ((B -> (C and B)) -> D)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-74032.        (A -> ((((B -> (C and B)) -> D) -> ((B -> (C and B)) -> D)) and A)), M:tm-5, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74033
in-theory        74033
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (A -> (B and A))) -> (((A -> (B and A)) -> C) -> C))
theorem-size     23
proof            (modus-ponens tm-2 tm-850 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> Am (and Bm Am))) (C Cm)))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-74033.        ((((A -> (B and A)) -> C) -> (A -> (B and A))) -> (((A -> (B and A)) -> C) -> C)), M:tm-2, m:tm-850, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> Am (and Bm Am))) (C Cm))
================================================================
tm-name          tm-74034
in-theory        74034
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C and B)) -> D) -> ((B -> (C and B)) -> D)))
theorem-size     17
proof            (modus-ponens tm-1 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-1 tm-2 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-74034.        (A -> (((B -> (C and B)) -> D) -> ((B -> (C and B)) -> D))), M:tm-1, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74035
in-theory        74035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     39
proof            (modus-ponens tm-808 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9)
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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-74035.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-808, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74036
in-theory        74036
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((D and (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C))))
theorem-size     76
proof            (modus-ponens tm-798 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
proof-size       224
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-74036.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((D and (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C)))), M:tm-798, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74037
in-theory        74037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     39
proof            (modus-ponens tm-757 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-74037.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-757, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74038
in-theory        74038
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) and D) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C))))
theorem-size     76
proof            (modus-ponens tm-747 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       224
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-48.           (((A -> (B and 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-74038.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) and D) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C)))), M:tm-747, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74039
in-theory        74039
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G))))
theorem-size     53
proof            (modus-ponens tm-708 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-74039.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G)))), M:tm-708, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74040
in-theory        74040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     41
proof            (modus-ponens tm-665 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-74040.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-665, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74041
in-theory        74041
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((not ((B or (A -> (B and A))) -> C)) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C))))
theorem-size     66
proof            (modus-ponens tm-654 tm-851 ((A (-> (-> Am (and Bm Am)) Cm)) (B (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (C (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       220
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-48.           (((A -> (B and 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-74041.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((not ((B or (A -> (B and A))) -> C)) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C)))), M:tm-654, m:tm-851, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (C (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74042
in-theory        74042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (D or (not ((A -> (B and A)) -> C))))
theorem-size     29
proof            (modus-ponens tm-623 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-74042.        ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (D or (not ((A -> (B and A)) -> C)))), M:tm-623, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74043
in-theory        74043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-622 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74043.        ((A -> (B -> (C or B))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-622, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74044
in-theory        74044
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B and A)) -> (C or (A -> (B and A)))) -> (not ((B or (A -> (B and A))) -> (C or (A -> (B and A)))))))
theorem-size     31
proof            (modus-ponens tm-618 tm-851 ((A (-> (-> (-> Am (and Bm Am)) (or C (-> Am (and Bm Am)))) (not (-> (or Bm (-> Am (and Bm Am))) (or C (-> Am (and Bm Am))))))) (B (-> Am (and Bm Am))) (Cm (or C (-> Am (and Bm Am))))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-5)
proof-size       145
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-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-74044.        (not (((A -> (B and A)) -> (C or (A -> (B and A)))) -> (not ((B or (A -> (B and A))) -> (C or (A -> (B and A))))))), M:tm-618, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) (or C (-> Am (and Bm Am)))) (not (-> (or Bm (-> Am (and Bm Am))) (or C (-> Am (and Bm Am))))))) (B (-> Am (and Bm Am))) (Cm (or C (-> Am (and Bm Am)))))
================================================================
tm-name          tm-74045
in-theory        74045
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (E or D)))
theorem-size     33
proof            (modus-ponens tm-609 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74045.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (E or D))), M:tm-609, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74046
in-theory        74046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     37
proof            (modus-ponens tm-605 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74046.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-605, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74047
in-theory        74047
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (E or D)) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-74047.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (E or D)) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))), M:tm-595, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74048
in-theory        74048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-550 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74048.        (((A -> (B or A)) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-550, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74049
in-theory        74049
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-540 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74049.        ((A or (B -> (C or B))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-540, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74050
in-theory        74050
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-530 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74050.        ((A or (B -> (B or C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-530, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74051
in-theory        74051
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     37
proof            (modus-ponens tm-520 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74051.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-520, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74052
in-theory        74052
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-510 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74052.        ((A or ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-510, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74053
in-theory        74053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-500 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74053.        ((A or ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-500, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74054
in-theory        74054
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G))))
theorem-size     43
proof            (modus-ponens tm-490 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74054.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G)))), M:tm-490, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74055
in-theory        74055
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-480 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74055.        ((A or (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-480, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74056
in-theory        74056
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> ((not ((A -> (B and A)) -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-470 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-74056.        ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> ((not ((A -> (B and A)) -> C)) or D)), M:tm-470, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74057
in-theory        74057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-469 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74057.        ((A -> (B -> (B or C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-469, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74058
in-theory        74058
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B and A)) -> ((A -> (B and A)) or C)) -> (not ((B or (A -> (B and A))) -> ((A -> (B and A)) or C)))))
theorem-size     31
proof            (modus-ponens tm-465 tm-851 ((A (-> (-> (-> Am (and Bm Am)) (or (-> Am (and Bm Am)) C)) (not (-> (or Bm (-> Am (and Bm Am))) (or (-> Am (and Bm Am)) C))))) (B (-> Am (and Bm Am))) (Cm (or (-> Am (and Bm Am)) C))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-5)
proof-size       145
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-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-74058.        (not (((A -> (B and A)) -> ((A -> (B and A)) or C)) -> (not ((B or (A -> (B and A))) -> ((A -> (B and A)) or C))))), M:tm-465, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) (or (-> Am (and Bm Am)) C)) (not (-> (or Bm (-> Am (and Bm Am))) (or (-> Am (and Bm Am)) C))))) (B (-> Am (and Bm Am))) (Cm (or (-> Am (and Bm Am)) C)))
================================================================
tm-name          tm-74059
in-theory        74059
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (D or E)))
theorem-size     33
proof            (modus-ponens tm-456 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74059.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (D or E))), M:tm-456, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74060
in-theory        74060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     37
proof            (modus-ponens tm-453 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74060.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-453, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74061
in-theory        74061
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (D or E)) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-74061.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (D or E)) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))), M:tm-443, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74062
in-theory        74062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-409 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74062.        (((A -> (A or B)) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-409, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74063
in-theory        74063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     37
proof            (modus-ponens tm-400 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74063.        (((A -> (B -> (A and B))) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-400, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74064
in-theory        74064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-391 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74064.        ((((A and B) -> B) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-391, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74065
in-theory        74065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-382 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74065.        ((((A and B) -> A) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-382, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74066
in-theory        74066
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G))))
theorem-size     43
proof            (modus-ponens tm-373 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74066.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G)))), M:tm-373, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74067
in-theory        74067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-364 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74067.        (((A -> (B -> A)) or C) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-364, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74068
in-theory        74068
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (D -> ((not ((A -> (B and A)) -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74068.        ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (D -> ((not ((A -> (B and A)) -> C)) and D))), M:tm-355, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74069
in-theory        74069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     37
proof            (modus-ponens tm-354 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74069.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-354, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74070
in-theory        74070
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B and A)) -> (C -> ((A -> (B and A)) and C))) -> (not ((B or (A -> (B and A))) -> (C -> ((A -> (B and A)) and C))))))
theorem-size     35
proof            (modus-ponens tm-350 tm-851 ((A (-> (-> (-> Am (and Bm Am)) (-> C (and (-> Am (and Bm Am)) C))) (not (-> (or Bm (-> Am (and Bm Am))) (-> C (and (-> Am (and Bm Am)) C)))))) (B (-> Am (and Bm Am))) (Cm (-> C (and (-> Am (and Bm Am)) C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-8)
proof-size       155
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-48.           (((A -> (B and 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-74070.        (not (((A -> (B and A)) -> (C -> ((A -> (B and A)) and C))) -> (not ((B or (A -> (B and A))) -> (C -> ((A -> (B and A)) and C)))))), M:tm-350, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) (-> C (and (-> Am (and Bm Am)) C))) (not (-> (or Bm (-> Am (and Bm Am))) (-> C (and (-> Am (and Bm Am)) C)))))) (B (-> Am (and Bm Am))) (Cm (-> C (and (-> Am (and Bm Am)) C))))
================================================================
tm-name          tm-74071
in-theory        74071
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (E -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-341 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74071.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74072
in-theory        74072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E))))
theorem-size     37
proof            (modus-ponens tm-338 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-74072.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E)))), M:tm-338, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74073
in-theory        74073
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) and (not ((A -> (B and A)) -> C)))))
theorem-size     74
proof            (modus-ponens tm-328 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       220
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-48.           (((A -> (B and 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-74073.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) and (not ((A -> (B and A)) -> C))))), M:tm-328, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74074
in-theory        74074
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (E -> (D and E))) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-74074.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (E -> (D and E))) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))), M:tm-327, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74075
in-theory        74075
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((D and E) -> E) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-74075.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((D and E) -> E) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))), M:tm-326, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74076
in-theory        74076
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((D and E) -> D) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-74076.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((D and E) -> D) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))), M:tm-325, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74077
in-theory        74077
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-74077.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))), M:tm-324, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74078
in-theory        74078
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (E -> D)) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-74078.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (E -> D)) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))), M:tm-323, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74079
in-theory        74079
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D and E) -> E))
theorem-size     33
proof            (modus-ponens tm-322 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74079.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74080
in-theory        74080
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D and E) -> D))
theorem-size     33
proof            (modus-ponens tm-320 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74080.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74081
in-theory        74081
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-318 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74081.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74082
in-theory        74082
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))))
theorem-size     65
proof            (modus-ponens tm-316 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-48.           (((A -> (B and 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-74082.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))))), M:tm-316, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74083
in-theory        74083
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (E -> D)))
theorem-size     33
proof            (modus-ponens tm-315 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74083.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74084
in-theory        74084
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not (not ((A -> (B and A)) -> C)))) -> (not (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))))))
theorem-size     76
proof            (modus-ponens tm-313 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       206
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-74084.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not (not ((A -> (B and A)) -> C)))) -> (not (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))))), M:tm-313, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74085
in-theory        74085
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((not ((A -> (B and A)) -> C)) -> D) -> (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) or (not ((A -> (B and A)) -> C))) -> D)))
theorem-size     68
proof            (modus-ponens tm-312 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       202
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-48.           (((A -> (B and 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-74085.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (((not ((A -> (B and A)) -> C)) -> D) -> (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) or (not ((A -> (B and A)) -> C))) -> D))), M:tm-312, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74086
in-theory        74086
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D or ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-74086.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D or ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))), M:tm-311, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74087
in-theory        74087
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((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))) or D))
theorem-size     57
proof            (modus-ponens tm-310 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-74087.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((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))) or D)), M:tm-310, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74088
in-theory        74088
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and D)))
theorem-size     59
proof            (modus-ponens tm-309 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
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-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-48.           (((A -> (B and 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-74088.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and D))), M:tm-309, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74089
in-theory        74089
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-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-48.           (((A -> (B and 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-74089.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) and (D -> ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))), M:tm-305, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74090
in-theory        74090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     39
proof            (modus-ponens tm-303 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74090.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-303, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74091
in-theory        74091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     37
proof            (modus-ponens tm-270 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74091.        ((A -> (((B and C) -> C) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-270, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74092
in-theory        74092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     37
proof            (modus-ponens tm-239 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74092.        ((A -> (((B and C) -> B) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-239, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74093
in-theory        74093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G))))
theorem-size     45
proof            (modus-ponens tm-210 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 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-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-74093.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G)))), M:tm-210, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74094
in-theory        74094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     37
proof            (modus-ponens tm-183 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74094.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-183, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74095
in-theory        74095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-157 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74095.        ((A -> ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-157, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74096
in-theory        74096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     43
proof            (modus-ponens tm-147 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74096.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-147, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74097
in-theory        74097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-134 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74097.        ((A -> ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-134, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74098
in-theory        74098
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     43
proof            (modus-ponens tm-125 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74098.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-125, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74099
in-theory        74099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G))))
theorem-size     43
proof            (modus-ponens tm-113 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74099.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G)))), M:tm-113, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74100
in-theory        74100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     47
proof            (modus-ponens tm-105 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-48.           (((A -> (B and 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-74100.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-105, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74101
in-theory        74101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E))))
theorem-size     35
proof            (modus-ponens tm-95 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74101.        (((A -> B) -> (A -> A)) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E)))), M:tm-95, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74102
in-theory        74102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (D -> (not ((A -> (B and A)) -> C))))
theorem-size     29
proof            (modus-ponens tm-84 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-1 tm-9 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-74102.        ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (D -> (not ((A -> (B and A)) -> C)))), M:tm-84, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74103
in-theory        74103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     35
proof            (modus-ponens tm-83 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74103.        ((A -> (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-83, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74104
in-theory        74104
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B and A)) -> (C -> (A -> (B and A)))) -> (not ((B or (A -> (B and A))) -> (C -> (A -> (B and A)))))))
theorem-size     31
proof            (modus-ponens tm-79 tm-851 ((A (-> (-> (-> Am (and Bm Am)) (-> C (-> Am (and Bm Am)))) (not (-> (or Bm (-> Am (and Bm Am))) (-> C (-> Am (and Bm Am))))))) (B (-> Am (and Bm Am))) (Cm (-> C (-> Am (and Bm Am))))))
axioms-used      (tm-9 tm-1 tm-8 tm-5)
proof-size       145
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-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-74104.        (not (((A -> (B and A)) -> (C -> (A -> (B and A)))) -> (not ((B or (A -> (B and A))) -> (C -> (A -> (B and A))))))), M:tm-79, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) (-> C (-> Am (and Bm Am)))) (not (-> (or Bm (-> Am (and Bm Am))) (-> C (-> Am (and Bm Am))))))) (B (-> Am (and Bm Am))) (Cm (-> C (-> Am (and Bm Am)))))
================================================================
tm-name          tm-74105
in-theory        74105
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((B -> (C and B)) -> D))))
theorem-size     33
proof            (modus-ponens tm-76 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74105.        (((not (not A)) -> A) and ((((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((B -> (C and B)) -> D)))), M:tm-76, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74106
in-theory        74106
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))))) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C)))
theorem-size     48
proof            (modus-ponens tm-73 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-5)
proof-size       152
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-48.           (((A -> (B and 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-74106.        (((not (not (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))))) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C))), M:tm-73, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74107
in-theory        74107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E))))
theorem-size     39
proof            (modus-ponens tm-69 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-48.           (((A -> (B and 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-74107.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E)))), M:tm-69, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74108
in-theory        74108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     41
proof            (modus-ponens tm-54 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-48.           (((A -> (B and 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-74108.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-54, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74109
in-theory        74109
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D)))) or (((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D)))) -> (not ((B -> (C and B)) -> D)))
theorem-size     48
proof            (modus-ponens tm-47 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-5)
proof-size       152
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-48.           (((A -> (B and 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-74109.        (((A and (((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D)))) or (((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D)))) -> (not ((B -> (C and B)) -> D))), M:tm-47, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74110
in-theory        74110
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) and D) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C)))
theorem-size     48
proof            (modus-ponens tm-46 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-5)
proof-size       152
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-48.           (((A -> (B and 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-74110.        ((((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) and D) or (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))) -> (not ((A -> (B and A)) -> C))), M:tm-46, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74111
in-theory        74111
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A or (B -> (A and B))) -> C)) or (((B -> (A and B)) -> C) -> (not ((A or (B -> (A and B))) -> C)))) -> (not ((B -> (A and B)) -> C)))
theorem-size     38
proof            (modus-ponens tm-44 tm-851 ((A (-> (-> Am (and Bm Am)) Cm)) (B (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (C (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-5)
proof-size       144
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-48.           (((A -> (B and 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-74111.        (((not ((A or (B -> (A and B))) -> C)) or (((B -> (A and B)) -> C) -> (not ((A or (B -> (A and B))) -> C)))) -> (not ((B -> (A and B)) -> C))), M:tm-44, m:tm-851, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (C (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74112
in-theory        74112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E))))
theorem-size     33
proof            (modus-ponens tm-42 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74112.        ((A -> (B or A)) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E)))), M:tm-42, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74113
in-theory        74113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E))))
theorem-size     33
proof            (modus-ponens tm-32 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74113.        ((A -> (A or B)) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E)))), M:tm-32, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74114
in-theory        74114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) and (not ((A -> (B and A)) -> C))))
theorem-size     46
proof            (modus-ponens tm-24 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74114.        ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) and (not ((A -> (B and A)) -> C)))), M:tm-24, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74115
in-theory        74115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E))))
theorem-size     35
proof            (modus-ponens tm-23 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74115.        ((A -> (B -> (A and B))) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E)))), M:tm-23, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74116
in-theory        74116
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E))))
theorem-size     33
proof            (modus-ponens tm-22 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74116.        (((A and B) -> B) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E)))), M:tm-22, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74117
in-theory        74117
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E))))
theorem-size     33
proof            (modus-ponens tm-21 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74117.        (((A and B) -> A) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E)))), M:tm-21, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74118
in-theory        74118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     41
proof            (modus-ponens tm-20 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74118.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-20, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74119
in-theory        74119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E))))
theorem-size     33
proof            (modus-ponens tm-19 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-74119.        ((A -> (B -> A)) and ((((C -> (D and C)) -> E) -> (not ((D or (C -> (D and C))) -> E))) -> (not ((C -> (D and C)) -> E)))), M:tm-19, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74120
in-theory        74120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))))
theorem-size     37
proof            (modus-ponens tm-12 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8 tm-5)
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-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-74120.        ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))), M:tm-12, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74121
in-theory        74121
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not (not ((A -> (B and A)) -> C)))) -> (not (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C)))))
theorem-size     48
proof            (modus-ponens tm-9 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-9 tm-8 tm-5)
proof-size       134
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-48.           (((A -> (B and 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-74121.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not (not ((A -> (B and A)) -> C)))) -> (not (((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))))), M:tm-9, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74122
in-theory        74122
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> (B and A)) -> C)) -> D) -> (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) or (not ((A -> (B and A)) -> C))) -> D))
theorem-size     40
proof            (modus-ponens tm-8 tm-851 ((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       128
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-48.           (((A -> (B and 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-74122.        (((not ((A -> (B and A)) -> C)) -> D) -> (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) or (not ((A -> (B and A)) -> C))) -> D)), M:tm-8, m:tm-851, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm)))) (B (not (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-74123
in-theory        74123
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((B -> (C and B)) -> D))))
theorem-size     29
proof            (modus-ponens tm-7 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-7 tm-9 tm-8 tm-5)
proof-size       109
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-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-74123.        (A or ((((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((B -> (C and B)) -> D)))), M:tm-7, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74124
in-theory        74124
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) or D)
theorem-size     29
proof            (modus-ponens tm-6 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-6 tm-9 tm-8 tm-5)
proof-size       109
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-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-74124.        (((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))) or D), M:tm-6, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74125
in-theory        74125
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((B -> (C and B)) -> D))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       113
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-48.           (((A -> (B and 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-74125.        (A -> (((((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((B -> (C and B)) -> D))) and A)), M:tm-5, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74126
in-theory        74126
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((B -> (C and B)) -> D))))
theorem-size     29
proof            (modus-ponens tm-1 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-1 tm-9 tm-8 tm-5)
proof-size       109
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-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-74126.        (A -> ((((B -> (C and B)) -> D) -> (not ((C or (B -> (C and B))) -> D))) -> (not ((B -> (C and B)) -> D)))), M:tm-1, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-74127
in-theory        74127
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((B or (A -> (B and A))) -> C)))
theorem-size     29
proof            (modus-ponens tm-852 tm-1 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       115
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-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-1.            (A -> (B -> A)), axiom
tm-74127.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-1, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74128
in-theory        74128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C -> D)) or ((B or (A -> (B and A))) -> (C -> D))) -> (((B or (A -> (B and A))) -> C) -> ((B or (A -> (B and A))) -> D)))
theorem-size     41
proof            (modus-ponens tm-852 tm-2 ((Am (or A (-> B (and A B)))) (C (-> Bm Cm)) (D (-> (-> (or A (-> B (and A B))) Bm) (-> (or A (-> B (and A B))) Cm)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       135
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-74128.        ((((A -> (B and A)) -> (C -> D)) or ((B or (A -> (B and A))) -> (C -> D))) -> (((B or (A -> (B and A))) -> C) -> ((B or (A -> (B and A))) -> D))), M:tm-852, m:tm-2, u:((Am (or A (-> B (and A B)))) (C (-> Bm Cm)) (D (-> (-> (or A (-> B (and A B))) Bm) (-> (or A (-> B (and A B))) Cm))))
================================================================
tm-name          tm-74129
in-theory        74129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (((B or (A -> (B and A))) -> C) and D)))
theorem-size     31
proof            (modus-ponens tm-852 tm-5 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> (or A (-> B (and A B))) C) Bm)))))
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-48.           (((A -> (B and 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-74129.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (((B or (A -> (B and A))) -> C) and D))), M:tm-852, m:tm-5, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> (or A (-> B (and A B))) C) Bm))))
================================================================
tm-name          tm-74130
in-theory        74130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) or D))
theorem-size     29
proof            (modus-ponens tm-852 tm-6 ((Am (-> (or A (-> B (and A B))) C)) (D (or (-> (or A (-> B (and A B))) C) Bm))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       115
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-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-6.            (A -> (A or B)), axiom
tm-74130.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) or D)), M:tm-852, m:tm-6, u:((Am (-> (or A (-> B (and A B))) C)) (D (or (-> (or A (-> B (and A B))) C) Bm)))
================================================================
tm-name          tm-74131
in-theory        74131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((B or (A -> (B and A))) -> C)))
theorem-size     29
proof            (modus-ponens tm-852 tm-7 ((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       115
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-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-7.            (A -> (B or A)), axiom
tm-74131.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-7, u:((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74132
in-theory        74132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((C -> D) -> (((B or (A -> (B and A))) or C) -> D)))
theorem-size     33
proof            (modus-ponens tm-852 tm-8 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (-> Bm Cm) (-> (or (or A (-> B (and A B))) Bm) Cm)))))
axioms-used      (tm-8 tm-5)
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-48.           (((A -> (B and 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-74132.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((C -> D) -> (((B or (A -> (B and A))) or C) -> D))), M:tm-852, m:tm-8, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (-> Bm Cm) (-> (or (or A (-> B (and A B))) Bm) Cm))))
================================================================
tm-name          tm-74133
in-theory        74133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> (not C)) -> (not (B or (A -> (B and A))))))
theorem-size     37
proof            (modus-ponens tm-852 tm-9 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (-> (or A (-> B (and A B))) (not Bm)) (not (or A (-> B (and A B))))))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       129
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-74133.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> (not C)) -> (not (B or (A -> (B and A)))))), M:tm-852, m:tm-9, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (-> (or A (-> B (and A B))) (not Bm)) (not (or A (-> B (and A B)))))))
================================================================
tm-name          tm-74134
in-theory        74134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-852 tm-11 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm Bm)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-74134.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> D))), M:tm-852, m:tm-11, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-74135
in-theory        74135
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (B or (A -> (B and A)))))
theorem-size     33
proof            (modus-ponens tm-852 tm-12 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       139
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-74135.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (B or (A -> (B and A))))), M:tm-852, m:tm-12, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (or A (-> B (and A B))))))
================================================================
tm-name          tm-74136
in-theory        74136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-852 tm-14 ((Am (-> (or 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       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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-74136.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-852, m:tm-14, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-74137
in-theory        74137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-852 tm-16 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-74137.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D and E) -> D)), M:tm-852, m:tm-16, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-74138
in-theory        74138
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-852 tm-18 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-74138.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D and E) -> E)), M:tm-852, m:tm-18, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-74139
in-theory        74139
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     33
proof            (modus-ponens tm-852 tm-19 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1)
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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-74139.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-19, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74140
in-theory        74140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A -> (B and A))) -> C)))
theorem-size     41
proof            (modus-ponens tm-852 tm-20 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (-> B (and A B))) C)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-74140.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-20, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74141
in-theory        74141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and E) -> D) and ((B or (A -> (B and A))) -> C)))
theorem-size     33
proof            (modus-ponens tm-852 tm-21 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (and Bm Cm) Bm) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-3)
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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-74141.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and E) -> D) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-21, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (and Bm Cm) Bm) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74142
in-theory        74142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and E) -> E) and ((B or (A -> (B and A))) -> C)))
theorem-size     33
proof            (modus-ponens tm-852 tm-22 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (and Bm Cm) Cm) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-4)
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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-74142.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and E) -> E) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-22, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (and Bm Cm) Cm) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74143
in-theory        74143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (D and E))) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-23 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
proof-size       141
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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-74143.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (D and E))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-23, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74144
in-theory        74144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> ((B or (A -> (B and A))) and C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-24 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (and (or A (-> B (and A B))) Bm)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-74144.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> ((B or (A -> (B and A))) and C))), M:tm-852, m:tm-24, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (and (or A (-> B (and A B))) Bm))))
================================================================
tm-name          tm-74145
in-theory        74145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-852 tm-25 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-74145.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (D and E)))), M:tm-852, m:tm-25, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-74146
in-theory        74146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (D or E)) and ((B or (A -> (B and A))) -> C)))
theorem-size     33
proof            (modus-ponens tm-852 tm-32 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (or Bm Cm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-74146.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (D or E)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-32, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (or Bm Cm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74147
in-theory        74147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-852 tm-33 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-74147.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (D or E))), M:tm-852, m:tm-33, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-74148
in-theory        74148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E or D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     33
proof            (modus-ponens tm-852 tm-42 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (or Cm Bm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-74148.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E or D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-42, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (or Cm Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74149
in-theory        74149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-852 tm-43 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-74149.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E or D))), M:tm-852, m:tm-43, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-74150
in-theory        74150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((B or (A -> (B and A))) and D) or (B or (A -> (B and A)))) -> C))
theorem-size     37
proof            (modus-ponens tm-852 tm-46 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or (and (or A (-> B (and A B))) Cm) (or A (-> B (and A B)))) Bm))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-74150.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((B or (A -> (B and A))) and D) or (B or (A -> (B and A)))) -> C)), M:tm-852, m:tm-46, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or (and (or A (-> B (and A B))) Cm) (or A (-> B (and A B)))) Bm)))
================================================================
tm-name          tm-74151
in-theory        74151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and (B or (A -> (B and A)))) or (B or (A -> (B and A)))) -> C))
theorem-size     37
proof            (modus-ponens tm-852 tm-47 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or (and Cm (or A (-> B (and A B)))) (or A (-> B (and A B)))) Bm))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-74151.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and (B or (A -> (B and A)))) or (B or (A -> (B and A)))) -> C)), M:tm-852, m:tm-47, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or (and Cm (or A (-> B (and A B)))) (or A (-> B (and A B)))) Bm)))
================================================================
tm-name          tm-74152
in-theory        74152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (B or (A -> (B and A)))) -> C))
theorem-size     29
proof            (modus-ponens tm-852 tm-49 ((A Am) (Bm (-> B (and Am B))) (C Cm) (D (-> (or Am (or Am (-> B (and Am B)))) Cm))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       141
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-74152.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (B or (A -> (B and A)))) -> C)), M:tm-852, m:tm-49, u:((A Am) (Bm (-> B (and Am B))) (C Cm) (D (-> (or Am (or Am (-> B (and Am B)))) Cm)))
================================================================
tm-name          tm-74153
in-theory        74153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((A -> (B and A)) or (B or (A -> (B and A)))) -> C))
theorem-size     33
proof            (modus-ponens tm-852 tm-50 ((A Am) (Bm (-> B (and Am B))) (C Cm) (D (-> (or (-> B (and Am B)) (or Am (-> B (and Am B)))) Cm))))
axioms-used      (tm-8 tm-5 tm-7)
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-74153.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((A -> (B and A)) or (B or (A -> (B and A)))) -> C)), M:tm-852, m:tm-50, u:((A Am) (Bm (-> B (and Am B))) (C Cm) (D (-> (or (-> B (and Am B)) (or Am (-> B (and Am B)))) Cm)))
================================================================
tm-name          tm-74154
in-theory        74154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B or (A -> (B and A))) -> C)))
theorem-size     41
proof            (modus-ponens tm-852 tm-54 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
proof-size       159
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-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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-74154.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-54, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74155
in-theory        74155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-852 tm-56 ((Am (-> (or 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       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-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-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-74155.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-852, m:tm-56, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-74156
in-theory        74156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (C -> (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (C -> (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A)))))
theorem-size     44
proof            (modus-ponens tm-852 tm-57 ((Am (or A (-> B (and A B)))) (C (not (-> Bm (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-1)
proof-size       150
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-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-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-74156.        ((((A -> (B and A)) -> (not (C -> (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (C -> (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-57, u:((Am (or A (-> B (and A B)))) (C (not (-> Bm (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74157
in-theory        74157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (C -> ((B or (A -> (B and A))) and C)))) or ((B or (A -> (B and A))) -> (not (C -> ((B or (A -> (B and A))) and C))))) -> (not (B or (A -> (B and A)))))
theorem-size     48
proof            (modus-ponens tm-852 tm-61 ((Am (or A (-> B (and A B)))) (C (not (-> Bm (and (or A (-> B (and A B))) Bm)))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       158
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-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-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-74157.        ((((A -> (B and A)) -> (not (C -> ((B or (A -> (B and A))) and C)))) or ((B or (A -> (B and A))) -> (not (C -> ((B or (A -> (B and A))) and C))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-61, u:((Am (or A (-> B (and A B)))) (C (not (-> Bm (and (or A (-> B (and A B))) Bm)))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74158
in-theory        74158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not ((B or (A -> (B and A))) or C))) or ((B or (A -> (B and A))) -> (not ((B or (A -> (B and A))) or C)))) -> (not (B or (A -> (B and A)))))
theorem-size     44
proof            (modus-ponens tm-852 tm-62 ((Am (or A (-> B (and A B)))) (C (not (or (or A (-> B (and A B))) Bm))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-6)
proof-size       150
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-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-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-74158.        ((((A -> (B and A)) -> (not ((B or (A -> (B and A))) or C))) or ((B or (A -> (B and A))) -> (not ((B or (A -> (B and A))) or C)))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-62, u:((Am (or A (-> B (and A B)))) (C (not (or (or A (-> B (and A B))) Bm))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74159
in-theory        74159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (C or (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (C or (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A)))))
theorem-size     44
proof            (modus-ponens tm-852 tm-63 ((Am (or A (-> B (and A B)))) (C (not (or Bm (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-7)
proof-size       150
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-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-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-74159.        ((((A -> (B and A)) -> (not (C or (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (C or (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-63, u:((Am (or A (-> B (and A B)))) (C (not (or Bm (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74160
in-theory        74160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B or (A -> (B and A))) -> C)))
theorem-size     39
proof            (modus-ponens tm-852 tm-69 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-9)
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-74160.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-69, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74161
in-theory        74161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-852 tm-71 ((Am (-> (or 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       139
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-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-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-74161.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-852, m:tm-71, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-74162
in-theory        74162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((not (not (B or (A -> (B and A))))) or (B or (A -> (B and A)))) -> C))
theorem-size     37
proof            (modus-ponens tm-852 tm-73 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or (not (not (or A (-> B (and A B))))) (or A (-> B (and A B)))) Bm))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-74162.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((not (not (B or (A -> (B and A))))) or (B or (A -> (B and A)))) -> C)), M:tm-852, m:tm-73, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or (not (not (or A (-> B (and A B))))) (or A (-> B (and A B)))) Bm)))
================================================================
tm-name          tm-74163
in-theory        74163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((not (not D)) -> D) and ((B or (A -> (B and A))) -> C)))
theorem-size     33
proof            (modus-ponens tm-852 tm-76 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (not (not Bm)) Bm) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-10)
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-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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-74163.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((not (not D)) -> D) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-76, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (not (not Bm)) Bm) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74164
in-theory        74164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((not (not D)) -> D))
theorem-size     23
proof            (modus-ponens tm-852 tm-78 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-10)
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-48.           (((A -> (B and 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-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-74164.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((not (not D)) -> D)), M:tm-852, m:tm-78, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-74165
in-theory        74165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (C -> (D -> C)))) or ((B or (A -> (B and A))) -> (not (C -> (D -> C))))) -> (not (B or (A -> (B and A)))))
theorem-size     36
proof            (modus-ponens tm-852 tm-79 ((Am (or A (-> B (and A B)))) (C (not (-> Bm (-> Cm Bm)))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-1)
proof-size       156
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-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-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-74165.        ((((A -> (B and A)) -> (not (C -> (D -> C)))) or ((B or (A -> (B and A))) -> (not (C -> (D -> C))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-79, u:((Am (or A (-> B (and A B)))) (C (not (-> Bm (-> Cm Bm)))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74166
in-theory        74166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (F -> E))) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-83 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-74166.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (F -> E))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-83, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74167
in-theory        74167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (D -> C)))
theorem-size     29
proof            (modus-ponens tm-852 tm-84 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (-> Cm 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-74167.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (D -> C))), M:tm-852, m:tm-84, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (-> Cm Bm))))
================================================================
tm-name          tm-74168
in-theory        74168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-852 tm-85 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-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-74168.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (F -> E)))), M:tm-852, m:tm-85, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-74169
in-theory        74169
times-derived    3
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> C))
theorem-size     27
proof            (modus-ponens tm-852 tm-86 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (or A (-> B (and A B))) C))))
axioms-used      (tm-8 tm-5 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74169.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> C)), M:tm-852, m:tm-86, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (or A (-> B (and A B))) C)))
================================================================
tm-name          tm-74170
in-theory        74170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C -> D)) or ((B or (A -> (B and A))) -> (C -> D))) -> ((B or (A -> (B and A))) -> (C -> D)))
theorem-size     33
proof            (modus-ponens tm-852 tm-87 ((Am (or A (-> B (and A B)))) (C (-> Bm Cm)) (D (-> (or A (-> B (and A B))) (-> Bm Cm)))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74170.        ((((A -> (B and A)) -> (C -> D)) or ((B or (A -> (B and A))) -> (C -> D))) -> ((B or (A -> (B and A))) -> (C -> D))), M:tm-852, m:tm-87, u:((Am (or A (-> B (and A B)))) (C (-> Bm Cm)) (D (-> (or A (-> B (and A B))) (-> Bm Cm))))
================================================================
tm-name          tm-74171
in-theory        74171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> (D -> D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-95 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or A (-> B (and A B))) C)))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-74171.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> (D -> D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-95, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74172
in-theory        74172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> (D -> D)))
theorem-size     25
proof            (modus-ponens tm-852 tm-97 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
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-48.           (((A -> (B and 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-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-74172.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> (D -> D))), M:tm-852, m:tm-97, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-74173
in-theory        74173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> ((C -> (B or (A -> (B and A)))) -> D)) or ((B or (A -> (B and A))) -> ((C -> (B or (A -> (B and A)))) -> D))) -> ((B or (A -> (B and A))) -> D))
theorem-size     47
proof            (modus-ponens tm-852 tm-98 ((Am (or A (-> B (and A B)))) (C (-> (-> Bm (or A (-> B (and A B)))) Cm)) (D (-> (or A (-> B (and A B))) Cm))))
axioms-used      (tm-8 tm-5 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74173.        ((((A -> (B and A)) -> ((C -> (B or (A -> (B and A)))) -> D)) or ((B or (A -> (B and A))) -> ((C -> (B or (A -> (B and A)))) -> D))) -> ((B or (A -> (B and A))) -> D)), M:tm-852, m:tm-98, u:((Am (or A (-> B (and A B)))) (C (-> (-> Bm (or A (-> B (and A B)))) Cm)) (D (-> (or A (-> B (and A B))) Cm)))
================================================================
tm-name          tm-74174
in-theory        74174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> ((B or (A -> (B and A))) -> C)) or ((B or (A -> (B and A))) -> ((B or (A -> (B and A))) -> C))) -> ((B or (A -> (B and A))) -> C))
theorem-size     43
proof            (modus-ponens tm-852 tm-99 ((Am (or A (-> B (and A B)))) (C (-> (or A (-> B (and A B))) Bm)) (D (-> (or A (-> B (and A B))) Bm))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74174.        ((((A -> (B and A)) -> ((B or (A -> (B and A))) -> C)) or ((B or (A -> (B and A))) -> ((B or (A -> (B and A))) -> C))) -> ((B or (A -> (B and A))) -> C)), M:tm-852, m:tm-99, u:((Am (or A (-> B (and A B)))) (C (-> (or A (-> B (and A B))) Bm)) (D (-> (or A (-> B (and A B))) Bm)))
================================================================
tm-name          tm-74175
in-theory        74175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B or (A -> (B and A))) -> C)))
theorem-size     47
proof            (modus-ponens tm-852 tm-105 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or A (-> B (and A B))) C)))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-74175.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-105, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74176
in-theory        74176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-852 tm-107 ((Am (-> (or 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       189
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-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-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-74176.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-852, m:tm-107, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-74177
in-theory        74177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or ((B or (A -> (B and A))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (B or (A -> (B and A)))))
theorem-size     52
proof            (modus-ponens tm-852 tm-109 ((Am (or A (-> B (and A B)))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-1 tm-2)
proof-size       196
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-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-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-74177.        ((((A -> (B and A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or ((B or (A -> (B and A))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-109, u:((Am (or A (-> B (and A B)))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74178
in-theory        74178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A -> (B and A))) -> C)))
theorem-size     43
proof            (modus-ponens tm-852 tm-113 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (-> B (and A B))) C)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-74178.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-113, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74179
in-theory        74179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C -> (D -> E))) or ((B or (A -> (B and A))) -> (C -> (D -> E)))) -> ((B or (A -> (B and A))) -> ((C -> D) -> (C -> E))))
theorem-size     41
proof            (modus-ponens tm-852 tm-114 ((Am (or A (-> B (and A B)))) (C (-> Bm (-> Cm Dm))) (D (-> (or A (-> B (and A B))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
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-48.           (((A -> (B and 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-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-74179.        ((((A -> (B and A)) -> (C -> (D -> E))) or ((B or (A -> (B and A))) -> (C -> (D -> E)))) -> ((B or (A -> (B and A))) -> ((C -> D) -> (C -> E)))), M:tm-852, m:tm-114, u:((Am (or A (-> B (and A B)))) (C (-> Bm (-> Cm Dm))) (D (-> (or A (-> B (and A B))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-74180
in-theory        74180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-852 tm-115 ((Am (-> (or 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       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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-74180.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-852, m:tm-115, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-74181
in-theory        74181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B or (A -> (B and A))) -> C)))
theorem-size     43
proof            (modus-ponens tm-852 tm-125 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or A (-> B (and A B))) C)))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-74181.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-125, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74182
in-theory        74182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-852 tm-127 ((Am (-> (or 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       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-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-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-74182.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-852, m:tm-127, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-74183
in-theory        74183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not ((C and D) -> C))) or ((B or (A -> (B and A))) -> (not ((C and D) -> C)))) -> (not (B or (A -> (B and A)))))
theorem-size     36
proof            (modus-ponens tm-852 tm-130 ((Am (or A (-> B (and A B)))) (C (not (-> (and Bm Cm) Bm))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-1 tm-3)
proof-size       156
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-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-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-74183.        ((((A -> (B and A)) -> (not ((C and D) -> C))) or ((B or (A -> (B and A))) -> (not ((C and D) -> C)))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-130, u:((Am (or A (-> B (and A B)))) (C (not (-> (and Bm Cm) Bm))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74184
in-theory        74184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E and F) -> E)) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-134 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-74184.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E and F) -> E)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-134, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74185
in-theory        74185
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C and D)) or ((B or (A -> (B and A))) -> (C and D))) -> ((B or (A -> (B and A))) -> C))
theorem-size     31
proof            (modus-ponens tm-852 tm-135 ((Am (or A (-> B (and A B)))) (C (and Bm Cm)) (D (-> (or A (-> B (and A B))) 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-48.           (((A -> (B and 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-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-74185.        ((((A -> (B and A)) -> (C and D)) or ((B or (A -> (B and A))) -> (C and D))) -> ((B or (A -> (B and A))) -> C)), M:tm-852, m:tm-135, u:((Am (or A (-> B (and A B)))) (C (and Bm Cm)) (D (-> (or A (-> B (and A B))) Bm)))
================================================================
tm-name          tm-74186
in-theory        74186
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-852 tm-136 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-74186.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E and F) -> E))), M:tm-852, m:tm-136, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-74187
in-theory        74187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B or (A -> (B and A))) -> C)))
theorem-size     43
proof            (modus-ponens tm-852 tm-147 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-74187.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-147, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74188
in-theory        74188
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-852 tm-149 ((Am (-> (or 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       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-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-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-74188.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-852, m:tm-149, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-74189
in-theory        74189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not ((C and D) -> D))) or ((B or (A -> (B and A))) -> (not ((C and D) -> D)))) -> (not (B or (A -> (B and A)))))
theorem-size     36
proof            (modus-ponens tm-852 tm-153 ((Am (or A (-> B (and A B)))) (C (not (-> (and Bm Cm) Cm))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-1 tm-4)
proof-size       156
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-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-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-74189.        ((((A -> (B and A)) -> (not ((C and D) -> D))) or ((B or (A -> (B and A))) -> (not ((C and D) -> D)))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-153, u:((Am (or A (-> B (and A B)))) (C (not (-> (and Bm Cm) Cm))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74190
in-theory        74190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E and F) -> F)) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-157 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-74190.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E and F) -> F)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-157, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74191
in-theory        74191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C and D)) or ((B or (A -> (B and A))) -> (C and D))) -> ((B or (A -> (B and A))) -> D))
theorem-size     31
proof            (modus-ponens tm-852 tm-158 ((Am (or A (-> B (and A B)))) (C (and Bm Cm)) (D (-> (or A (-> B (and A B))) Cm))))
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-48.           (((A -> (B and 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-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-74191.        ((((A -> (B and A)) -> (C and D)) or ((B or (A -> (B and A))) -> (C and D))) -> ((B or (A -> (B and A))) -> D)), M:tm-852, m:tm-158, u:((Am (or A (-> B (and A B)))) (C (and Bm Cm)) (D (-> (or A (-> B (and A B))) Cm)))
================================================================
tm-name          tm-74192
in-theory        74192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-852 tm-159 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-74192.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E and F) -> F))), M:tm-852, m:tm-159, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-74193
in-theory        74193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not ((C -> (D -> C)) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not ((C -> (D -> C)) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A)))))
theorem-size     52
proof            (modus-ponens tm-852 tm-179 ((Am (or A (-> B (and A B)))) (C (not (and (-> Bm (-> Cm Bm)) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-1)
proof-size       178
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-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-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-74193.        ((((A -> (B and A)) -> (not ((C -> (D -> C)) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not ((C -> (D -> C)) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-179, u:((Am (or A (-> B (and A B)))) (C (not (and (-> Bm (-> Cm Bm)) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74194
in-theory        74194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-852 tm-183 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-74194.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-183, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74195
in-theory        74195
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     27
proof            (modus-ponens tm-852 tm-184 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
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-48.           (((A -> (B and 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-1.            (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-74195.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (F -> E)) and D))), M:tm-852, m:tm-184, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-74196
in-theory        74196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A)))))
theorem-size     68
proof            (modus-ponens tm-852 tm-206 ((Am (or A (-> B (and A B)))) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-2)
proof-size       218
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-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-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-74196.        ((((A -> (B and A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-206, u:((Am (or A (-> B (and A B)))) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74197
in-theory        74197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     45
proof            (modus-ponens tm-852 tm-210 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       191
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-74197.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-210, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74198
in-theory        74198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     35
proof            (modus-ponens tm-852 tm-211 ((Am (-> (or 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       177
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-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-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-74198.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-852, m:tm-211, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-74199
in-theory        74199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (((C and D) -> C) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (((C and D) -> C) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A)))))
theorem-size     52
proof            (modus-ponens tm-852 tm-235 ((Am (or A (-> B (and A B)))) (C (not (and (-> (and Bm Cm) Bm) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-3)
proof-size       178
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-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-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-74199.        ((((A -> (B and A)) -> (not (((C and D) -> C) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (((C and D) -> C) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-235, u:((Am (or A (-> B (and A B)))) (C (not (and (-> (and Bm Cm) Bm) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74200
in-theory        74200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-852 tm-239 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-74200.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-239, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74201
in-theory        74201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (((E and F) -> E) and D)))
theorem-size     27
proof            (modus-ponens tm-852 tm-240 ((Am (-> (or 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       145
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-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-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-74201.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (((E and F) -> E) and D))), M:tm-852, m:tm-240, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-74202
in-theory        74202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (((C and D) -> D) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (((C and D) -> D) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A)))))
theorem-size     52
proof            (modus-ponens tm-852 tm-266 ((Am (or A (-> B (and A B)))) (C (not (and (-> (and Bm Cm) Cm) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-4)
proof-size       178
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-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-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-74202.        ((((A -> (B and A)) -> (not (((C and D) -> D) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not (((C and D) -> D) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-266, u:((Am (or A (-> B (and A B)))) (C (not (and (-> (and Bm Cm) Cm) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74203
in-theory        74203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-852 tm-270 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-74203.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-270, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74204
in-theory        74204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (((E and F) -> F) and D)))
theorem-size     27
proof            (modus-ponens tm-852 tm-271 ((Am (-> (or 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       145
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-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-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-74204.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (((E and F) -> F) and D))), M:tm-852, m:tm-271, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-74205
in-theory        74205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not ((C -> (D -> (C and D))) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not ((C -> (D -> (C and D))) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A)))))
theorem-size     56
proof            (modus-ponens tm-852 tm-299 ((Am (or A (-> B (and A B)))) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       188
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-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-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-74205.        ((((A -> (B and A)) -> (not ((C -> (D -> (C and D))) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not ((C -> (D -> (C and D))) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-299, u:((Am (or A (-> B (and A B)))) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74206
in-theory        74206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     39
proof            (modus-ponens tm-852 tm-303 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-74206.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-303, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74207
in-theory        74207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     29
proof            (modus-ponens tm-852 tm-304 ((Am (-> (or 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       153
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-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-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-74207.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-852, m:tm-304, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-74208
in-theory        74208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> ((B or (A -> (B and A))) -> C))))
theorem-size     39
proof            (modus-ponens tm-852 tm-305 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (-> (or A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       161
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-74208.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> ((B or (A -> (B and A))) -> C)))), M:tm-852, m:tm-305, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (-> (or A (-> B (and A B))) C)))))
================================================================
tm-name          tm-74209
in-theory        74209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C -> D)) or ((B or (A -> (B and A))) -> (C -> D))) -> (((B or (A -> (B and A))) -> (C -> D)) and (((B or (A -> (B and A))) -> C) -> ((B or (A -> (B and A))) -> D))))
theorem-size     53
proof            (modus-ponens tm-852 tm-306 ((Am (or A (-> B (and A B)))) (C (-> Bm Cm)) (D (and (-> (or A (-> B (and A B))) (-> Bm Cm)) (-> (-> (or A (-> B (and A B))) Bm) (-> (or A (-> B (and A B))) Cm))))))
axioms-used      (tm-8 tm-5 tm-2)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-74209.        ((((A -> (B and A)) -> (C -> D)) or ((B or (A -> (B and A))) -> (C -> D))) -> (((B or (A -> (B and A))) -> (C -> D)) and (((B or (A -> (B and A))) -> C) -> ((B or (A -> (B and A))) -> D)))), M:tm-852, m:tm-306, u:((Am (or A (-> B (and A B)))) (C (-> Bm Cm)) (D (and (-> (or A (-> B (and A B))) (-> Bm Cm)) (-> (-> (or A (-> B (and A B))) Bm) (-> (or A (-> B (and A B))) Cm)))))
================================================================
tm-name          tm-74210
in-theory        74210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (((B or (A -> (B and A))) -> C) and D))))
theorem-size     41
proof            (modus-ponens tm-852 tm-309 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (and (-> (or A (-> B (and A B))) C) Bm))))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-74210.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (((B or (A -> (B and A))) -> C) and D)))), M:tm-852, m:tm-309, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (and (-> (or A (-> B (and A B))) C) Bm)))))
================================================================
tm-name          tm-74211
in-theory        74211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((B or (A -> (B and A))) -> C) or D)))
theorem-size     39
proof            (modus-ponens tm-852 tm-310 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (or (-> (or A (-> B (and A B))) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       161
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-74211.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((B or (A -> (B and A))) -> C) or D))), M:tm-852, m:tm-310, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (or (-> (or A (-> B (and A B))) C) Bm))))
================================================================
tm-name          tm-74212
in-theory        74212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D or ((B or (A -> (B and A))) -> C))))
theorem-size     39
proof            (modus-ponens tm-852 tm-311 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (or Bm (-> (or A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       161
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-74212.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D or ((B or (A -> (B and A))) -> C)))), M:tm-852, m:tm-311, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (or Bm (-> (or A (-> B (and A B))) C)))))
================================================================
tm-name          tm-74213
in-theory        74213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((C -> D) -> (((B or (A -> (B and A))) or C) -> D))))
theorem-size     43
proof            (modus-ponens tm-852 tm-312 ((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (-> Bm Cm) (-> (or (or A (-> B (and A B))) Bm) Cm))))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-74213.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((C -> D) -> (((B or (A -> (B and A))) or C) -> D)))), M:tm-852, m:tm-312, u:((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (-> Bm Cm) (-> (or (or A (-> B (and A B))) Bm) Cm)))))
================================================================
tm-name          tm-74214
in-theory        74214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((B or (A -> (B and A))) -> (not C)) -> (not (B or (A -> (B and A)))))))
theorem-size     47
proof            (modus-ponens tm-852 tm-313 ((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (-> (or A (-> B (and A B))) (not Bm)) (not (or A (-> B (and A B)))))))))
axioms-used      (tm-8 tm-5 tm-2 tm-9)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-74214.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((B or (A -> (B and A))) -> (not C)) -> (not (B or (A -> (B and A))))))), M:tm-852, m:tm-313, u:((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (-> (or A (-> B (and A B))) (not Bm)) (not (or A (-> B (and A B))))))))
================================================================
tm-name          tm-74215
in-theory        74215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (E -> D))))
theorem-size     33
proof            (modus-ponens tm-852 tm-315 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-74215.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (E -> D)))), M:tm-852, m:tm-315, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-74216
in-theory        74216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((B or (A -> (B and A))) -> (B or (A -> (B and A))))))
theorem-size     43
proof            (modus-ponens tm-852 tm-316 ((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (or A (-> B (and A B))) (or A (-> B (and A B))))))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-74216.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((B or (A -> (B and A))) -> (B or (A -> (B and A)))))), M:tm-852, m:tm-316, u:((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (or A (-> B (and A B))) (or A (-> B (and A B)))))))
================================================================
tm-name          tm-74217
in-theory        74217
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-852 tm-318 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-74217.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-852, m:tm-318, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-74218
in-theory        74218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D and E) -> D)))
theorem-size     33
proof            (modus-ponens tm-852 tm-320 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-74218.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D and E) -> D))), M:tm-852, m:tm-320, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-74219
in-theory        74219
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D and E) -> E)))
theorem-size     33
proof            (modus-ponens tm-852 tm-322 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-4)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-74219.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D and E) -> E))), M:tm-852, m:tm-322, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-74220
in-theory        74220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (E -> D)) and ((B or (A -> (B and A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-852 tm-323 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> Bm (-> Cm Bm)) (-> (or A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-74220.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (E -> D)) and ((B or (A -> (B and A))) -> C)))), M:tm-852, m:tm-323, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> Bm (-> Cm Bm)) (-> (or A (-> B (and A B))) C)))))
================================================================
tm-name          tm-74221
in-theory        74221
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A -> (B and A))) -> C))))
theorem-size     51
proof            (modus-ponens tm-852 tm-324 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-74221.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A -> (B and A))) -> C)))), M:tm-852, m:tm-324, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (-> B (and A B))) C)))))
================================================================
tm-name          tm-74222
in-theory        74222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((D and E) -> D) and ((B or (A -> (B and A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-852 tm-325 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> (and Bm Cm) Bm) (-> (or A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-74222.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((D and E) -> D) and ((B or (A -> (B and A))) -> C)))), M:tm-852, m:tm-325, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> (and Bm Cm) Bm) (-> (or A (-> B (and A B))) C)))))
================================================================
tm-name          tm-74223
in-theory        74223
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((D and E) -> E) and ((B or (A -> (B and A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-852 tm-326 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> (and Bm Cm) Cm) (-> (or A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-74223.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((D and E) -> E) and ((B or (A -> (B and A))) -> C)))), M:tm-852, m:tm-326, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> (and Bm Cm) Cm) (-> (or A (-> B (and A B))) C)))))
================================================================
tm-name          tm-74224
in-theory        74224
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (E -> (D and E))) and ((B or (A -> (B and A))) -> C))))
theorem-size     45
proof            (modus-ponens tm-852 tm-327 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-74224.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (E -> (D and E))) and ((B or (A -> (B and A))) -> C)))), M:tm-852, m:tm-327, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (-> B (and A B))) C)))))
================================================================
tm-name          tm-74225
in-theory        74225
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((B or (A -> (B and A))) -> ((B or (A -> (B and A))) and C))))
theorem-size     45
proof            (modus-ponens tm-852 tm-328 ((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (or A (-> B (and A B))) (and (or A (-> B (and A B))) Bm))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-74225.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((B or (A -> (B and A))) -> ((B or (A -> (B and A))) and C)))), M:tm-852, m:tm-328, u:((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (or A (-> B (and A B))) (and (or A (-> B (and A B))) Bm)))))
================================================================
tm-name          tm-74226
in-theory        74226
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-852 tm-338 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-74226.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-338, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74227
in-theory        74227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-852 tm-340 ((Am (-> (or 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       153
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-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-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-74227.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> (D -> (D and E)))), M:tm-852, m:tm-340, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-74228
in-theory        74228
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-852 tm-341 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (-> Cm (and Bm Cm)))))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-74228.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (E -> (D and E))))), M:tm-852, m:tm-341, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-74229
in-theory        74229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> ((C -> ((B or (A -> (B and A))) and C)) -> D)) or ((B or (A -> (B and A))) -> ((C -> ((B or (A -> (B and A))) and C)) -> D))) -> ((B or (A -> (B and A))) -> D))
theorem-size     51
proof            (modus-ponens tm-852 tm-349 ((Am (or A (-> B (and A B)))) (C (-> (-> Bm (and (or A (-> B (and A B))) Bm)) Cm)) (D (-> (or A (-> B (and A B))) Cm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74229.        ((((A -> (B and A)) -> ((C -> ((B or (A -> (B and A))) and C)) -> D)) or ((B or (A -> (B and A))) -> ((C -> ((B or (A -> (B and A))) and C)) -> D))) -> ((B or (A -> (B and A))) -> D)), M:tm-852, m:tm-349, u:((Am (or A (-> B (and A B)))) (C (-> (-> Bm (and (or A (-> B (and A B))) Bm)) Cm)) (D (-> (or A (-> B (and A B))) Cm)))
================================================================
tm-name          tm-74230
in-theory        74230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (C -> (D -> (C and D))))) or ((B or (A -> (B and A))) -> (not (C -> (D -> (C and D)))))) -> (not (B or (A -> (B and A)))))
theorem-size     40
proof            (modus-ponens tm-852 tm-350 ((Am (or A (-> B (and A B)))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-1)
proof-size       166
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-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-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-74230.        ((((A -> (B and A)) -> (not (C -> (D -> (C and D))))) or ((B or (A -> (B and A))) -> (not (C -> (D -> (C and D)))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-350, u:((Am (or A (-> B (and A B)))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74231
in-theory        74231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-852 tm-354 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-74231.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-354, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74232
in-theory        74232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (D -> (C and D))))
theorem-size     31
proof            (modus-ponens tm-852 tm-355 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       157
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-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-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-74232.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (D -> (C and D)))), M:tm-852, m:tm-355, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-74233
in-theory        74233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-852 tm-356 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-1)
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-48.           (((A -> (B and 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-1.            (A -> (B -> 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-74233.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (F -> (E and F))))), M:tm-852, m:tm-356, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-74234
in-theory        74234
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> D)) or F) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-364 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-74234.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> D)) or F) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-364, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74235
in-theory        74235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> D)) or F))
theorem-size     25
proof            (modus-ponens tm-852 tm-365 ((Am (-> (or A (-> B (and A B))) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 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-48.           (((A -> (B and 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-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-74235.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> D)) or F)), M:tm-852, m:tm-365, u:((Am (-> (or A (-> B (and A B))) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-74236
in-theory        74236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B or (A -> (B and A))) -> C)))
theorem-size     43
proof            (modus-ponens tm-852 tm-373 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-74236.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-373, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74237
in-theory        74237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     33
proof            (modus-ponens tm-852 tm-374 ((Am (-> (or 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       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-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-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-74237.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-852, m:tm-374, u:((Am (-> (or A (-> B (and A B))) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-74238
in-theory        74238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D and E) -> D) or F) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-382 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-74238.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D and E) -> D) or F) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-382, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74239
in-theory        74239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and E) -> D) or F))
theorem-size     25
proof            (modus-ponens tm-852 tm-383 ((Am (-> (or 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       137
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-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-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-74239.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and E) -> D) or F)), M:tm-852, m:tm-383, u:((Am (-> (or A (-> B (and A B))) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-74240
in-theory        74240
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D and E) -> E) or F) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-391 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-74240.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D and E) -> E) or F) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-391, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74241
in-theory        74241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and E) -> E) or F))
theorem-size     25
proof            (modus-ponens tm-852 tm-392 ((Am (-> (or 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       137
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-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-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-74241.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D and E) -> E) or F)), M:tm-852, m:tm-392, u:((Am (-> (or A (-> B (and A B))) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-74242
in-theory        74242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> (D and E))) or F) and ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-852 tm-400 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-74242.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E -> (D and E))) or F) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-400, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74243
in-theory        74243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (D and E))) or F))
theorem-size     27
proof            (modus-ponens tm-852 tm-401 ((Am (-> (or 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       145
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-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-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-74243.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (D and E))) or F)), M:tm-852, m:tm-401, u:((Am (-> (or A (-> B (and A B))) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-74244
in-theory        74244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (D or E)) or F) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-409 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-74244.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (D or E)) or F) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-409, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74245
in-theory        74245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (D or E)) or F))
theorem-size     25
proof            (modus-ponens tm-852 tm-410 ((Am (-> (or 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       137
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-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-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-74245.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (D or E)) or F)), M:tm-852, m:tm-410, u:((Am (-> (or A (-> B (and A B))) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-74246
in-theory        74246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (D or E)) and ((B or (A -> (B and A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-852 tm-443 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> Bm (or Bm Cm)) (-> (or A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-74246.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (D or E)) and ((B or (A -> (B and A))) -> C)))), M:tm-852, m:tm-443, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> Bm (or Bm Cm)) (-> (or A (-> B (and A B))) C)))))
================================================================
tm-name          tm-74247
in-theory        74247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not ((C -> (C or D)) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not ((C -> (C or D)) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A)))))
theorem-size     52
proof            (modus-ponens tm-852 tm-449 ((Am (or A (-> B (and A B)))) (C (not (and (-> Bm (or Bm Cm)) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-6)
proof-size       178
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-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-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-74247.        ((((A -> (B and A)) -> (not ((C -> (C or D)) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not ((C -> (C or D)) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-449, u:((Am (or A (-> B (and A B)))) (C (not (and (-> Bm (or Bm Cm)) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74248
in-theory        74248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-852 tm-453 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-74248.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-453, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74249
in-theory        74249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     27
proof            (modus-ponens tm-852 tm-454 ((Am (-> (or 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       145
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-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-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-74249.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (E or F)) and D))), M:tm-852, m:tm-454, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-74250
in-theory        74250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (D or E))))
theorem-size     33
proof            (modus-ponens tm-852 tm-456 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-74250.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (D or E)))), M:tm-852, m:tm-456, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-74251
in-theory        74251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (((B or (A -> (B and A))) or C) -> D)) or ((B or (A -> (B and A))) -> (((B or (A -> (B and A))) or C) -> D))) -> ((B or (A -> (B and A))) -> D))
theorem-size     47
proof            (modus-ponens tm-852 tm-464 ((Am (or A (-> B (and A B)))) (C (-> (or (or A (-> B (and A B))) Bm) Cm)) (D (-> (or A (-> B (and A B))) Cm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74251.        ((((A -> (B and A)) -> (((B or (A -> (B and A))) or C) -> D)) or ((B or (A -> (B and A))) -> (((B or (A -> (B and A))) or C) -> D))) -> ((B or (A -> (B and A))) -> D)), M:tm-852, m:tm-464, u:((Am (or A (-> B (and A B)))) (C (-> (or (or A (-> B (and A B))) Bm) Cm)) (D (-> (or A (-> B (and A B))) Cm)))
================================================================
tm-name          tm-74252
in-theory        74252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (C -> (C or D)))) or ((B or (A -> (B and A))) -> (not (C -> (C or D))))) -> (not (B or (A -> (B and A)))))
theorem-size     36
proof            (modus-ponens tm-852 tm-465 ((Am (or A (-> B (and A B)))) (C (not (-> Bm (or Bm Cm)))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-1 tm-6)
proof-size       156
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-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-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-74252.        ((((A -> (B and A)) -> (not (C -> (C or D)))) or ((B or (A -> (B and A))) -> (not (C -> (C or D))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-465, u:((Am (or A (-> B (and A B)))) (C (not (-> Bm (or Bm Cm)))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74253
in-theory        74253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (E or F))) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-469 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-74253.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (E or F))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-469, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74254
in-theory        74254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (C or D)))
theorem-size     29
proof            (modus-ponens tm-852 tm-470 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-74254.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (C or D))), M:tm-852, m:tm-470, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (or Bm Cm))))
================================================================
tm-name          tm-74255
in-theory        74255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-852 tm-471 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-74255.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (E or F)))), M:tm-852, m:tm-471, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-74256
in-theory        74256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or (E -> (F -> E))) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-480 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-74256.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or (E -> (F -> E))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-480, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74257
in-theory        74257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-852 tm-481 ((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 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-48.           (((A -> (B and 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-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-74257.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or (E -> (F -> E)))), M:tm-852, m:tm-481, u:((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-74258
in-theory        74258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A -> (B and A))) -> C)))
theorem-size     43
proof            (modus-ponens tm-852 tm-490 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-74258.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-490, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74259
in-theory        74259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-852 tm-491 ((Am (-> (or 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       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-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-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-74259.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-852, m:tm-491, u:((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-74260
in-theory        74260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or ((E and F) -> E)) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-500 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-74260.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or ((E and F) -> E)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-500, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74261
in-theory        74261
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-852 tm-501 ((Am (-> (or 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       137
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-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-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-74261.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((E and F) -> E))), M:tm-852, m:tm-501, u:((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-74262
in-theory        74262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or ((E and F) -> F)) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-510 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-74262.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or ((E and F) -> F)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-510, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74263
in-theory        74263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-852 tm-511 ((Am (-> (or 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       137
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-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-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-74263.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((E and F) -> F))), M:tm-852, m:tm-511, u:((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-74264
in-theory        74264
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-852 tm-520 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-74264.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-520, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74265
in-theory        74265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-852 tm-521 ((Am (-> (or 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       145
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-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-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-74265.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or (E -> (F -> (E and F))))), M:tm-852, m:tm-521, u:((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-74266
in-theory        74266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or (E -> (E or F))) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-530 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-74266.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or (E -> (E or F))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-530, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74267
in-theory        74267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-852 tm-531 ((Am (-> (or 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       137
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-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-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-74267.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or (E -> (E or F)))), M:tm-852, m:tm-531, u:((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-74268
in-theory        74268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or (E -> (F or E))) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-540 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-74268.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or (E -> (F or E))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-540, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74269
in-theory        74269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-852 tm-541 ((Am (-> (or 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       137
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-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-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-74269.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or (E -> (F or E)))), M:tm-852, m:tm-541, u:((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-74270
in-theory        74270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E or D)) or F) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-550 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-74270.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E or D)) or F) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-550, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74271
in-theory        74271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E or D)) or F))
theorem-size     25
proof            (modus-ponens tm-852 tm-551 ((Am (-> (or 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       137
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-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-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-74271.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E or D)) or F)), M:tm-852, m:tm-551, u:((Am (-> (or A (-> B (and A B))) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-74272
in-theory        74272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (E or D)) and ((B or (A -> (B and A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-852 tm-595 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> Bm (or Cm Bm)) (-> (or A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-74272.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((D -> (E or D)) and ((B or (A -> (B and A))) -> C)))), M:tm-852, m:tm-595, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (and (-> Bm (or Cm Bm)) (-> (or A (-> B (and A B))) C)))))
================================================================
tm-name          tm-74273
in-theory        74273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not ((C -> (D or C)) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not ((C -> (D or C)) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A)))))
theorem-size     52
proof            (modus-ponens tm-852 tm-601 ((Am (or A (-> B (and A B)))) (C (not (and (-> Bm (or Cm Bm)) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-7)
proof-size       178
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-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-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-74273.        ((((A -> (B and A)) -> (not ((C -> (D or C)) and (B or (A -> (B and A)))))) or ((B or (A -> (B and A))) -> (not ((C -> (D or C)) and (B or (A -> (B and A))))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-601, u:((Am (or A (-> B (and A B)))) (C (not (and (-> Bm (or Cm Bm)) (or A (-> B (and A B)))))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74274
in-theory        74274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-852 tm-605 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-74274.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-605, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74275
in-theory        74275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     27
proof            (modus-ponens tm-852 tm-606 ((Am (-> (or 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       145
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-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-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-74275.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> ((E -> (F or E)) and D))), M:tm-852, m:tm-606, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-74276
in-theory        74276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (E or D))))
theorem-size     33
proof            (modus-ponens tm-852 tm-609 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-74276.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (D -> (E or D)))), M:tm-852, m:tm-609, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (or A (-> B (and A B))) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-74277
in-theory        74277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> ((C or (B or (A -> (B and A)))) -> D)) or ((B or (A -> (B and A))) -> ((C or (B or (A -> (B and A)))) -> D))) -> ((B or (A -> (B and A))) -> D))
theorem-size     47
proof            (modus-ponens tm-852 tm-617 ((Am (or A (-> B (and A B)))) (C (-> (or Bm (or A (-> B (and A B)))) Cm)) (D (-> (or A (-> B (and A B))) Cm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74277.        ((((A -> (B and A)) -> ((C or (B or (A -> (B and A)))) -> D)) or ((B or (A -> (B and A))) -> ((C or (B or (A -> (B and A)))) -> D))) -> ((B or (A -> (B and A))) -> D)), M:tm-852, m:tm-617, u:((Am (or A (-> B (and A B)))) (C (-> (or Bm (or A (-> B (and A B)))) Cm)) (D (-> (or A (-> B (and A B))) Cm)))
================================================================
tm-name          tm-74278
in-theory        74278
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (C -> (D or C)))) or ((B or (A -> (B and A))) -> (not (C -> (D or C))))) -> (not (B or (A -> (B and A)))))
theorem-size     36
proof            (modus-ponens tm-852 tm-618 ((Am (or A (-> B (and A B)))) (C (not (-> Bm (or Cm Bm)))) (D (not (or A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-9 tm-1 tm-7)
proof-size       156
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-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-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-74278.        ((((A -> (B and A)) -> (not (C -> (D or C)))) or ((B or (A -> (B and A))) -> (not (C -> (D or C))))) -> (not (B or (A -> (B and A))))), M:tm-852, m:tm-618, u:((Am (or A (-> B (and A B)))) (C (not (-> Bm (or Cm Bm)))) (D (not (or A (-> B (and A B))))))
================================================================
tm-name          tm-74279
in-theory        74279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (F or E))) and ((B or (A -> (B and A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-852 tm-622 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-74279.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> (E -> (F or E))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-622, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74280
in-theory        74280
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (D or C)))
theorem-size     29
proof            (modus-ponens tm-852 tm-623 ((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-74280.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((B or (A -> (B and A))) -> (D or C))), M:tm-852, m:tm-623, u:((Am (or A (-> B (and A B)))) (C Bm) (D (-> (or A (-> B (and A B))) (or Cm Bm))))
================================================================
tm-name          tm-74281
in-theory        74281
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-852 tm-624 ((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-74281.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D -> (E -> (F or E)))), M:tm-852, m:tm-624, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-74282
in-theory        74282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B or (A -> (B and A))) -> C)))
theorem-size     41
proof            (modus-ponens tm-852 tm-665 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-74282.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-665, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74283
in-theory        74283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-852 tm-667 ((Am (-> (or 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       163
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-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-1.            (A -> (B -> A)), 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-74283.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-852, m:tm-667, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-74284
in-theory        74284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B or (A -> (B and A))) -> C)))
theorem-size     53
proof            (modus-ponens tm-852 tm-708 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       221
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-74284.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-708, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74285
in-theory        74285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-852 tm-710 ((Am (-> (or 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       207
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-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-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-74285.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-852, m:tm-710, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-74286
in-theory        74286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((((B or (A -> (B and A))) and D) or (B or (A -> (B and A)))) -> C)))
theorem-size     47
proof            (modus-ponens tm-852 tm-747 ((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (or (and (or A (-> B (and A B))) Cm) (or A (-> B (and A B)))) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-74286.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((((B or (A -> (B and A))) and D) or (B or (A -> (B and A)))) -> C))), M:tm-852, m:tm-747, u:((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (or (and (or A (-> B (and A B))) Cm) (or A (-> B (and A B)))) Bm))))
================================================================
tm-name          tm-74287
in-theory        74287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B or (A -> (B and A))) -> C)))
theorem-size     39
proof            (modus-ponens tm-852 tm-757 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-74287.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-757, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74288
in-theory        74288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-852 tm-759 ((Am (-> (or 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       157
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-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-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-74288.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-852, m:tm-759, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-74289
in-theory        74289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((D and (B or (A -> (B and A)))) or (B or (A -> (B and A)))) -> C)))
theorem-size     47
proof            (modus-ponens tm-852 tm-798 ((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (or (and Cm (or A (-> B (and A B)))) (or A (-> B (and A B)))) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-74289.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((D and (B or (A -> (B and A)))) or (B or (A -> (B and A)))) -> C))), M:tm-852, m:tm-798, u:((Am (or A (-> B (and A B)))) (C Bm) (D (and (-> (or A (-> B (and A B))) Bm) (-> (or (and Cm (or A (-> B (and A B)))) (or A (-> B (and A B)))) Bm))))
================================================================
tm-name          tm-74290
in-theory        74290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B or (A -> (B and A))) -> C)))
theorem-size     39
proof            (modus-ponens tm-852 tm-808 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-74290.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-808, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-74291
in-theory        74291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-852 tm-810 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       157
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-74291.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-852, m:tm-810, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-74292
in-theory        74292
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> (D and ((A or (B -> (A and B))) -> C))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> (D and ((A or (B -> (A and B))) -> C))))
theorem-size     51
proof            (modus-ponens tm-850 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (and B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (and B (-> (or Am (-> Bm (and Am Bm))) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-74292.        ((((A or (B -> (A and B))) -> C) -> (D and ((A or (B -> (A and B))) -> C))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> (D and ((A or (B -> (A and B))) -> C)))), M:tm-850, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (and B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (and B (-> (or Am (-> Bm (and Am Bm))) Cm)))))
================================================================
tm-name          tm-74293
in-theory        74293
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> (D and ((A or (B -> (A and B))) -> C))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> (D and ((A or (B -> (A and B))) -> C)))) and ((D or (((A or (B -> (A and B))) -> C) -> (D and ((A or (B -> (A and B))) -> C)))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> (D and ((A or (B -> (A and B))) -> C)))))
theorem-size     105
proof            (modus-ponens tm-844 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (and B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (and B (-> (or Am (-> Bm (and Am Bm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
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-48.           (((A -> (B and 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-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-74293.        (((((A or (B -> (A and B))) -> C) -> (D and ((A or (B -> (A and B))) -> C))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> (D and ((A or (B -> (A and B))) -> C)))) and ((D or (((A or (B -> (A and B))) -> C) -> (D and ((A or (B -> (A and B))) -> C)))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> (D and ((A or (B -> (A and B))) -> C))))), M:tm-844, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (and B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (and B (-> (or Am (-> Bm (and Am Bm))) Cm)))))
================================================================
tm-name          tm-74294
in-theory        74294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-808 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-74294.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-808, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74295
in-theory        74295
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((E and (((A or (B -> (A and B))) -> C) -> D)) or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))
theorem-size     77
proof            (modus-ponens tm-798 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-74295.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((E and (((A or (B -> (A and B))) -> C) -> D)) or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))), M:tm-798, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74296
in-theory        74296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-757 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-74296.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-757, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74297
in-theory        74297
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((((((A or (B -> (A and B))) -> C) -> D) and E) or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))
theorem-size     77
proof            (modus-ponens tm-747 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-74297.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((((((A or (B -> (A and B))) -> C) -> D) and E) or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))), M:tm-747, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74298
in-theory        74298
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-708 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
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-48.           (((A -> (B and 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-74298.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H))), M:tm-708, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74299
in-theory        74299
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> D)))
theorem-size     47
proof            (modus-ponens tm-703 tm-852 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or Am (-> Bm (and Am Bm))) C)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74299.        ((((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> D))), M:tm-703, m:tm-852, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or Am (-> Bm (and Am Bm))) C)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or Am (-> Bm (and Am Bm))) C))))
================================================================
tm-name          tm-74300
in-theory        74300
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> D))) and ((((A or (B -> (A and B))) -> (C -> D)) or (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> D))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> D))))
theorem-size     107
proof            (modus-ponens tm-697 tm-852 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or Am (-> Bm (and Am Bm))) C)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or Am (-> Bm (and Am Bm))) C)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       303
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-74300.        (((((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> D))) and ((((A or (B -> (A and B))) -> (C -> D)) or (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> D))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> D)))), M:tm-697, m:tm-852, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or Am (-> Bm (and Am Bm))) C)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or Am (-> Bm (and Am Bm))) C))))
================================================================
tm-name          tm-74301
in-theory        74301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-665 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-74301.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-665, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74302
in-theory        74302
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((D or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))
theorem-size     65
proof            (modus-ponens tm-654 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (B Dm) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-74302.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((D or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))), M:tm-654, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (B Dm) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74303
in-theory        74303
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> (E or ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-623 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-74303.        ((((A or (B -> (A and B))) -> C) -> D) -> (E or ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))), M:tm-623, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74304
in-theory        74304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-622 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-48.           (((A -> (B and 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-74304.        ((A -> (B -> (C or B))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-622, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74305
in-theory        74305
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> (B and C))) -> D) -> (E or ((B or (C -> (B and C))) -> D)))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (E or ((B or (C -> (B and C))) -> D))))
theorem-size     53
proof            (modus-ponens tm-619 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (or B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (or B (-> (or Am (-> Bm (and Am Bm))) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       181
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-48.           (((A -> (B and 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-74305.        ((A or (((B or (C -> (B and C))) -> D) -> (E or ((B or (C -> (B and C))) -> D)))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (E or ((B or (C -> (B and C))) -> D)))), M:tm-619, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (or B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (or B (-> (or Am (-> Bm (and Am Bm))) Cm)))))
================================================================
tm-name          tm-74306
in-theory        74306
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (F or E)))
theorem-size     37
proof            (modus-ponens tm-609 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74306.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74307
in-theory        74307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-605 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-74307.        ((A -> ((B -> (C or B)) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-605, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74308
in-theory        74308
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (F or E)) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     69
proof            (modus-ponens tm-595 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-74308.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (F or E)) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-595, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74309
in-theory        74309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-550 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-48.           (((A -> (B and 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-74309.        (((A -> (B or A)) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-550, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74310
in-theory        74310
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-540 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-74310.        ((A or (B -> (C or B))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-540, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74311
in-theory        74311
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-530 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-48.           (((A -> (B and 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-74311.        ((A or (B -> (B or C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-530, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74312
in-theory        74312
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-520 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-74312.        ((A or (B -> (C -> (B and C)))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-520, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74313
in-theory        74313
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-510 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-48.           (((A -> (B and 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-74313.        ((A or ((B and C) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-510, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74314
in-theory        74314
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-500 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-48.           (((A -> (B and 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-74314.        ((A or ((B and C) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-500, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74315
in-theory        74315
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-490 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-48.           (((A -> (B and 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-74315.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H))), M:tm-490, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74316
in-theory        74316
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-480 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-48.           (((A -> (B and 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-74316.        ((A or (B -> (C -> B))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-480, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74317
in-theory        74317
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> (((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D) or E))
theorem-size     33
proof            (modus-ponens tm-470 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-74317.        ((((A or (B -> (A and B))) -> C) -> D) -> (((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D) or E)), M:tm-470, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74318
in-theory        74318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-469 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-48.           (((A -> (B and 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-74318.        ((A -> (B -> (B or C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-469, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74319
in-theory        74319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> (B and C))) -> D) -> (((B or (C -> (B and C))) -> D) or E))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (((B or (C -> (B and C))) -> D) or E)))
theorem-size     53
proof            (modus-ponens tm-466 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (or (-> (or Am (-> Bm (and Am Bm))) Cm) B)) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (or (-> (or Am (-> Bm (and Am Bm))) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       181
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-48.           (((A -> (B and 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-74319.        ((A or (((B or (C -> (B and C))) -> D) -> (((B or (C -> (B and C))) -> D) or E))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (((B or (C -> (B and C))) -> D) or E))), M:tm-466, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (or (-> (or Am (-> Bm (and Am Bm))) Cm) B)) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (or (-> (or Am (-> Bm (and Am Bm))) Cm) B))))
================================================================
tm-name          tm-74320
in-theory        74320
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (E or F)))
theorem-size     37
proof            (modus-ponens tm-456 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74320.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74321
in-theory        74321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-453 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-74321.        ((A -> ((B -> (B or C)) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-453, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74322
in-theory        74322
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (E or F)) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     69
proof            (modus-ponens tm-443 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-74322.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (E or F)) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-443, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74323
in-theory        74323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-409 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-74323.        (((A -> (A or B)) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-409, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74324
in-theory        74324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-400 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-74324.        (((A -> (B -> (A and B))) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-400, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74325
in-theory        74325
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-391 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-48.           (((A -> (B and 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-74325.        ((((A and B) -> B) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-391, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74326
in-theory        74326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-382 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-48.           (((A -> (B and 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-74326.        ((((A and B) -> A) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-382, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74327
in-theory        74327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-373 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-48.           (((A -> (B and 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-74327.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H))), M:tm-373, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74328
in-theory        74328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-364 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-48.           (((A -> (B and 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-74328.        (((A -> (B -> A)) or C) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-364, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74329
in-theory        74329
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> (E -> (((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D) and E)))
theorem-size     35
proof            (modus-ponens tm-355 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74329.        ((((A or (B -> (A and B))) -> C) -> D) -> (E -> (((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D) and E))), M:tm-355, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74330
in-theory        74330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-354 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-74330.        ((A -> (B -> (C -> (B and C)))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-354, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74331
in-theory        74331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> (B and C))) -> D) -> (E -> (((B or (C -> (B and C))) -> D) and E)))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (E -> (((B or (C -> (B and C))) -> D) and E))))
theorem-size     57
proof            (modus-ponens tm-351 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (-> B (and (-> (or Am (-> Bm (and Am Bm))) Cm) B))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> B (and (-> (or Am (-> Bm (and Am Bm))) Cm) B))))))
axioms-used      (tm-8 tm-1 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-5.            (A -> (B -> (A and 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-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-74331.        ((A or (((B or (C -> (B and C))) -> D) -> (E -> (((B or (C -> (B and C))) -> D) and E)))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (E -> (((B or (C -> (B and C))) -> D) and E)))), M:tm-351, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (-> B (and (-> (or Am (-> Bm (and Am Bm))) Cm) B))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> B (and (-> (or Am (-> Bm (and Am Bm))) Cm) B)))))
================================================================
tm-name          tm-74332
in-theory        74332
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     39
proof            (modus-ponens tm-341 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-74332.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74333
in-theory        74333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-338 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-74333.        (((A -> B) -> (A -> (A and B))) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F))), M:tm-338, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74334
in-theory        74334
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) or (((A or (B -> (A and B))) -> C) -> (((A or (B -> (A and B))) -> C) and D))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> (((A or (B -> (A and B))) -> C) and D)))
theorem-size     63
proof            (modus-ponens tm-335 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (and (-> (or Am (-> Bm (and Am Bm))) Cm) B)) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (and (-> (or Am (-> Bm (and Am Bm))) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5)
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-5.            (A -> (B -> (A and B))), axiom
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-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-74334.        (((((A or (B -> (A and B))) -> C) -> D) or (((A or (B -> (A and B))) -> C) -> (((A or (B -> (A and B))) -> C) and D))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> (((A or (B -> (A and B))) -> C) and D))), M:tm-335, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (and (-> (or Am (-> Bm (and Am Bm))) Cm) B)) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (and (-> (or Am (-> Bm (and Am Bm))) Cm) B))))
================================================================
tm-name          tm-74335
in-theory        74335
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((A or (B -> (A and B))) -> C) -> D) and ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     75
proof            (modus-ponens tm-328 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-328.          ((A -> 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-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-74335.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((A or (B -> (A and B))) -> C) -> D) and ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-328, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74336
in-theory        74336
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     71
proof            (modus-ponens tm-327 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-74336.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-327, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74337
in-theory        74337
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((E and F) -> F) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     69
proof            (modus-ponens tm-326 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-74337.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((E and F) -> F) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-326, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74338
in-theory        74338
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((E and F) -> E) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     69
proof            (modus-ponens tm-325 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-74338.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((E and F) -> E) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-325, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74339
in-theory        74339
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     77
proof            (modus-ponens tm-324 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-74339.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-324, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74340
in-theory        74340
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (F -> E)) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     69
proof            (modus-ponens tm-323 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-74340.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (F -> E)) and ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-323, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74341
in-theory        74341
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E and F) -> F))
theorem-size     37
proof            (modus-ponens tm-322 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74341.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74342
in-theory        74342
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E and F) -> E))
theorem-size     37
proof            (modus-ponens tm-320 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74342.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74343
in-theory        74343
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-318 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74343.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74344
in-theory        74344
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((((A or (B -> (A and B))) -> C) -> D) -> (((A or (B -> (A and B))) -> C) -> D)))
theorem-size     55
proof            (modus-ponens tm-316 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74344.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((((A or (B -> (A and B))) -> C) -> D) -> (((A or (B -> (A and B))) -> C) -> D))), M:tm-316, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74345
in-theory        74345
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (F -> E)))
theorem-size     37
proof            (modus-ponens tm-315 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74345.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74346
in-theory        74346
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((((A or (B -> (A and B))) -> C) -> D) -> (not ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))) -> (not (((A or (B -> (A and B))) -> C) -> D))))
theorem-size     77
proof            (modus-ponens tm-313 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-74346.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((((A or (B -> (A and B))) -> C) -> D) -> (not ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))) -> (not (((A or (B -> (A and B))) -> C) -> D)))), M:tm-313, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74347
in-theory        74347
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D) -> E) -> (((((A or (B -> (A and B))) -> C) -> D) or ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) -> E)))
theorem-size     87
proof            (modus-ponens tm-312 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-74347.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and ((((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D) -> E) -> (((((A or (B -> (A and B))) -> C) -> D) or ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) -> E))), M:tm-312, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74348
in-theory        74348
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E or ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     65
proof            (modus-ponens tm-311 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
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-7.            (A -> (B or 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-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-74348.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E or ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-311, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74349
in-theory        74349
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) or E))
theorem-size     65
proof            (modus-ponens tm-310 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
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-6.            (A -> (A or 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-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-74349.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) or E)), M:tm-310, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74350
in-theory        74350
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and E)))
theorem-size     67
proof            (modus-ponens tm-309 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
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-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-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-74350.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and E))), M:tm-309, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74351
in-theory        74351
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((((A or (B -> (A and B))) -> C) -> D) -> (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C))) -> ((((A or (B -> (A and B))) -> C) -> D) -> D)))
theorem-size     75
proof            (modus-ponens tm-306 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (C Dm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-74351.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (((((A or (B -> (A and B))) -> C) -> D) -> (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C))) -> ((((A or (B -> (A and B))) -> C) -> D) -> D))), M:tm-306, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (C Dm))
================================================================
tm-name          tm-74352
in-theory        74352
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))))
theorem-size     65
proof            (modus-ponens tm-305 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am 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-1.            (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-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-74352.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) and (E -> ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))), M:tm-305, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74353
in-theory        74353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-303 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-74353.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-303, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74354
in-theory        74354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-270 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
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-48.           (((A -> (B and 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-74354.        ((A -> (((B and C) -> C) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-270, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74355
in-theory        74355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-239 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
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-48.           (((A -> (B and 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-74355.        ((A -> (((B and C) -> B) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-239, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74356
in-theory        74356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-210 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-74356.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H))), M:tm-210, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74357
in-theory        74357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-183 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-74357.        ((A -> ((B -> (C -> B)) and A)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-183, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74358
in-theory        74358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-157 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-48.           (((A -> (B and 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-74358.        ((A -> ((B and C) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-157, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74359
in-theory        74359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     47
proof            (modus-ponens tm-147 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-74359.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-147, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74360
in-theory        74360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-134 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-48.           (((A -> (B and 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-74360.        ((A -> ((B and C) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-134, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74361
in-theory        74361
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     47
proof            (modus-ponens tm-125 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-74361.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-125, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74362
in-theory        74362
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> (D -> E)) -> (((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> E)))
theorem-size     53
proof            (modus-ponens tm-114 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) (-> C D))) (B (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       197
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-48.           (((A -> (B and 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-74362.        ((((A or (B -> (A and B))) -> C) -> (D -> E)) -> (((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> E))), M:tm-114, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) (-> C D))) (B (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-74363
in-theory        74363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-113 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74363.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H))), M:tm-113, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74364
in-theory        74364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> (B and C))) -> (D -> E)) -> (((B or (C -> (B and C))) -> D) -> ((B or (C -> (B and C))) -> E)))) -> ((((C -> (B and C)) -> (D -> E)) or ((B or (C -> (B and C))) -> (D -> E))) -> (((B or (C -> (B and C))) -> D) -> ((B or (C -> (B and C))) -> E))))
theorem-size     75
proof            (modus-ponens tm-110 tm-852 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B C)) (Dm (-> (-> (or Am (-> Bm (and Am Bm))) B) (-> (or Am (-> Bm (and Am Bm))) C))) (D (-> (or (-> (-> Bm (and Am Bm)) (-> B C)) (-> (or Am (-> Bm (and Am Bm))) (-> B C))) (-> (-> (or Am (-> Bm (and Am Bm))) B) (-> (or Am (-> Bm (and Am Bm))) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       235
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-48.           (((A -> (B and 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-74364.        ((A or (((B or (C -> (B and C))) -> (D -> E)) -> (((B or (C -> (B and C))) -> D) -> ((B or (C -> (B and C))) -> E)))) -> ((((C -> (B and C)) -> (D -> E)) or ((B or (C -> (B and C))) -> (D -> E))) -> (((B or (C -> (B and C))) -> D) -> ((B or (C -> (B and C))) -> E)))), M:tm-110, m:tm-852, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B C)) (Dm (-> (-> (or Am (-> Bm (and Am Bm))) B) (-> (or Am (-> Bm (and Am Bm))) C))) (D (-> (or (-> (-> Bm (and Am Bm)) (-> B C)) (-> (or Am (-> Bm (and Am Bm))) (-> B C))) (-> (-> (or Am (-> Bm (and Am Bm))) B) (-> (or Am (-> Bm (and Am Bm))) C)))))
================================================================
tm-name          tm-74365
in-theory        74365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     51
proof            (modus-ponens tm-105 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-74365.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-105, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74366
in-theory        74366
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> (C -> D)) -> ((A or (B -> (A and B))) -> C)) or (((A or (B -> (A and B))) -> (C -> D)) -> ((A or (B -> (A and B))) -> D))) -> ((((B -> (A and B)) -> (C -> D)) or ((A or (B -> (A and B))) -> (C -> D))) -> ((A or (B -> (A and B))) -> D)))
theorem-size     75
proof            (modus-ponens tm-102 tm-852 ((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B C)) (Dm (-> (or Am (-> Bm (and Am Bm))) C)) (D (-> (or (-> (-> Bm (and Am Bm)) (-> B C)) (-> (or Am (-> Bm (and Am Bm))) (-> B C))) (-> (or Am (-> Bm (and Am Bm))) C)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       247
proof-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-48.           (((A -> (B and 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-74366.        (((((A or (B -> (A and B))) -> (C -> D)) -> ((A or (B -> (A and B))) -> C)) or (((A or (B -> (A and B))) -> (C -> D)) -> ((A or (B -> (A and B))) -> D))) -> ((((B -> (A and B)) -> (C -> D)) or ((A or (B -> (A and B))) -> (C -> D))) -> ((A or (B -> (A and B))) -> D))), M:tm-102, m:tm-852, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (-> B C)) (Dm (-> (or Am (-> Bm (and Am Bm))) C)) (D (-> (or (-> (-> Bm (and Am Bm)) (-> B C)) (-> (or Am (-> Bm (and Am Bm))) (-> B C))) (-> (or Am (-> Bm (and Am Bm))) C))))
================================================================
tm-name          tm-74367
in-theory        74367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F)))
theorem-size     39
proof            (modus-ponens tm-95 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) 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-48.           (((A -> (B and 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-74367.        (((A -> B) -> (A -> A)) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F))), M:tm-95, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74368
in-theory        74368
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) or (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> C))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> C)))
theorem-size     59
proof            (modus-ponens tm-92 tm-852 ((Dm (-> (or Am (-> Bm (and Am Bm))) Cm)) (A (-> (or Am (-> Bm (and Am Bm))) Cm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or Am (-> Bm (and Am Bm))) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
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-1.            (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-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-74368.        (((((A or (B -> (A and B))) -> C) -> D) or (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> C))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> C))), M:tm-92, m:tm-852, u:((Dm (-> (or Am (-> Bm (and Am Bm))) Cm)) (A (-> (or Am (-> Bm (and Am Bm))) Cm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or Am (-> Bm (and Am Bm))) Cm))))
================================================================
tm-name          tm-74369
in-theory        74369
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> (E -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-84 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-74369.        ((((A or (B -> (A and B))) -> C) -> D) -> (E -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))), M:tm-84, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74370
in-theory        74370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-83 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-74370.        ((A -> (B -> (C -> B))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-83, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74371
in-theory        74371
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> (B and C))) -> D) -> (E -> ((B or (C -> (B and C))) -> D)))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (E -> ((B or (C -> (B and C))) -> D))))
theorem-size     53
proof            (modus-ponens tm-80 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (-> B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> B (-> (or Am (-> Bm (and Am Bm))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       181
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-48.           (((A -> (B and 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-74371.        ((A or (((B or (C -> (B and C))) -> D) -> (E -> ((B or (C -> (B and C))) -> D)))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (E -> ((B or (C -> (B and C))) -> D)))), M:tm-80, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (-> B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> B (-> (or Am (-> Bm (and Am Bm))) Cm)))))
================================================================
tm-name          tm-74372
in-theory        74372
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or (C -> (B and C))) -> D) -> E) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E)))
theorem-size     37
proof            (modus-ponens tm-76 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8)
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-48.           (((A -> (B and 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-74372.        (((not (not A)) -> A) and ((((B or (C -> (B and C))) -> D) -> E) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E))), M:tm-76, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74373
in-theory        74373
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A or (B -> (A and B))) -> C) -> D))) or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))
theorem-size     45
proof            (modus-ponens tm-73 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       155
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-48.           (((A -> (B and 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-74373.        (((not (not (((A or (B -> (A and B))) -> C) -> D))) or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)), M:tm-73, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74374
in-theory        74374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F)))
theorem-size     43
proof            (modus-ponens tm-69 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8)
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-48.           (((A -> (B and 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-74374.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F))), M:tm-69, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74375
in-theory        74375
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) or (((A or (B -> (A and B))) -> (not C)) -> (not (A or (B -> (A and B)))))) -> ((((B -> (A and B)) -> (not C)) or ((A or (B -> (A and B))) -> (not C))) -> (not (A or (B -> (A and B))))))
theorem-size     58
proof            (modus-ponens tm-66 tm-852 ((A (or Am (-> Bm (and Am Bm)))) (Cm (not B)) (Dm (not (or Am (-> Bm (and Am Bm))))) (C (-> (or (-> (-> Bm (and Am Bm)) (not B)) (-> (or Am (-> Bm (and Am Bm))) (not B))) (not (or Am (-> Bm (and Am Bm))))))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       186
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-48.           (((A -> (B and 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-74375.        ((((A or (B -> (A and B))) -> C) or (((A or (B -> (A and B))) -> (not C)) -> (not (A or (B -> (A and B)))))) -> ((((B -> (A and B)) -> (not C)) or ((A or (B -> (A and B))) -> (not C))) -> (not (A or (B -> (A and B)))))), M:tm-66, m:tm-852, u:((A (or Am (-> Bm (and Am Bm)))) (Cm (not B)) (Dm (not (or Am (-> Bm (and Am Bm))))) (C (-> (or (-> (-> Bm (and Am Bm)) (not B)) (-> (or Am (-> Bm (and Am Bm))) (not B))) (not (or Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-74376
in-theory        74376
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C))) -> ((((A or (B -> (A and B))) -> C) or (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C))) -> (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C))))
theorem-size     73
proof            (modus-ponens tm-55 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (B (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-8 tm-5)
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-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-74376.        ((((A or (B -> (A and B))) -> C) -> (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C))) -> ((((A or (B -> (A and B))) -> C) or (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C))) -> (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)))), M:tm-55, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (B (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))))
================================================================
tm-name          tm-74377
in-theory        74377
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-54 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-74377.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-54, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74378
in-theory        74378
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or (C -> (B and C)))) or (((B or (C -> (B and C))) -> D) -> ((A or (B or (C -> (B and C)))) -> D))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> ((A or (B or (C -> (B and C)))) -> D)))
theorem-size     61
proof            (modus-ponens tm-51 tm-852 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or C (or Am (-> Bm (and Am Bm)))) Cm)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or C (or Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-8 tm-5)
proof-size       195
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-48.           (((A -> (B and 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-74378.        (((A -> (B or (C -> (B and C)))) or (((B or (C -> (B and C))) -> D) -> ((A or (B or (C -> (B and C)))) -> D))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> ((A or (B or (C -> (B and C)))) -> D))), M:tm-51, m:tm-852, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or C (or Am (-> Bm (and Am Bm)))) Cm)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or C (or Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-74379
in-theory        74379
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or (C -> (B and C))) -> D) -> (A and ((B or (C -> (B and C))) -> D)))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (A and ((B or (C -> (B and C))) -> D))))
theorem-size     53
proof            (modus-ponens tm-48 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (and B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (and B (-> (or Am (-> Bm (and Am Bm))) Cm))))))
axioms-used      (tm-8 tm-5)
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-48.           (((A -> (B and 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-74379.        ((A or (((B or (C -> (B and C))) -> D) -> (A and ((B or (C -> (B and C))) -> D)))) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> (A and ((B or (C -> (B and C))) -> D)))), M:tm-48, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (Dm (and B (-> (or Am (-> Bm (and Am Bm))) Cm))) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (and B (-> (or Am (-> Bm (and Am Bm))) Cm)))))
================================================================
tm-name          tm-74380
in-theory        74380
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B or (C -> (B and C))) -> D) -> E)) or (((B or (C -> (B and C))) -> D) -> E)) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E))
theorem-size     45
proof            (modus-ponens tm-47 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       155
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-48.           (((A -> (B and 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-74380.        (((A and (((B or (C -> (B and C))) -> D) -> E)) or (((B or (C -> (B and C))) -> D) -> E)) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E)), M:tm-47, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74381
in-theory        74381
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or (B -> (A and B))) -> C) -> D) and E) or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))
theorem-size     45
proof            (modus-ponens tm-46 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       155
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-48.           (((A -> (B and 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-74381.        ((((((A or (B -> (A and B))) -> C) -> D) and E) or (((A or (B -> (A and B))) -> C) -> D)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)), M:tm-46, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74382
in-theory        74382
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> (C -> D)) or (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> D))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> D)))
theorem-size     59
proof            (modus-ponens tm-45 tm-852 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or Am (-> Bm (and Am Bm))) C)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or Am (-> Bm (and Am Bm))) C)))))
axioms-used      (tm-8 tm-2 tm-5)
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-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-74382.        ((((A or (B -> (A and B))) -> (C -> D)) or (((A or (B -> (A and B))) -> C) -> ((A or (B -> (A and B))) -> D))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((A or (B -> (A and B))) -> D))), M:tm-45, m:tm-852, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or Am (-> Bm (and Am Bm))) C)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or Am (-> Bm (and Am Bm))) C))))
================================================================
tm-name          tm-74383
in-theory        74383
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or (C -> (B and C))) -> D) -> A)) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> A))
theorem-size     33
proof            (modus-ponens tm-44 tm-852 ((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (B Dm) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5)
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-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-74383.        ((A or (((B or (C -> (B and C))) -> D) -> A)) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> A)), M:tm-44, m:tm-852, u:((A (-> (or Am (-> Bm (and Am Bm))) Cm)) (B Dm) (C (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74384
in-theory        74384
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-42 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-74384.        ((A -> (B or A)) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F))), M:tm-42, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74385
in-theory        74385
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-32 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-74385.        ((A -> (A or B)) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F))), M:tm-32, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74386
in-theory        74386
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> ((((A or (B -> (A and B))) -> C) -> D) and ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)))
theorem-size     43
proof            (modus-ponens tm-24 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-74386.        ((((A or (B -> (A and B))) -> C) -> D) -> ((((A or (B -> (A and B))) -> C) -> D) and ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))), M:tm-24, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74387
in-theory        74387
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F)))
theorem-size     39
proof            (modus-ponens tm-23 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-74387.        ((A -> (B -> (A and B))) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F))), M:tm-23, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74388
in-theory        74388
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-22 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
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-48.           (((A -> (B and 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-74388.        (((A and B) -> B) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F))), M:tm-22, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74389
in-theory        74389
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-21 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
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-48.           (((A -> (B and 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-74389.        (((A and B) -> A) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F))), M:tm-21, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74390
in-theory        74390
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-20 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) 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-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-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-74390.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-20, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74391
in-theory        74391
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-19 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-74391.        ((A -> (B -> A)) and ((((C or (D -> (C and D))) -> E) -> F) -> ((((D -> (C and D)) -> E) or ((C or (D -> (C and D))) -> E)) -> F))), M:tm-19, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74392
in-theory        74392
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> (((A or (B -> (A and B))) -> C) -> D))
theorem-size     23
proof            (modus-ponens tm-12 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
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-12.           ((A -> B) -> (A -> A)), M: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-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-74392.        ((((A or (B -> (A and B))) -> C) -> D) -> (((A or (B -> (A and B))) -> C) -> D)), M:tm-12, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74393
in-theory        74393
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> (not ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))) -> (not (((A or (B -> (A and B))) -> C) -> D)))
theorem-size     45
proof            (modus-ponens tm-9 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-5)
proof-size       137
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-48.           (((A -> (B and 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-74393.        (((((A or (B -> (A and B))) -> C) -> D) -> (not ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))) -> (not (((A or (B -> (A and B))) -> C) -> D))), M:tm-9, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74394
in-theory        74394
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> D) -> E) -> (((((B or (A -> (B and A))) -> C) -> D) or ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> D)) -> E))
theorem-size     55
proof            (modus-ponens tm-8 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-5)
proof-size       149
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-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-74394.        ((((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> D) -> E) -> (((((B or (A -> (B and A))) -> C) -> D) or ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> D)) -> E)), M:tm-8, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-74395
in-theory        74395
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B or (C -> (B and C))) -> D) -> E) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-7 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-5)
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-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-74395.        (A or ((((B or (C -> (B and C))) -> D) -> E) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E))), M:tm-7, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74396
in-theory        74396
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) or E)
theorem-size     33
proof            (modus-ponens tm-6 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-5)
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-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-74396.        (((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)) or E), M:tm-6, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74397
in-theory        74397
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B or (C -> (B and C))) -> D) -> E) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E)) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-74397.        (A -> (((((B or (C -> (B and C))) -> D) -> E) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E)) and A)), M:tm-5, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74398
in-theory        74398
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> D) -> (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C))) -> ((((A or (B -> (A and B))) -> C) -> D) -> D))
theorem-size     43
proof            (modus-ponens tm-2 tm-852 ((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       137
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-48.           (((A -> (B and 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-74398.        (((((A or (B -> (A and B))) -> C) -> D) -> (((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C))) -> ((((A or (B -> (A and B))) -> C) -> D) -> D)), M:tm-2, m:tm-852, u:((A (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm)) (B (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm))) (C Dm))
================================================================
tm-name          tm-74399
in-theory        74399
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B or (C -> (B and C))) -> D) -> E) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-1 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       119
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-48.           (((A -> (B and 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-74399.        (A -> ((((B or (C -> (B and C))) -> D) -> E) -> ((((C -> (B and C)) -> D) or ((B or (C -> (B and C))) -> D)) -> E))), M:tm-1, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-74400
in-theory        74400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), 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-74400.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-808, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74401
in-theory        74401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-7.            (A -> (B or A)), 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-74401.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-757, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74402
in-theory        74402
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-7.            (A -> (B or A)), 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-74402.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-708, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74403
in-theory        74403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-7.            (A -> (B or A)), 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-74403.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-665, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74404
in-theory        74404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-74404.        ((A -> (B -> (C or B))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-622, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74405
in-theory        74405
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-74405.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F or E))), M:tm-609, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74406
in-theory        74406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-74406.        ((A -> ((B -> (C or B)) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-605, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74407
in-theory        74407
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F or E)) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-74407.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F or E)) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-595, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74408
in-theory        74408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-74408.        (((A -> (B or A)) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-550, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74409
in-theory        74409
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-74409.        ((A or (B -> (C or B))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-540, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74410
in-theory        74410
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-74410.        ((A or (B -> (B or C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-530, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74411
in-theory        74411
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-74411.        ((A or (B -> (C -> (B and C)))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-520, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74412
in-theory        74412
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-48.           (((A -> (B and 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-74412.        ((A or ((B and C) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-510, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74413
in-theory        74413
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm 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-48.           (((A -> (B and 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-74413.        ((A or ((B and C) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-500, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74414
in-theory        74414
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-74414.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-490, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74415
in-theory        74415
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-74415.        ((A or (B -> (C -> B))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-480, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74416
in-theory        74416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-74416.        ((A -> (B -> (B or C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-469, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74417
in-theory        74417
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-74417.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (E or F))), M:tm-456, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74418
in-theory        74418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-48.           (((A -> (B and 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-74418.        ((A -> ((B -> (B or C)) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-453, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74419
in-theory        74419
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (E or F)) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-74419.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (E or F)) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-443, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74420
in-theory        74420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-48.           (((A -> (B and 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-74420.        (((A -> (A or B)) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-409, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74421
in-theory        74421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-48.           (((A -> (B and 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-74421.        (((A -> (B -> (A and B))) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-400, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74422
in-theory        74422
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-48.           (((A -> (B and 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-74422.        ((((A and B) -> B) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-391, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74423
in-theory        74423
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-48.           (((A -> (B and 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-74423.        ((((A and B) -> A) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-382, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74424
in-theory        74424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 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-7.            (A -> (B or A)), 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-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-74424.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-373, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74425
in-theory        74425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-74425.        (((A -> (B -> A)) or C) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-364, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74426
in-theory        74426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-48.           (((A -> (B and 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-74426.        ((A -> (B -> (C -> (B and C)))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-354, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74427
in-theory        74427
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-74427.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74428
in-theory        74428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), 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-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-74428.        (((A -> B) -> (A -> (A and B))) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-338, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74429
in-theory        74429
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> (E and F))) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-74429.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> (E and F))) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-327, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74430
in-theory        74430
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and F) -> F) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-74430.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and F) -> F) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-326, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74431
in-theory        74431
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and F) -> E) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-74431.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and F) -> E) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-325, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74432
in-theory        74432
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-74432.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-324, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74433
in-theory        74433
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> E)) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-74433.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> E)) and (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-323, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74434
in-theory        74434
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-74434.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74435
in-theory        74435
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-74435.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74436
in-theory        74436
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-74436.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74437
in-theory        74437
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-74437.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74438
in-theory        74438
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E or (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-74438.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E or (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-311, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74439
in-theory        74439
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-74439.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) or E)), M:tm-310, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74440
in-theory        74440
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), 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-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-74440.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and E))), M:tm-309, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74441
in-theory        74441
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-48.           (((A -> (B and 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-74441.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-305, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74442
in-theory        74442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-7 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-7.            (A -> (B or A)), 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-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-74442.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-303, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74443
in-theory        74443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), 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-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-74443.        ((A -> (((B and C) -> C) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-270, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74444
in-theory        74444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 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-7.            (A -> (B or A)), 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-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-74444.        ((A -> (((B and C) -> B) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-239, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74445
in-theory        74445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), 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-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-74445.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-210, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74446
in-theory        74446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-48.           (((A -> (B and 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-74446.        ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-183, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74447
in-theory        74447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-74447.        ((A -> ((B and C) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-157, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74448
in-theory        74448
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-74448.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-147, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74449
in-theory        74449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-74449.        ((A -> ((B and C) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-134, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74450
in-theory        74450
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-74450.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-125, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74451
in-theory        74451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 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-7.            (A -> (B or A)), 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-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-74451.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-113, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74452
in-theory        74452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), 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-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-74452.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-105, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74453
in-theory        74453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-48.           (((A -> (B and 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-74453.        (((A -> B) -> (A -> A)) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-95, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74454
in-theory        74454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-74454.        ((A -> (B -> (C -> B))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-83, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74455
in-theory        74455
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 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-7.            (A -> (B or A)), 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-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-74455.        (((not (not A)) -> A) and (B or (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-76, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74456
in-theory        74456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 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-7.            (A -> (B or A)), 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-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-74456.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-69, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74457
in-theory        74457
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), 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-74457.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-54, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74458
in-theory        74458
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-74458.        ((A -> (B or A)) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-42, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74459
in-theory        74459
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), 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-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-74459.        ((A -> (A or B)) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-32, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74460
in-theory        74460
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-7 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-7.            (A -> (B or A)), 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-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-74460.        ((A -> (B -> (A and B))) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-23, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74461
in-theory        74461
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), 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-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-74461.        (((A and B) -> B) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-22, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74462
in-theory        74462
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 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-7.            (A -> (B or A)), 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-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-74462.        (((A and B) -> A) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-21, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74463
in-theory        74463
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-7.            (A -> (B or A)), 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-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-74463.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-20, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74464
in-theory        74464
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), 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-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-74464.        ((A -> (B -> A)) and (C or (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-19, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74465
in-theory        74465
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-7 tm-8 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-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-74465.        (A or (B or (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-7, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74466
in-theory        74466
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-6 tm-7 tm-8 tm-5)
proof-size       87
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-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-74466.        ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) or E), M:tm-6, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74467
in-theory        74467
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       91
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-48.           (((A -> (B and 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-74467.        (A -> ((B or (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and A)), M:tm-5, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74468
in-theory        74468
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-1 tm-7 tm-8 tm-5)
proof-size       87
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-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-74468.        (A -> (B or (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-1, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-74469
in-theory        74469
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     25
proof            (modus-ponens tm-841 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> B (and C B)) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 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-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-6.            (A -> (A or B)), axiom
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-74469.        ((A or (B -> (A and B))) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-841, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> B (and C B)) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74470
in-theory        74470
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-837 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> B (and C B)) (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) (-> B (and C B)))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-74470.        ((A or (B -> (A and B))) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (B -> (A and B)))), M:tm-837, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> B (and C B)) (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) (-> B (and C B))))))
================================================================
tm-name          tm-74471
in-theory        74471
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B))
theorem-size     25
proof            (modus-ponens tm-836 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74471.        (((A and B) or B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B)), M:tm-836, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74472
in-theory        74472
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and A))
theorem-size     25
proof            (modus-ponens tm-835 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74472.        (((A and B) or A) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and A)), M:tm-835, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74473
in-theory        74473
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-834 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       231
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-74473.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> (A -> C)))), M:tm-834, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-74474
in-theory        74474
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (B -> A)))
theorem-size     27
proof            (modus-ponens tm-833 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> B C) (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) (-> B C))))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74474.        ((A or (B -> A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (B -> A))), M:tm-833, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> B C) (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) (-> B C)))))
================================================================
tm-name          tm-74475
in-theory        74475
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-831 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74475.        ((A -> (B or A)) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C))), M:tm-831, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74476
in-theory        74476
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-829 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-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-74476.        ((A -> (A or B)) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C))), M:tm-829, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74477
in-theory        74477
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))
theorem-size     23
proof            (modus-ponens tm-827 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74477.        (A -> (A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))), M:tm-827, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74478
in-theory        74478
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C)))
theorem-size     29
proof            (modus-ponens tm-826 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74478.        ((A -> (B -> (A and B))) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C))), M:tm-826, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74479
in-theory        74479
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-825 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74479.        (((A and B) -> B) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C))), M:tm-825, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74480
in-theory        74480
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-824 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74480.        (((A and B) -> A) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C))), M:tm-824, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74481
in-theory        74481
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-823 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-74481.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-823, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74482
in-theory        74482
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-822 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74482.        ((A -> (B -> A)) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C))), M:tm-822, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74483
in-theory        74483
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))) -> (not A))
theorem-size     25
proof            (modus-ponens tm-816 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-9 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74483.        ((A -> (not ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))) -> (not A)), M:tm-816, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74484
in-theory        74484
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and D) -> E) -> ((D or ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and D)) -> E))
theorem-size     45
proof            (modus-ponens tm-815 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74484.        ((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and D) -> E) -> ((D or ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and D)) -> E)), M:tm-815, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74485
in-theory        74485
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B)))
theorem-size     23
proof            (modus-ponens tm-814 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74485.        (A or (B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B))), M:tm-814, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74486
in-theory        74486
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) or E)
theorem-size     23
proof            (modus-ponens tm-813 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-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-74486.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) or E), M:tm-813, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74487
in-theory        74487
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B)) and A))
theorem-size     25
proof            (modus-ponens tm-812 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74487.        (A -> ((B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B)) and A)), M:tm-812, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74488
in-theory        74488
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B)))
theorem-size     23
proof            (modus-ponens tm-811 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-74488.        (A -> (B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B))), M:tm-811, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (and (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B))))
================================================================
tm-name          tm-74489
in-theory        74489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     31
proof            (modus-ponens tm-808 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or 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-74489.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-808, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74490
in-theory        74490
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-795 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-6 tm-5)
proof-size       157
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), 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-74490.        (((A and B) or B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-795, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74491
in-theory        74491
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> (C and B)) -> D) -> (C or (B -> (C and B))))) or (((B -> (C and B)) -> D) -> (C or (B -> (C and B))))) -> (((B -> (C and B)) -> D) -> D))
theorem-size     43
proof            (modus-ponens tm-794 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-6 tm-5)
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), 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-74491.        (((A and (((B -> (C and B)) -> D) -> (C or (B -> (C and B))))) or (((B -> (C and B)) -> D) -> (C or (B -> (C and B))))) -> (((B -> (C and B)) -> D) -> D)), M:tm-794, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74492
in-theory        74492
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)) or G))
theorem-size     31
proof            (modus-ponens tm-757 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 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-6.            (A -> (A or 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-74492.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-757, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74493
in-theory        74493
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-744 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-6 tm-5)
proof-size       157
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-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-74493.        (((A and B) or A) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-744, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74494
in-theory        74494
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) and D) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C))
theorem-size     43
proof            (modus-ponens tm-743 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-6 tm-5)
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-3.            ((A and B) -> A), axiom
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-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-74494.        ((((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) and D) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C)), M:tm-743, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74495
in-theory        74495
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)) or H))
theorem-size     45
proof            (modus-ponens tm-708 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-48.           (((A -> (B and 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-74495.        (((((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)) or H)), M:tm-708, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74496
in-theory        74496
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-694 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-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-74496.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-694, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74497
in-theory        74497
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) or (((B -> (A and B)) -> C) -> (A or (B -> (A and B))))) -> (((B -> (A and B)) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-692 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-5)
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-1.            (A -> (B -> A)), 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-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-74497.        (((A or (B -> (A and B))) or (((B -> (A and B)) -> C) -> (A or (B -> (A and B))))) -> (((B -> (A and B)) -> C) -> C)), M:tm-692, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74498
in-theory        74498
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-690 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6)
proof-size       191
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-48.           (((A -> (B and 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-74498.        ((A -> (B or A)) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E))), M:tm-690, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74499
in-theory        74499
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-688 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       191
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-48.           (((A -> (B and 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-74499.        ((A -> (A or B)) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E))), M:tm-688, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74500
in-theory        74500
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) and (((A -> (B and A)) -> C) -> C)))
theorem-size     41
proof            (modus-ponens tm-686 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
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-5.            (A -> (B -> (A and B))), axiom
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-48.           (((A -> (B and 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-74500.        ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) and (((A -> (B and A)) -> C) -> C))), M:tm-686, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74501
in-theory        74501
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E)))
theorem-size     33
proof            (modus-ponens tm-685 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
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-48.           (((A -> (B and 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-74501.        ((A -> (B -> (A and B))) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E))), M:tm-685, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74502
in-theory        74502
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-684 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-6)
proof-size       191
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-48.           (((A -> (B and 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-74502.        (((A and B) -> B) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E))), M:tm-684, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74503
in-theory        74503
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-683 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-6)
proof-size       191
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-48.           (((A -> (B and 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-74503.        (((A and B) -> A) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E))), M:tm-683, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74504
in-theory        74504
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     39
proof            (modus-ponens tm-682 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-20.           (A -> (((B -> (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-48.           (((A -> (B and 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-74504.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-682, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74505
in-theory        74505
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-681 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       191
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-48.           (((A -> (B and 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-74505.        ((A -> (B -> A)) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E))), M:tm-681, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74506
in-theory        74506
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> (B or (A -> (B and A)))))
theorem-size     31
proof            (modus-ponens tm-676 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-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-74506.        ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))), M:tm-676, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74507
in-theory        74507
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (not (((A -> (B and A)) -> C) -> C))) -> (not (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))))
theorem-size     43
proof            (modus-ponens tm-674 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-9 tm-6 tm-5)
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-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-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-74507.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (not (((A -> (B and A)) -> C) -> C))) -> (not (((A -> (B and A)) -> C) -> (B or (A -> (B and A)))))), M:tm-674, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74508
in-theory        74508
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> C) -> D) -> (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) or (((A -> (B and A)) -> C) -> C)) -> D))
theorem-size     39
proof            (modus-ponens tm-673 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-6 tm-5)
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-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-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-74508.        (((((A -> (B and A)) -> C) -> C) -> D) -> (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) or (((A -> (B and A)) -> C) -> C)) -> D)), M:tm-673, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74509
in-theory        74509
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C and B)) -> D) -> (C or (B -> (C and B)))) -> (((B -> (C and B)) -> D) -> D)))
theorem-size     27
proof            (modus-ponens tm-672 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-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-74509.        (A or ((((B -> (C and B)) -> D) -> (C or (B -> (C and B)))) -> (((B -> (C and B)) -> D) -> D))), M:tm-672, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74510
in-theory        74510
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) or D)
theorem-size     27
proof            (modus-ponens tm-671 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-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-74510.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) or D), M:tm-671, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74511
in-theory        74511
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C and B)) -> D) -> (C or (B -> (C and B)))) -> (((B -> (C and B)) -> D) -> D)) and A))
theorem-size     29
proof            (modus-ponens tm-670 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-48.           (((A -> (B and 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-74511.        (A -> (((((B -> (C and B)) -> D) -> (C or (B -> (C and B)))) -> (((B -> (C and B)) -> D) -> D)) and A)), M:tm-670, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74512
in-theory        74512
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((A -> (B and A)) -> C)) -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> C))
theorem-size     41
proof            (modus-ponens tm-669 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-6 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-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-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-74512.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((A -> (B and A)) -> C)) -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> C)), M:tm-669, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74513
in-theory        74513
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B -> (C and B)) -> D) -> (C or (B -> (C and B)))) -> (((B -> (C and B)) -> D) -> D)))
theorem-size     27
proof            (modus-ponens tm-668 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-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-74513.        (A -> ((((B -> (C and B)) -> D) -> (C or (B -> (C and B)))) -> (((B -> (C and B)) -> D) -> D))), M:tm-668, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-74514
in-theory        74514
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)) or G))
theorem-size     33
proof            (modus-ponens tm-665 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 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-6.            (A -> (A or 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-74514.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-665, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74515
in-theory        74515
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-651 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> B C) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       161
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-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-74515.        ((A or (B -> A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-651, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (-> B C) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74516
in-theory        74516
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-649 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6)
proof-size       153
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-48.           (((A -> (B and 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-74516.        ((A -> (B or A)) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-649, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74517
in-theory        74517
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-647 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       153
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-48.           (((A -> (B and 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-74517.        ((A -> (A or B)) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-647, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74518
in-theory        74518
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))
theorem-size     21
proof            (modus-ponens tm-645 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       153
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-48.           (((A -> (B and 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-74518.        (A -> (A and (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))), M:tm-645, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74519
in-theory        74519
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     27
proof            (modus-ponens tm-644 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       161
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-48.           (((A -> (B and 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-74519.        ((A -> (B -> (A and B))) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-644, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74520
in-theory        74520
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-643 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4 tm-6)
proof-size       153
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-48.           (((A -> (B and 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-74520.        (((A and B) -> B) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-643, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74521
in-theory        74521
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-642 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3 tm-6)
proof-size       153
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-48.           (((A -> (B and 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-74521.        (((A and B) -> A) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-642, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74522
in-theory        74522
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-641 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6)
proof-size       185
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-48.           (((A -> (B and 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-74522.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-641, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74523
in-theory        74523
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     25
proof            (modus-ponens tm-640 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       153
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-48.           (((A -> (B and 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-74523.        ((A -> (B -> A)) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-640, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74524
in-theory        74524
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E)) -> E)
theorem-size     23
proof            (modus-ponens tm-638 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (and B (-> (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) C)) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-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-74524.        ((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E)) -> E), M:tm-638, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (and B (-> (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) C)) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74525
in-theory        74525
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) and E) -> D)
theorem-size     23
proof            (modus-ponens tm-636 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (and (-> (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B) C) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-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-74525.        ((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) and E) -> D), M:tm-636, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> (and (-> (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) B) C) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74526
in-theory        74526
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((B or (A -> (B and A))) -> C) -> D)) -> (((A -> (B and A)) -> C) -> D))
theorem-size     29
proof            (modus-ponens tm-634 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> (or Bm (-> Am (and Bm Am))) Cm) C)) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-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-74526.        ((((A -> (B and A)) -> C) -> (((B or (A -> (B and A))) -> C) -> D)) -> (((A -> (B and A)) -> C) -> D)), M:tm-634, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)) (Dm (-> (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> (or Bm (-> Am (and Bm Am))) Cm) C)) (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74527
in-theory        74527
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-631 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-9 tm-6 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-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-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-74527.        ((A -> (not (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))) -> (not A)), M:tm-631, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74528
in-theory        74528
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) -> ((E or (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))) -> D))
theorem-size     41
proof            (modus-ponens tm-630 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
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-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-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-74528.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) -> ((E or (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))) -> D)), M:tm-630, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74529
in-theory        74529
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     21
proof            (modus-ponens tm-629 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 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-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-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-74529.        (A or (B -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-629, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74530
in-theory        74530
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) or E)
theorem-size     21
proof            (modus-ponens tm-628 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-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-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-74530.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) or E), M:tm-628, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74531
in-theory        74531
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-627 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
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-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-48.           (((A -> (B and 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-74531.        (A -> ((B -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and A)), M:tm-627, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74532
in-theory        74532
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C and B)) -> D)) -> (A -> ((C or (B -> (C and B))) -> D)))
theorem-size     21
proof            (modus-ponens tm-626 tm-854 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)) (Dm (-> C (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 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-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-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-74532.        ((A -> ((B -> (C and B)) -> D)) -> (A -> ((C or (B -> (C and B))) -> D))), M:tm-626, m:tm-854, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)) (Dm (-> C (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74533
in-theory        74533
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     21
proof            (modus-ponens tm-625 tm-854 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
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-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-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-74533.        (A -> (B -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-625, m:tm-854, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))) (Dm (-> B (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-74534
in-theory        74534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-622 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-74534.        ((A -> (B -> (C or B))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-622, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74535
in-theory        74535
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-74535.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (F or E))), M:tm-609, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74536
in-theory        74536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-605 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-48.           (((A -> (B and 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-74536.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-605, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74537
in-theory        74537
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (F or E)) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)))
theorem-size     45
proof            (modus-ponens tm-595 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-74537.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (F or E)) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))), M:tm-595, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74538
in-theory        74538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-550 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-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-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-74538.        (((A -> (B or A)) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-550, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74539
in-theory        74539
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-540 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-48.           (((A -> (B and 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-74539.        ((A or (B -> (C or B))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-540, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74540
in-theory        74540
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-530 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-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-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-74540.        ((A or (B -> (B or C))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-530, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74541
in-theory        74541
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-520 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-48.           (((A -> (B and 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-74541.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-520, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74542
in-theory        74542
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-510 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-48.           (((A -> (B and 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-74542.        ((A or ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-510, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74543
in-theory        74543
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-500 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-48.           (((A -> (B and 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-74543.        ((A or ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-500, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74544
in-theory        74544
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)) or H))
theorem-size     35
proof            (modus-ponens tm-490 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 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-6.            (A -> (A or 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-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-74544.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H)), M:tm-490, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74545
in-theory        74545
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-480 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-74545.        ((A or (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-480, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74546
in-theory        74546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-469 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-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-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-74546.        ((A -> (B -> (B or C))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-469, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74547
in-theory        74547
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-48.           (((A -> (B and 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-74547.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (E or F))), M:tm-456, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74548
in-theory        74548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-453 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-74548.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-453, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74549
in-theory        74549
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (E or F)) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)))
theorem-size     45
proof            (modus-ponens tm-443 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-48.           (((A -> (B and 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-74549.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (E or F)) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))), M:tm-443, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74550
in-theory        74550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-409 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-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-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-74550.        (((A -> (A or B)) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-409, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74551
in-theory        74551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-400 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-74551.        (((A -> (B -> (A and B))) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-400, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74552
in-theory        74552
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-391 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-48.           (((A -> (B and 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-74552.        ((((A and B) -> B) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-391, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74553
in-theory        74553
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-382 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) 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-48.           (((A -> (B and 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-74553.        ((((A and B) -> A) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-382, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74554
in-theory        74554
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)) or H))
theorem-size     35
proof            (modus-ponens tm-373 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-48.           (((A -> (B and 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-74554.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H)), M:tm-373, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74555
in-theory        74555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-364 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-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-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-74555.        (((A -> (B -> A)) or C) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-364, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74556
in-theory        74556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-354 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-48.           (((A -> (B and 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-74556.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-354, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74557
in-theory        74557
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-74557.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74558
in-theory        74558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F))
theorem-size     29
proof            (modus-ponens tm-338 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or 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-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-74558.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F)), M:tm-338, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74559
in-theory        74559
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)))
theorem-size     47
proof            (modus-ponens tm-327 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-74559.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))), M:tm-327, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74560
in-theory        74560
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (((E and F) -> F) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)))
theorem-size     45
proof            (modus-ponens tm-326 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-74560.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (((E and F) -> F) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))), M:tm-326, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74561
in-theory        74561
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (((E and F) -> E) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)))
theorem-size     45
proof            (modus-ponens tm-325 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-74561.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (((E and F) -> E) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))), M:tm-325, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74562
in-theory        74562
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)))
theorem-size     53
proof            (modus-ponens tm-324 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-74562.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))), M:tm-324, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74563
in-theory        74563
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (F -> E)) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)))
theorem-size     45
proof            (modus-ponens tm-323 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-74563.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (F -> E)) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))), M:tm-323, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74564
in-theory        74564
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-74564.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E and F) -> F)), M:tm-322, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74565
in-theory        74565
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-74565.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E and F) -> E)), M:tm-320, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74566
in-theory        74566
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-74566.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74567
in-theory        74567
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-74567.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (F -> E))), M:tm-315, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74568
in-theory        74568
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E or ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)))
theorem-size     41
proof            (modus-ponens tm-311 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-74568.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E or ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))), M:tm-311, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74569
in-theory        74569
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-48.           (((A -> (B and 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-74569.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) or E)), M:tm-310, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74570
in-theory        74570
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-74570.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and E))), M:tm-309, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74571
in-theory        74571
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)))
theorem-size     41
proof            (modus-ponens tm-305 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-48.           (((A -> (B and 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-74571.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) and (E -> ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))), M:tm-305, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74572
in-theory        74572
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)) or G))
theorem-size     31
proof            (modus-ponens tm-303 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-48.           (((A -> (B and 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-74572.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-303, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74573
in-theory        74573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-270 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 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-6.            (A -> (A or 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-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-74573.        ((A -> (((B and C) -> C) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-270, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74574
in-theory        74574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-239 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 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-6.            (A -> (A or 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-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-74574.        ((A -> (((B and C) -> B) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-239, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74575
in-theory        74575
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)) or H))
theorem-size     37
proof            (modus-ponens tm-210 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or 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-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-74575.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H)), M:tm-210, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74576
in-theory        74576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-183 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-48.           (((A -> (B and 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-74576.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-183, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74577
in-theory        74577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-157 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-74577.        ((A -> ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-157, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74578
in-theory        74578
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)) or G))
theorem-size     35
proof            (modus-ponens tm-147 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-74578.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-147, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74579
in-theory        74579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-134 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-74579.        ((A -> ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-134, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74580
in-theory        74580
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)) or G))
theorem-size     35
proof            (modus-ponens tm-125 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-74580.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-125, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74581
in-theory        74581
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)) or H))
theorem-size     35
proof            (modus-ponens tm-113 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 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-6.            (A -> (A or 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-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-74581.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H)), M:tm-113, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74582
in-theory        74582
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)) or G))
theorem-size     39
proof            (modus-ponens tm-105 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or 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-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-74582.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-105, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74583
in-theory        74583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F))
theorem-size     27
proof            (modus-ponens tm-95 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-48.           (((A -> (B and 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-74583.        (((A -> B) -> (A -> A)) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F)), M:tm-95, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74584
in-theory        74584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-83 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-74584.        ((A -> (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-83, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74585
in-theory        74585
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-76 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 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-6.            (A -> (A or 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-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-74585.        (((not (not A)) -> A) and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) or E)), M:tm-76, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74586
in-theory        74586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F))
theorem-size     31
proof            (modus-ponens tm-69 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 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-6.            (A -> (A or 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-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-74586.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F)), M:tm-69, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74587
in-theory        74587
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-54 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or 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-74587.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-54, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74588
in-theory        74588
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-42 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or 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-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-74588.        ((A -> (B or A)) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F)), M:tm-42, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74589
in-theory        74589
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-32 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-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-74589.        ((A -> (A or B)) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F)), M:tm-32, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74590
in-theory        74590
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F))
theorem-size     27
proof            (modus-ponens tm-23 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-6 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-6.            (A -> (A or 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-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-74590.        ((A -> (B -> (A and B))) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F)), M:tm-23, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74591
in-theory        74591
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-22 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 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-6.            (A -> (A or 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-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-74591.        (((A and B) -> B) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F)), M:tm-22, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74592
in-theory        74592
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-21 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 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-6.            (A -> (A or 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-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-74592.        (((A and B) -> A) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F)), M:tm-21, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74593
in-theory        74593
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-20 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) 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-6.            (A -> (A or 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-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-74593.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-20, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74594
in-theory        74594
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-19 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or 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-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-74594.        ((A -> (B -> A)) and ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) or F)), M:tm-19, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74595
in-theory        74595
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) or E))
theorem-size     21
proof            (modus-ponens tm-7 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-7 tm-6 tm-8 tm-5)
proof-size       87
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-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-74595.        (A or ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) or E)), M:tm-7, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74596
in-theory        74596
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-6 tm-8 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-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-74596.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D) or E), M:tm-6, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74597
in-theory        74597
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) or E) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       91
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-48.           (((A -> (B and 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-74597.        (A -> (((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) or E) and A)), M:tm-5, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74598
in-theory        74598
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) or E))
theorem-size     21
proof            (modus-ponens tm-1 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-1 tm-6 tm-8 tm-5)
proof-size       87
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-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-74598.        (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) or E)), M:tm-1, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-74599
in-theory        74599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8)
proof-size       109
proof-steps      7
----------------------------------------------------------------
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-74599.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-855, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-74600
in-theory        74600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-74600.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-855, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-74601
in-theory        74601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((not (not D)) -> D))
theorem-size     23
proof            (modus-ponens tm-855 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-8 tm-10)
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-48.           (((A -> (B and 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-10.           ((not (not A)) -> A), axiom
tm-74601.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((not (not D)) -> D)), M:tm-855, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-74602
in-theory        74602
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-855 tm-11 ((A (-> Am (-> Bm (-> Cm 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-74602.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> E)))), M:tm-855, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-74603
in-theory        74603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> D)))
theorem-size     25
proof            (modus-ponens tm-855 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-74603.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> D))), M:tm-855, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-74604
in-theory        74604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-855 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-74604.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-855, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-74605
in-theory        74605
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-74605.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-855, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-74606
in-theory        74606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-855 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       131
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-74606.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-855, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-74607
in-theory        74607
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-855 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-74607.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E and F) -> E))), M:tm-855, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-74608
in-theory        74608
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-855 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       131
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-74608.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-855, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-74609
in-theory        74609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-855 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-74609.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E and F) -> F))), M:tm-855, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-74610
in-theory        74610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-74610.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> E)) and D))), M:tm-855, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-74611
in-theory        74611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     35
proof            (modus-ponens tm-855 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-74611.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-855, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-74612
in-theory        74612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and F) -> E) and D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-74612.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and F) -> E) and D))), M:tm-855, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-74613
in-theory        74613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and F) -> F) and D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-74613.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and F) -> F) and D))), M:tm-855, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-74614
in-theory        74614
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-74614.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-855, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-74615
in-theory        74615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-855 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-74615.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (D and E)))), M:tm-855, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-74616
in-theory        74616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-25 ((A (-> Am (-> Bm (-> Cm (and 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-74616.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (E and F))))), M:tm-855, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-74617
in-theory        74617
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) or F))
theorem-size     25
proof            (modus-ponens tm-855 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-74617.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) or F)), M:tm-855, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-74618
in-theory        74618
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     33
proof            (modus-ponens tm-855 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-74618.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-855, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-74619
in-theory        74619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) or F))
theorem-size     25
proof            (modus-ponens tm-855 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-74619.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) or F)), M:tm-855, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-74620
in-theory        74620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) or F))
theorem-size     25
proof            (modus-ponens tm-855 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-74620.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) or F)), M:tm-855, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-74621
in-theory        74621
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) or F))
theorem-size     27
proof            (modus-ponens tm-855 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-74621.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) or F)), M:tm-855, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-74622
in-theory        74622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) or F))
theorem-size     25
proof            (modus-ponens tm-855 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-74622.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) or F)), M:tm-855, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-74623
in-theory        74623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (E or F)) and D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-74623.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (E or F)) and D))), M:tm-855, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-74624
in-theory        74624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-855 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-74624.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (E or F)))), M:tm-855, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-74625
in-theory        74625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-855 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-74625.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> E)))), M:tm-855, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-74626
in-theory        74626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-74626.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-855, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-74627
in-theory        74627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-855 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-74627.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E and F) -> E))), M:tm-855, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-74628
in-theory        74628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-855 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-74628.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E and F) -> F))), M:tm-855, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-74629
in-theory        74629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-74629.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (E and F))))), M:tm-855, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-74630
in-theory        74630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-855 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-74630.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (E or F)))), M:tm-855, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-74631
in-theory        74631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-855 tm-40 ((A (or Am (-> Bm (or Cm 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-74631.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F or E)))), M:tm-855, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-74632
in-theory        74632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) or F))
theorem-size     25
proof            (modus-ponens tm-855 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-74632.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) or F)), M:tm-855, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-74633
in-theory        74633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F or E)) and D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-74633.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F or E)) and D))), M:tm-855, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-74634
in-theory        74634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-855 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-74634.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F or E)))), M:tm-855, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-74635
in-theory        74635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-855 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-74635.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-855, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-74636
in-theory        74636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-855 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       159
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-74636.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-855, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-74637
in-theory        74637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-855 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-74637.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-855, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-74638
in-theory        74638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-855 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-74638.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-855, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-74639
in-theory        74639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-855 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-74639.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-855, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-74640
in-theory        74640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-855 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-74640.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-855, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-74641
in-theory        74641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-855 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-74641.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-855, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-74642
in-theory        74642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     45
proof            (modus-ponens tm-855 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       163
proof-steps      9
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-74642.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-855, 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-74643
in-theory        74643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74643.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-855, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-74644
in-theory        74644
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     33
proof            (modus-ponens tm-855 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74644.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-855, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-74645
in-theory        74645
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     35
proof            (modus-ponens tm-855 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-74645.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-855, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-74646
in-theory        74646
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-855 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74646.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-855, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-74647
in-theory        74647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74647.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-855, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-74648
in-theory        74648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-48.           (((A -> (B and 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-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-74648.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> D))) -> (not D))), M:tm-855, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-74649
in-theory        74649
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-855 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       149
proof-steps      9
----------------------------------------------------------------
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-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-74649.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-855, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-74650
in-theory        74650
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-3)
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-48.           (((A -> (B and 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-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-74650.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-855, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-74651
in-theory        74651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-4)
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-48.           (((A -> (B and 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-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-74651.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-855, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-74652
in-theory        74652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74652.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-855, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-74653
in-theory        74653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-48.           (((A -> (B and 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-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-74653.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (D or E))) -> (not D))), M:tm-855, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-74654
in-theory        74654
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-48.           (((A -> (B and 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-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-74654.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E or D))) -> (not D))), M:tm-855, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-74655
in-theory        74655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     37
proof            (modus-ponens tm-855 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       145
proof-steps      9
----------------------------------------------------------------
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-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-74655.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-855, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-74656
in-theory        74656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     35
proof            (modus-ponens tm-855 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74656.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-855, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-74657
in-theory        74657
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     41
proof            (modus-ponens tm-855 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       153
proof-steps      9
----------------------------------------------------------------
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-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-74657.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-855, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-74658
in-theory        74658
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74658.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-855, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-74659
in-theory        74659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     31
proof            (modus-ponens tm-855 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74659.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-855, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-74660
in-theory        74660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     33
proof            (modus-ponens tm-855 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-74660.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-855, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-74661
in-theory        74661
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     33
proof            (modus-ponens tm-855 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
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-48.           (((A -> (B and 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-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-74661.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-855, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-74662
in-theory        74662
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not 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-48.           (((A -> (B and 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-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-74662.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-855, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-74663
in-theory        74663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     29
proof            (modus-ponens tm-855 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-8 tm-9 tm-10)
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-48.           (((A -> (B and 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-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-74663.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-855, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-74664
in-theory        74664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-855 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-10)
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-48.           (((A -> (B and 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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-74664.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-855, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-74665
in-theory        74665
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((not (not E)) -> E)))
theorem-size     25
proof            (modus-ponens tm-855 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74665.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((not (not E)) -> E))), M:tm-855, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-74666
in-theory        74666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((not (not D)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-855 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74666.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((not (not D)) -> D) or E)), M:tm-855, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-74667
in-theory        74667
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-10)
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-48.           (((A -> (B and 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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-74667.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((not (not E)) -> E) and D))), M:tm-855, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-74668
in-theory        74668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     33
proof            (modus-ponens tm-855 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       131
proof-steps      9
----------------------------------------------------------------
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-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-74668.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-855, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-74669
in-theory        74669
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((not (not E)) -> E)))
theorem-size     25
proof            (modus-ponens tm-855 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-74669.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((not (not E)) -> E))), M:tm-855, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-74670
in-theory        74670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-48.           (((A -> (B and 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-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-74670.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-855, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-74671
in-theory        74671
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-855 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74671.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-855, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-74672
in-theory        74672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-81 ((A (or Am (-> Bm (-> Cm (-> 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-48.           (((A -> (B and 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-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-74672.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (G -> F))))), M:tm-855, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-74673
in-theory        74673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (F -> E))) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
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-48.           (((A -> (B and 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-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-74673.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (F -> E))) or G)), M:tm-855, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-74674
in-theory        74674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-74674.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-855, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-74675
in-theory        74675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-855 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-74675.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (F -> E)))), M:tm-855, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-74676
in-theory        74676
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-85 ((A (-> Am (-> Bm (-> Cm (-> 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-48.           (((A -> (B and 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-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-74676.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (G -> F))))), M:tm-855, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-74677
in-theory        74677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> D))
theorem-size     21
proof            (modus-ponens tm-855 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74677.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> D)), M:tm-855, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-74678
in-theory        74678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74678.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-855, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-74679
in-theory        74679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> (D and E)))
theorem-size     25
proof            (modus-ponens tm-855 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74679.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> (D and E))), M:tm-855, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-74680
in-theory        74680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> E)))
theorem-size     25
proof            (modus-ponens tm-855 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74680.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> E))), M:tm-855, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-74681
in-theory        74681
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((not (not D)) -> (not (not D))))
theorem-size     25
proof            (modus-ponens tm-855 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-10)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74681.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((not (not D)) -> (not (not D)))), M:tm-855, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-74682
in-theory        74682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-855 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       145
proof-steps      11
----------------------------------------------------------------
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-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-74682.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-855, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-74683
in-theory        74683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-855 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74683.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-855, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-74684
in-theory        74684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> (E -> E))))
theorem-size     27
proof            (modus-ponens tm-855 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74684.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> (E -> E)))), M:tm-855, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-74685
in-theory        74685
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (D -> D)) or F))
theorem-size     27
proof            (modus-ponens tm-855 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74685.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (D -> D)) or F)), M:tm-855, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-74686
in-theory        74686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-74686.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-855, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-74687
in-theory        74687
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74687.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-855, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-74688
in-theory        74688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     27
proof            (modus-ponens tm-855 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
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-48.           (((A -> (B and 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-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-74688.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> (E -> E)))), M:tm-855, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-74689
in-theory        74689
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74689.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-855, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-74690
in-theory        74690
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     27
proof            (modus-ponens tm-855 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74690.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D -> E)) -> (D -> E))), M:tm-855, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-74691
in-theory        74691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     37
proof            (modus-ponens tm-855 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74691.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-855, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-74692
in-theory        74692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     49
proof            (modus-ponens tm-855 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       201
proof-steps      11
----------------------------------------------------------------
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-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-74692.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-855, 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-74693
in-theory        74693
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     51
proof            (modus-ponens tm-855 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       207
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-74693.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-855, 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-74694
in-theory        74694
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-855 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       175
proof-steps      11
----------------------------------------------------------------
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-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-74694.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-855, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-74695
in-theory        74695
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     39
proof            (modus-ponens tm-855 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       175
proof-steps      11
----------------------------------------------------------------
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-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-74695.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-855, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-74696
in-theory        74696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     41
proof            (modus-ponens tm-855 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       181
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-74696.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-855, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-74697
in-theory        74697
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     47
proof            (modus-ponens tm-855 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-74697.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-855, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-74698
in-theory        74698
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-855 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       175
proof-steps      11
----------------------------------------------------------------
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-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-74698.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-855, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-74699
in-theory        74699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-855 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       207
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74699.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-855, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-74700
in-theory        74700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     37
proof            (modus-ponens tm-855 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       165
proof-steps      11
----------------------------------------------------------------
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-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-74700.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-855, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-74701
in-theory        74701
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     51
proof            (modus-ponens tm-855 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       195
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-74701.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-855, 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-74702
in-theory        74702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74702.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-855, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-74703
in-theory        74703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74703.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-855, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-74704
in-theory        74704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     37
proof            (modus-ponens tm-855 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       161
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-74704.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-855, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-74705
in-theory        74705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-855 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-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-74705.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-855, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-74706
in-theory        74706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-855 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-74706.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-855, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-74707
in-theory        74707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) and D) -> E))
theorem-size     25
proof            (modus-ponens tm-855 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-74707.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) and D) -> E)), M:tm-855, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-74708
in-theory        74708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     29
proof            (modus-ponens tm-855 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-74708.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-855, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-74709
in-theory        74709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     37
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-74709.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-855, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-74710
in-theory        74710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     39
proof            (modus-ponens tm-855 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       203
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-74710.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-855, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-74711
in-theory        74711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     33
proof            (modus-ponens tm-855 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       171
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74711.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-855, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-74712
in-theory        74712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     43
proof            (modus-ponens tm-855 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       177
proof-steps      11
----------------------------------------------------------------
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-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-74712.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-855, 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-74713
in-theory        74713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     45
proof            (modus-ponens tm-855 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       183
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-74713.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-855, 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-74714
in-theory        74714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74714.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-855, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-74715
in-theory        74715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74715.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-855, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-74716
in-theory        74716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     37
proof            (modus-ponens tm-855 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       161
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-74716.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-855, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-74717
in-theory        74717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     41
proof            (modus-ponens tm-855 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       175
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-74717.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-855, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-74718
in-theory        74718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74718.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-855, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-74719
in-theory        74719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     29
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-74719.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-855, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-74720
in-theory        74720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     31
proof            (modus-ponens tm-855 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       171
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74720.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-855, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-74721
in-theory        74721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-855 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       133
proof-steps      11
----------------------------------------------------------------
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-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-74721.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-855, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-74722
in-theory        74722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     35
proof            (modus-ponens tm-855 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       147
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-74722.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-855, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-74723
in-theory        74723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-855 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74723.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F and G) -> F)))), M:tm-855, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-74724
in-theory        74724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74724.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E and F) -> E)) or G)), M:tm-855, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-74725
in-theory        74725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-74725.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-855, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-74726
in-theory        74726
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     27
proof            (modus-ponens tm-855 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-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-74726.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E and F)) -> (D -> E))), M:tm-855, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-74727
in-theory        74727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-855 tm-136 ((A (-> Am (-> Bm (-> (and Cm 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-74727.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F and G) -> F)))), M:tm-855, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-74728
in-theory        74728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and (D -> E)) -> E))
theorem-size     25
proof            (modus-ponens tm-855 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-74728.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and (D -> E)) -> E)), M:tm-855, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-74729
in-theory        74729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     29
proof            (modus-ponens tm-855 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-74729.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-855, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-74730
in-theory        74730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     37
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-74730.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-855, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-74731
in-theory        74731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     29
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-74731.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-855, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-74732
in-theory        74732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     39
proof            (modus-ponens tm-855 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       203
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-74732.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-855, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-74733
in-theory        74733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     33
proof            (modus-ponens tm-855 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       171
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-74733.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-855, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-74734
in-theory        74734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     43
proof            (modus-ponens tm-855 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       177
proof-steps      11
----------------------------------------------------------------
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-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-74734.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-855, 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-74735
in-theory        74735
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-855 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       183
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-74735.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-855, 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-74736
in-theory        74736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74736.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-855, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-74737
in-theory        74737
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74737.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-855, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-74738
in-theory        74738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     37
proof            (modus-ponens tm-855 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       161
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-74738.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-855, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-74739
in-theory        74739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     41
proof            (modus-ponens tm-855 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       175
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-74739.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-855, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-74740
in-theory        74740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74740.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-855, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-74741
in-theory        74741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     29
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-74741.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-855, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-74742
in-theory        74742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     29
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-74742.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-855, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-74743
in-theory        74743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     31
proof            (modus-ponens tm-855 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       171
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74743.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-855, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-74744
in-theory        74744
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-855 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       133
proof-steps      11
----------------------------------------------------------------
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-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-74744.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-855, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-74745
in-theory        74745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-855 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       147
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-74745.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-855, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-74746
in-theory        74746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-855 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74746.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F and G) -> G)))), M:tm-855, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-74747
in-theory        74747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E and F) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74747.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E and F) -> F)) or G)), M:tm-855, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-74748
in-theory        74748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-74748.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-855, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-74749
in-theory        74749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-855 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-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-74749.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E and F)) -> (D -> F))), M:tm-855, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-74750
in-theory        74750
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-855 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-74750.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F and G) -> G)))), M:tm-855, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-74751
in-theory        74751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> 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-48.           (((A -> (B and 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-1.            (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-74751.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-855, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-74752
in-theory        74752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-74752.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-74753
in-theory        74753
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (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-74753.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-855, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-74754
in-theory        74754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (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-74754.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-855, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-74755
in-theory        74755
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (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-74755.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-855, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-74756
in-theory        74756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-74756.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-855, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-74757
in-theory        74757
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-74757.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-855, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-74758
in-theory        74758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-1.            (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-74758.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-855, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-74759
in-theory        74759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     35
proof            (modus-ponens tm-855 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       149
proof-steps      11
----------------------------------------------------------------
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-1.            (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-74759.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-855, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-74760
in-theory        74760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
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-48.           (((A -> (B and 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-1.            (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-74760.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-855, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-74761
in-theory        74761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em 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-48.           (((A -> (B and 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-1.            (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-74761.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-855, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-74762
in-theory        74762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-74762.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-855, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-74763
in-theory        74763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-855 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       199
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-74763.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-855, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-74764
in-theory        74764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-74764.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-74765
in-theory        74765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-74765.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-855, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-74766
in-theory        74766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (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-74766.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-855, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-74767
in-theory        74767
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-74767.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-855, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-74768
in-theory        74768
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (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-74768.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-855, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-74769
in-theory        74769
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (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-74769.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-855, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-74770
in-theory        74770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-48.           (((A -> (B and 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-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-74770.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-855, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-74771
in-theory        74771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-855 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       159
proof-steps      11
----------------------------------------------------------------
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-1.            (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-74771.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-855, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-74772
in-theory        74772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74772.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-855, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-74773
in-theory        74773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     29
proof            (modus-ponens tm-855 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74773.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-855, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-74774
in-theory        74774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-74774.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-855, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-74775
in-theory        74775
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
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-48.           (((A -> (B and 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-1.            (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-74775.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-855, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-74776
in-theory        74776
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 (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-74776.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-855, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-74777
in-theory        74777
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 ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-855 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       187
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74777.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-855, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-74778
in-theory        74778
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 ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74778.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-855, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-74779
in-theory        74779
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 ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74779.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-855, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-74780
in-theory        74780
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 (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-855 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       169
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74780.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-855, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-74781
in-theory        74781
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 (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74781.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-855, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-74782
in-theory        74782
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 (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74782.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-855, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-74783
in-theory        74783
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 ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     45
proof            (modus-ponens tm-855 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       187
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74783.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-855, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-74784
in-theory        74784
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 ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     43
proof            (modus-ponens tm-855 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       181
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74784.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-855, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-74785
in-theory        74785
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 ((not (not G)) -> G)))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74785.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-855, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-74786
in-theory        74786
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 (G -> (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-74786.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-855, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-74787
in-theory        74787
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 ((G -> H) -> (G -> G))))
theorem-size     39
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-74787.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-855, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-74788
in-theory        74788
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 (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     51
proof            (modus-ponens tm-855 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       231
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74788.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-855, 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-74789
in-theory        74789
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 (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-855 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       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-74789.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-855, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-74790
in-theory        74790
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 ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     47
proof            (modus-ponens tm-855 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       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74790.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-855, 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-74791
in-theory        74791
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 (G -> ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-74791.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-855, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-74792
in-theory        74792
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 (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     47
proof            (modus-ponens tm-855 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       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74792.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-855, 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-74793
in-theory        74793
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 (G -> ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-74793.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-855, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-74794
in-theory        74794
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 (G -> ((H -> (I -> H)) and G))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-74794.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-855, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-74795
in-theory        74795
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 (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     49
proof            (modus-ponens tm-855 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       219
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74795.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-855, 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-74796
in-theory        74796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-74796.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-855, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-74797
in-theory        74797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     39
proof            (modus-ponens tm-855 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       173
proof-steps      11
----------------------------------------------------------------
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-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-74797.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-855, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-74798
in-theory        74798
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 G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-855 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       207
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74798.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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-855, 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-74799
in-theory        74799
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-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-74799.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-855, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-74800
in-theory        74800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-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-74800.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-855, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-74801
in-theory        74801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     39
proof            (modus-ponens tm-855 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       169
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-74801.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-855, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-74802
in-theory        74802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-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-74802.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-855, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-74803
in-theory        74803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-74803.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-855, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-74804
in-theory        74804
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-74804.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-74805
in-theory        74805
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm 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-48.           (((A -> (B and 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-3.            ((A and B) -> 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-74805.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-855, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-74806
in-theory        74806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-3.            ((A and B) -> 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-74806.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-855, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-74807
in-theory        74807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> 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-74807.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-855, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-74808
in-theory        74808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-74808.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-855, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-74809
in-theory        74809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-74809.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-855, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-74810
in-theory        74810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-74810.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-855, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-74811
in-theory        74811
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     35
proof            (modus-ponens tm-855 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       149
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-74811.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-855, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-74812
in-theory        74812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
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-48.           (((A -> (B and 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-3.            ((A and B) -> 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-74812.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-855, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-74813
in-theory        74813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-74813.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-855, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-74814
in-theory        74814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     31
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-74814.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-855, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-74815
in-theory        74815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-855 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       199
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-74815.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-855, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-74816
in-theory        74816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-74816.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-74817
in-theory        74817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-74817.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-855, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-74818
in-theory        74818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-74818.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-855, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-74819
in-theory        74819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-74819.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-855, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-74820
in-theory        74820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-74820.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-855, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-74821
in-theory        74821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-74821.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-855, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-74822
in-theory        74822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-74822.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-855, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-74823
in-theory        74823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-74823.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-855, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-74824
in-theory        74824
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 (G -> (((H and I) -> H) and G))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74824.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-855, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-74825
in-theory        74825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-1.            (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-74825.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-855, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-74826
in-theory        74826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-855 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       141
proof-steps      11
----------------------------------------------------------------
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-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-74826.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-855, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-74827
in-theory        74827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-855 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       159
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-74827.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-855, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-74828
in-theory        74828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74828.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-855, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-74829
in-theory        74829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     29
proof            (modus-ponens tm-855 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74829.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-855, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-74830
in-theory        74830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-74830.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-855, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-74831
in-theory        74831
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-74831.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-855, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-74832
in-theory        74832
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-74832.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-855, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-74833
in-theory        74833
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-74833.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-74834
in-theory        74834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> 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-74834.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-855, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-74835
in-theory        74835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-4.            ((A and B) -> 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-74835.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-855, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-74836
in-theory        74836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-4.            ((A and B) -> 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-74836.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-855, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-74837
in-theory        74837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-74837.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-855, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-74838
in-theory        74838
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-74838.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-855, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-74839
in-theory        74839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-74839.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-855, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-74840
in-theory        74840
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     35
proof            (modus-ponens tm-855 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       149
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-74840.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-855, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-74841
in-theory        74841
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-10)
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-48.           (((A -> (B and 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-4.            ((A and B) -> 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-74841.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-855, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-74842
in-theory        74842
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-74842.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-855, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-74843
in-theory        74843
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     31
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-74843.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-855, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-74844
in-theory        74844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-855 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       199
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-74844.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-855, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-74845
in-theory        74845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-74845.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-74846
in-theory        74846
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-74846.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-855, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-74847
in-theory        74847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-74847.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-855, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-74848
in-theory        74848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-74848.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-855, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-74849
in-theory        74849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-74849.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-855, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-74850
in-theory        74850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-74850.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-855, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-74851
in-theory        74851
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-74851.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-855, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-74852
in-theory        74852
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-74852.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-855, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-74853
in-theory        74853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-74853.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-855, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-74854
in-theory        74854
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-74854.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-855, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-74855
in-theory        74855
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 (G -> (((H and I) -> I) and G))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74855.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-855, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-74856
in-theory        74856
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-1.            (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-74856.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-855, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-74857
in-theory        74857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-855 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       141
proof-steps      11
----------------------------------------------------------------
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-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-74857.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-855, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-74858
in-theory        74858
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-855 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       159
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-74858.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-855, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-74859
in-theory        74859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74859.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-855, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-74860
in-theory        74860
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     29
proof            (modus-ponens tm-855 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74860.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-855, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-74861
in-theory        74861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-74861.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-855, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-74862
in-theory        74862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-74862.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-855, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-74863
in-theory        74863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B 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-74863.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-855, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-74864
in-theory        74864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-74864.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-74865
in-theory        74865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-855 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-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-74865.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-855, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-74866
in-theory        74866
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-855 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74866.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-855, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-74867
in-theory        74867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-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-74867.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-855, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-74868
in-theory        74868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-855 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and 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-74868.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-855, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-74869
in-theory        74869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and 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-74869.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-855, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-74870
in-theory        74870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     39
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-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-74870.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-855, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-74871
in-theory        74871
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     37
proof            (modus-ponens tm-855 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       157
proof-steps      11
----------------------------------------------------------------
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-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-74871.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-855, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-74872
in-theory        74872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-855 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-10)
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-48.           (((A -> (B and 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-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-74872.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-855, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-74873
in-theory        74873
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B 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-74873.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-855, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-74874
in-theory        74874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     33
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-74874.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-855, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-74875
in-theory        74875
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     45
proof            (modus-ponens tm-855 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       207
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-74875.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-855, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-74876
in-theory        74876
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-74876.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-74877
in-theory        74877
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-74877.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-855, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-74878
in-theory        74878
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-74878.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-855, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-74879
in-theory        74879
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-74879.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-855, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-74880
in-theory        74880
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-74880.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-855, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-74881
in-theory        74881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-74881.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-855, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-74882
in-theory        74882
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     43
proof            (modus-ponens tm-855 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       195
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-74882.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-855, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-74883
in-theory        74883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-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-74883.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-855, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-74884
in-theory        74884
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-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-74884.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-855, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-74885
in-theory        74885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     37
proof            (modus-ponens tm-855 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       171
proof-steps      13
----------------------------------------------------------------
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-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-74885.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-855, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-74886
in-theory        74886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-74886.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-855, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-74887
in-theory        74887
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-74887.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-855, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-74888
in-theory        74888
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 (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     43
proof            (modus-ponens tm-855 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       195
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74888.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-855, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-74889
in-theory        74889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-1.            (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-74889.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-855, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-74890
in-theory        74890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-855 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9)
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-48.           (((A -> (B and 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-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-74890.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-855, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-74891
in-theory        74891
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-855 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       171
proof-steps      11
----------------------------------------------------------------
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-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-74891.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-855, 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-74892
in-theory        74892
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     31
proof            (modus-ponens tm-855 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74892.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-855, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-74893
in-theory        74893
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     31
proof            (modus-ponens tm-855 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74893.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-855, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-74894
in-theory        74894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     33
proof            (modus-ponens tm-855 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-74894.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-855, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-74895
in-theory        74895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     31
proof            (modus-ponens tm-855 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-74895.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-855, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-74896
in-theory        74896
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-855 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-74896.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> D)))), M:tm-855, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-74897
in-theory        74897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-855 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-74897.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-855, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-74898
in-theory        74898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> ((D and E) and D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-74898.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> ((D and E) and D))), M:tm-855, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-74899
in-theory        74899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> ((D and E) and E)))
theorem-size     27
proof            (modus-ponens tm-855 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-74899.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> ((D and E) and E))), M:tm-855, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-74900
in-theory        74900
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-74900.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (D and E))))), M:tm-855, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-74901
in-theory        74901
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (D or E))))
theorem-size     25
proof            (modus-ponens tm-855 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-74901.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (D or E)))), M:tm-855, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-74902
in-theory        74902
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E or D))))
theorem-size     25
proof            (modus-ponens tm-855 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-74902.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E or D)))), M:tm-855, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-74903
in-theory        74903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-855 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-74903.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-74904
in-theory        74904
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     33
proof            (modus-ponens tm-855 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       153
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-74904.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-855, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-74905
in-theory        74905
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-74905.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-855, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-74906
in-theory        74906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (F -> E)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-74906.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (F -> E))))), M:tm-855, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-74907
in-theory        74907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-74907.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-855, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-74908
in-theory        74908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     47
proof            (modus-ponens tm-855 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-74908.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-855, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-74909
in-theory        74909
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     35
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-74909.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-855, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-74910
in-theory        74910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     41
proof            (modus-ponens tm-855 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-74910.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-855, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-74911
in-theory        74911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E and F) -> E))))
theorem-size     27
proof            (modus-ponens tm-855 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-74911.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E and F) -> E)))), M:tm-855, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-74912
in-theory        74912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     41
proof            (modus-ponens tm-855 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-74912.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-855, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-74913
in-theory        74913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E and F) -> F))))
theorem-size     27
proof            (modus-ponens tm-855 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-74913.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E and F) -> F)))), M:tm-855, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-74914
in-theory        74914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-74914.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-855, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-74915
in-theory        74915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     37
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-74915.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-855, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-74916
in-theory        74916
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-74916.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-855, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-74917
in-theory        74917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-74917.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-855, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-74918
in-theory        74918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     31
proof            (modus-ponens tm-855 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-74918.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-855, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-74919
in-theory        74919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-74919.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-855, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-74920
in-theory        74920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-855 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       171
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-74920.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-855, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-74921
in-theory        74921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-74921.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-855, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-74922
in-theory        74922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-74922.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-855, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-74923
in-theory        74923
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 ((G -> H) -> (G -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-855 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       195
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-74923.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-855, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-74924
in-theory        74924
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-74924.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-855, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-74925
in-theory        74925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-855 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       153
proof-steps      11
----------------------------------------------------------------
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-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-74925.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-855, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-74926
in-theory        74926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-74926.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-855, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-74927
in-theory        74927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-855 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74927.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-855, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-74928
in-theory        74928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     29
proof            (modus-ponens tm-855 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74928.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-855, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-74929
in-theory        74929
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-74929.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-855, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-74930
in-theory        74930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-855 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-74930.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-855, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-74931
in-theory        74931
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-855 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-74931.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-855, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-74932
in-theory        74932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     29
proof            (modus-ponens tm-855 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-74932.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-855, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-74933
in-theory        74933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-74933.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-855, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-74934
in-theory        74934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-74934.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-855, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-74935
in-theory        74935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-74935.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-855, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-74936
in-theory        74936
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 (G -> (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-74936.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-855, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-74937
in-theory        74937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (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-74937.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-855, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-74938
in-theory        74938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     31
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-74938.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-855, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-74939
in-theory        74939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     31
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-74939.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-855, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-74940
in-theory        74940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     31
proof            (modus-ponens tm-855 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-74940.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-855, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-74941
in-theory        74941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-48.           (((A -> (B and 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-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-74941.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-855, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-74942
in-theory        74942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     39
proof            (modus-ponens tm-855 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       159
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> 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-74942.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-855, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-74943
in-theory        74943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-855 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74943.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-855, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-74944
in-theory        74944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     29
proof            (modus-ponens tm-855 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-74944.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-855, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-74945
in-theory        74945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-74945.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-855, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-74946
in-theory        74946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-855 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
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-48.           (((A -> (B and 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-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-74946.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-855, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-74947
in-theory        74947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-855 tm-356 ((A (-> 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-48.           (((A -> (B and 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-1.            (A -> (B -> 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-74947.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-855, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-74948
in-theory        74948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-74948.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-855, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-74949
in-theory        74949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-74949.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-855, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-74950
in-theory        74950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-74950.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-855, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-74951
in-theory        74951
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 ((G -> (H -> G)) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74951.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-855, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-74952
in-theory        74952
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-74952.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-855, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-74953
in-theory        74953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (F -> E)) or G)))
theorem-size     27
proof            (modus-ponens tm-855 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74953.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (F -> E)) or G))), M:tm-855, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-74954
in-theory        74954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> D)) or F) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-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-74954.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> D)) or F) or G)), M:tm-855, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-74955
in-theory        74955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-74955.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-855, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-74956
in-theory        74956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     27
proof            (modus-ponens tm-855 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) 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-48.           (((A -> (B and 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-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-74956.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> E)) or G))), M:tm-855, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-74957
in-theory        74957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-74957.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-855, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-74958
in-theory        74958
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-74958.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-855, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-74959
in-theory        74959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-74959.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-855, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-74960
in-theory        74960
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 (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     47
proof            (modus-ponens tm-855 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       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74960.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-855, 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-74961
in-theory        74961
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-74961.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-855, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-74962
in-theory        74962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74962.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-855, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-74963
in-theory        74963
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-74963.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-855, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-74964
in-theory        74964
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     37
proof            (modus-ponens tm-855 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       161
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-74964.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-855, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-74965
in-theory        74965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-74965.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-855, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-74966
in-theory        74966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-74966.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-855, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-74967
in-theory        74967
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-74967.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-855, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-74968
in-theory        74968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-74968.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-855, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-74969
in-theory        74969
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 (((G and H) -> G) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74969.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-855, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-74970
in-theory        74970
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-74970.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-855, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-74971
in-theory        74971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E and F) -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-855 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       123
proof-steps      11
----------------------------------------------------------------
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-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-74971.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E and F) -> E) or G))), M:tm-855, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-74972
in-theory        74972
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) -> D) or F) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-74972.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) -> D) or F) or G)), M:tm-855, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-74973
in-theory        74973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-74973.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-855, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-74974
in-theory        74974
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and F) -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-855 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-74974.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and F) -> E) or G))), M:tm-855, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-74975
in-theory        74975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-74975.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-855, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-74976
in-theory        74976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-74976.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-855, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-74977
in-theory        74977
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-74977.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-855, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-74978
in-theory        74978
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 (((G and H) -> H) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74978.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-855, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-74979
in-theory        74979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-74979.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-855, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-74980
in-theory        74980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E and F) -> F) or G)))
theorem-size     27
proof            (modus-ponens tm-855 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       123
proof-steps      11
----------------------------------------------------------------
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-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-74980.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E and F) -> F) or G))), M:tm-855, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-74981
in-theory        74981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) -> E) or F) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-74981.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) -> E) or F) or G)), M:tm-855, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-74982
in-theory        74982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-74982.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-855, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-74983
in-theory        74983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and F) -> F) or G)))
theorem-size     27
proof            (modus-ponens tm-855 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-74983.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E and F) -> F) or G))), M:tm-855, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-74984
in-theory        74984
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-74984.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-855, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-74985
in-theory        74985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-74985.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-855, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-74986
in-theory        74986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-74986.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-855, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-74987
in-theory        74987
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 ((G -> (H -> (G and H))) or I)))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74987.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-855, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-74988
in-theory        74988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-74988.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-855, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-74989
in-theory        74989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-74989.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-855, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-74990
in-theory        74990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     29
proof            (modus-ponens tm-855 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-74990.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-855, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-74991
in-theory        74991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-74991.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-855, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-74992
in-theory        74992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-74992.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-855, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-74993
in-theory        74993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-74993.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-855, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-74994
in-theory        74994
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-74994.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-855, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-74995
in-theory        74995
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-74995.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-855, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-74996
in-theory        74996
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 ((G -> (G or H)) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-74996.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-855, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-74997
in-theory        74997
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-74997.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-855, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-74998
in-theory        74998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (E or F)) or G)))
theorem-size     27
proof            (modus-ponens tm-855 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
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-48.           (((A -> (B and 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-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-74998.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (E or F)) or G))), M:tm-855, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-74999
in-theory        74999
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (D or E)) or F) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
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-48.           (((A -> (B and 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-6.            (A -> (A 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-74999.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (D or E)) or F) or G)), M:tm-855, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-75000
in-theory        75000
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-75000.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-855, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-75001
in-theory        75001
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (E or F)) or G)))
theorem-size     27
proof            (modus-ponens tm-855 tm-410 ((A (-> Am (or (-> Bm (or Bm 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-48.           (((A -> (B and 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-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-75001.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (E or F)) or G))), M:tm-855, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-75002
in-theory        75002
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75002.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-855, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-75003
in-theory        75003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-75003.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-75004
in-theory        75004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or 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-75004.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-855, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-75005
in-theory        75005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or 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-75005.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-855, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-75006
in-theory        75006
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or 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-75006.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-855, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-75007
in-theory        75007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
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-48.           (((A -> (B and 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-6.            (A -> (A or 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-75007.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-855, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-75008
in-theory        75008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75008.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-855, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-75009
in-theory        75009
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-75009.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-855, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-75010
in-theory        75010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     35
proof            (modus-ponens tm-855 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       149
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-75010.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-855, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-75011
in-theory        75011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-10)
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-48.           (((A -> (B and 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-6.            (A -> (A or 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-75011.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-855, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-75012
in-theory        75012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75012.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-855, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-75013
in-theory        75013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     31
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-75013.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-855, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-75014
in-theory        75014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-855 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       199
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-75014.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-855, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-75015
in-theory        75015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75015.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-75016
in-theory        75016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-75016.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-855, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-75017
in-theory        75017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75017.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-855, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-75018
in-theory        75018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-75018.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-855, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-75019
in-theory        75019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75019.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-855, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-75020
in-theory        75020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75020.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-855, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-75021
in-theory        75021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-75021.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-855, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-75022
in-theory        75022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-75022.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-855, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-75023
in-theory        75023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-75023.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-855, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-75024
in-theory        75024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-75024.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-855, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-75025
in-theory        75025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-75025.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-855, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-75026
in-theory        75026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75026.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-855, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-75027
in-theory        75027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75027.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-855, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-75028
in-theory        75028
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-75028.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-855, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-75029
in-theory        75029
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-75029.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-855, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-75030
in-theory        75030
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-75030.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-855, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-75031
in-theory        75031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-75031.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-855, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-75032
in-theory        75032
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or 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-75032.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-855, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-75033
in-theory        75033
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-75033.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-855, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-75034
in-theory        75034
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-75034.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-855, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-75035
in-theory        75035
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75035.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-855, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-75036
in-theory        75036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75036.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-855, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-75037
in-theory        75037
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75037.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-855, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-75038
in-theory        75038
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 (G -> ((H -> (H or I)) and G))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75038.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-855, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-75039
in-theory        75039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75039.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-855, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-75040
in-theory        75040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-855 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       141
proof-steps      11
----------------------------------------------------------------
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-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-75040.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-855, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-75041
in-theory        75041
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-855 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       159
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-75041.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-855, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-75042
in-theory        75042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-75042.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-855, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-75043
in-theory        75043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     29
proof            (modus-ponens tm-855 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
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-48.           (((A -> (B and 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-6.            (A -> (A or 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-75043.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-855, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-75044
in-theory        75044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-75044.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-855, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-75045
in-theory        75045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-75045.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-855, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-75046
in-theory        75046
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75046.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-855, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75047
in-theory        75047
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (E or F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-75047.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (E or F))))), M:tm-855, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-75048
in-theory        75048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-75048.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-855, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75049
in-theory        75049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-75049.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-855, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75050
in-theory        75050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-75050.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-855, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75051
in-theory        75051
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 (G -> (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-75051.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-855, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-75052
in-theory        75052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75052.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-855, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75053
in-theory        75053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     29
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-75053.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-855, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-75054
in-theory        75054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     29
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-75054.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-855, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-75055
in-theory        75055
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-75055.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-855, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-75056
in-theory        75056
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-855 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       133
proof-steps      11
----------------------------------------------------------------
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-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-75056.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-855, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-75057
in-theory        75057
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     35
proof            (modus-ponens tm-855 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       147
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-75057.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-855, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-75058
in-theory        75058
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-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-75058.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (F or G))))), M:tm-855, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-75059
in-theory        75059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (E or F))) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
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-48.           (((A -> (B and 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-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-75059.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (E or F))) or G)), M:tm-855, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-75060
in-theory        75060
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-75060.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-855, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-75061
in-theory        75061
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-855 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-75061.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (E or F)))), M:tm-855, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-75062
in-theory        75062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-471 ((A (-> Am (-> Bm (-> Cm (or 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-75062.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (F or G))))), M:tm-855, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-75063
in-theory        75063
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75063.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-855, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-75064
in-theory        75064
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75064.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-855, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-75065
in-theory        75065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75065.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-855, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-75066
in-theory        75066
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75066.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-855, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-75067
in-theory        75067
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 (G or (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75067.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-855, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-75068
in-theory        75068
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75068.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-855, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-75069
in-theory        75069
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-478 ((A (or Am (or Bm (-> Cm (-> 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-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-75069.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or (F -> (G -> F))))), M:tm-855, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-75070
in-theory        75070
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (F -> E))) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-75070.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (F -> E))) or G)), M:tm-855, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-75071
in-theory        75071
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-75071.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-855, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-75072
in-theory        75072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-481 ((A (-> Am (or Bm (-> Cm (-> 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-48.           (((A -> (B and 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-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-75072.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or (F -> (G -> F))))), M:tm-855, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-75073
in-theory        75073
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75073.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-75074
in-theory        75074
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75074.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-75075
in-theory        75075
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75075.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-75076
in-theory        75076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75076.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-75077
in-theory        75077
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 (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-855 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       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75077.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-855, 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-75078
in-theory        75078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75078.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-75079
in-theory        75079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-75079.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-855, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-75080
in-theory        75080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-75080.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-855, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-75081
in-theory        75081
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     37
proof            (modus-ponens tm-855 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       161
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-75081.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-855, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-75082
in-theory        75082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-75082.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-855, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-75083
in-theory        75083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75083.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-855, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-75084
in-theory        75084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75084.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-855, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-75085
in-theory        75085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75085.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-855, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-75086
in-theory        75086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75086.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-855, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-75087
in-theory        75087
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 (G or ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75087.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-855, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-75088
in-theory        75088
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75088.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-855, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-75089
in-theory        75089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-855 tm-498 ((A (or Am (or Bm (-> (and Cm 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-75089.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or ((F and G) -> F)))), M:tm-855, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-75090
in-theory        75090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-855 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       123
proof-steps      11
----------------------------------------------------------------
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-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-75090.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E and F) -> E)) or G)), M:tm-855, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-75091
in-theory        75091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-75091.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-855, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-75092
in-theory        75092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-855 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-75092.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or ((F and G) -> F)))), M:tm-855, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-75093
in-theory        75093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75093.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-855, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-75094
in-theory        75094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75094.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-855, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-75095
in-theory        75095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75095.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-855, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-75096
in-theory        75096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75096.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-855, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-75097
in-theory        75097
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 (G or ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75097.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-855, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-75098
in-theory        75098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75098.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-855, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-75099
in-theory        75099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-855 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-75099.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or ((F and G) -> G)))), M:tm-855, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-75100
in-theory        75100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E and F) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-855 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       123
proof-steps      11
----------------------------------------------------------------
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-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-75100.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E and F) -> F)) or G)), M:tm-855, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-75101
in-theory        75101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-75101.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-855, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-75102
in-theory        75102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-855 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-75102.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or ((F and G) -> G)))), M:tm-855, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-75103
in-theory        75103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75103.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-855, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-75104
in-theory        75104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75104.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-855, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-75105
in-theory        75105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75105.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-855, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-75106
in-theory        75106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75106.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-855, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-75107
in-theory        75107
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 (G or (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75107.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-855, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-75108
in-theory        75108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75108.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-855, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-75109
in-theory        75109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-855 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), 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-75109.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-855, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-75110
in-theory        75110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     29
proof            (modus-ponens tm-855 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-75110.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-855, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-75111
in-theory        75111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-75111.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-855, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-75112
in-theory        75112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-855 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-75112.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-855, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-75113
in-theory        75113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75113.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-855, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75114
in-theory        75114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75114.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-855, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75115
in-theory        75115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75115.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-855, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75116
in-theory        75116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75116.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-855, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75117
in-theory        75117
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 (G or (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75117.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-855, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-75118
in-theory        75118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75118.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-855, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75119
in-theory        75119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A 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-75119.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or (F -> (F or G))))), M:tm-855, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-75120
in-theory        75120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (E or F))) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
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-48.           (((A -> (B and 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-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-75120.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (E or F))) or G)), M:tm-855, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-75121
in-theory        75121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-75121.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-855, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-75122
in-theory        75122
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-75122.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or (F -> (F or G))))), M:tm-855, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-75123
in-theory        75123
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75123.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-855, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75124
in-theory        75124
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75124.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-855, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75125
in-theory        75125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75125.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-855, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75126
in-theory        75126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75126.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-855, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75127
in-theory        75127
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 (G or (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75127.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-855, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-75128
in-theory        75128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75128.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-855, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75129
in-theory        75129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-538 ((A (or Am (or Bm (-> Cm (or 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-48.           (((A -> (B and 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-7.            (A -> (B 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-75129.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or (F -> (G or F))))), M:tm-855, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-75130
in-theory        75130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (F or E))) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
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-48.           (((A -> (B and 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-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-75130.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (F or E))) or G)), M:tm-855, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-75131
in-theory        75131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-75131.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-855, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-75132
in-theory        75132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-541 ((A (-> Am (or Bm (-> Cm (or 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-48.           (((A -> (B and 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-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-75132.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or (F -> (G or F))))), M:tm-855, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-75133
in-theory        75133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75133.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-855, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-75134
in-theory        75134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75134.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-855, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-75135
in-theory        75135
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75135.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-855, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-75136
in-theory        75136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75136.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-855, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-75137
in-theory        75137
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 ((G -> (H or G)) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75137.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-855, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-75138
in-theory        75138
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75138.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-855, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-75139
in-theory        75139
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (F or E)) or G)))
theorem-size     27
proof            (modus-ponens tm-855 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
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-48.           (((A -> (B and 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-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-75139.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> (F or E)) or G))), M:tm-855, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-75140
in-theory        75140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E or D)) or F) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B 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-75140.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E or D)) or F) or G)), M:tm-855, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-75141
in-theory        75141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-75141.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-855, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-75142
in-theory        75142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F or E)) or G)))
theorem-size     27
proof            (modus-ponens tm-855 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-75142.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F or E)) or G))), M:tm-855, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-75143
in-theory        75143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75143.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-855, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-75144
in-theory        75144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-75144.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-75145
in-theory        75145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or 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-75145.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-855, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-75146
in-theory        75146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or 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-75146.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-855, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-75147
in-theory        75147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or 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-75147.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-855, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-75148
in-theory        75148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75148.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-855, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-75149
in-theory        75149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or 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-48.           (((A -> (B and 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-7.            (A -> (B or 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-75149.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-855, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-75150
in-theory        75150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-75150.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-855, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-75151
in-theory        75151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     35
proof            (modus-ponens tm-855 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       149
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-75151.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-855, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-75152
in-theory        75152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-10)
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-48.           (((A -> (B and 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-7.            (A -> (B or 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-75152.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-855, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-75153
in-theory        75153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75153.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-855, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-75154
in-theory        75154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     31
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-75154.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-855, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-75155
in-theory        75155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-855 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       199
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-75155.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-855, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-75156
in-theory        75156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75156.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-75157
in-theory        75157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-75157.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-855, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-75158
in-theory        75158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75158.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-855, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-75159
in-theory        75159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-75159.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-855, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-75160
in-theory        75160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75160.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-855, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-75161
in-theory        75161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75161.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-855, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-75162
in-theory        75162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-75162.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-855, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-75163
in-theory        75163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-75163.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-855, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-75164
in-theory        75164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-75164.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-855, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-75165
in-theory        75165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-75165.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-855, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-75166
in-theory        75166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-75166.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-855, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-75167
in-theory        75167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75167.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-855, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-75168
in-theory        75168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75168.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-855, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-75169
in-theory        75169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75169.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-855, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-75170
in-theory        75170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75170.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-855, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-75171
in-theory        75171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75171.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-855, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-75172
in-theory        75172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75172.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-855, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-75173
in-theory        75173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75173.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-855, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-75174
in-theory        75174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75174.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-855, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-75175
in-theory        75175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75175.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-855, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75176
in-theory        75176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75176.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-855, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-75177
in-theory        75177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-75177.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-855, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-75178
in-theory        75178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-75178.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-855, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-75179
in-theory        75179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-75179.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-855, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-75180
in-theory        75180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-75180.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-855, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-75181
in-theory        75181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75181.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-855, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-75182
in-theory        75182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or 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-75182.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-855, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75183
in-theory        75183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-75183.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-855, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-75184
in-theory        75184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-75184.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-855, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-75185
in-theory        75185
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-75185.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-855, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-75186
in-theory        75186
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-75186.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-855, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-75187
in-theory        75187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     35
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-75187.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-855, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-75188
in-theory        75188
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-75188.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-855, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-75189
in-theory        75189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-75189.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-855, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-75190
in-theory        75190
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 (G -> ((H -> (I or H)) and G))))
theorem-size     41
proof            (modus-ponens tm-855 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       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75190.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-855, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-75191
in-theory        75191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75191.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-855, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-75192
in-theory        75192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-855 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       141
proof-steps      11
----------------------------------------------------------------
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-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-75192.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-855, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-75193
in-theory        75193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-855 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       159
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-75193.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-855, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-75194
in-theory        75194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
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-48.           (((A -> (B and 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-7.            (A -> (B or 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-75194.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-855, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-75195
in-theory        75195
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     29
proof            (modus-ponens tm-855 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-75195.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-855, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-75196
in-theory        75196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-75196.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-855, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-75197
in-theory        75197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-75197.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-855, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-75198
in-theory        75198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75198.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-855, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75199
in-theory        75199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75199.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-855, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75200
in-theory        75200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (F or E)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-75200.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D and (E -> (F or E))))), M:tm-855, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-75201
in-theory        75201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-75201.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-855, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75202
in-theory        75202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-75202.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-855, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75203
in-theory        75203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-75203.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-855, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75204
in-theory        75204
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 (G -> (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-855 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       179
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-75204.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-855, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-75205
in-theory        75205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-75205.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-855, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-75206
in-theory        75206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     29
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-75206.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-855, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-75207
in-theory        75207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     29
proof            (modus-ponens tm-855 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       155
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-75207.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-855, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-75208
in-theory        75208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-75208.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-855, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-75209
in-theory        75209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-855 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       133
proof-steps      11
----------------------------------------------------------------
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-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-75209.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-855, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-75210
in-theory        75210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-855 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       147
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-75210.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-855, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-75211
in-theory        75211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-620 ((A (or Am (-> Bm (-> Cm (or 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-48.           (((A -> (B and 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-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-75211.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E -> (F -> (G or F))))), M:tm-855, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-75212
in-theory        75212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (F or E))) or G))
theorem-size     27
proof            (modus-ponens tm-855 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-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-75212.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (F or E))) or G)), M:tm-855, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-75213
in-theory        75213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     29
proof            (modus-ponens tm-855 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-75213.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-855, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-75214
in-theory        75214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-855 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-75214.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> (D -> (F or E)))), M:tm-855, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-75215
in-theory        75215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-855 tm-624 ((A (-> Am (-> Bm (-> Cm (or 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-75215.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (F -> (G or F))))), M:tm-855, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-75216
in-theory        75216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75216.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-855, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-75217
in-theory        75217
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     35
proof            (modus-ponens tm-855 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       161
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-75217.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-855, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-75218
in-theory        75218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75218.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-855, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-75219
in-theory        75219
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75219.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-855, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-75220
in-theory        75220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75220.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-855, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-75221
in-theory        75221
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     33
proof            (modus-ponens tm-855 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75221.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-855, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-75222
in-theory        75222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-855 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75222.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-855, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-75223
in-theory        75223
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75223.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-855, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-75224
in-theory        75224
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     27
proof            (modus-ponens tm-855 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-75224.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (E -> E))), M:tm-855, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-75225
in-theory        75225
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-855 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       205
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-75225.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-855, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-75226
in-theory        75226
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       185
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-75226.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-75227
in-theory        75227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-855 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       181
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-75227.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-855, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-75228
in-theory        75228
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75228.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-855, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-75229
in-theory        75229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-855 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       181
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-75229.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-855, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-75230
in-theory        75230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75230.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-855, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-75231
in-theory        75231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-855 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75231.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-855, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-75232
in-theory        75232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     41
proof            (modus-ponens tm-855 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       197
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-75232.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-855, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-75233
in-theory        75233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-855 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       165
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-75233.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-855, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-75234
in-theory        75234
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-855 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       165
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-75234.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-855, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-75235
in-theory        75235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     35
proof            (modus-ponens tm-855 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       173
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-75235.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-855, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-75236
in-theory        75236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-75236.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-855, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-75237
in-theory        75237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75237.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-855, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-75238
in-theory        75238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-855 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       165
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-75238.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-855, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-75239
in-theory        75239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75239.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-855, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-75240
in-theory        75240
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-855 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       165
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-75240.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-855, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-75241
in-theory        75241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75241.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-855, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-75242
in-theory        75242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     33
proof            (modus-ponens tm-855 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75242.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-855, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-75243
in-theory        75243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 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       173
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-75243.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-855, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-75244
in-theory        75244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 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       173
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-75244.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-855, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-75245
in-theory        75245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     37
proof            (modus-ponens tm-855 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-75245.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-855, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-75246
in-theory        75246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 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       181
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-75246.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-855, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-75247
in-theory        75247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 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       173
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-75247.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-855, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-75248
in-theory        75248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 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       173
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-75248.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-855, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-75249
in-theory        75249
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 (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-855 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       205
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-75249.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-855, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-75250
in-theory        75250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 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       173
proof-steps      13
----------------------------------------------------------------
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-1.            (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-75250.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-855, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-75251
in-theory        75251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-75251.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-855, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-75252
in-theory        75252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     39
proof            (modus-ponens tm-855 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       167
proof-steps      11
----------------------------------------------------------------
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-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-75252.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-855, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-75253
in-theory        75253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-855 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       177
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-75253.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-855, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-75254
in-theory        75254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-855 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       149
proof-steps      11
----------------------------------------------------------------
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-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-75254.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-855, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-75255
in-theory        75255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-855 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       149
proof-steps      11
----------------------------------------------------------------
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-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-75255.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-855, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-75256
in-theory        75256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-855 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-75256.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-855, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-75257
in-theory        75257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     37
proof            (modus-ponens tm-855 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       165
proof-steps      11
----------------------------------------------------------------
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-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-75257.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-855, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-75258
in-theory        75258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-855 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75258.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-855, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-75259
in-theory        75259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-855 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       185
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75259.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-855, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-75260
in-theory        75260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     43
proof            (modus-ponens tm-855 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       197
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75260.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-855, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-75261
in-theory        75261
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     43
proof            (modus-ponens tm-855 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       191
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75261.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-855, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-75262
in-theory        75262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     41
proof            (modus-ponens tm-855 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       185
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75262.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-855, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-75263
in-theory        75263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-855 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       185
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75263.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-855, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-75264
in-theory        75264
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-855 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       205
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75264.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-855, 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-75265
in-theory        75265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     45
proof            (modus-ponens tm-855 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75265.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-855, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-75266
in-theory        75266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-855 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       189
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75266.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-855, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-75267
in-theory        75267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     39
proof            (modus-ponens tm-855 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75267.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-855, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-75268
in-theory        75268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-855 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       233
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75268.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-855, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-75269
in-theory        75269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-855 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       221
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75269.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-855, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-75270
in-theory        75270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-855 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       189
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75270.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-855, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-75271
in-theory        75271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-855 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       189
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75271.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-855, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-75272
in-theory        75272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-855 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       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75272.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-855, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-75273
in-theory        75273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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     53
proof            (modus-ponens tm-855 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       241
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75273.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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-855, 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-75274
in-theory        75274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-855 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       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75274.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-855, 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-75275
in-theory        75275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-855 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       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75275.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-855, 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-75276
in-theory        75276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     47
proof            (modus-ponens tm-855 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       217
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75276.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-855, 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-75277
in-theory        75277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-855 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       213
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75277.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-855, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-75278
in-theory        75278
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-855 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       197
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75278.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-855, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-75279
in-theory        75279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-855 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       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75279.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-855, 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-75280
in-theory        75280
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-855 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       189
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75280.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-855, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-75281
in-theory        75281
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-855 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       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75281.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-855, 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-75282
in-theory        75282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-855 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       189
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75282.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-855, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-75283
in-theory        75283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-855 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       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-75283.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-855, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-75284
in-theory        75284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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     61
proof            (modus-ponens tm-855 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       271
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75284.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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-855, 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-75285
in-theory        75285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     45
proof            (modus-ponens tm-855 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       219
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-75285.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-855, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-75286
in-theory        75286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     49
proof            (modus-ponens tm-855 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       217
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-75286.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-855, 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-75287
in-theory        75287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     49
proof            (modus-ponens tm-855 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       217
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-75287.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-855, 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-75288
in-theory        75288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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     53
proof            (modus-ponens tm-855 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       233
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-75288.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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-855, 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-75289
in-theory        75289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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     51
proof            (modus-ponens tm-855 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       225
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-75289.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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-855, 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-75290
in-theory        75290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     49
proof            (modus-ponens tm-855 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       217
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-75290.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-855, 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-75291
in-theory        75291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     49
proof            (modus-ponens tm-855 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       217
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-75291.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-855, 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-75292
in-theory        75292
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 ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     57
proof            (modus-ponens tm-855 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       249
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-75292.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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-855, 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-75293
in-theory        75293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     49
proof            (modus-ponens tm-855 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       217
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-75293.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-855, 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-75294
in-theory        75294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-855 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       197
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-75294.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-855, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-75295
in-theory        75295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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     55
proof            (modus-ponens tm-855 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       219
proof-steps      11
----------------------------------------------------------------
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-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-75295.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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-855, 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-75296
in-theory        75296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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     63
proof            (modus-ponens tm-855 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       237
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-75296.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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-855, 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-75297
in-theory        75297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     45
proof            (modus-ponens tm-855 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       193
proof-steps      11
----------------------------------------------------------------
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-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-75297.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-855, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-75298
in-theory        75298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     45
proof            (modus-ponens tm-855 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       193
proof-steps      11
----------------------------------------------------------------
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-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-75298.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-855, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-75299
in-theory        75299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     47
proof            (modus-ponens tm-855 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-75299.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-855, 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-75300
in-theory        75300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     53
proof            (modus-ponens tm-855 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       217
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75300.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-855, 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-75301
in-theory        75301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     45
proof            (modus-ponens tm-855 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       193
proof-steps      11
----------------------------------------------------------------
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-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-75301.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-855, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-75302
in-theory        75302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75302.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> D))), M:tm-855, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-75303
in-theory        75303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-855 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       167
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-75303.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-855, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-75304
in-theory        75304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     29
proof            (modus-ponens tm-855 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
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-75304.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-855, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-75305
in-theory        75305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     29
proof            (modus-ponens tm-855 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       139
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-75305.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-855, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-75306
in-theory        75306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
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-75306.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-855, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-75307
in-theory        75307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (D or F)))
theorem-size     27
proof            (modus-ponens tm-855 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
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-75307.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (D or F))), M:tm-855, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-75308
in-theory        75308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F or D)))
theorem-size     27
proof            (modus-ponens tm-855 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
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-75308.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F or D))), M:tm-855, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-75309
in-theory        75309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-75309.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-855, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-75310
in-theory        75310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     35
proof            (modus-ponens tm-855 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       157
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-75310.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-855, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-75311
in-theory        75311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     29
proof            (modus-ponens tm-855 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       139
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-75311.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-855, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-75312
in-theory        75312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75312.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-855, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-75313
in-theory        75313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     31
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-75313.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-855, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-75314
in-theory        75314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     49
proof            (modus-ponens tm-855 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       219
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-75314.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-855, 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-75315
in-theory        75315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75315.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-75316
in-theory        75316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     43
proof            (modus-ponens tm-855 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       195
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-75316.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-855, 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-75317
in-theory        75317
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75317.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-855, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-75318
in-theory        75318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     43
proof            (modus-ponens tm-855 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       195
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-75318.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-855, 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-75319
in-theory        75319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75319.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-855, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-75320
in-theory        75320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-855 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       159
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75320.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-855, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-75321
in-theory        75321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     39
proof            (modus-ponens tm-855 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-75321.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-855, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-75322
in-theory        75322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
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-75322.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-855, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-75323
in-theory        75323
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     31
proof            (modus-ponens tm-855 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       159
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-75323.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-855, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-75324
in-theory        75324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     33
proof            (modus-ponens tm-855 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       167
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-75324.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-855, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-75325
in-theory        75325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-855 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       171
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-75325.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-855, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-75326
in-theory        75326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 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       159
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75326.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-855, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-75327
in-theory        75327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     31
proof            (modus-ponens tm-855 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       159
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-75327.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-855, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-75328
in-theory        75328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75328.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-855, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-75329
in-theory        75329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     31
proof            (modus-ponens tm-855 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       159
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-75329.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-855, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-75330
in-theory        75330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75330.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-855, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-75331
in-theory        75331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     39
proof            (modus-ponens tm-855 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       185
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-75331.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-855, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-75332
in-theory        75332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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     55
proof            (modus-ponens tm-855 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       237
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-75332.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and 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-855, 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-75333
in-theory        75333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     35
proof            (modus-ponens tm-855 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       175
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-75333.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-855, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-75334
in-theory        75334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-855 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       217
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75334.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-855, 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-75335
in-theory        75335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     31
proof            (modus-ponens tm-855 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       169
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-75335.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-855, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-75336
in-theory        75336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 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       167
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-75336.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-855, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-75337
in-theory        75337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 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       167
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-75337.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-855, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-75338
in-theory        75338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-855 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       171
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-75338.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-855, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-75339
in-theory        75339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-855 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       175
proof-steps      13
----------------------------------------------------------------
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-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-75339.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-855, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-75340
in-theory        75340
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 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       167
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-75340.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-855, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-75341
in-theory        75341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 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       167
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-75341.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-855, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-75342
in-theory        75342
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 ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-855 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       199
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-75342.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-855, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-75343
in-theory        75343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 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       167
proof-steps      13
----------------------------------------------------------------
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-1.            (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-75343.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-855, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-75344
in-theory        75344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     35
proof            (modus-ponens tm-855 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       157
proof-steps      11
----------------------------------------------------------------
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-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-75344.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-855, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-75345
in-theory        75345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-855 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       171
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-75345.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-855, 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-75346
in-theory        75346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-855 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       143
proof-steps      11
----------------------------------------------------------------
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-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-75346.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-855, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-75347
in-theory        75347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     31
proof            (modus-ponens tm-855 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       143
proof-steps      11
----------------------------------------------------------------
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-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-75347.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-855, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-75348
in-theory        75348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     33
proof            (modus-ponens tm-855 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-75348.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-855, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-75349
in-theory        75349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     33
proof            (modus-ponens tm-855 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       155
proof-steps      11
----------------------------------------------------------------
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-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-75349.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-855, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-75350
in-theory        75350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-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-75350.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-855, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-75351
in-theory        75351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-855 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-75351.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> E))), M:tm-855, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-75352
in-theory        75352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-855 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       167
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-75352.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-855, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-75353
in-theory        75353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     29
proof            (modus-ponens tm-855 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       139
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-75353.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-855, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-75354
in-theory        75354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     29
proof            (modus-ponens tm-855 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75354.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-855, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-75355
in-theory        75355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75355.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-855, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-75356
in-theory        75356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-855 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75356.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (E or F))), M:tm-855, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-75357
in-theory        75357
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-855 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75357.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F or E))), M:tm-855, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-75358
in-theory        75358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-855 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       163
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-75358.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-855, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-75359
in-theory        75359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     35
proof            (modus-ponens tm-855 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       157
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-75359.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-855, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-75360
in-theory        75360
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     29
proof            (modus-ponens tm-855 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       139
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-75360.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-855, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-75361
in-theory        75361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-75361.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-855, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-75362
in-theory        75362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     31
proof            (modus-ponens tm-855 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       163
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-75362.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-855, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-75363
in-theory        75363
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     49
proof            (modus-ponens tm-855 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       219
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-75363.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-855, 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-75364
in-theory        75364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-75364.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-75365
in-theory        75365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     43
proof            (modus-ponens tm-855 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       195
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-75365.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-855, 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-75366
in-theory        75366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 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       151
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-75366.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-855, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-75367
in-theory        75367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     43
proof            (modus-ponens tm-855 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       195
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-75367.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-855, 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-75368
in-theory        75368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-75368.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-855, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-75369
in-theory        75369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     31
proof            (modus-ponens tm-855 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       159
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-75369.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-855, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-75370
in-theory        75370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     39
proof            (modus-ponens tm-855 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-75370.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-855, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-75371
in-theory        75371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     31
proof            (modus-ponens tm-855 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       159
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-75371.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-855, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-75372
in-theory        75372
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     31
proof            (modus-ponens tm-855 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75372.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-855, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-75373
in-theory        75373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     33
proof            (modus-ponens tm-855 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       167
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-75373.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-855, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-75374
in-theory        75374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-855 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       171
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-75374.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-855, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-75375
in-theory        75375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), 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-75375.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-855, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-75376
in-theory        75376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     31
proof            (modus-ponens tm-855 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-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-75376.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-855, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-75377
in-theory        75377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-75377.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-855, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-75378
in-theory        75378
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     31
proof            (modus-ponens tm-855 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-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-75378.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-855, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-75379
in-theory        75379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-75379.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-855, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-75380
in-theory        75380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-855 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-75380.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-855, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-75381
in-theory        75381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     55
proof            (modus-ponens tm-855 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-75381.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-855, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-75382
in-theory        75382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     35
proof            (modus-ponens tm-855 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75382.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-855, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-75383
in-theory        75383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     35
proof            (modus-ponens tm-855 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75383.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-855, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-75384
in-theory        75384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     35
proof            (modus-ponens tm-855 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
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-75384.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-855, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-75385
in-theory        75385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-855 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75385.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-855, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-75386
in-theory        75386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     31
proof            (modus-ponens tm-855 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75386.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-855, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-75387
in-theory        75387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or 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-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-75387.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-855, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-75388
in-theory        75388
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or 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-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-75388.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-855, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-75389
in-theory        75389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-855 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-75389.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-855, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-75390
in-theory        75390
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-855 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-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-75390.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-855, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-75391
in-theory        75391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-75391.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-855, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-75392
in-theory        75392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-3.            ((A and B) -> 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-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-75392.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-855, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-75393
in-theory        75393
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 ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-855 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-75393.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-855, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-75394
in-theory        75394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-855 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (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-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-75394.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-855, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-75395
in-theory        75395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     35
proof            (modus-ponens tm-855 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 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-48.           (((A -> (B and 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
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-75395.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-855, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-75396
in-theory        75396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-855 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75396.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-855, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-75397
in-theory        75397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
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-75397.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-855, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-75398
in-theory        75398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     31
proof            (modus-ponens tm-855 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
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-75398.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-855, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-75399
in-theory        75399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     33
proof            (modus-ponens tm-855 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75399.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-855, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-75400
in-theory        75400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     33
proof            (modus-ponens tm-855 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-75400.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-855, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-75401
in-theory        75401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-75401.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-855, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-75402
in-theory        75402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-75402.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-855, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-75403
in-theory        75403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     35
proof            (modus-ponens tm-855 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-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-75403.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-855, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-75404
in-theory        75404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     33
proof            (modus-ponens tm-855 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-75404.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-855, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-75405
in-theory        75405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-75405.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-855, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-75406
in-theory        75406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-855 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-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-75406.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-855, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-75407
in-theory        75407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     35
proof            (modus-ponens tm-855 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-9)
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-48.           (((A -> (B and 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-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-75407.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-855, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-75408
in-theory        75408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-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-75408.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-855, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-75409
in-theory        75409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     29
proof            (modus-ponens tm-855 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-75409.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-855, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-75410
in-theory        75410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-75410.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-75411
in-theory        75411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-855 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-75411.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-855, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-75412
in-theory        75412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-855 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-75412.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-855, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-75413
in-theory        75413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-855 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-1.            (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-75413.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-855, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-75414
in-theory        75414
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     45
proof            (modus-ponens tm-855 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-75414.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-855, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-75415
in-theory        75415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-855 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-3.            ((A and B) -> 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-75415.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-855, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-75416
in-theory        75416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-855 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-4.            ((A and B) -> 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-75416.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-855, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-75417
in-theory        75417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-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-75417.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-855, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-75418
in-theory        75418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-75418.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-855, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-75419
in-theory        75419
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-855 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> 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-75419.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-855, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-75420
in-theory        75420
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-855 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or 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-75420.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-855, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-75421
in-theory        75421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-855 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-75421.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-855, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-75422
in-theory        75422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-855 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or 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-75422.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-855, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-75423
in-theory        75423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-75423.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-855, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-75424
in-theory        75424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     41
proof            (modus-ponens tm-855 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-75424.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-855, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-75425
in-theory        75425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     61
proof            (modus-ponens tm-855 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-75425.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-855, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-75426
in-theory        75426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-855 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
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-75426.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-855, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-75427
in-theory        75427
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-855 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-75427.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-855, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-75428
in-theory        75428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     49
proof            (modus-ponens tm-855 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-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-75428.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-855, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-75429
in-theory        75429
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     45
proof            (modus-ponens tm-855 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-75429.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-855, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75430
in-theory        75430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     45
proof            (modus-ponens tm-855 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
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-75430.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-855, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-75431
in-theory        75431
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     47
proof            (modus-ponens tm-855 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
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-75431.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-855, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-75432
in-theory        75432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     37
proof            (modus-ponens tm-855 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
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-75432.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-855, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-75433
in-theory        75433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-855 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-75433.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-855, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-75434
in-theory        75434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-855 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-75434.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-855, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-75435
in-theory        75435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     43
proof            (modus-ponens tm-855 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-75435.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-855, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-75436
in-theory        75436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-855 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-75436.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-855, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-75437
in-theory        75437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-855 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-75437.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-855, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-75438
in-theory        75438
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-855 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-75438.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-855, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-75439
in-theory        75439
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 (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-855 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
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-75439.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-855, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-75440
in-theory        75440
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-855 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-75440.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-855, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-75441
in-theory        75441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     33
proof            (modus-ponens tm-855 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
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-75441.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-855, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-75442
in-theory        75442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     45
proof            (modus-ponens tm-855 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
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-75442.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-855, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-75443
in-theory        75443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     49
proof            (modus-ponens tm-855 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-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-75443.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-855, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-75444
in-theory        75444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     37
proof            (modus-ponens tm-855 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
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-75444.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-855, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75445
in-theory        75445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     37
proof            (modus-ponens tm-855 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-75445.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-855, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-75446
in-theory        75446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     39
proof            (modus-ponens tm-855 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-75446.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-855, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75447
in-theory        75447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B or (A -> (B and A))) -> C)))
theorem-size     45
proof            (modus-ponens tm-852 tm-855 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
proof-size       191
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-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-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-75447.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-855, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-75448
in-theory        75448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> (B and A))))
theorem-size     29
proof            (modus-ponens tm-850 tm-855 ((Am (-> A (and B A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (and B A))))))
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-12.           ((A -> B) -> (A -> A)), M: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-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-75448.        ((A -> (B and A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> (B and A)))), M:tm-850, m:tm-855, u:((Am (-> A (and B A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-75449
in-theory        75449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> (B and A)))))
theorem-size     61
proof            (modus-ponens tm-844 tm-855 ((Am (-> A (and B A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 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-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-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-75449.        (((A -> (B and A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> (B and A))))), M:tm-844, m:tm-855, u:((Am (-> A (and B A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-75450
in-theory        75450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-808 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-75450.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-808, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75451
in-theory        75451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((C and A) or A) -> B)))
theorem-size     37
proof            (modus-ponens tm-805 tm-855 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5)
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-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-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-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-75451.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((C and A) or A) -> B))), M:tm-805, m:tm-855, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-75452
in-theory        75452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((E and A) or A) -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))
theorem-size     47
proof            (modus-ponens tm-798 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-75452.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((E and A) or A) -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))), M:tm-798, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75453
in-theory        75453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-757 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-75453.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-757, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75454
in-theory        75454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((A and C) or A) -> B)))
theorem-size     37
proof            (modus-ponens tm-754 tm-855 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 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-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-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-75454.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((A and C) or A) -> B))), M:tm-754, m:tm-855, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-75455
in-theory        75455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((A and E) or A) -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))
theorem-size     47
proof            (modus-ponens tm-747 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) 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-48.           (((A -> (B and 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-75455.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((A and E) or A) -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))), M:tm-747, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75456
in-theory        75456
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E)))
theorem-size     47
proof            (modus-ponens tm-708 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) 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-48.           (((A -> (B and 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-75456.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E))), M:tm-708, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75457
in-theory        75457
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     59
proof            (modus-ponens tm-705 tm-855 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (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-48.           (((A -> (B and 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-75457.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-855, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-75458
in-theory        75458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-703 tm-855 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> 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-48.           (((A -> (B and 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-75458.        (((A -> B) -> (A -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-855, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-75459
in-theory        75459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> (A -> C)))))
theorem-size     73
proof            (modus-ponens tm-697 tm-855 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> 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-48.           (((A -> (B and 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-75459.        ((((A -> B) -> (A -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-855, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-75460
in-theory        75460
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-665 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-75460.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-665, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75461
in-theory        75461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B or (A -> B)) -> C)))
theorem-size     39
proof            (modus-ponens tm-662 tm-855 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 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-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-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-75461.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-855, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-75462
in-theory        75462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> B)))
theorem-size     25
proof            (modus-ponens tm-660 tm-855 ((Am (-> A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> 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-48.           (((A -> (B and 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-75462.        ((A -> B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> B))), M:tm-660, m:tm-855, u:((Am (-> A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A B))))
================================================================
tm-name          tm-75463
in-theory        75463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> B))))
theorem-size     53
proof            (modus-ponens tm-654 tm-855 ((Am (-> A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> 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-48.           (((A -> (B and 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-75463.        (((A -> B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> B)))), M:tm-654, m:tm-855, u:((Am (-> A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A B))))
================================================================
tm-name          tm-75464
in-theory        75464
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and A)))
theorem-size     23
proof            (modus-ponens tm-623 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-75464.        (A -> (B or ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and A))), M:tm-623, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75465
in-theory        75465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-622 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-75465.        ((A -> (B -> (C or B))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-622, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75466
in-theory        75466
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (B -> (C or B))))
theorem-size     31
proof            (modus-ponens tm-619 tm-855 ((Am (-> A (or B A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 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-7.            (A -> (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-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-75466.        ((A or (B -> (C or B))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (B -> (C or B)))), M:tm-619, m:tm-855, u:((Am (-> A (or B A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (or B A)))))
================================================================
tm-name          tm-75467
in-theory        75467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-75467.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (F or E))), M:tm-609, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75468
in-theory        75468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-605 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-75468.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-605, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75469
in-theory        75469
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> (C or B)) and A)))
theorem-size     35
proof            (modus-ponens tm-602 tm-855 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-48.           (((A -> (B and 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-75469.        ((A or ((B -> (C or B)) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-855, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-75470
in-theory        75470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     49
proof            (modus-ponens tm-595 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-75470.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-595, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75471
in-theory        75471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-550 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-75471.        (((A -> (B or A)) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-550, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75472
in-theory        75472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-540 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-75472.        ((A or (B -> (C or B))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-540, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75473
in-theory        75473
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-530 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-75473.        ((A or (B -> (B or C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-530, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75474
in-theory        75474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-520 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-75474.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-520, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75475
in-theory        75475
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-510 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-75475.        ((A or ((B and C) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-510, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75476
in-theory        75476
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-500 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-75476.        ((A or ((B and C) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-500, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75477
in-theory        75477
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E)))
theorem-size     37
proof            (modus-ponens tm-490 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-75477.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E))), M:tm-490, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75478
in-theory        75478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-480 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-75478.        ((A or (B -> (C -> B))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-480, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75479
in-theory        75479
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-75479.        (A -> (((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A) or E)), M:tm-470, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75480
in-theory        75480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-469 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-75480.        ((A -> (B -> (B or C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-469, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75481
in-theory        75481
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (B -> (B or C))))
theorem-size     31
proof            (modus-ponens tm-466 tm-855 ((Am (-> A (or A B))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 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-6.            (A -> (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-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-75481.        ((A or (B -> (B or C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (B -> (B or C)))), M:tm-466, m:tm-855, u:((Am (-> A (or A B))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (or A B)))))
================================================================
tm-name          tm-75482
in-theory        75482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-75482.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (E or F))), M:tm-456, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75483
in-theory        75483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-453 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-75483.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-453, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75484
in-theory        75484
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> (B or C)) and A)))
theorem-size     35
proof            (modus-ponens tm-450 tm-855 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-75484.        ((A or ((B -> (B or C)) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-855, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-75485
in-theory        75485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     49
proof            (modus-ponens tm-443 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-75485.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-443, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75486
in-theory        75486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-409 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-75486.        (((A -> (A or B)) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-409, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75487
in-theory        75487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-400 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-75487.        (((A -> (B -> (A and B))) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-400, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75488
in-theory        75488
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-391 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-75488.        ((((A and B) -> B) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-391, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75489
in-theory        75489
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-382 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-75489.        ((((A and B) -> A) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-382, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75490
in-theory        75490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E)))
theorem-size     37
proof            (modus-ponens tm-373 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-75490.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E))), M:tm-373, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75491
in-theory        75491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-364 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-75491.        (((A -> (B -> A)) or C) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-364, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75492
in-theory        75492
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and A) and B)))
theorem-size     25
proof            (modus-ponens tm-355 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-75492.        (A -> (B -> (((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and A) and B))), M:tm-355, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75493
in-theory        75493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-354 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-75493.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-354, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75494
in-theory        75494
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (B -> (C -> (B and C)))))
theorem-size     35
proof            (modus-ponens tm-351 tm-855 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
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-48.           (((A -> (B and 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-75494.        ((A or (B -> (C -> (B and C)))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-855, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-75495
in-theory        75495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-75495.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75496
in-theory        75496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C)))
theorem-size     31
proof            (modus-ponens tm-338 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-75496.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C))), M:tm-338, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75497
in-theory        75497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> (A and B))))
theorem-size     33
proof            (modus-ponens tm-335 tm-855 ((Am (-> A (and A B))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> 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-48.           (((A -> (B and 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-75497.        (((A -> B) or (A -> (A and B))) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> (A and B)))), M:tm-335, m:tm-855, u:((Am (-> A (and A B))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (and A B)))))
================================================================
tm-name          tm-75498
in-theory        75498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (A -> (A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     45
proof            (modus-ponens tm-328 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-75498.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (A -> (A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-328, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75499
in-theory        75499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     51
proof            (modus-ponens tm-327 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-75499.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-327, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75500
in-theory        75500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     49
proof            (modus-ponens tm-326 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-75500.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-326, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75501
in-theory        75501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     49
proof            (modus-ponens tm-325 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-75501.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-325, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75502
in-theory        75502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     57
proof            (modus-ponens tm-324 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-75502.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-324, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75503
in-theory        75503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     49
proof            (modus-ponens tm-323 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-75503.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-323, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75504
in-theory        75504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-75504.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75505
in-theory        75505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-75505.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75506
in-theory        75506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-75506.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75507
in-theory        75507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (A -> A))
theorem-size     25
proof            (modus-ponens tm-316 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-75507.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (A -> A)), M:tm-316, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75508
in-theory        75508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-75508.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75509
in-theory        75509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((A -> (not ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))) -> (not A)))
theorem-size     47
proof            (modus-ponens tm-313 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
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-48.           (((A -> (B and 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-75509.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((A -> (not ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))) -> (not A))), M:tm-313, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75510
in-theory        75510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A) -> E) -> ((A or ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) -> E)))
theorem-size     67
proof            (modus-ponens tm-312 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) 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-48.           (((A -> (B and 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-75510.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A) -> E) -> ((A or ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) -> E))), M:tm-312, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75511
in-theory        75511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E or (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     45
proof            (modus-ponens tm-311 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-75511.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E or (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-311, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75512
in-theory        75512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-75512.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) or E)), M:tm-310, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75513
in-theory        75513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
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-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-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-75513.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and E))), M:tm-309, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75514
in-theory        75514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))))
theorem-size     45
proof            (modus-ponens tm-305 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-75514.        ((A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)) and (E -> (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)))), M:tm-305, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75515
in-theory        75515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-303 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-8)
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-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-75515.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-303, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75516
in-theory        75516
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> (C -> (B and C))) and A)))
theorem-size     39
proof            (modus-ponens tm-300 tm-855 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
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-48.           (((A -> (B and 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-75516.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-855, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-75517
in-theory        75517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-270 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-75517.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-270, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75518
in-theory        75518
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((B and C) -> C) and A)))
theorem-size     35
proof            (modus-ponens tm-267 tm-855 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4)
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-48.           (((A -> (B and 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-75518.        ((A or (((B and C) -> C) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((B and C) -> C) and A))), M:tm-267, m:tm-855, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-75519
in-theory        75519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-239 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-75519.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-239, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75520
in-theory        75520
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((B and C) -> B) and A)))
theorem-size     35
proof            (modus-ponens tm-236 tm-855 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3)
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-48.           (((A -> (B and 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-75520.        ((A or (((B and C) -> B) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((B and C) -> B) and A))), M:tm-236, m:tm-855, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-75521
in-theory        75521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E)))
theorem-size     39
proof            (modus-ponens tm-210 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-75521.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E))), M:tm-210, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75522
in-theory        75522
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     51
proof            (modus-ponens tm-207 tm-855 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (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-48.           (((A -> (B and 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-75522.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-855, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-75523
in-theory        75523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-183 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-75523.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-183, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75524
in-theory        75524
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> (C -> B)) and A)))
theorem-size     35
proof            (modus-ponens tm-180 tm-855 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
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-48.           (((A -> (B and 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-75524.        ((A or ((B -> (C -> B)) and A)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-855, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-75525
in-theory        75525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-157 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-75525.        ((A -> ((B and C) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-157, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75526
in-theory        75526
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B and C) -> C)))
theorem-size     31
proof            (modus-ponens tm-154 tm-855 ((Am (-> (and A B) B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 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-4.            ((A 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-48.           (((A -> (B and 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-75526.        ((A or ((B and C) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B and C) -> C))), M:tm-154, m:tm-855, u:((Am (-> (and A B) B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (and A B) B))))
================================================================
tm-name          tm-75527
in-theory        75527
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     37
proof            (modus-ponens tm-147 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-75527.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-147, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75528
in-theory        75528
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A and (B -> C)) -> C)))
theorem-size     41
proof            (modus-ponens tm-144 tm-855 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (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-48.           (((A -> (B and 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-75528.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-855, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-75529
in-theory        75529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-134 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-75529.        ((A -> ((B and C) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-134, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75530
in-theory        75530
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-131 tm-855 ((Am (-> (and A B) A)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 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-3.            ((A 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-48.           (((A -> (B and 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-75530.        ((A or ((B and C) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B and C) -> B))), M:tm-131, m:tm-855, u:((Am (-> (and A B) A)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (and A B) A))))
================================================================
tm-name          tm-75531
in-theory        75531
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     37
proof            (modus-ponens tm-125 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-75531.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-125, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75532
in-theory        75532
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((A -> B) and C) -> B)))
theorem-size     41
proof            (modus-ponens tm-122 tm-855 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (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-48.           (((A -> (B and 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-75532.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-855, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-75533
in-theory        75533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E)))
theorem-size     37
proof            (modus-ponens tm-113 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-75533.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E))), M:tm-113, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75534
in-theory        75534
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     47
proof            (modus-ponens tm-110 tm-855 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> 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-48.           (((A -> (B and 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-75534.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-855, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-75535
in-theory        75535
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     41
proof            (modus-ponens tm-105 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-75535.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-105, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75536
in-theory        75536
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-102 tm-855 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> 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-48.           (((A -> (B and 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-75536.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-855, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-75537
in-theory        75537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C)))
theorem-size     29
proof            (modus-ponens tm-95 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-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-75537.        (((A -> B) -> (A -> A)) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C))), M:tm-95, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75538
in-theory        75538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> A)))
theorem-size     29
proof            (modus-ponens tm-92 tm-855 ((Am (-> A A)) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> 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-48.           (((A -> (B and 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-75538.        (((A -> B) or (A -> A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A -> A))), M:tm-92, m:tm-855, u:((Am (-> A A)) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A A))))
================================================================
tm-name          tm-75539
in-theory        75539
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and A)))
theorem-size     23
proof            (modus-ponens tm-84 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-75539.        (A -> (B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and A))), M:tm-84, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75540
in-theory        75540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-83 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-75540.        ((A -> (B -> (C -> B))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-83, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75541
in-theory        75541
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (B -> (C -> B))))
theorem-size     31
proof            (modus-ponens tm-80 tm-855 ((Am (-> A (-> B A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-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-75541.        ((A or (B -> (C -> B))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and (B -> (C -> B)))), M:tm-80, m:tm-855, u:((Am (-> A (-> B A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> A (-> B A)))))
================================================================
tm-name          tm-75542
in-theory        75542
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B)))
theorem-size     27
proof            (modus-ponens tm-76 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8)
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-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-75542.        (((not (not A)) -> A) and (B -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and B))), M:tm-76, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75543
in-theory        75543
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))
theorem-size     25
proof            (modus-ponens tm-73 tm-855 ((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
axioms-used      (tm-8 tm-10 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-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-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-75543.        (((not (not A)) or A) -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)), M:tm-73, m:tm-855, u:((A Am) (B (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))
================================================================
tm-name          tm-75544
in-theory        75544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C)))
theorem-size     33
proof            (modus-ponens tm-69 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8)
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-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-75544.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and C))), M:tm-69, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75545
in-theory        75545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and ((A -> (not B)) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-66 tm-855 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5)
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-48.           (((A -> (B and 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-75545.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-855, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-75546
in-theory        75546
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-54 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-75546.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-54, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-75547
in-theory        75547
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-51 tm-855 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5)
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-48.           (((A -> (B and 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-75547.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-855, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-75548
in-theory        75548
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (B or A)))
theorem-size     27
proof            (modus-ponens tm-50 tm-855 ((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5)
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-48.           (((A -> (B and 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-75548.        ((A or (B or A)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (B or A))), M:tm-50, m:tm-855, u:((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B))))
================================================================
tm-name          tm-75549
in-theory        75549
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B)))
theorem-size     27
proof            (modus-ponens tm-49 tm-855 ((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5)
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-48.           (((A -> (B and 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-75549.        ((A or (A or B)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B))), M:tm-49, m:tm-855, u:((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B))))
================================================================
tm-name          tm-75550
in-theory        75550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) -> D) -> D)
theorem-size     13
proof            (modus-ponens tm-856 tm-365 ((Am (-> (-> A (and (-> Bm (-> Cm Bm)) A)) C)) (B (-> Bm (-> Cm Bm))) (Dm (-> A (and (-> Bm (-> Cm Bm)) A)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-6)
proof-size       119
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-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-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-75550.        (((A -> ((B -> (C -> B)) and A)) -> D) -> D), M:tm-856, m:tm-365, u:((Am (-> (-> A (and (-> Bm (-> Cm Bm)) A)) C)) (B (-> Bm (-> Cm Bm))) (Dm (-> A (and (-> Bm (-> Cm Bm)) A))))
================================================================
tm-name          tm-75551
in-theory        75551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> E)
theorem-size     21
proof            (modus-ponens tm-856 tm-374 ((Am (-> (-> A (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) A)) C)) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (-> A (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) A)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-6)
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-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-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-75551.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> E), M:tm-856, m:tm-374, u:((Am (-> (-> A (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) A)) C)) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (-> A (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) A))))
================================================================
tm-name          tm-75552
in-theory        75552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) -> D) -> D)
theorem-size     13
proof            (modus-ponens tm-856 tm-383 ((Am (-> (-> A (and (-> (and Bm Cm) Bm) A)) C)) (B (-> (and Bm Cm) Bm)) (Dm (-> A (and (-> (and Bm Cm) Bm) A)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-6 tm-3)
proof-size       119
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-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-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-75552.        (((A -> (((B and C) -> B) and A)) -> D) -> D), M:tm-856, m:tm-383, u:((Am (-> (-> A (and (-> (and Bm Cm) Bm) A)) C)) (B (-> (and Bm Cm) Bm)) (Dm (-> A (and (-> (and Bm Cm) Bm) A))))
================================================================
tm-name          tm-75553
in-theory        75553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) -> D) -> D)
theorem-size     13
proof            (modus-ponens tm-856 tm-392 ((Am (-> (-> A (and (-> (and Bm Cm) Cm) A)) C)) (B (-> (and Bm Cm) Cm)) (Dm (-> A (and (-> (and Bm Cm) Cm) A)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-6 tm-4)
proof-size       119
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-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-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-75553.        (((A -> (((B and C) -> C) and A)) -> D) -> D), M:tm-856, m:tm-392, u:((Am (-> (-> A (and (-> (and Bm Cm) Cm) A)) C)) (B (-> (and Bm Cm) Cm)) (Dm (-> A (and (-> (and Bm Cm) Cm) A))))
================================================================
tm-name          tm-75554
in-theory        75554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) -> D) -> D)
theorem-size     15
proof            (modus-ponens tm-856 tm-401 ((Am (-> (-> A (and (-> Bm (-> Cm (and Bm Cm))) A)) C)) (B (-> Bm (-> Cm (and Bm Cm)))) (Dm (-> A (and (-> Bm (-> Cm (and Bm Cm))) A)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-6)
proof-size       127
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-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-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-75554.        (((A -> ((B -> (C -> (B and C))) and A)) -> D) -> D), M:tm-856, m:tm-401, u:((Am (-> (-> A (and (-> Bm (-> Cm (and Bm Cm))) A)) C)) (B (-> Bm (-> Cm (and Bm Cm)))) (Dm (-> A (and (-> Bm (-> Cm (and Bm Cm))) A))))
================================================================
tm-name          tm-75555
in-theory        75555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) -> D) -> D)
theorem-size     13
proof            (modus-ponens tm-856 tm-410 ((Am (-> (-> A (and (-> Bm (or Bm Cm)) A)) C)) (B (-> Bm (or Bm Cm))) (Dm (-> A (and (-> Bm (or Bm Cm)) A)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-6)
proof-size       119
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-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-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-75555.        (((A -> ((B -> (B or C)) and A)) -> D) -> D), M:tm-856, m:tm-410, u:((Am (-> (-> A (and (-> Bm (or Bm Cm)) A)) C)) (B (-> Bm (or Bm Cm))) (Dm (-> A (and (-> Bm (or Bm Cm)) A))))
================================================================
tm-name          tm-75556
in-theory        75556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) -> D) -> D)
theorem-size     13
proof            (modus-ponens tm-856 tm-551 ((Am (-> (-> A (and (-> Bm (or Cm Bm)) A)) C)) (B (-> Bm (or Cm Bm))) (Dm (-> A (and (-> Bm (or Cm Bm)) A)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-6 tm-7)
proof-size       119
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-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-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-75556.        (((A -> ((B -> (C or B)) and A)) -> D) -> D), M:tm-856, m:tm-551, u:((Am (-> (-> A (and (-> Bm (or Cm Bm)) A)) C)) (B (-> Bm (or Cm Bm))) (Dm (-> A (and (-> Bm (or Cm Bm)) A))))
================================================================
tm-name          tm-75557
in-theory        75557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     43
proof            (modus-ponens tm-855 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-75557.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-855, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75558
in-theory        75558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     37
proof            (modus-ponens tm-808 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-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-75558.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-808, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75559
in-theory        75559
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((D and (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C)))
theorem-size     69
proof            (modus-ponens tm-798 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-75559.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((D and (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C))), M:tm-798, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75560
in-theory        75560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     37
proof            (modus-ponens tm-757 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-48.           (((A -> (B and 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-75560.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-757, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75561
in-theory        75561
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) and D) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C)))
theorem-size     69
proof            (modus-ponens tm-747 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-75561.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) and D) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C))), M:tm-747, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75562
in-theory        75562
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)))) -> (((E -> (F and E)) -> G) -> G)))
theorem-size     51
proof            (modus-ponens tm-708 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2)
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-48.           (((A -> (B and 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-75562.        (((((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)))) -> (((E -> (F and E)) -> G) -> G))), M:tm-708, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75563
in-theory        75563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     39
proof            (modus-ponens tm-665 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-48.           (((A -> (B and 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-75563.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-665, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75564
in-theory        75564
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((B or (A -> (B and A))) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C)))
theorem-size     59
proof            (modus-ponens tm-654 tm-856 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-75564.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((B or (A -> (B and A))) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C))), M:tm-654, m:tm-856, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75565
in-theory        75565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (D or (((A -> (B and A)) -> C) -> C)))
theorem-size     27
proof            (modus-ponens tm-623 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
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-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-75565.        ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (D or (((A -> (B and A)) -> C) -> C))), M:tm-623, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75566
in-theory        75566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-622 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-75566.        ((A -> (B -> (C or B))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-622, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75567
in-theory        75567
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (E or D)))
theorem-size     31
proof            (modus-ponens tm-609 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-75567.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (E or D))), M:tm-609, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75568
in-theory        75568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-605 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-48.           (((A -> (B and 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-75568.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-605, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75569
in-theory        75569
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (E or D)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))))
theorem-size     57
proof            (modus-ponens tm-595 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-48.           (((A -> (B and 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-75569.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (E or D)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))), M:tm-595, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75570
in-theory        75570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-550 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75570.        (((A -> (B or A)) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-550, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75571
in-theory        75571
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-540 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75571.        ((A or (B -> (C or B))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-540, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75572
in-theory        75572
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-530 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75572.        ((A or (B -> (B or C))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-530, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75573
in-theory        75573
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-520 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-48.           (((A -> (B and 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-75573.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-520, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75574
in-theory        75574
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-510 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75574.        ((A or ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-510, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75575
in-theory        75575
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-500 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75575.        ((A or ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-500, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75576
in-theory        75576
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)))) -> (((E -> (F and E)) -> G) -> G)))
theorem-size     41
proof            (modus-ponens tm-490 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-48.           (((A -> (B and 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-75576.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G))), M:tm-490, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75577
in-theory        75577
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-480 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75577.        ((A or (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-480, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75578
in-theory        75578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((((A -> (B and A)) -> C) -> C) or D))
theorem-size     27
proof            (modus-ponens tm-470 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
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-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-75578.        ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((((A -> (B and A)) -> C) -> C) or D)), M:tm-470, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75579
in-theory        75579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-469 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-75579.        ((A -> (B -> (B or C))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-469, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75580
in-theory        75580
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (D or E)))
theorem-size     31
proof            (modus-ponens tm-456 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-75580.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (D or E))), M:tm-456, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75581
in-theory        75581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-453 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-48.           (((A -> (B and 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-75581.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-453, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75582
in-theory        75582
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (D or E)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))))
theorem-size     57
proof            (modus-ponens tm-443 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-48.           (((A -> (B and 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-75582.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (D or E)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))), M:tm-443, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75583
in-theory        75583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-409 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75583.        (((A -> (A or B)) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-409, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75584
in-theory        75584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-400 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-48.           (((A -> (B and 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-75584.        (((A -> (B -> (A and B))) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-400, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75585
in-theory        75585
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-391 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75585.        ((((A and B) -> B) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-391, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75586
in-theory        75586
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-382 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75586.        ((((A and B) -> A) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-382, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75587
in-theory        75587
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)))) -> (((E -> (F and E)) -> G) -> G)))
theorem-size     41
proof            (modus-ponens tm-373 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-48.           (((A -> (B and 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-75587.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G))), M:tm-373, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75588
in-theory        75588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-364 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75588.        (((A -> (B -> A)) or C) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-364, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75589
in-theory        75589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (D -> ((((A -> (B and A)) -> C) -> C) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-75589.        ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (D -> ((((A -> (B and A)) -> C) -> C) and D))), M:tm-355, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75590
in-theory        75590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-354 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-48.           (((A -> (B and 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-75590.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-354, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75591
in-theory        75591
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (E -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-341 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-75591.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75592
in-theory        75592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E)))
theorem-size     35
proof            (modus-ponens tm-338 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-75592.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E))), M:tm-338, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75593
in-theory        75593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) and (((A -> (B and A)) -> C) -> C))))
theorem-size     67
proof            (modus-ponens tm-328 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) 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-328.          ((A -> 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-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-75593.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) and (((A -> (B and A)) -> C) -> C)))), M:tm-328, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75594
in-theory        75594
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (E -> (D and E))) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))))
theorem-size     59
proof            (modus-ponens tm-327 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-75594.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (E -> (D and E))) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))), M:tm-327, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75595
in-theory        75595
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((D and E) -> E) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))))
theorem-size     57
proof            (modus-ponens tm-326 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-75595.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((D and E) -> E) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))), M:tm-326, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75596
in-theory        75596
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((D and E) -> D) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))))
theorem-size     57
proof            (modus-ponens tm-325 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-75596.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((D and E) -> D) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))), M:tm-325, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75597
in-theory        75597
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))))
theorem-size     65
proof            (modus-ponens tm-324 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-75597.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))), M:tm-324, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75598
in-theory        75598
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (E -> D)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))))
theorem-size     57
proof            (modus-ponens tm-323 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-48.           (((A -> (B and 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-75598.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (E -> D)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))), M:tm-323, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75599
in-theory        75599
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D and E) -> E))
theorem-size     31
proof            (modus-ponens tm-322 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-48.           (((A -> (B and 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-75599.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75600
in-theory        75600
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D and E) -> D))
theorem-size     31
proof            (modus-ponens tm-320 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-48.           (((A -> (B and 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-75600.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75601
in-theory        75601
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-318 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-75601.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75602
in-theory        75602
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))))
theorem-size     57
proof            (modus-ponens tm-316 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-75602.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> (B or (A -> (B and A)))))), M:tm-316, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75603
in-theory        75603
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (E -> D)))
theorem-size     31
proof            (modus-ponens tm-315 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-75603.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75604
in-theory        75604
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (not (((A -> (B and A)) -> C) -> C))) -> (not (((A -> (B and A)) -> C) -> (B or (A -> (B and A)))))))
theorem-size     69
proof            (modus-ponens tm-313 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-75604.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (not (((A -> (B and A)) -> C) -> C))) -> (not (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))))), M:tm-313, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75605
in-theory        75605
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((((A -> (B and A)) -> C) -> C) -> D) -> (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) or (((A -> (B and A)) -> C) -> C)) -> D)))
theorem-size     65
proof            (modus-ponens tm-312 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) 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-312.          ((A -> B) -> ((A -> B) and ((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-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-75605.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((((A -> (B and A)) -> C) -> C) -> D) -> (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) or (((A -> (B and A)) -> C) -> C)) -> D))), M:tm-312, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75606
in-theory        75606
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D or ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))))
theorem-size     53
proof            (modus-ponens tm-311 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-48.           (((A -> (B and 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-75606.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D or ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))), M:tm-311, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75607
in-theory        75607
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) or D))
theorem-size     53
proof            (modus-ponens tm-310 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-48.           (((A -> (B and 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-75607.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) or D)), M:tm-310, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75608
in-theory        75608
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and D)))
theorem-size     55
proof            (modus-ponens tm-309 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-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-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-75608.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and D))), M:tm-309, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75609
in-theory        75609
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((A -> (B and A)) -> C)) -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> C)))
theorem-size     67
proof            (modus-ponens tm-306 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> Am (and Bm Am)) Cm)) (C Cm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-75609.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> ((A -> (B and A)) -> C)) -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> C))), M:tm-306, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> Am (and Bm Am)) Cm)) (C Cm))
================================================================
tm-name          tm-75610
in-theory        75610
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))))
theorem-size     53
proof            (modus-ponens tm-305 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-48.           (((A -> (B and 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-75610.        (((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)) and (D -> ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))), M:tm-305, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75611
in-theory        75611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     37
proof            (modus-ponens tm-303 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75611.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-303, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75612
in-theory        75612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-270 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75612.        ((A -> (((B and C) -> C) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-270, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75613
in-theory        75613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-239 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75613.        ((A -> (((B and C) -> B) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-239, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75614
in-theory        75614
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)))) -> (((E -> (F and E)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-210 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-75614.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G))), M:tm-210, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75615
in-theory        75615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-183 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-48.           (((A -> (B and 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-75615.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-183, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75616
in-theory        75616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-157 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-75616.        ((A -> ((B and C) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-157, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75617
in-theory        75617
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)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     41
proof            (modus-ponens tm-147 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-48.           (((A -> (B and 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-75617.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-147, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75618
in-theory        75618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-134 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-75618.        ((A -> ((B and C) -> B)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-134, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75619
in-theory        75619
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)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     41
proof            (modus-ponens tm-125 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-48.           (((A -> (B and 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-75619.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-125, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75620
in-theory        75620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (C -> D)) -> (B or (A -> (B and A)))) -> ((((A -> (B and A)) -> (C -> D)) -> C) -> (((A -> (B and A)) -> (C -> D)) -> D)))
theorem-size     41
proof            (modus-ponens tm-114 tm-856 ((A (-> (-> (-> Am (and Bm Am)) (-> C D)) (or Bm (-> Am (and Bm Am))))) (B (-> (-> Am (and Bm Am)) (-> C D))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       179
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-48.           (((A -> (B and 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-75620.        ((((A -> (B and A)) -> (C -> D)) -> (B or (A -> (B and A)))) -> ((((A -> (B and A)) -> (C -> D)) -> C) -> (((A -> (B and A)) -> (C -> D)) -> D))), M:tm-114, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) (-> C D)) (or Bm (-> Am (and Bm Am))))) (B (-> (-> Am (and Bm Am)) (-> C D))) (Cm (-> C D)))
================================================================
tm-name          tm-75621
in-theory        75621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G)))
theorem-size     41
proof            (modus-ponens tm-113 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-48.           (((A -> (B and 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-75621.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G))), M:tm-113, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75622
in-theory        75622
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)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     45
proof            (modus-ponens tm-105 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-75622.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-105, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75623
in-theory        75623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E)))
theorem-size     33
proof            (modus-ponens tm-95 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-75623.        (((A -> B) -> (A -> A)) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E))), M:tm-95, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75624
in-theory        75624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (D -> (((A -> (B and A)) -> C) -> C)))
theorem-size     27
proof            (modus-ponens tm-84 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-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-75624.        ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (D -> (((A -> (B and A)) -> C) -> C))), M:tm-84, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75625
in-theory        75625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-83 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-75625.        ((A -> (B -> (C -> B))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-83, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75626
in-theory        75626
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C and B)) -> D) -> (C or (B -> (C and B)))) -> (((B -> (C and B)) -> D) -> D)))
theorem-size     31
proof            (modus-ponens tm-76 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75626.        (((not (not A)) -> A) and ((((B -> (C and B)) -> D) -> (C or (B -> (C and B)))) -> (((B -> (C and B)) -> D) -> D))), M:tm-76, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75627
in-theory        75627
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B and A)) -> C) -> (B or (A -> (B and A)))))) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C))
theorem-size     43
proof            (modus-ponens tm-73 tm-856 ((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
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-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-75627.        (((not (not (((A -> (B and A)) -> C) -> (B or (A -> (B and A)))))) or (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C)), M:tm-73, m:tm-856, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am))))) (B (-> (-> (-> Am (and Bm Am)) Cm) Cm)))
================================================================
tm-name          tm-75628
in-theory        75628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (not (B or (A -> (B and A))))) -> (B or (A -> (B and A)))) -> (not ((A -> (B and A)) -> (not (B or (A -> (B and A)))))))
theorem-size     38
proof            (modus-ponens tm-70 tm-856 ((B (or Bm (-> Am (and Bm Am)))) (A (-> (-> Am (and Bm Am)) (not (or Bm (-> Am (and Bm Am)))))) (Cm (not (or Bm (-> Am (and Bm Am)))))))
axioms-used      (tm-2 tm-9 tm-8 tm-5)
proof-size       152
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-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-75628.        ((((A -> (B and A)) -> (not (B or (A -> (B and A))))) -> (B or (A -> (B and A)))) -> (not ((A -> (B and A)) -> (not (B or (A -> (B and A))))))), M:tm-70, m:tm-856, u:((B (or Bm (-> Am (and Bm Am)))) (A (-> (-> Am (and Bm Am)) (not (or Bm (-> Am (and Bm Am)))))) (Cm (not (or Bm (-> Am (and Bm Am))))))
================================================================
tm-name          tm-75629
in-theory        75629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E)))
theorem-size     37
proof            (modus-ponens tm-69 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-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-75629.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D and C)) -> E) -> (D or (C -> (D and C)))) -> (((C -> (D and C)) -> E) -> E))), M:tm-69, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75630
in-theory        75630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     39
proof            (modus-ponens tm-54 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-48.           (((A -> (B and 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-75630.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-54, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-75631
in-theory        75631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     37
proof            (modus-ponens tm-855 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
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-75631.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-855, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75632
in-theory        75632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-852 tm-857 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-5 tm-1)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
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-75632.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-852, m:tm-857, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75633
in-theory        75633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-850 tm-857 ((Am (-> A (and B A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-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-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-75633.        ((A -> (B and A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-850, m:tm-857, u:((Am (-> A (and B A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75634
in-theory        75634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((B or (A -> (B and A))) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     49
proof            (modus-ponens tm-844 tm-857 ((Am (-> A (and B A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
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-75634.        (((A -> (B and A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((B or (A -> (B and A))) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-844, m:tm-857, u:((Am (-> A (and B A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75635
in-theory        75635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-75635.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-808, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75636
in-theory        75636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-805 tm-857 ((Am (-> (or (and A B) B) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
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-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-1.            (A -> (B -> A)), 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-75636.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-805, m:tm-857, u:((Am (-> (or (and A B) B) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75637
in-theory        75637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and A) or A) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))
theorem-size     43
proof            (modus-ponens tm-798 tm-857 ((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-75637.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and A) or A) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))), M:tm-798, m:tm-857, u:((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75638
in-theory        75638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-1.            (A -> (B -> A)), 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-75638.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-757, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75639
in-theory        75639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-754 tm-857 ((Am (-> (or (and A B) A) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
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-48.           (((A -> (B and 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-75639.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-754, m:tm-857, u:((Am (-> (or (and A B) A) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75640
in-theory        75640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((A and E) or A) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))
theorem-size     43
proof            (modus-ponens tm-747 tm-857 ((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75640.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((A and E) or A) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))), M:tm-747, m:tm-857, u:((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75641
in-theory        75641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and 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-48.           (((A -> (B and 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-75641.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-708, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75642
in-theory        75642
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-705 tm-857 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75642.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-705, m:tm-857, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75643
in-theory        75643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-703 tm-857 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75643.        (((A -> B) -> (A -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-703, m:tm-857, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75644
in-theory        75644
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     57
proof            (modus-ponens tm-697 tm-857 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-48.           (((A -> (B and 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-75644.        ((((A -> B) -> (A -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-697, m:tm-857, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75645
in-theory        75645
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-75645.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-665, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75646
in-theory        75646
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-662 tm-857 ((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5)
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-48.           (((A -> (B and 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-75646.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-662, m:tm-857, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75647
in-theory        75647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     21
proof            (modus-ponens tm-660 tm-857 ((Am (-> A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-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-48.           (((A -> (B and 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-75647.        ((A -> B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-660, m:tm-857, u:((Am (-> A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75648
in-theory        75648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((B or (A -> B)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     45
proof            (modus-ponens tm-654 tm-857 ((Am (-> A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75648.        (((A -> B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((B or (A -> B)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-654, m:tm-857, u:((Am (-> A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75649
in-theory        75649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-75649.        ((A -> (B -> (C or B))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-622, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75650
in-theory        75650
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-619 tm-857 ((Am (-> A (or B A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 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-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-75650.        ((A or (B -> (C or B))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-619, m:tm-857, u:((Am (-> A (or B A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75651
in-theory        75651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-75651.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F or E))), M:tm-609, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75652
in-theory        75652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-48.           (((A -> (B and 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-75652.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-605, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75653
in-theory        75653
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-602 tm-857 ((Am (and (-> A (or B A)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-75653.        ((A or ((B -> (C or B)) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-602, m:tm-857, u:((Am (and (-> A (or B A)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75654
in-theory        75654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F or E)) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-75654.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F or E)) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-595, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75655
in-theory        75655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-48.           (((A -> (B and 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-75655.        (((A -> (B or A)) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-550, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75656
in-theory        75656
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-48.           (((A -> (B and 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-75656.        ((A or (B -> (C or B))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-540, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75657
in-theory        75657
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-48.           (((A -> (B and 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-75657.        ((A or (B -> (B or C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-530, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75658
in-theory        75658
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-48.           (((A -> (B and 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-75658.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-520, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75659
in-theory        75659
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-48.           (((A -> (B and 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-75659.        ((A or ((B and C) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-510, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75660
in-theory        75660
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-48.           (((A -> (B and 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-75660.        ((A or ((B and C) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-500, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75661
in-theory        75661
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 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-1.            (A -> (B -> A)), 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-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-75661.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-490, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75662
in-theory        75662
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-75662.        ((A or (B -> (C -> B))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-480, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75663
in-theory        75663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-75663.        ((A -> (B -> (B or C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-469, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75664
in-theory        75664
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-466 tm-857 ((Am (-> A (or A B))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-6 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-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-75664.        ((A or (B -> (B or C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-466, m:tm-857, u:((Am (-> A (or A B))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75665
in-theory        75665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-75665.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (E or F))), M:tm-456, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75666
in-theory        75666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-48.           (((A -> (B and 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-75666.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-453, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75667
in-theory        75667
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-450 tm-857 ((Am (and (-> A (or A B)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-75667.        ((A or ((B -> (B or C)) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-450, m:tm-857, u:((Am (and (-> A (or A B)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75668
in-theory        75668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (E or F)) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-75668.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (E or F)) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-443, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75669
in-theory        75669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-48.           (((A -> (B and 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-75669.        (((A -> (A or B)) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-409, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75670
in-theory        75670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-48.           (((A -> (B and 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-75670.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-400, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75671
in-theory        75671
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-48.           (((A -> (B and 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-75671.        ((((A and B) -> B) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-391, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75672
in-theory        75672
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-48.           (((A -> (B and 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-75672.        ((((A and B) -> A) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-382, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75673
in-theory        75673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 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-1.            (A -> (B -> A)), 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-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-75673.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-373, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75674
in-theory        75674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-75674.        (((A -> (B -> A)) or C) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-364, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75675
in-theory        75675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-75675.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-354, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75676
in-theory        75676
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-351 tm-857 ((Am (-> A (-> B (and A B)))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-1 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-5.            (A -> (B -> (A and 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-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-75676.        ((A or (B -> (C -> (B and C)))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-351, m:tm-857, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75677
in-theory        75677
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> (A and (C -> (B and C)))))
theorem-size     17
proof            (modus-ponens tm-349 tm-857 ((A Am) (B (-> Bm (and Cm Bm))) (Dm (and Am (-> Bm (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
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-5.            (A -> (B -> (A and 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-48.           (((A -> (B and 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-75677.        (A -> ((B or (C -> (B and C))) -> (A and (C -> (B and C))))), M:tm-349, m:tm-857, u:((A Am) (B (-> Bm (and Cm Bm))) (Dm (and Am (-> Bm (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-75678
in-theory        75678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-75678.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75679
in-theory        75679
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) -> ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and D))
theorem-size     39
proof            (modus-ponens tm-339 tm-857 ((Am (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B)) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-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-48.           (((A -> (B and 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-75679.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) -> ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and D)), M:tm-339, m:tm-857, u:((Am (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B)) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75680
in-theory        75680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-75680.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-338, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75681
in-theory        75681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     27
proof            (modus-ponens tm-335 tm-857 ((Am (-> A (and A B))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75681.        (((A -> B) or (A -> (A and B))) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-335, m:tm-857, u:((Am (-> A (and A B))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75682
in-theory        75682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (A -> (A and (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     41
proof            (modus-ponens tm-328 tm-857 ((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-328.          ((A -> 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-48.           (((A -> (B and 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-75682.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (A -> (A and (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-328, m:tm-857, u:((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75683
in-theory        75683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-75683.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-327, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75684
in-theory        75684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and F) -> F) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-75684.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and F) -> F) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-326, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75685
in-theory        75685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and F) -> E) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-75685.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E and F) -> E) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-325, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75686
in-theory        75686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-75686.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-324, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75687
in-theory        75687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> E)) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-75687.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> E)) and (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-323, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75688
in-theory        75688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-48.           (((A -> (B and 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-75688.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75689
in-theory        75689
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E)) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E)) -> E))
theorem-size     63
proof            (modus-ponens tm-321 tm-857 ((Am (and A (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) C))) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-48.           (((A -> (B and 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-75689.        (((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E)) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E)) -> E)), M:tm-321, m:tm-857, u:((Am (and A (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) C))) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75690
in-theory        75690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm 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-48.           (((A -> (B and 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-75690.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75691
in-theory        75691
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) and E) -> (((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)) -> D) and E) -> D))
theorem-size     63
proof            (modus-ponens tm-319 tm-857 ((Am (and (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B) C)) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-48.           (((A -> (B and 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-75691.        (((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) and E) -> (((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)) -> D) and E) -> D)), M:tm-319, m:tm-857, u:((Am (and (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B) C)) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75692
in-theory        75692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-75692.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75693
in-theory        75693
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> (((B or (A -> (B and A))) -> C) -> D)) -> (((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) -> D)) -> (((A -> (B and A)) -> C) -> D)))
theorem-size     67
proof            (modus-ponens tm-317 tm-857 ((Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (-> (or Cm (-> Bm (and Cm Bm))) Dm) C))) (A (-> (-> Bm (and Cm Bm)) Dm)) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-13.           (((A -> (B -> C)) -> (A -> 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-48.           (((A -> (B and 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-75693.        (((((A -> (B and A)) -> C) -> (((B or (A -> (B and A))) -> C) -> D)) -> (((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) -> D)) -> (((A -> (B and A)) -> C) -> D))), M:tm-317, m:tm-857, u:((Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (-> (or Cm (-> Bm (and Cm Bm))) Dm) C))) (A (-> (-> Bm (and Cm Bm)) Dm)) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-75694
in-theory        75694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-857 ((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-75694.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (A -> A)), M:tm-316, m:tm-857, u:((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75695
in-theory        75695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-75695.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75696
in-theory        75696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A -> (not (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-857 ((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-8)
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-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-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-75696.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A -> (not (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))) -> (not A))), M:tm-313, m:tm-857, u:((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75697
in-theory        75697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E) -> ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) -> E)))
theorem-size     61
proof            (modus-ponens tm-312 tm-857 ((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75697.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E) -> ((A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) -> E))), M:tm-312, m:tm-857, u:((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75698
in-theory        75698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E or (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-75698.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E or (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-311, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75699
in-theory        75699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-75699.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) or E)), M:tm-310, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75700
in-theory        75700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm 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-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-48.           (((A -> (B and 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-75700.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and E))), M:tm-309, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75701
in-theory        75701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A -> ((B -> (C and B)) -> D)) -> (A -> ((C or (B -> (C and B))) -> D))))
theorem-size     41
proof            (modus-ponens tm-306 tm-857 ((A Am) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) 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-306.          ((A -> (B -> C)) -> ((A -> (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-48.           (((A -> (B and 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-75701.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and ((A -> ((B -> (C and B)) -> D)) -> (A -> ((C or (B -> (C and B))) -> D)))), M:tm-306, m:tm-857, u:((A Am) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-75702
in-theory        75702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-75702.        ((A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))) and (E -> (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))))), M:tm-305, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75703
in-theory        75703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-1 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-1.            (A -> (B -> A)), 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-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-75703.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-303, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75704
in-theory        75704
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-300 tm-857 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75704.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-300, m:tm-857, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75705
in-theory        75705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 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-1.            (A -> (B -> A)), 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-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-75705.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-270, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75706
in-theory        75706
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-267 tm-857 ((Am (and (-> (and A B) B) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-5 tm-4 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-4.            ((A and B) -> 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-48.           (((A -> (B and 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-75706.        ((A or (((B and C) -> C) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-267, m:tm-857, u:((Am (and (-> (and A B) B) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75707
in-theory        75707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 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-1.            (A -> (B -> A)), 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-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-75707.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-239, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75708
in-theory        75708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-236 tm-857 ((Am (and (-> (and A B) A) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-5 tm-3 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-3.            ((A and B) -> 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-48.           (((A -> (B and 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-75708.        ((A or (((B and C) -> B) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-236, m:tm-857, u:((Am (and (-> (and A B) A) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75709
in-theory        75709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-75709.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-210, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75710
in-theory        75710
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-207 tm-857 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75710.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-207, m:tm-857, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75711
in-theory        75711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-75711.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-183, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75712
in-theory        75712
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-180 tm-857 ((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-5 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-1.            (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-48.           (((A -> (B and 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-75712.        ((A or ((B -> (C -> B)) and A)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-180, m:tm-857, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75713
in-theory        75713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-48.           (((A -> (B and 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-75713.        ((A -> ((B and C) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-157, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75714
in-theory        75714
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-154 tm-857 ((Am (-> (and A B) B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-4 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-4.            ((A 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-48.           (((A -> (B and 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-75714.        ((A or ((B and C) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-154, m:tm-857, u:((Am (-> (and A B) B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75715
in-theory        75715
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))
theorem-size     19
proof            (modus-ponens tm-152 tm-857 ((Am (and A (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 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-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-75715.        ((A and ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)), M:tm-152, m:tm-857, u:((Am (and A (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-75716
in-theory        75716
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-75716.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-147, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75717
in-theory        75717
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-144 tm-857 ((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75717.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-144, m:tm-857, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75718
in-theory        75718
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E)) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))
theorem-size     39
proof            (modus-ponens tm-142 tm-857 ((Am (and A (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) C))) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 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-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-75718.        ((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> E)) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))), M:tm-142, m:tm-857, u:((Am (and A (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) C))) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75719
in-theory        75719
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D))
theorem-size     37
proof            (modus-ponens tm-141 tm-857 ((Am (and A (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> Bm (and Cm Bm)) Dm)))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-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-75719.        ((A and ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) -> ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D)), M:tm-141, m:tm-857, u:((Am (and A (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> Bm (and Cm Bm)) Dm)))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-75720
in-theory        75720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm 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-48.           (((A -> (B and 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-75720.        ((A -> ((B and C) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-134, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75721
in-theory        75721
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-131 tm-857 ((Am (-> (and A B) A)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75721.        ((A or ((B and C) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-131, m:tm-857, u:((Am (-> (and A B) A)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75722
in-theory        75722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) and D) -> ((B or (A -> (B and A))) -> C))
theorem-size     19
proof            (modus-ponens tm-129 tm-857 ((Am (and (-> (-> Bm (and Cm Bm)) Dm) B)) (A (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 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-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-75722.        ((((A -> (B and A)) -> C) and D) -> ((B or (A -> (B and A))) -> C)), M:tm-129, m:tm-857, u:((Am (and (-> (-> Bm (and Cm Bm)) Dm) B)) (A (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-75723
in-theory        75723
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-75723.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-125, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75724
in-theory        75724
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-122 tm-857 ((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75724.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-122, m:tm-857, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75725
in-theory        75725
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) and E) -> (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))
theorem-size     39
proof            (modus-ponens tm-120 tm-857 ((Am (and (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B) C)) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 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-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-75725.        ((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) and E) -> (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))), M:tm-120, m:tm-857, u:((Am (and (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B) C)) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75726
in-theory        75726
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> ((A -> (B and A)) -> C)) and D) -> ((B or (A -> (B and A))) -> C))
theorem-size     37
proof            (modus-ponens tm-119 tm-857 ((Am (and (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) C)) (A (-> (-> Bm (and Cm Bm)) Dm)) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-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-75726.        ((((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> ((A -> (B and A)) -> C)) and D) -> ((B or (A -> (B and A))) -> C)), M:tm-119, m:tm-857, u:((Am (and (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) C)) (A (-> (-> Bm (and Cm Bm)) Dm)) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-75727
in-theory        75727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-75727.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-113, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75728
in-theory        75728
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-110 tm-857 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75728.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-110, m:tm-857, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75729
in-theory        75729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and A) -> C)) -> ((B or (A -> (B and A))) -> (A -> C)))
theorem-size     19
proof            (modus-ponens tm-108 tm-857 ((Am (-> Bm (-> (and Cm Bm) C))) (A Bm) (B (and Cm Bm)) (Dm (-> Bm C)) (D (-> (or Cm (-> Bm (and Cm Bm))) (-> Bm C)))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-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-75729.        ((A -> ((B and A) -> C)) -> ((B or (A -> (B and A))) -> (A -> C))), M:tm-108, m:tm-857, u:((Am (-> Bm (-> (and Cm Bm) C))) (A Bm) (B (and Cm Bm)) (Dm (-> Bm C)) (D (-> (or Cm (-> Bm (and Cm Bm))) (-> Bm C))))
================================================================
tm-name          tm-75730
in-theory        75730
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C))
theorem-size     43
proof            (modus-ponens tm-106 tm-857 ((Am (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> (-> Bm (and Cm Bm)) Dm) (or Cm (-> Bm (and Cm Bm)))))) (A (-> (-> Bm (and Cm Bm)) Dm)) (B (or Cm (-> Bm (and Cm Bm)))) (C Dm)))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       191
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-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-75730.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> (((A -> (B and A)) -> C) -> (B or (A -> (B and A))))) -> (((A -> (B and A)) -> C) -> C)), M:tm-106, m:tm-857, u:((Am (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> (-> Bm (and Cm Bm)) Dm) (or Cm (-> Bm (and Cm Bm)))))) (A (-> (-> Bm (and Cm Bm)) Dm)) (B (or Cm (-> Bm (and Cm Bm)))) (C Dm))
================================================================
tm-name          tm-75731
in-theory        75731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-48.           (((A -> (B and 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-75731.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-105, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75732
in-theory        75732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-102 tm-857 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75732.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-102, m:tm-857, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75733
in-theory        75733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (((B or (A -> (B and A))) -> C) -> D)) -> (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-100 tm-857 ((Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (-> (or Cm (-> Bm (and Cm Bm))) Dm) C))) (A (-> (-> Bm (and Cm Bm)) Dm)) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
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-13.           (((A -> (B -> C)) -> (A -> 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-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-75733.        ((((A -> (B and A)) -> C) -> (((B or (A -> (B and A))) -> C) -> D)) -> (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))), M:tm-100, m:tm-857, u:((Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (-> (or Cm (-> Bm (and Cm Bm))) Dm) C))) (A (-> (-> Bm (and Cm Bm)) Dm)) (B (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-75734
in-theory        75734
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (B and C))) -> A))
theorem-size     11
proof            (modus-ponens tm-98 tm-857 ((Dm Am) (B (-> Bm (and Cm Bm))) (A Am) (C (-> (or Cm (-> Bm (and Cm 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-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-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-75734.        (A -> ((B or (C -> (B and C))) -> A)), M:tm-98, m:tm-857, u:((Dm Am) (B (-> Bm (and Cm Bm))) (A Am) (C (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-75735
in-theory        75735
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) -> (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-96 tm-857 ((Am (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B)) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 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-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-75735.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) -> (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))), M:tm-96, m:tm-857, u:((Am (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B)) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75736
in-theory        75736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-48.           (((A -> (B and 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-75736.        (((A -> B) -> (A -> A)) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-95, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75737
in-theory        75737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     25
proof            (modus-ponens tm-92 tm-857 ((Am (-> A A)) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-48.           (((A -> (B and 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-75737.        (((A -> B) or (A -> A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-92, m:tm-857, u:((Am (-> A A)) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75738
in-theory        75738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
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-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-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-75738.        ((A -> (B -> (C -> B))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-83, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75739
in-theory        75739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-80 tm-857 ((Am (-> A (-> B A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-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-75739.        ((A or (B -> (C -> B))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-80, m:tm-857, u:((Am (-> A (-> B A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75740
in-theory        75740
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-77 tm-857 ((Am (not (not (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B)))) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-8 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-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-75740.        ((not (not ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D))) -> D), M:tm-77, m:tm-857, u:((Am (not (not (-> (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) B)))) (A (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75741
in-theory        75741
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 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-1.            (A -> (B -> A)), 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-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-75741.        (((not (not A)) -> A) and (B -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-76, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75742
in-theory        75742
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))
theorem-size     23
proof            (modus-ponens tm-73 tm-857 ((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
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-48.           (((A -> (B and 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-75742.        (((not (not A)) or A) -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))), M:tm-73, m:tm-857, u:((A Am) (B (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75743
in-theory        75743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 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-1.            (A -> (B -> A)), 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-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-75743.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-69, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75744
in-theory        75744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-66 tm-857 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-5)
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-48.           (((A -> (B and 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-75744.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-66, m:tm-857, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75745
in-theory        75745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C and B)) -> D)) -> ((A or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-55 tm-857 ((Am (-> A (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
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-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-48.           (((A -> (B and 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-75745.        ((A -> ((B -> (C and B)) -> D)) -> ((A or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))), M:tm-55, m:tm-857, u:((Am (-> A (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-75746
in-theory        75746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), 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-75746.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-54, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-75747
in-theory        75747
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-51 tm-857 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5)
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-48.           (((A -> (B and 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-75747.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-51, m:tm-857, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75748
in-theory        75748
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-50 tm-857 ((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
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-48.           (((A -> (B and 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-75748.        ((A or (B or A)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-50, m:tm-857, u:((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75749
in-theory        75749
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-49 tm-857 ((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
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-48.           (((A -> (B and 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-75749.        ((A or (A or B)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-49, m:tm-857, u:((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-75750
in-theory        75750
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75750.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-855, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75751
in-theory        75751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75751.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-808, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75752
in-theory        75752
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (((D and (A or (A or B))) or (A or (A or B))) -> (C -> (A or B))))
theorem-size     31
proof            (modus-ponens tm-798 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75752.        (((A or (A or B)) -> (C -> (A or B))) and (((D and (A or (A or B))) or (A or (A or B))) -> (C -> (A or B)))), M:tm-798, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75753
in-theory        75753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75753.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-757, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75754
in-theory        75754
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((((A or (A or B)) and D) or (A or (A or B))) -> (C -> (A or B))))
theorem-size     31
proof            (modus-ponens tm-747 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75754.        (((A or (A or B)) -> (C -> (A or B))) and ((((A or (A or B)) and D) or (A or (A or B))) -> (C -> (A or B)))), M:tm-747, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75755
in-theory        75755
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (E or F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75755.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (E or F)))), M:tm-708, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75756
in-theory        75756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75756.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-665, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75757
in-theory        75757
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D -> (A or B))))
theorem-size     13
proof            (modus-ponens tm-623 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75757.        ((A or (A or B)) -> (C or (D -> (A or B)))), M:tm-623, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75758
in-theory        75758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75758.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-622, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75759
in-theory        75759
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75759.        (((A or (A or B)) -> (C -> (A or B))) and (D -> (E or D))), M:tm-609, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75760
in-theory        75760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75760.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-605, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75761
in-theory        75761
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((D -> (E or D)) and ((A or (A or B)) -> (C -> (A or B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-75761.        (((A or (A or B)) -> (C -> (A or B))) and ((D -> (E or D)) and ((A or (A or B)) -> (C -> (A or B))))), M:tm-595, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75762
in-theory        75762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75762.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-550, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75763
in-theory        75763
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75763.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-540, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75764
in-theory        75764
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75764.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-530, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75765
in-theory        75765
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75765.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-520, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75766
in-theory        75766
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75766.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-510, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75767
in-theory        75767
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75767.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-500, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75768
in-theory        75768
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75768.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (E or F)))), M:tm-490, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75769
in-theory        75769
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75769.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-480, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75770
in-theory        75770
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (A or B)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75770.        ((A or (A or B)) -> ((C -> (A or B)) or D)), M:tm-470, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75771
in-theory        75771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75771.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-469, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75772
in-theory        75772
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75772.        (((A or (A or B)) -> (C -> (A or B))) and (D -> (D or E))), M:tm-456, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75773
in-theory        75773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75773.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-453, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75774
in-theory        75774
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((D -> (D or E)) and ((A or (A or B)) -> (C -> (A or B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75774.        (((A or (A or B)) -> (C -> (A or B))) and ((D -> (D or E)) and ((A or (A or B)) -> (C -> (A or B))))), M:tm-443, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75775
in-theory        75775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75775.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-409, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75776
in-theory        75776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75776.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-400, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75777
in-theory        75777
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75777.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-391, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75778
in-theory        75778
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75778.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-382, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75779
in-theory        75779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75779.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (E or F)))), M:tm-373, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75780
in-theory        75780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75780.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-364, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75781
in-theory        75781
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (A or B)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75781.        ((A or (A or B)) -> (C -> ((D -> (A or B)) and C))), M:tm-355, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75782
in-theory        75782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75782.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-354, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75783
in-theory        75783
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75783.        (((A or (A or B)) -> (C -> (A or B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75784
in-theory        75784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (C or D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75784.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (C or D)))), M:tm-338, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75785
in-theory        75785
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (A or B)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-75785.        (((A or (A or B)) -> (C -> (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (A or B))))), M:tm-328, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75786
in-theory        75786
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> (C -> (A or B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-75786.        (((A or (A or B)) -> (C -> (A or B))) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> (C -> (A or B))))), M:tm-327, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75787
in-theory        75787
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (((D and E) -> E) and ((A or (A or B)) -> (C -> (A or B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-75787.        (((A or (A or B)) -> (C -> (A or B))) and (((D and E) -> E) and ((A or (A or B)) -> (C -> (A or B))))), M:tm-326, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75788
in-theory        75788
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (((D and E) -> D) and ((A or (A or B)) -> (C -> (A or B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-75788.        (((A or (A or B)) -> (C -> (A or B))) and (((D and E) -> D) and ((A or (A or B)) -> (C -> (A or B))))), M:tm-325, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75789
in-theory        75789
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> (C -> (A or B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-75789.        (((A or (A or B)) -> (C -> (A or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> (C -> (A or B))))), M:tm-324, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75790
in-theory        75790
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((D -> (E -> D)) and ((A or (A or B)) -> (C -> (A or B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75790.        (((A or (A or B)) -> (C -> (A or B))) and ((D -> (E -> D)) and ((A or (A or B)) -> (C -> (A or B))))), M:tm-323, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75791
in-theory        75791
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75791.        (((A or (A or B)) -> (C -> (A or B))) and ((D and E) -> E)), M:tm-322, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75792
in-theory        75792
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75792.        (((A or (A or B)) -> (C -> (A or B))) and ((D and E) -> D)), M:tm-320, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75793
in-theory        75793
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75793.        (((A or (A or B)) -> (C -> (A or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75794
in-theory        75794
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-316 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75794.        (((A or (A or B)) -> (C -> (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75795
in-theory        75795
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75795.        (((A or (A or B)) -> (C -> (A or B))) and (D -> (E -> D))), M:tm-315, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75796
in-theory        75796
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (((A or (A or B)) -> (not (C -> (A or B)))) -> (not (A or (A or B)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-75796.        (((A or (A or B)) -> (C -> (A or B))) and (((A or (A or B)) -> (not (C -> (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75797
in-theory        75797
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (((C -> (A or B)) -> D) -> (((A or (A or B)) or (C -> (A or B))) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-75797.        (((A or (A or B)) -> (C -> (A or B))) and (((C -> (A or B)) -> D) -> (((A or (A or B)) or (C -> (A or B))) -> D))), M:tm-312, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75798
in-theory        75798
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (D or ((A or (A or B)) -> (C -> (A or B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-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-75798.        (((A or (A or B)) -> (C -> (A or B))) and (D or ((A or (A or B)) -> (C -> (A or B))))), M:tm-311, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75799
in-theory        75799
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (((A or (A or B)) -> (C -> (A or B))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75799.        (((A or (A or B)) -> (C -> (A or B))) and (((A or (A or B)) -> (C -> (A or B))) or D)), M:tm-310, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75800
in-theory        75800
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (D -> (((A or (A or B)) -> (C -> (A or B))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75800.        (((A or (A or B)) -> (C -> (A or B))) and (D -> (((A or (A or B)) -> (C -> (A or B))) and D))), M:tm-309, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75801
in-theory        75801
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (A or B))))
theorem-size     29
proof            (modus-ponens tm-306 tm-858 ((A (or Am (or Am Bm))) (B Cm) (C (or Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75801.        (((A or (A or B)) -> (C -> (A or B))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (A or B)))), M:tm-306, m:tm-858, u:((A (or Am (or Am Bm))) (B Cm) (C (or Am Bm)))
================================================================
tm-name          tm-75802
in-theory        75802
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (D -> ((A or (A or B)) -> (C -> (A or B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75802.        (((A or (A or B)) -> (C -> (A or B))) and (D -> ((A or (A or B)) -> (C -> (A or B))))), M:tm-305, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75803
in-theory        75803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75803.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-303, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75804
in-theory        75804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75804.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-270, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75805
in-theory        75805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75805.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-239, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75806
in-theory        75806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (E or F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-75806.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (E or F)))), M:tm-210, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75807
in-theory        75807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75807.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-183, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75808
in-theory        75808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75808.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-157, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75809
in-theory        75809
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75809.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-147, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75810
in-theory        75810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75810.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-134, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75811
in-theory        75811
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75811.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-125, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75812
in-theory        75812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75812.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (E or F)))), M:tm-113, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75813
in-theory        75813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75813.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-105, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75814
in-theory        75814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (C or D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75814.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (C or D)))), M:tm-95, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75815
in-theory        75815
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> (A or B))))
theorem-size     13
proof            (modus-ponens tm-84 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75815.        ((A or (A or B)) -> (C -> (D -> (A or B)))), M:tm-84, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75816
in-theory        75816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75816.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-83, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75817
in-theory        75817
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (B or C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75817.        (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (B or C)))), M:tm-76, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75818
in-theory        75818
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-73 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75818.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (A or B))), M:tm-73, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75819
in-theory        75819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (C or D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75819.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (C or D)))), M:tm-69, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75820
in-theory        75820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75820.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-54, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75821
in-theory        75821
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (C -> (A or B)))
theorem-size     15
proof            (modus-ponens tm-50 tm-858 ((A Am) (B (or Am Bm)) (C (-> Cm (or Am Bm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75821.        (((A or B) or (A or (A or B))) -> (C -> (A or B))), M:tm-50, m:tm-858, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75822
in-theory        75822
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (C -> (A or B)))
theorem-size     13
proof            (modus-ponens tm-49 tm-858 ((A Am) (B (or Am Bm)) (C (-> Cm (or Am Bm)))))
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-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-75822.        ((A or (A or (A or B))) -> (C -> (A or B))), M:tm-49, m:tm-858, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75823
in-theory        75823
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (B or C)))
theorem-size     19
proof            (modus-ponens tm-47 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75823.        (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (B or C))), M:tm-47, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75824
in-theory        75824
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-46 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75824.        ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (A or B))), M:tm-46, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75825
in-theory        75825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (E -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75825.        ((A -> (B or A)) and ((C or (C or D)) -> (E -> (C or D)))), M:tm-42, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75826
in-theory        75826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (E -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75826.        ((A -> (A or B)) and ((C or (C or D)) -> (E -> (C or D)))), M:tm-32, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75827
in-theory        75827
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (C -> (A or B))))
theorem-size     17
proof            (modus-ponens tm-24 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75827.        ((A or (A or B)) -> ((A or (A or B)) and (C -> (A or B)))), M:tm-24, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75828
in-theory        75828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (C or D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-75828.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (C or D)))), M:tm-23, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75829
in-theory        75829
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (E -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75829.        (((A and B) -> B) and ((C or (C or D)) -> (E -> (C or D)))), M:tm-22, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75830
in-theory        75830
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (E -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75830.        (((A and B) -> A) and ((C or (C or D)) -> (E -> (C or D)))), M:tm-21, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75831
in-theory        75831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75831.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-20, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75832
in-theory        75832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75832.        ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (C or D)))), M:tm-19, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75833
in-theory        75833
times-derived    19
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (A or (A or B)))
theorem-size     11
proof            (modus-ponens tm-12 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-75833.        ((A or (A or B)) -> (A or (A or B))), M:tm-12, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75834
in-theory        75834
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (C -> (A or B)))) -> (not (A or (A or B))))
theorem-size     19
proof            (modus-ponens tm-9 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75834.        (((A or (A or B)) -> (not (C -> (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75835
in-theory        75835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or C)) -> D) -> (((B or (B or C)) or (A -> (B or C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-858 ((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       81
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-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-75835.        (((A -> (B or C)) -> D) -> (((B or (B or C)) or (A -> (B or C))) -> D)), M:tm-8, m:tm-858, u:((A (or Am (or Am Bm))) (B (-> Cm (or Am Bm))))
================================================================
tm-name          tm-75836
in-theory        75836
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (D -> (B or C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75836.        (A or ((B or (B or C)) -> (D -> (B or C)))), M:tm-7, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75837
in-theory        75837
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-49.           (((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-75837.        (((A or (A or B)) -> (C -> (A or B))) or D), M:tm-6, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75838
in-theory        75838
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (D -> (B or C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75838.        (A -> (((B or (B or C)) -> (D -> (B or C))) and A)), M:tm-5, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75839
in-theory        75839
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> C) -> ((A or (A or B)) -> (A or B)))
theorem-size     17
proof            (modus-ponens tm-2 tm-858 ((A (or Am (or Am Bm))) (B Cm) (C (or Am Bm))))
axioms-used      (tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75839.        (((A or (A or B)) -> C) -> ((A or (A or B)) -> (A or B))), M:tm-2, m:tm-858, u:((A (or Am (or Am Bm))) (B Cm) (C (or Am Bm)))
================================================================
tm-name          tm-75840
in-theory        75840
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (D -> (B or C))))
theorem-size     13
proof            (modus-ponens tm-1 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75840.        (A -> ((B or (B or C)) -> (D -> (B or C)))), M:tm-1, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-75841
in-theory        75841
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75841.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-855, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75842
in-theory        75842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75842.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-808, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75843
in-theory        75843
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (((D and (A or (A or B))) or (A or (A or B))) -> (C -> ((A or B) and C))))
theorem-size     35
proof            (modus-ponens tm-798 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75843.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (((D and (A or (A or B))) or (A or (A or B))) -> (C -> ((A or B) and C)))), M:tm-798, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75844
in-theory        75844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-75844.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-757, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75845
in-theory        75845
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((((A or (A or B)) and D) or (A or (A or B))) -> (C -> ((A or B) and C))))
theorem-size     35
proof            (modus-ponens tm-747 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-75845.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((((A or (A or B)) and D) or (A or (A or B))) -> (C -> ((A or B) and C)))), M:tm-747, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75846
in-theory        75846
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> ((E or F) and G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-75846.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> ((E or F) and G)))), M:tm-708, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75847
in-theory        75847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75847.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-665, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75848
in-theory        75848
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D -> ((A or B) and D))))
theorem-size     15
proof            (modus-ponens tm-623 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75848.        ((A or (A or B)) -> (C or (D -> ((A or B) and D)))), M:tm-623, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75849
in-theory        75849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75849.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-622, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75850
in-theory        75850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C or (A or (A or B)))))
theorem-size     17
proof            (modus-ponens tm-617 tm-859 ((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (and (or Am Bm) (or B (or Am (or Am Bm)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75850.        ((A or (A or B)) -> ((A or B) and (C or (A or (A or B))))), M:tm-617, m:tm-859, u:((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (and (or Am Bm) (or B (or Am (or Am Bm))))))
================================================================
tm-name          tm-75851
in-theory        75851
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75851.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (E or D))), M:tm-609, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75852
in-theory        75852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75852.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-605, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75853
in-theory        75853
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (E or D)) and ((A or (A or B)) -> (C -> ((A or B) and C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-75853.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (E or D)) and ((A or (A or B)) -> (C -> ((A or B) and C))))), M:tm-595, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75854
in-theory        75854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75854.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-550, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75855
in-theory        75855
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-75855.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-540, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75856
in-theory        75856
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75856.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-530, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75857
in-theory        75857
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75857.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-520, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75858
in-theory        75858
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-75858.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-510, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75859
in-theory        75859
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-75859.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-500, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75860
in-theory        75860
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> ((E or F) and G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75860.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> ((E or F) and G)))), M:tm-490, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75861
in-theory        75861
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75861.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-480, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75862
in-theory        75862
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> ((A or B) and C)) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) 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-49.           (((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-75862.        ((A or (A or B)) -> ((C -> ((A or B) and C)) or D)), M:tm-470, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75863
in-theory        75863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75863.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-469, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75864
in-theory        75864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and ((A or (A or B)) or C)))
theorem-size     17
proof            (modus-ponens tm-464 tm-859 ((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (and (or Am Bm) (or (or Am (or Am Bm)) 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-49.           (((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-75864.        ((A or (A or B)) -> ((A or B) and ((A or (A or B)) or C))), M:tm-464, m:tm-859, u:((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (and (or Am Bm) (or (or Am (or Am Bm)) B))))
================================================================
tm-name          tm-75865
in-theory        75865
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75865.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (D or E))), M:tm-456, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75866
in-theory        75866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-75866.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-453, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75867
in-theory        75867
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (D or E)) and ((A or (A or B)) -> (C -> ((A or B) and C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-75867.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (D or E)) and ((A or (A or B)) -> (C -> ((A or B) and C))))), M:tm-443, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75868
in-theory        75868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75868.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-409, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75869
in-theory        75869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-75869.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-400, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75870
in-theory        75870
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75870.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-391, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75871
in-theory        75871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75871.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-382, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75872
in-theory        75872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> ((E or F) and G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75872.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> ((E or F) and G)))), M:tm-373, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75873
in-theory        75873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75873.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-364, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75874
in-theory        75874
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> ((A or B) and D)) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75874.        ((A or (A or B)) -> (C -> ((D -> ((A or B) and D)) and C))), M:tm-355, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75875
in-theory        75875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75875.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-354, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75876
in-theory        75876
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C -> ((A or (A or B)) and C))))
theorem-size     19
proof            (modus-ponens tm-349 tm-859 ((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (and (or Am Bm) (-> B (and (or Am (or Am Bm)) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75876.        ((A or (A or B)) -> ((A or B) and (C -> ((A or (A or B)) and C)))), M:tm-349, m:tm-859, u:((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (and (or Am Bm) (-> B (and (or Am (or Am Bm)) B)))))
================================================================
tm-name          tm-75877
in-theory        75877
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75877.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75878
in-theory        75878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> ((C or D) and E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75878.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> ((C or D) and E)))), M:tm-338, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75879
in-theory        75879
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> ((A or B) and C)))))
theorem-size     33
proof            (modus-ponens tm-328 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-75879.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> ((A or B) and C))))), M:tm-328, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75880
in-theory        75880
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> (C -> ((A or B) and C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-75880.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> (C -> ((A or B) and C))))), M:tm-327, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75881
in-theory        75881
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (((D and E) -> E) and ((A or (A or B)) -> (C -> ((A or B) and C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-75881.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (((D and E) -> E) and ((A or (A or B)) -> (C -> ((A or B) and C))))), M:tm-326, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75882
in-theory        75882
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (((D and E) -> D) and ((A or (A or B)) -> (C -> ((A or B) and C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-75882.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (((D and E) -> D) and ((A or (A or B)) -> (C -> ((A or B) and C))))), M:tm-325, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75883
in-theory        75883
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> (C -> ((A or B) and C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-75883.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> (C -> ((A or B) and C))))), M:tm-324, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75884
in-theory        75884
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (E -> D)) and ((A or (A or B)) -> (C -> ((A or B) and C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-75884.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (E -> D)) and ((A or (A or B)) -> (C -> ((A or B) and C))))), M:tm-323, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75885
in-theory        75885
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75885.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D and E) -> E)), M:tm-322, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75886
in-theory        75886
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75886.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D and E) -> D)), M:tm-320, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75887
in-theory        75887
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75887.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75888
in-theory        75888
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     25
proof            (modus-ponens tm-316 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-75888.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75889
in-theory        75889
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75889.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (E -> D))), M:tm-315, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75890
in-theory        75890
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (((A or (A or B)) -> (not (C -> ((A or B) and C)))) -> (not (A or (A or B)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-75890.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (((A or (A or B)) -> (not (C -> ((A or B) and C)))) -> (not (A or (A or B))))), M:tm-313, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75891
in-theory        75891
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (((C -> ((A or B) and C)) -> D) -> (((A or (A or B)) or (C -> ((A or B) and C))) -> D)))
theorem-size     39
proof            (modus-ponens tm-312 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-312.          ((A -> B) -> ((A -> B) and ((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-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-75891.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (((C -> ((A or B) and C)) -> D) -> (((A or (A or B)) or (C -> ((A or B) and C))) -> D))), M:tm-312, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75892
in-theory        75892
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (D or ((A or (A or B)) -> (C -> ((A or B) and C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-75892.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (D or ((A or (A or B)) -> (C -> ((A or B) and C))))), M:tm-311, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75893
in-theory        75893
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (((A or (A or B)) -> (C -> ((A or B) and C))) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-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-75893.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (((A or (A or B)) -> (C -> ((A or B) and C))) or D)), M:tm-310, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75894
in-theory        75894
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (((A or (A or B)) -> (C -> ((A or B) and C))) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-75894.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> (((A or (A or B)) -> (C -> ((A or B) and C))) and D))), M:tm-309, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75895
in-theory        75895
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> ((A or B) and C))))
theorem-size     33
proof            (modus-ponens tm-306 tm-859 ((A (or Am (or Am Bm))) (B Cm) (C (and (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-75895.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> ((A or B) and C)))), M:tm-306, m:tm-859, u:((A (or Am (or Am Bm))) (B Cm) (C (and (or Am Bm) Cm)))
================================================================
tm-name          tm-75896
in-theory        75896
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> ((A or (A or B)) -> (C -> ((A or B) and C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-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-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-75896.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (D -> ((A or (A or B)) -> (C -> ((A or B) and C))))), M:tm-305, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75897
in-theory        75897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75897.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-303, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75898
in-theory        75898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75898.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-270, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75899
in-theory        75899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75899.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-239, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75900
in-theory        75900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> ((E or F) and G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75900.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> ((E or F) and G)))), M:tm-210, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75901
in-theory        75901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75901.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-183, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75902
in-theory        75902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75902.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-157, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75903
in-theory        75903
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75903.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-147, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75904
in-theory        75904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75904.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-134, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75905
in-theory        75905
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75905.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-125, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75906
in-theory        75906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> ((E or F) and G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75906.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> ((E or F) and G)))), M:tm-113, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75907
in-theory        75907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-75907.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-105, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75908
in-theory        75908
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (A or (A or B))))
theorem-size     15
proof            (modus-ponens tm-99 tm-859 ((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (and (or Am Bm) (or Am (or Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75908.        ((A or (A or B)) -> ((A or B) and (A or (A or B)))), M:tm-99, m:tm-859, u:((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (and (or Am Bm) (or Am (or Am Bm)))))
================================================================
tm-name          tm-75909
in-theory        75909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C -> (A or (A or B)))))
theorem-size     17
proof            (modus-ponens tm-98 tm-859 ((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (and (or Am Bm) (-> B (or Am (or Am Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75909.        ((A or (A or B)) -> ((A or B) and (C -> (A or (A or B))))), M:tm-98, m:tm-859, u:((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (and (or Am Bm) (-> B (or Am (or Am Bm))))))
================================================================
tm-name          tm-75910
in-theory        75910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> ((C or D) and E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75910.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> ((C or D) and E)))), M:tm-95, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75911
in-theory        75911
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> ((A or B) and D))))
theorem-size     15
proof            (modus-ponens tm-84 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75911.        ((A or (A or B)) -> (C -> (D -> ((A or B) and D)))), M:tm-84, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75912
in-theory        75912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75912.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-83, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75913
in-theory        75913
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (D -> ((B or C) and D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75913.        (((not (not A)) -> A) and ((B or (B or C)) -> (D -> ((B or C) and D)))), M:tm-76, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75914
in-theory        75914
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> ((A or B) and C)))
theorem-size     21
proof            (modus-ponens tm-73 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75914.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> ((A or B) and C))), M:tm-73, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75915
in-theory        75915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> ((C or D) and E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75915.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> ((C or D) and E)))), M:tm-69, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75916
in-theory        75916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75916.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-54, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75917
in-theory        75917
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (C -> ((A or B) and C)))
theorem-size     17
proof            (modus-ponens tm-50 tm-859 ((A Am) (B (or Am Bm)) (C (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75917.        (((A or B) or (A or (A or B))) -> (C -> ((A or B) and C))), M:tm-50, m:tm-859, u:((A Am) (B (or Am Bm)) (C (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75918
in-theory        75918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (C -> ((A or B) and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-859 ((A Am) (B (or Am Bm)) (C (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-6 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-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-75918.        ((A or (A or (A or B))) -> (C -> ((A or B) and C))), M:tm-49, m:tm-859, u:((A Am) (B (or Am Bm)) (C (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75919
in-theory        75919
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (D -> ((B or C) and D)))
theorem-size     21
proof            (modus-ponens tm-47 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75919.        (((A and (B or (B or C))) or (B or (B or C))) -> (D -> ((B or C) and D))), M:tm-47, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75920
in-theory        75920
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> ((A or B) and D)))
theorem-size     21
proof            (modus-ponens tm-46 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75920.        ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> ((A or B) and D))), M:tm-46, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75921
in-theory        75921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (E -> ((C or D) and E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75921.        ((A -> (B or A)) and ((C or (C or D)) -> (E -> ((C or D) and E)))), M:tm-42, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75922
in-theory        75922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (E -> ((C or D) and E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-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-75922.        ((A -> (A or B)) and ((C or (C or D)) -> (E -> ((C or D) and E)))), M:tm-32, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75923
in-theory        75923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (C -> ((A or B) and C))))
theorem-size     19
proof            (modus-ponens tm-24 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75923.        ((A or (A or B)) -> ((A or (A or B)) and (C -> ((A or B) and C)))), M:tm-24, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75924
in-theory        75924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> ((C or D) and E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75924.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> ((C or D) and E)))), M:tm-23, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75925
in-theory        75925
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (E -> ((C or D) and E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75925.        (((A and B) -> B) and ((C or (C or D)) -> (E -> ((C or D) and E)))), M:tm-22, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75926
in-theory        75926
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (E -> ((C or D) and E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75926.        (((A and B) -> A) and ((C or (C or D)) -> (E -> ((C or D) and E)))), M:tm-21, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75927
in-theory        75927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75927.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-20, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75928
in-theory        75928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (E -> ((C or D) and E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75928.        ((A -> (B -> A)) and ((C or (C or D)) -> (E -> ((C or D) and E)))), M:tm-19, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75929
in-theory        75929
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (C -> ((A or B) and C)))) -> (not (A or (A or B))))
theorem-size     21
proof            (modus-ponens tm-9 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75929.        (((A or (A or B)) -> (not (C -> ((A or B) and C)))) -> (not (A or (A or B)))), M:tm-9, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75930
in-theory        75930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or C) and A)) -> D) -> (((B or (B or C)) or (A -> ((B or C) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-859 ((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       89
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-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-75930.        (((A -> ((B or C) and A)) -> D) -> (((B or (B or C)) or (A -> ((B or C) and A))) -> D)), M:tm-8, m:tm-859, u:((A (or Am (or Am Bm))) (B (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-75931
in-theory        75931
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (D -> ((B or C) and D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75931.        (A or ((B or (B or C)) -> (D -> ((B or C) and D)))), M:tm-7, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75932
in-theory        75932
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-6 tm-8 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-49.           (((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-75932.        (((A or (A or B)) -> (C -> ((A or B) and C))) or D), M:tm-6, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75933
in-theory        75933
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (D -> ((B or C) and D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-75933.        (A -> (((B or (B or C)) -> (D -> ((B or C) and D))) and A)), M:tm-5, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75934
in-theory        75934
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> C) -> ((A or (A or B)) -> ((A or B) and C)))
theorem-size     19
proof            (modus-ponens tm-2 tm-859 ((A (or Am (or Am Bm))) (B Cm) (C (and (or Am Bm) Cm))))
axioms-used      (tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75934.        (((A or (A or B)) -> C) -> ((A or (A or B)) -> ((A or B) and C))), M:tm-2, m:tm-859, u:((A (or Am (or Am Bm))) (B Cm) (C (and (or Am Bm) Cm)))
================================================================
tm-name          tm-75935
in-theory        75935
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (D -> ((B or C) and D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75935.        (A -> ((B or (B or C)) -> (D -> ((B or C) and D)))), M:tm-1, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-75936
in-theory        75936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75936.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-855, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75937
in-theory        75937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75937.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-808, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75938
in-theory        75938
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (((D and (A or (A or B))) or (A or (A or B))) -> ((A or B) or C)))
theorem-size     31
proof            (modus-ponens tm-798 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75938.        (((A or (A or B)) -> ((A or B) or C)) and (((D and (A or (A or B))) or (A or (A or B))) -> ((A or B) or C))), M:tm-798, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-75939
in-theory        75939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-75939.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-757, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75940
in-theory        75940
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((((A or (A or B)) and D) or (A or (A or B))) -> ((A or B) or C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75940.        (((A or (A or B)) -> ((A or B) or C)) and ((((A or (A or B)) and D) or (A or (A or B))) -> ((A or B) or C))), M:tm-747, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-75941
in-theory        75941
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((E or F) or G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-75941.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((E or F) or G))), M:tm-708, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75942
in-theory        75942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-49.           (((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-75942.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-665, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75943
in-theory        75943
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((A or B) or D)))
theorem-size     13
proof            (modus-ponens tm-623 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75943.        ((A or (A or B)) -> (C or ((A or B) or D))), M:tm-623, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-75944
in-theory        75944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75944.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-622, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75945
in-theory        75945
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75945.        (((A or (A or B)) -> ((A or B) or C)) and (D -> (E or D))), M:tm-609, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75946
in-theory        75946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75946.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-605, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75947
in-theory        75947
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((D -> (E or D)) and ((A or (A or B)) -> ((A or B) or C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-75947.        (((A or (A or B)) -> ((A or B) or C)) and ((D -> (E or D)) and ((A or (A or B)) -> ((A or B) or C)))), M:tm-595, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75948
in-theory        75948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-49.           (((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-75948.        (((A -> (B or A)) or C) and ((D or (D or E)) -> ((D or E) or F))), M:tm-550, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75949
in-theory        75949
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-75949.        ((A or (B -> (C or B))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-540, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75950
in-theory        75950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-49.           (((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-75950.        ((A or (B -> (B or C))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-530, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75951
in-theory        75951
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75951.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-520, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75952
in-theory        75952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-75952.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-510, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75953
in-theory        75953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-75953.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-500, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75954
in-theory        75954
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((E or F) or G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75954.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((E or F) or G))), M:tm-490, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75955
in-theory        75955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75955.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-480, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75956
in-theory        75956
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((A or B) or C) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) 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-49.           (((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-75956.        ((A or (A or B)) -> (((A or B) or C) or D)), M:tm-470, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-75957
in-theory        75957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-49.           (((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-75957.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-469, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75958
in-theory        75958
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-49.           (((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-75958.        (((A or (A or B)) -> ((A or B) or C)) and (D -> (D or E))), M:tm-456, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75959
in-theory        75959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-75959.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-453, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75960
in-theory        75960
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((D -> (D or E)) and ((A or (A or B)) -> ((A or B) or C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-75960.        (((A or (A or B)) -> ((A or B) or C)) and ((D -> (D or E)) and ((A or (A or B)) -> ((A or B) or C)))), M:tm-443, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75961
in-theory        75961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-75961.        (((A -> (A or B)) or C) and ((D or (D or E)) -> ((D or E) or F))), M:tm-409, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75962
in-theory        75962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-75962.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((D or E) or F))), M:tm-400, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75963
in-theory        75963
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am 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-49.           (((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-75963.        ((((A and B) -> B) or C) and ((D or (D or E)) -> ((D or E) or F))), M:tm-391, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75964
in-theory        75964
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-49.           (((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-75964.        ((((A and B) -> A) or C) and ((D or (D or E)) -> ((D or E) or F))), M:tm-382, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75965
in-theory        75965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((E or F) or G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-75965.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((E or F) or G))), M:tm-373, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75966
in-theory        75966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-49.           (((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-75966.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((D or E) or F))), M:tm-364, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75967
in-theory        75967
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((A or B) or D) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75967.        ((A or (A or B)) -> (C -> (((A or B) or D) and C))), M:tm-355, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-75968
in-theory        75968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75968.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-354, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75969
in-theory        75969
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75969.        (((A or (A or B)) -> ((A or B) or C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75970
in-theory        75970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((C or D) or E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75970.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((C or D) or E))), M:tm-338, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75971
in-theory        75971
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((A or (A or B)) -> ((A or (A or B)) and ((A or B) or C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75971.        (((A or (A or B)) -> ((A or B) or C)) and ((A or (A or B)) -> ((A or (A or B)) and ((A or B) or C)))), M:tm-328, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-75972
in-theory        75972
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> ((A or B) or C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-75972.        (((A or (A or B)) -> ((A or B) or C)) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> ((A or B) or C)))), M:tm-327, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75973
in-theory        75973
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (((D and E) -> E) and ((A or (A or B)) -> ((A or B) or C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-75973.        (((A or (A or B)) -> ((A or B) or C)) and (((D and E) -> E) and ((A or (A or B)) -> ((A or B) or C)))), M:tm-326, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75974
in-theory        75974
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (((D and E) -> D) and ((A or (A or B)) -> ((A or B) or C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-75974.        (((A or (A or B)) -> ((A or B) or C)) and (((D and E) -> D) and ((A or (A or B)) -> ((A or B) or C)))), M:tm-325, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75975
in-theory        75975
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> ((A or B) or C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-75975.        (((A or (A or B)) -> ((A or B) or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> ((A or B) or C)))), M:tm-324, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75976
in-theory        75976
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((D -> (E -> D)) and ((A or (A or B)) -> ((A or B) or C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75976.        (((A or (A or B)) -> ((A or B) or C)) and ((D -> (E -> D)) and ((A or (A or B)) -> ((A or B) or C)))), M:tm-323, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75977
in-theory        75977
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75977.        (((A or (A or B)) -> ((A or B) or C)) and ((D and E) -> E)), M:tm-322, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75978
in-theory        75978
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75978.        (((A or (A or B)) -> ((A or B) or C)) and ((D and E) -> D)), M:tm-320, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75979
in-theory        75979
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75979.        (((A or (A or B)) -> ((A or B) or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75980
in-theory        75980
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-316 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75980.        (((A or (A or B)) -> ((A or B) or C)) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-75981
in-theory        75981
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75981.        (((A or (A or B)) -> ((A or B) or C)) and (D -> (E -> D))), M:tm-315, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75982
in-theory        75982
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (((A or (A or B)) -> (not ((A or B) or C))) -> (not (A or (A or B)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-75982.        (((A or (A or B)) -> ((A or B) or C)) and (((A or (A or B)) -> (not ((A or B) or C))) -> (not (A or (A or B))))), M:tm-313, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-75983
in-theory        75983
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((((A or B) or C) -> D) -> (((A or (A or B)) or ((A or B) or C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75983.        (((A or (A or B)) -> ((A or B) or C)) and ((((A or B) or C) -> D) -> (((A or (A or B)) or ((A or B) or C)) -> D))), M:tm-312, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-75984
in-theory        75984
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (D or ((A or (A or B)) -> ((A or B) or C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-75984.        (((A or (A or B)) -> ((A or B) or C)) and (D or ((A or (A or B)) -> ((A or B) or C)))), M:tm-311, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75985
in-theory        75985
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (((A or (A or B)) -> ((A or B) or C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-75985.        (((A or (A or B)) -> ((A or B) or C)) and (((A or (A or B)) -> ((A or B) or C)) or D)), M:tm-310, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75986
in-theory        75986
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (D -> (((A or (A or B)) -> ((A or B) or C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75986.        (((A or (A or B)) -> ((A or B) or C)) and (D -> (((A or (A or B)) -> ((A or B) or C)) and D))), M:tm-309, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75987
in-theory        75987
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (D -> ((A or (A or B)) -> ((A or B) or C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-860 ((A (-> (or Am (or Am Bm)) (or (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-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-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-75987.        (((A or (A or B)) -> ((A or B) or C)) and (D -> ((A or (A or B)) -> ((A or B) or C)))), M:tm-305, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75988
in-theory        75988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75988.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-303, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75989
in-theory        75989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75989.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-270, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75990
in-theory        75990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75990.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-239, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75991
in-theory        75991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((E or F) or G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75991.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((E or F) or G))), M:tm-210, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75992
in-theory        75992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75992.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-183, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75993
in-theory        75993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75993.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-157, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75994
in-theory        75994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75994.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-147, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75995
in-theory        75995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75995.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-134, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75996
in-theory        75996
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75996.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-125, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75997
in-theory        75997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((E or F) or G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75997.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((E or F) or G))), M:tm-113, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75998
in-theory        75998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-75998.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-105, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-75999
in-theory        75999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((C or D) or E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-75999.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((C or D) or E))), M:tm-95, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76000
in-theory        76000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((A or B) or D)))
theorem-size     13
proof            (modus-ponens tm-84 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76000.        ((A or (A or B)) -> (C -> ((A or B) or D))), M:tm-84, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-76001
in-theory        76001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76001.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-83, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76002
in-theory        76002
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> ((B or C) or D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76002.        (((not (not A)) -> A) and ((B or (B or C)) -> ((B or C) or D))), M:tm-76, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76003
in-theory        76003
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> ((A or B) or C))
theorem-size     19
proof            (modus-ponens tm-73 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-8 tm-10 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76003.        (((not (not (A or (A or B)))) or (A or (A or B))) -> ((A or B) or C)), M:tm-73, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-76004
in-theory        76004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((C or D) or E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76004.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((C or D) or E))), M:tm-69, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76005
in-theory        76005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76005.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-54, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76006
in-theory        76006
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> ((A or B) or C))
theorem-size     15
proof            (modus-ponens tm-50 tm-860 ((A Am) (B (or Am Bm)) (C (or (or Am Bm) Cm))))
axioms-used      (tm-8 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76006.        (((A or B) or (A or (A or B))) -> ((A or B) or C)), M:tm-50, m:tm-860, u:((A Am) (B (or Am Bm)) (C (or (or Am Bm) Cm)))
================================================================
tm-name          tm-76007
in-theory        76007
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> ((A or B) or C))
theorem-size     13
proof            (modus-ponens tm-49 tm-860 ((A Am) (B (or Am Bm)) (C (or (or Am Bm) Cm))))
axioms-used      (tm-8 tm-6)
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-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-76007.        ((A or (A or (A or B))) -> ((A or B) or C)), M:tm-49, m:tm-860, u:((A Am) (B (or Am Bm)) (C (or (or Am Bm) Cm)))
================================================================
tm-name          tm-76008
in-theory        76008
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> ((B or C) or D))
theorem-size     19
proof            (modus-ponens tm-47 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-8 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76008.        (((A and (B or (B or C))) or (B or (B or C))) -> ((B or C) or D)), M:tm-47, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-76009
in-theory        76009
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> ((A or B) or D))
theorem-size     19
proof            (modus-ponens tm-46 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-8 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76009.        ((((A or (A or B)) and C) or (A or (A or B))) -> ((A or B) or D)), M:tm-46, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-76010
in-theory        76010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> ((C or D) or E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76010.        ((A -> (B or A)) and ((C or (C or D)) -> ((C or D) or E))), M:tm-42, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76011
in-theory        76011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> ((C or D) or E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-76011.        ((A -> (A or B)) and ((C or (C or D)) -> ((C or D) or E))), M:tm-32, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76012
in-theory        76012
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and ((A or B) or C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76012.        ((A or (A or B)) -> ((A or (A or B)) and ((A or B) or C))), M:tm-24, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-76013
in-theory        76013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((C or D) or E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76013.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((C or D) or E))), M:tm-23, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76014
in-theory        76014
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> ((C or D) or E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76014.        (((A and B) -> B) and ((C or (C or D)) -> ((C or D) or E))), M:tm-22, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76015
in-theory        76015
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> ((C or D) or E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76015.        (((A and B) -> A) and ((C or (C or D)) -> ((C or D) or E))), M:tm-21, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76016
in-theory        76016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76016.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((D or E) or F))), M:tm-20, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76017
in-theory        76017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> ((C or D) or E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76017.        ((A -> (B -> A)) and ((C or (C or D)) -> ((C or D) or E))), M:tm-19, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76018
in-theory        76018
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not ((A or B) or C))) -> (not (A or (A or B))))
theorem-size     19
proof            (modus-ponens tm-9 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-9 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76018.        (((A or (A or B)) -> (not ((A or B) or C))) -> (not (A or (A or B)))), M:tm-9, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-76019
in-theory        76019
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) or C) -> D) -> (((A or (A or B)) or ((A or B) or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-860 ((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm))))
axioms-used      (tm-8 tm-6)
proof-size       81
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-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-76019.        ((((A or B) or C) -> D) -> (((A or (A or B)) or ((A or B) or C)) -> D)), M:tm-8, m:tm-860, u:((A (or Am (or Am Bm))) (B (or (or Am Bm) Cm)))
================================================================
tm-name          tm-76020
in-theory        76020
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> ((B or C) or D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76020.        (A or ((B or (B or C)) -> ((B or C) or D))), M:tm-7, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76021
in-theory        76021
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-6 tm-8)
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-49.           (((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-76021.        (((A or (A or B)) -> ((A or B) or C)) or D), M:tm-6, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76022
in-theory        76022
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> ((B or C) or D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76022.        (A -> (((B or (B or C)) -> ((B or C) or D)) and A)), M:tm-5, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76023
in-theory        76023
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> ((B or C) or D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76023.        (A -> ((B or (B or C)) -> ((B or C) or D))), M:tm-1, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-76024
in-theory        76024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     29
proof            (modus-ponens tm-855 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76024.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-855, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76025
in-theory        76025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     23
proof            (modus-ponens tm-808 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76025.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-808, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76026
in-theory        76026
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (((D and (A or (A or B))) or (A or (A or B))) -> (C or (A or B))))
theorem-size     31
proof            (modus-ponens tm-798 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76026.        (((A or (A or B)) -> (C or (A or B))) and (((D and (A or (A or B))) or (A or (A or B))) -> (C or (A or B)))), M:tm-798, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76027
in-theory        76027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76027.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-757, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76028
in-theory        76028
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((((A or (A or B)) and D) or (A or (A or B))) -> (C or (A or B))))
theorem-size     31
proof            (modus-ponens tm-747 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76028.        (((A or (A or B)) -> (C or (A or B))) and ((((A or (A or B)) and D) or (A or (A or B))) -> (C or (A or B)))), M:tm-747, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76029
in-theory        76029
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G or (E or F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76029.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G or (E or F)))), M:tm-708, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76030
in-theory        76030
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76030.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-665, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76031
in-theory        76031
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D or (A or B))))
theorem-size     13
proof            (modus-ponens tm-623 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76031.        ((A or (A or B)) -> (C or (D or (A or B)))), M:tm-623, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76032
in-theory        76032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76032.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-622, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76033
in-theory        76033
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76033.        (((A or (A or B)) -> (C or (A or B))) and (D -> (E or D))), M:tm-609, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76034
in-theory        76034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76034.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-605, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76035
in-theory        76035
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((D -> (E or D)) and ((A or (A or B)) -> (C or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-76035.        (((A or (A or B)) -> (C or (A or B))) and ((D -> (E or D)) and ((A or (A or B)) -> (C or (A or B))))), M:tm-595, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76036
in-theory        76036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76036.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (F or (D or E)))), M:tm-550, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76037
in-theory        76037
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-76037.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-540, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76038
in-theory        76038
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76038.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-530, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76039
in-theory        76039
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76039.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-520, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76040
in-theory        76040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-76040.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-510, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76041
in-theory        76041
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-76041.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-500, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76042
in-theory        76042
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G or (E or F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76042.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G or (E or F)))), M:tm-490, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76043
in-theory        76043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76043.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-480, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76044
in-theory        76044
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or (A or B)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
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-49.           (((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-76044.        ((A or (A or B)) -> ((C or (A or B)) or D)), M:tm-470, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76045
in-theory        76045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
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-49.           (((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-76045.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-469, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76046
in-theory        76046
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
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-49.           (((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-76046.        (((A or (A or B)) -> (C or (A or B))) and (D -> (D or E))), M:tm-456, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76047
in-theory        76047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-76047.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-453, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76048
in-theory        76048
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((D -> (D or E)) and ((A or (A or B)) -> (C or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-76048.        (((A or (A or B)) -> (C or (A or B))) and ((D -> (D or E)) and ((A or (A or B)) -> (C or (A or B))))), M:tm-443, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76049
in-theory        76049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-76049.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (F or (D or E)))), M:tm-409, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76050
in-theory        76050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-76050.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F or (D or E)))), M:tm-400, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76051
in-theory        76051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-76051.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (F or (D or E)))), M:tm-391, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76052
in-theory        76052
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-76052.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (F or (D or E)))), M:tm-382, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76053
in-theory        76053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G or (E or F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-49.           (((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-76053.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G or (E or F)))), M:tm-373, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76054
in-theory        76054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
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-49.           (((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-76054.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F or (D or E)))), M:tm-364, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76055
in-theory        76055
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D or (A or B)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76055.        ((A or (A or B)) -> (C -> ((D or (A or B)) and C))), M:tm-355, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76056
in-theory        76056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76056.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-354, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76057
in-theory        76057
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-76057.        (((A or (A or B)) -> (C or (A or B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76058
in-theory        76058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E or (C or D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76058.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E or (C or D)))), M:tm-338, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76059
in-theory        76059
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (C or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-76059.        (((A or (A or B)) -> (C or (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (C or (A or B))))), M:tm-328, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76060
in-theory        76060
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> (C or (A or B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-76060.        (((A or (A or B)) -> (C or (A or B))) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> (C or (A or B))))), M:tm-327, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76061
in-theory        76061
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (((D and E) -> E) and ((A or (A or B)) -> (C or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-76061.        (((A or (A or B)) -> (C or (A or B))) and (((D and E) -> E) and ((A or (A or B)) -> (C or (A or B))))), M:tm-326, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76062
in-theory        76062
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (((D and E) -> D) and ((A or (A or B)) -> (C or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-76062.        (((A or (A or B)) -> (C or (A or B))) and (((D and E) -> D) and ((A or (A or B)) -> (C or (A or B))))), M:tm-325, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76063
in-theory        76063
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> (C or (A or B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76063.        (((A or (A or B)) -> (C or (A or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> (C or (A or B))))), M:tm-324, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76064
in-theory        76064
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((D -> (E -> D)) and ((A or (A or B)) -> (C or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-76064.        (((A or (A or B)) -> (C or (A or B))) and ((D -> (E -> D)) and ((A or (A or B)) -> (C or (A or B))))), M:tm-323, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76065
in-theory        76065
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76065.        (((A or (A or B)) -> (C or (A or B))) and ((D and E) -> E)), M:tm-322, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76066
in-theory        76066
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76066.        (((A or (A or B)) -> (C or (A or B))) and ((D and E) -> D)), M:tm-320, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76067
in-theory        76067
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76067.        (((A or (A or B)) -> (C or (A or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76068
in-theory        76068
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-316 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-76068.        (((A or (A or B)) -> (C or (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76069
in-theory        76069
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76069.        (((A or (A or B)) -> (C or (A or B))) and (D -> (E -> D))), M:tm-315, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76070
in-theory        76070
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (((A or (A or B)) -> (not (C or (A or B)))) -> (not (A or (A or B)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-76070.        (((A or (A or B)) -> (C or (A or B))) and (((A or (A or B)) -> (not (C or (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76071
in-theory        76071
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (((C or (A or B)) -> D) -> (((A or (A or B)) or (C or (A or B))) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-76071.        (((A or (A or B)) -> (C or (A or B))) and (((C or (A or B)) -> D) -> (((A or (A or B)) or (C or (A or B))) -> D))), M:tm-312, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76072
in-theory        76072
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (D or ((A or (A or B)) -> (C or (A or B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-76072.        (((A or (A or B)) -> (C or (A or B))) and (D or ((A or (A or B)) -> (C or (A or B))))), M:tm-311, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76073
in-theory        76073
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (((A or (A or B)) -> (C or (A or B))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-76073.        (((A or (A or B)) -> (C or (A or B))) and (((A or (A or B)) -> (C or (A or B))) or D)), M:tm-310, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76074
in-theory        76074
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (D -> (((A or (A or B)) -> (C or (A or B))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76074.        (((A or (A or B)) -> (C or (A or B))) and (D -> (((A or (A or B)) -> (C or (A or B))) and D))), M:tm-309, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76075
in-theory        76075
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (D -> ((A or (A or B)) -> (C or (A or B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-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-76075.        (((A or (A or B)) -> (C or (A or B))) and (D -> ((A or (A or B)) -> (C or (A or B))))), M:tm-305, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76076
in-theory        76076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76076.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-303, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76077
in-theory        76077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76077.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-270, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76078
in-theory        76078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76078.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-239, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76079
in-theory        76079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G or (E or F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-76079.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G or (E or F)))), M:tm-210, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76080
in-theory        76080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76080.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-183, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76081
in-theory        76081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76081.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-157, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76082
in-theory        76082
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76082.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-147, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76083
in-theory        76083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76083.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-134, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76084
in-theory        76084
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76084.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-125, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76085
in-theory        76085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G or (E or F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76085.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G or (E or F)))), M:tm-113, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76086
in-theory        76086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76086.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-105, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76087
in-theory        76087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E or (C or D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76087.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E or (C or D)))), M:tm-95, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76088
in-theory        76088
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D or (A or B))))
theorem-size     13
proof            (modus-ponens tm-84 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76088.        ((A or (A or B)) -> (C -> (D or (A or B)))), M:tm-84, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76089
in-theory        76089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76089.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-83, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76090
in-theory        76090
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (D or (B or C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76090.        (((not (not A)) -> A) and ((B or (B or C)) -> (D or (B or C)))), M:tm-76, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76091
in-theory        76091
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (C or (A or B)))
theorem-size     19
proof            (modus-ponens tm-73 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76091.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (C or (A or B))), M:tm-73, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76092
in-theory        76092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E or (C or D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76092.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E or (C or D)))), M:tm-69, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76093
in-theory        76093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76093.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-54, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76094
in-theory        76094
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (C or (A or B)))
theorem-size     15
proof            (modus-ponens tm-50 tm-861 ((A Am) (B (or Am Bm)) (C (or Cm (or Am Bm)))))
axioms-used      (tm-8 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76094.        (((A or B) or (A or (A or B))) -> (C or (A or B))), M:tm-50, m:tm-861, u:((A Am) (B (or Am Bm)) (C (or Cm (or Am Bm))))
================================================================
tm-name          tm-76095
in-theory        76095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (C or (A or B)))
theorem-size     13
proof            (modus-ponens tm-49 tm-861 ((A Am) (B (or Am Bm)) (C (or Cm (or Am Bm)))))
axioms-used      (tm-8 tm-6 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-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-76095.        ((A or (A or (A or B))) -> (C or (A or B))), M:tm-49, m:tm-861, u:((A Am) (B (or Am Bm)) (C (or Cm (or Am Bm))))
================================================================
tm-name          tm-76096
in-theory        76096
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (D or (B or C)))
theorem-size     19
proof            (modus-ponens tm-47 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76096.        (((A and (B or (B or C))) or (B or (B or C))) -> (D or (B or C))), M:tm-47, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76097
in-theory        76097
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (D or (A or B)))
theorem-size     19
proof            (modus-ponens tm-46 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76097.        ((((A or (A or B)) and C) or (A or (A or B))) -> (D or (A or B))), M:tm-46, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76098
in-theory        76098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (E or (C or D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76098.        ((A -> (B or A)) and ((C or (C or D)) -> (E or (C or D)))), M:tm-42, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76099
in-theory        76099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (E or (C or D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-76099.        ((A -> (A or B)) and ((C or (C or D)) -> (E or (C or D)))), M:tm-32, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76100
in-theory        76100
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (C or (A or B))))
theorem-size     17
proof            (modus-ponens tm-24 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76100.        ((A or (A or B)) -> ((A or (A or B)) and (C or (A or B)))), M:tm-24, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76101
in-theory        76101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E or (C or D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-76101.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E or (C or D)))), M:tm-23, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76102
in-theory        76102
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (E or (C or D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76102.        (((A and B) -> B) and ((C or (C or D)) -> (E or (C or D)))), M:tm-22, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76103
in-theory        76103
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (E or (C or D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76103.        (((A and B) -> A) and ((C or (C or D)) -> (E or (C or D)))), M:tm-21, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76104
in-theory        76104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76104.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F or (D or E)))), M:tm-20, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76105
in-theory        76105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (E or (C or D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76105.        ((A -> (B -> A)) and ((C or (C or D)) -> (E or (C or D)))), M:tm-19, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76106
in-theory        76106
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (C or (A or B)))) -> (not (A or (A or B))))
theorem-size     19
proof            (modus-ponens tm-9 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76106.        (((A or (A or B)) -> (not (C or (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76107
in-theory        76107
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or C)) -> D) -> (((B or (B or C)) or (A or (B or C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-861 ((A (or Am (or Am Bm))) (B (or Cm (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-7)
proof-size       81
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-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-76107.        (((A or (B or C)) -> D) -> (((B or (B or C)) or (A or (B or C))) -> D)), M:tm-8, m:tm-861, u:((A (or Am (or Am Bm))) (B (or Cm (or Am Bm))))
================================================================
tm-name          tm-76108
in-theory        76108
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (D or (B or C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76108.        (A or ((B or (B or C)) -> (D or (B or C)))), M:tm-7, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76109
in-theory        76109
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-6 tm-8 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-49.           (((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-76109.        (((A or (A or B)) -> (C or (A or B))) or D), M:tm-6, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76110
in-theory        76110
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (D or (B or C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76110.        (A -> (((B or (B or C)) -> (D or (B or C))) and A)), M:tm-5, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76111
in-theory        76111
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (D or (B or C))))
theorem-size     13
proof            (modus-ponens tm-1 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76111.        (A -> ((B or (B or C)) -> (D or (B or C)))), M:tm-1, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-76112
in-theory        76112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76112.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-855, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76113
in-theory        76113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76113.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-808, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76114
in-theory        76114
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (((E and (A or (A or B))) or (A or (A or B))) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76114.        (((A or (A or B)) -> (C -> (D -> C))) and (((E and (A or (A or B))) or (A or (A or B))) -> (C -> (D -> C)))), M:tm-798, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76115
in-theory        76115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76115.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-757, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76116
in-theory        76116
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-76116.        (((A or (A or B)) -> (C -> (D -> C))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (C -> (D -> C)))), M:tm-747, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76117
in-theory        76117
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76117.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (H -> G)))), M:tm-708, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76118
in-theory        76118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76118.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-665, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76119
in-theory        76119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76119.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-622, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76120
in-theory        76120
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D or (A or (A or B)))))
theorem-size     15
proof            (modus-ponens tm-617 tm-862 ((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (-> Dm (or B (or Am (or Am Bm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76120.        ((A or (A or B)) -> (C -> (D or (A or (A or B))))), M:tm-617, m:tm-862, u:((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (-> Dm (or B (or Am (or Am Bm))))))
================================================================
tm-name          tm-76121
in-theory        76121
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76121.        (((A or (A or B)) -> (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76122
in-theory        76122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76122.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-605, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76123
in-theory        76123
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (F or E)) and ((A or (A or B)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76123.        (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (F or E)) and ((A or (A or B)) -> (C -> (D -> C))))), M:tm-595, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76124
in-theory        76124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76124.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-550, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76125
in-theory        76125
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76125.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-540, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76126
in-theory        76126
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76126.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-530, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76127
in-theory        76127
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76127.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-520, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76128
in-theory        76128
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76128.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-510, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76129
in-theory        76129
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76129.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-500, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76130
in-theory        76130
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76130.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H -> G)))), M:tm-490, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76131
in-theory        76131
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76131.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-480, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76132
in-theory        76132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76132.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-469, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76133
in-theory        76133
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((A or (A or B)) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-862 ((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (-> Dm (or (or Am (or Am Bm)) 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76133.        ((A or (A or B)) -> (C -> ((A or (A or B)) or D))), M:tm-464, m:tm-862, u:((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (-> Dm (or (or Am (or Am Bm)) B))))
================================================================
tm-name          tm-76134
in-theory        76134
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76134.        (((A or (A or B)) -> (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76135
in-theory        76135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76135.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-453, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76136
in-theory        76136
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (E or F)) and ((A or (A or B)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76136.        (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (E or F)) and ((A or (A or B)) -> (C -> (D -> C))))), M:tm-443, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76137
in-theory        76137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76137.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-409, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76138
in-theory        76138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76138.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-400, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76139
in-theory        76139
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76139.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-391, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76140
in-theory        76140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76140.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-382, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76141
in-theory        76141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76141.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (H -> G)))), M:tm-373, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76142
in-theory        76142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76142.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-364, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76143
in-theory        76143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76143.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-354, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76144
in-theory        76144
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> ((A or (A or B)) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-862 ((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (-> Dm (-> B (and (or Am (or Am Bm)) B))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76144.        ((A or (A or B)) -> (C -> (D -> ((A or (A or B)) and D)))), M:tm-349, m:tm-862, u:((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (-> Dm (-> B (and (or Am (or Am Bm)) B)))))
================================================================
tm-name          tm-76145
in-theory        76145
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76145.        (((A or (A or B)) -> (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76146
in-theory        76146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76146.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (F -> E)))), M:tm-338, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76147
in-theory        76147
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76147.        (((A or (A or B)) -> (C -> (D -> C))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (D -> C))))), M:tm-328, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76148
in-theory        76148
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76148.        (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (C -> (D -> C))))), M:tm-327, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76149
in-theory        76149
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (((E and F) -> F) and ((A or (A or B)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76149.        (((A or (A or B)) -> (C -> (D -> C))) and (((E and F) -> F) and ((A or (A or B)) -> (C -> (D -> C))))), M:tm-326, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76150
in-theory        76150
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (((E and F) -> E) and ((A or (A or B)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76150.        (((A or (A or B)) -> (C -> (D -> C))) and (((E and F) -> E) and ((A or (A or B)) -> (C -> (D -> C))))), M:tm-325, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76151
in-theory        76151
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-76151.        (((A or (A or B)) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (C -> (D -> C))))), M:tm-324, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76152
in-theory        76152
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (F -> E)) and ((A or (A or B)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76152.        (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (F -> E)) and ((A or (A or B)) -> (C -> (D -> C))))), M:tm-323, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76153
in-theory        76153
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76153.        (((A or (A or B)) -> (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76154
in-theory        76154
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76154.        (((A or (A or B)) -> (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76155
in-theory        76155
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76155.        (((A or (A or B)) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76156
in-theory        76156
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-316 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76156.        (((A or (A or B)) -> (C -> (D -> C))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76157
in-theory        76157
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76157.        (((A or (A or B)) -> (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76158
in-theory        76158
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (((A or (A or B)) -> (not (C -> (D -> C)))) -> (not (A or (A or B)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-76158.        (((A or (A or B)) -> (C -> (D -> C))) and (((A or (A or B)) -> (not (C -> (D -> C)))) -> (not (A or (A or B))))), M:tm-313, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76159
in-theory        76159
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> (((A or (A or B)) or (C -> (D -> C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76159.        (((A or (A or B)) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> (((A or (A or B)) or (C -> (D -> C))) -> E))), M:tm-312, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76160
in-theory        76160
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (E or ((A or (A or B)) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-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-76160.        (((A or (A or B)) -> (C -> (D -> C))) and (E or ((A or (A or B)) -> (C -> (D -> C))))), M:tm-311, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76161
in-theory        76161
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (((A or (A or B)) -> (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76161.        (((A or (A or B)) -> (C -> (D -> C))) and (((A or (A or B)) -> (C -> (D -> C))) or E)), M:tm-310, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76162
in-theory        76162
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (E -> (((A or (A or B)) -> (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-76162.        (((A or (A or B)) -> (C -> (D -> C))) and (E -> (((A or (A or B)) -> (C -> (D -> C))) and E))), M:tm-309, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76163
in-theory        76163
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D -> C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-862 ((A (or Am (or Am Bm))) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-76163.        (((A or (A or B)) -> (C -> (D -> C))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D -> C)))), M:tm-306, m:tm-862, u:((A (or Am (or Am Bm))) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-76164
in-theory        76164
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (E -> ((A or (A or B)) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm 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-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-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-76164.        (((A or (A or B)) -> (C -> (D -> C))) and (E -> ((A or (A or B)) -> (C -> (D -> C))))), M:tm-305, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76165
in-theory        76165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76165.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-303, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76166
in-theory        76166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76166.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-270, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76167
in-theory        76167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76167.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-239, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76168
in-theory        76168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76168.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (H -> G)))), M:tm-210, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76169
in-theory        76169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76169.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-183, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76170
in-theory        76170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76170.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-157, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76171
in-theory        76171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76171.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-147, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76172
in-theory        76172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76172.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-134, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76173
in-theory        76173
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76173.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-125, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76174
in-theory        76174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76174.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H -> G)))), M:tm-113, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76175
in-theory        76175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76175.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-105, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76176
in-theory        76176
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (A or (A or B))))
theorem-size     13
proof            (modus-ponens tm-99 tm-862 ((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (-> Dm (or Am (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76176.        ((A or (A or B)) -> (C -> (A or (A or B)))), M:tm-99, m:tm-862, u:((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (-> Dm (or Am (or Am Bm)))))
================================================================
tm-name          tm-76177
in-theory        76177
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> (A or (A or B)))))
theorem-size     15
proof            (modus-ponens tm-98 tm-862 ((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (-> Dm (-> B (or Am (or Am Bm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76177.        ((A or (A or B)) -> (C -> (D -> (A or (A or B))))), M:tm-98, m:tm-862, u:((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (-> Dm (-> B (or Am (or Am Bm))))))
================================================================
tm-name          tm-76178
in-theory        76178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76178.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (F -> E)))), M:tm-95, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76179
in-theory        76179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76179.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-83, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76180
in-theory        76180
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76180.        (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (E -> D)))), M:tm-76, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76181
in-theory        76181
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76181.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (D -> C))), M:tm-73, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76182
in-theory        76182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76182.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (F -> E)))), M:tm-69, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76183
in-theory        76183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76183.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-54, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76184
in-theory        76184
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-862 ((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76184.        (((A or B) or (A or (A or B))) -> (C -> (D -> C))), M:tm-50, m:tm-862, u:((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76185
in-theory        76185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-49 tm-862 ((A Am) (B (or Am Bm)) (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-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-76185.        ((A or (A or (A or B))) -> (C -> (D -> C))), M:tm-49, m:tm-862, u:((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76186
in-theory        76186
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76186.        (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (E -> D))), M:tm-47, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76187
in-theory        76187
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76187.        ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (E -> D))), M:tm-46, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76188
in-theory        76188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-76188.        ((A -> (B or A)) and ((C or (C or D)) -> (E -> (F -> E)))), M:tm-42, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76189
in-theory        76189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76189.        ((A -> (A or B)) and ((C or (C or D)) -> (E -> (F -> E)))), M:tm-32, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76190
in-theory        76190
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (C -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76190.        ((A or (A or B)) -> ((A or (A or B)) and (C -> (D -> C)))), M:tm-24, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76191
in-theory        76191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76191.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (F -> E)))), M:tm-23, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76192
in-theory        76192
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-76192.        (((A and B) -> B) and ((C or (C or D)) -> (E -> (F -> E)))), M:tm-22, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76193
in-theory        76193
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-76193.        (((A and B) -> A) and ((C or (C or D)) -> (E -> (F -> E)))), M:tm-21, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76194
in-theory        76194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-76194.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-20, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76195
in-theory        76195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76195.        ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (F -> E)))), M:tm-19, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76196
in-theory        76196
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (C -> (D -> C)))) -> (not (A or (A or B))))
theorem-size     19
proof            (modus-ponens tm-9 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76196.        (((A or (A or B)) -> (not (C -> (D -> C)))) -> (not (A or (A or B)))), M:tm-9, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76197
in-theory        76197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (((D or (D or E)) or (A -> (B -> A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-862 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-1)
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-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-76197.        (((A -> (B -> A)) -> C) -> (((D or (D or E)) or (A -> (B -> A))) -> C)), M:tm-8, m:tm-862, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-76198
in-theory        76198
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76198.        (A or ((B or (B or C)) -> (D -> (E -> D)))), M:tm-7, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76199
in-theory        76199
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-862 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76199.        (((A or (A or B)) -> (C -> (D -> C))) or E), M:tm-6, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76200
in-theory        76200
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76200.        (A -> (((B or (B or C)) -> (D -> (E -> D))) and A)), M:tm-5, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76201
in-theory        76201
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-862 ((A (or Am (or Am Bm))) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76201.        (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D -> C))), M:tm-2, m:tm-862, u:((A (or Am (or Am Bm))) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-76202
in-theory        76202
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76202.        (A -> ((B or (B or C)) -> (D -> (E -> D)))), M:tm-1, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-76203
in-theory        76203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76203.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76204
in-theory        76204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76204.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76205
in-theory        76205
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and (A or (A or B))) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-798 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76205.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and (A or (A or B))) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-798, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76206
in-theory        76206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76206.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76207
in-theory        76207
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A or (A or B)) and F) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-747 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76207.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A or (A or B)) and F) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-747, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76208
in-theory        76208
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76208.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76209
in-theory        76209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-863 ((A (-> (or 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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76209.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76210
in-theory        76210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76210.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76211
in-theory        76211
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-14.           (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-76211.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76212
in-theory        76212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76212.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76213
in-theory        76213
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76213.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76214
in-theory        76214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-76214.        (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76215
in-theory        76215
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76215.        ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76216
in-theory        76216
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-76216.        ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76217
in-theory        76217
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76217.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76218
in-theory        76218
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76218.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76219
in-theory        76219
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76219.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76220
in-theory        76220
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76220.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76221
in-theory        76221
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76221.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76222
in-theory        76222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-14.           (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-76222.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76223
in-theory        76223
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76223.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76224
in-theory        76224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-76224.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76225
in-theory        76225
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-14.           (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-76225.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76226
in-theory        76226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-76226.        (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76227
in-theory        76227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-76227.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76228
in-theory        76228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-76228.        ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76229
in-theory        76229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-76229.        ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76230
in-theory        76230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-14.           (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-76230.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76231
in-theory        76231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-14.           (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-76231.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76232
in-theory        76232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76232.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76233
in-theory        76233
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-14.           (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-76233.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76234
in-theory        76234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76234.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76235
in-theory        76235
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-328 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76235.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-328, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76236
in-theory        76236
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76236.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76237
in-theory        76237
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76237.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76238
in-theory        76238
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76238.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76239
in-theory        76239
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76239.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76240
in-theory        76240
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-14.           (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-76240.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76241
in-theory        76241
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-14.           (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-76241.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76242
in-theory        76242
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-14.           (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-76242.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76243
in-theory        76243
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A 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-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-76243.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76244
in-theory        76244
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     31
proof            (modus-ponens tm-316 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-14.           (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-76244.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76245
in-theory        76245
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-14.           (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-76245.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76246
in-theory        76246
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (A or B)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-76246.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (A or B))))), M:tm-313, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76247
in-theory        76247
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> (((A or (A or B)) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     57
proof            (modus-ponens tm-312 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76247.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> (((A or (A or B)) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-312, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76248
in-theory        76248
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-76248.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76249
in-theory        76249
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-14.           (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-76249.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76250
in-theory        76250
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-14.           (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-76250.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76251
in-theory        76251
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (A or B)) -> (C -> (D -> E))) -> ((A or (A or B)) -> ((C -> D) -> (C -> E)))))
theorem-size     45
proof            (modus-ponens tm-306 tm-863 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-76251.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (A or B)) -> (C -> (D -> E))) -> ((A or (A or B)) -> ((C -> D) -> (C -> E))))), M:tm-306, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-76252
in-theory        76252
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-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-14.           (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-76252.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76253
in-theory        76253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76253.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76254
in-theory        76254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76254.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76255
in-theory        76255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76255.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76256
in-theory        76256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76256.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76257
in-theory        76257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76257.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76258
in-theory        76258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76258.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76259
in-theory        76259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76259.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76260
in-theory        76260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76260.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76261
in-theory        76261
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76261.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76262
in-theory        76262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76262.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76263
in-theory        76263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76263.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76264
in-theory        76264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-14.           (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-76264.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76265
in-theory        76265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76265.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76266
in-theory        76266
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76266.        (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76267
in-theory        76267
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-73 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76267.        (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-73, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76268
in-theory        76268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76268.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76269
in-theory        76269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76269.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76270
in-theory        76270
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-50 tm-863 ((A Am) (B (or Am Bm)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76270.        (((A or B) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-50, m:tm-863, u:((A Am) (B (or Am Bm)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76271
in-theory        76271
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-49 tm-863 ((A Am) (B (or Am Bm)) (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-76271.        ((A or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-49, m:tm-863, u:((A Am) (B (or Am Bm)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76272
in-theory        76272
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-47 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76272.        (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-47, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76273
in-theory        76273
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-46 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76273.        ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-46, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76274
in-theory        76274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76274.        ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76275
in-theory        76275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-76275.        ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76276
in-theory        76276
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-24 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76276.        ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-24, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76277
in-theory        76277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76277.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76278
in-theory        76278
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76278.        (((A and B) -> B) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76279
in-theory        76279
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76279.        (((A and B) -> A) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76280
in-theory        76280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76280.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76281
in-theory        76281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76281.        ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76282
in-theory        76282
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (A or B))))
theorem-size     27
proof            (modus-ponens tm-9 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76282.        (((A or (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (A or B)))), M:tm-9, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76283
in-theory        76283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or (E or F)) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-863 ((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       133
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-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-76283.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or (E or F)) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-76284
in-theory        76284
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76284.        (A or ((B or (B or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76285
in-theory        76285
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> 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-49.           (((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-76285.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76286
in-theory        76286
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76286.        (A -> (((B or (B or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76287
in-theory        76287
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> E))) -> ((A or (A or B)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-2 tm-863 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76287.        (((A or (A or B)) -> (C -> (D -> E))) -> ((A or (A or B)) -> ((C -> D) -> (C -> E)))), M:tm-2, m:tm-863, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-76288
in-theory        76288
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-76288.        (A -> ((B or (B or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-76289
in-theory        76289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76289.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-855, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76290
in-theory        76290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76290.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-808, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76291
in-theory        76291
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-798 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76291.        (((A or (A or B)) -> ((C and D) -> C)) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C and D) -> C))), M:tm-798, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76292
in-theory        76292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76292.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-757, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76293
in-theory        76293
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (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-76293.        (((A or (A or B)) -> ((C and D) -> C)) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C and D) -> C))), M:tm-747, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76294
in-theory        76294
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76294.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G and H) -> G))), M:tm-708, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76295
in-theory        76295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76295.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-665, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76296
in-theory        76296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76296.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-622, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76297
in-theory        76297
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76297.        (((A or (A or B)) -> ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76298
in-theory        76298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76298.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-605, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76299
in-theory        76299
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (F or E)) and ((A or (A or B)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76299.        (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (F or E)) and ((A or (A or B)) -> ((C and D) -> C)))), M:tm-595, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76300
in-theory        76300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76300.        (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-550, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76301
in-theory        76301
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76301.        ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-540, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76302
in-theory        76302
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76302.        ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-530, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76303
in-theory        76303
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76303.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-520, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76304
in-theory        76304
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76304.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-510, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76305
in-theory        76305
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76305.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-500, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76306
in-theory        76306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76306.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G and H) -> G))), M:tm-490, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76307
in-theory        76307
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76307.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-480, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76308
in-theory        76308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-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-76308.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-469, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76309
in-theory        76309
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-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-76309.        (((A or (A or B)) -> ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76310
in-theory        76310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76310.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-453, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76311
in-theory        76311
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (E or F)) and ((A or (A or B)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76311.        (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (E or F)) and ((A or (A or B)) -> ((C and D) -> C)))), M:tm-443, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76312
in-theory        76312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76312.        (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-409, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76313
in-theory        76313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76313.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-400, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76314
in-theory        76314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76314.        ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-391, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76315
in-theory        76315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-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-76315.        ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-382, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76316
in-theory        76316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76316.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G and H) -> G))), M:tm-373, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76317
in-theory        76317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-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-76317.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-364, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76318
in-theory        76318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76318.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-354, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76319
in-theory        76319
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76319.        (((A or (A or B)) -> ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76320
in-theory        76320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76320.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E and F) -> E))), M:tm-338, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76321
in-theory        76321
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((A or (A or B)) -> ((A or (A or B)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76321.        (((A or (A or B)) -> ((C and D) -> C)) and ((A or (A or B)) -> ((A or (A or B)) and ((C and D) -> C)))), M:tm-328, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76322
in-theory        76322
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76322.        (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C and D) -> C)))), M:tm-327, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76323
in-theory        76323
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (((E and F) -> F) and ((A or (A or B)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76323.        (((A or (A or B)) -> ((C and D) -> C)) and (((E and F) -> F) and ((A or (A or B)) -> ((C and D) -> C)))), M:tm-326, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76324
in-theory        76324
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (((E and F) -> E) and ((A or (A or B)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76324.        (((A or (A or B)) -> ((C and D) -> C)) and (((E and F) -> E) and ((A or (A or B)) -> ((C and D) -> C)))), M:tm-325, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76325
in-theory        76325
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76325.        (((A or (A or B)) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C and D) -> C)))), M:tm-324, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76326
in-theory        76326
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A 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-76326.        (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C and D) -> C)))), M:tm-323, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76327
in-theory        76327
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76327.        (((A or (A or B)) -> ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76328
in-theory        76328
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76328.        (((A or (A or B)) -> ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76329
in-theory        76329
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-3.            ((A 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-76329.        (((A or (A or B)) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76330
in-theory        76330
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-316 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76330.        (((A or (A or B)) -> ((C and D) -> C)) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76331
in-theory        76331
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76331.        (((A or (A or B)) -> ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76332
in-theory        76332
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (((A or (A or B)) -> (not ((C and D) -> C))) -> (not (A or (A or B)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-76332.        (((A or (A or B)) -> ((C and D) -> C)) and (((A or (A or B)) -> (not ((C and D) -> C))) -> (not (A or (A or B))))), M:tm-313, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76333
in-theory        76333
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> (((A or (A or B)) or ((C and D) -> C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76333.        (((A or (A or B)) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> (((A or (A or B)) or ((C and D) -> C)) -> E))), M:tm-312, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76334
in-theory        76334
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (E or ((A or (A or B)) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-76334.        (((A or (A or B)) -> ((C and D) -> C)) and (E or ((A or (A or B)) -> ((C and D) -> C)))), M:tm-311, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76335
in-theory        76335
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (((A or (A or B)) -> ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76335.        (((A or (A or B)) -> ((C and D) -> C)) and (((A or (A or B)) -> ((C and D) -> C)) or E)), M:tm-310, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76336
in-theory        76336
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (E -> (((A or (A or B)) -> ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-76336.        (((A or (A or B)) -> ((C and D) -> C)) and (E -> (((A or (A or B)) -> ((C and D) -> C)) and E))), M:tm-309, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76337
in-theory        76337
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (((A or (A or B)) -> (C and D)) -> ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-306 tm-864 ((A (or Am (or Am Bm))) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-76337.        (((A or (A or B)) -> ((C and D) -> C)) and (((A or (A or B)) -> (C and D)) -> ((A or (A or B)) -> C))), M:tm-306, m:tm-864, u:((A (or Am (or Am Bm))) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-76338
in-theory        76338
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (E -> ((A or (A or B)) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-3.            ((A 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-76338.        (((A or (A or B)) -> ((C and D) -> C)) and (E -> ((A or (A or B)) -> ((C and D) -> C)))), M:tm-305, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76339
in-theory        76339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76339.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-303, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76340
in-theory        76340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76340.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-270, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76341
in-theory        76341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76341.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-239, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76342
in-theory        76342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76342.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G and H) -> G))), M:tm-210, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76343
in-theory        76343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76343.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-183, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76344
in-theory        76344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76344.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-157, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76345
in-theory        76345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76345.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-147, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76346
in-theory        76346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76346.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-134, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76347
in-theory        76347
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76347.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-125, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76348
in-theory        76348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76348.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G and H) -> G))), M:tm-113, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76349
in-theory        76349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76349.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-105, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76350
in-theory        76350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76350.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E and F) -> E))), M:tm-95, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76351
in-theory        76351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76351.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-83, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76352
in-theory        76352
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76352.        (((not (not A)) -> A) and ((B or (B or C)) -> ((D and E) -> D))), M:tm-76, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76353
in-theory        76353
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-73 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76353.        (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C and D) -> C)), M:tm-73, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76354
in-theory        76354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76354.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E and F) -> E))), M:tm-69, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76355
in-theory        76355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76355.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-54, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76356
in-theory        76356
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-50 tm-864 ((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76356.        (((A or B) or (A or (A or B))) -> ((C and D) -> C)), M:tm-50, m:tm-864, u:((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76357
in-theory        76357
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-49 tm-864 ((A Am) (B (or Am Bm)) (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-3.            ((A 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-76357.        ((A or (A or (A or B))) -> ((C and D) -> C)), M:tm-49, m:tm-864, u:((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76358
in-theory        76358
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-47 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76358.        (((A and (B or (B or C))) or (B or (B or C))) -> ((D and E) -> D)), M:tm-47, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76359
in-theory        76359
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-46 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76359.        ((((A or (A or B)) and C) or (A or (A or B))) -> ((D and E) -> D)), M:tm-46, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76360
in-theory        76360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76360.        ((A -> (B or A)) and ((C or (C or D)) -> ((E and F) -> E))), M:tm-42, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76361
in-theory        76361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76361.        ((A -> (A or B)) and ((C or (C or D)) -> ((E and F) -> E))), M:tm-32, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76362
in-theory        76362
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76362.        ((A or (A or B)) -> ((A or (A or B)) and ((C and D) -> C))), M:tm-24, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76363
in-theory        76363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76363.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E and F) -> E))), M:tm-23, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76364
in-theory        76364
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76364.        (((A and B) -> B) and ((C or (C or D)) -> ((E and F) -> E))), M:tm-22, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76365
in-theory        76365
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76365.        (((A and B) -> A) and ((C or (C or D)) -> ((E and F) -> E))), M:tm-21, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76366
in-theory        76366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76366.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-20, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76367
in-theory        76367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76367.        ((A -> (B -> A)) and ((C or (C or D)) -> ((E and F) -> E))), M:tm-19, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76368
in-theory        76368
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not ((C and D) -> C))) -> (not (A or (A or B))))
theorem-size     19
proof            (modus-ponens tm-9 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76368.        (((A or (A or B)) -> (not ((C and D) -> C))) -> (not (A or (A or B)))), M:tm-9, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76369
in-theory        76369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (((D or (D or E)) or ((A and B) -> A)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-864 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-76369.        ((((A and B) -> A) -> C) -> (((D or (D or E)) or ((A and B) -> A)) -> C)), M:tm-8, m:tm-864, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-76370
in-theory        76370
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76370.        (A or ((B or (B or C)) -> ((D and E) -> D))), M:tm-7, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76371
in-theory        76371
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-864 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76371.        (((A or (A or B)) -> ((C and D) -> C)) or E), M:tm-6, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76372
in-theory        76372
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76372.        (A -> (((B or (B or C)) -> ((D and E) -> D)) and A)), M:tm-5, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76373
in-theory        76373
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C and D)) -> ((A or (A or B)) -> C))
theorem-size     17
proof            (modus-ponens tm-2 tm-864 ((A (or Am (or Am Bm))) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76373.        (((A or (A or B)) -> (C and D)) -> ((A or (A or B)) -> C)), M:tm-2, m:tm-864, u:((A (or Am (or Am Bm))) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-76374
in-theory        76374
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76374.        (A -> ((B or (B or C)) -> ((D and E) -> D))), M:tm-1, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-76375
in-theory        76375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76375.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-855, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76376
in-theory        76376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76376.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-808, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76377
in-theory        76377
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-798 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76377.        (((A or (A or B)) -> ((C and D) -> D)) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C and D) -> D))), M:tm-798, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76378
in-theory        76378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76378.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-757, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76379
in-theory        76379
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-747 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76379.        (((A or (A or B)) -> ((C and D) -> D)) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C and D) -> D))), M:tm-747, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76380
in-theory        76380
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76380.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G and H) -> H))), M:tm-708, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76381
in-theory        76381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76381.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-665, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76382
in-theory        76382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76382.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-622, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76383
in-theory        76383
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76383.        (((A or (A or B)) -> ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76384
in-theory        76384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76384.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-605, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76385
in-theory        76385
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (F or E)) and ((A or (A or B)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76385.        (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (F or E)) and ((A or (A or B)) -> ((C and D) -> D)))), M:tm-595, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76386
in-theory        76386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76386.        (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-550, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76387
in-theory        76387
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76387.        ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-540, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76388
in-theory        76388
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76388.        ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-530, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76389
in-theory        76389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76389.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-520, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76390
in-theory        76390
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76390.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-510, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76391
in-theory        76391
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76391.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-500, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76392
in-theory        76392
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76392.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G and H) -> H))), M:tm-490, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76393
in-theory        76393
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76393.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-480, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76394
in-theory        76394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-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-76394.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-469, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76395
in-theory        76395
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-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-76395.        (((A or (A or B)) -> ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76396
in-theory        76396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76396.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-453, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76397
in-theory        76397
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (E or F)) and ((A or (A or B)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76397.        (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (E or F)) and ((A or (A or B)) -> ((C and D) -> D)))), M:tm-443, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76398
in-theory        76398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76398.        (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-409, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76399
in-theory        76399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76399.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-400, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76400
in-theory        76400
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-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-76400.        ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-391, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76401
in-theory        76401
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76401.        ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-382, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76402
in-theory        76402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76402.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G and H) -> H))), M:tm-373, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76403
in-theory        76403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-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-76403.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-364, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76404
in-theory        76404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76404.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-354, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76405
in-theory        76405
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76405.        (((A or (A or B)) -> ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76406
in-theory        76406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76406.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E and F) -> F))), M:tm-338, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76407
in-theory        76407
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((A or (A or B)) -> ((A or (A or B)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-328 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76407.        (((A or (A or B)) -> ((C and D) -> D)) and ((A or (A or B)) -> ((A or (A or B)) and ((C and D) -> D)))), M:tm-328, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76408
in-theory        76408
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76408.        (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C and D) -> D)))), M:tm-327, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76409
in-theory        76409
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (((E and F) -> F) and ((A or (A or B)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76409.        (((A or (A or B)) -> ((C and D) -> D)) and (((E and F) -> F) and ((A or (A or B)) -> ((C and D) -> D)))), M:tm-326, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76410
in-theory        76410
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (((E and F) -> E) and ((A or (A or B)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76410.        (((A or (A or B)) -> ((C and D) -> D)) and (((E and F) -> E) and ((A or (A or B)) -> ((C and D) -> D)))), M:tm-325, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76411
in-theory        76411
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76411.        (((A or (A or B)) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C and D) -> D)))), M:tm-324, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76412
in-theory        76412
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A 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-76412.        (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C and D) -> D)))), M:tm-323, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76413
in-theory        76413
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am 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-76413.        (((A or (A or B)) -> ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76414
in-theory        76414
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76414.        (((A or (A or B)) -> ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76415
in-theory        76415
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A 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-76415.        (((A or (A or B)) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76416
in-theory        76416
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-316 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76416.        (((A or (A or B)) -> ((C and D) -> D)) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76417
in-theory        76417
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76417.        (((A or (A or B)) -> ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76418
in-theory        76418
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (((A or (A or B)) -> (not ((C and D) -> D))) -> (not (A or (A or B)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-76418.        (((A or (A or B)) -> ((C and D) -> D)) and (((A or (A or B)) -> (not ((C and D) -> D))) -> (not (A or (A or B))))), M:tm-313, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76419
in-theory        76419
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> (((A or (A or B)) or ((C and D) -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76419.        (((A or (A or B)) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> (((A or (A or B)) or ((C and D) -> D)) -> E))), M:tm-312, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76420
in-theory        76420
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (E or ((A or (A or B)) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-76420.        (((A or (A or B)) -> ((C and D) -> D)) and (E or ((A or (A or B)) -> ((C and D) -> D)))), M:tm-311, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76421
in-theory        76421
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (((A or (A or B)) -> ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76421.        (((A or (A or B)) -> ((C and D) -> D)) and (((A or (A or B)) -> ((C and D) -> D)) or E)), M:tm-310, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76422
in-theory        76422
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (E -> (((A or (A or B)) -> ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-76422.        (((A or (A or B)) -> ((C and D) -> D)) and (E -> (((A or (A or B)) -> ((C and D) -> D)) and E))), M:tm-309, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76423
in-theory        76423
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (((A or (A or B)) -> (C and D)) -> ((A or (A or B)) -> D)))
theorem-size     29
proof            (modus-ponens tm-306 tm-865 ((A (or Am (or Am Bm))) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-76423.        (((A or (A or B)) -> ((C and D) -> D)) and (((A or (A or B)) -> (C and D)) -> ((A or (A or B)) -> D))), M:tm-306, m:tm-865, u:((A (or Am (or Am Bm))) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-76424
in-theory        76424
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (E -> ((A or (A or B)) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-4.            ((A 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-76424.        (((A or (A or B)) -> ((C and D) -> D)) and (E -> ((A or (A or B)) -> ((C and D) -> D)))), M:tm-305, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76425
in-theory        76425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76425.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-303, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76426
in-theory        76426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76426.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-270, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76427
in-theory        76427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76427.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-239, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76428
in-theory        76428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76428.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G and H) -> H))), M:tm-210, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76429
in-theory        76429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76429.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-183, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76430
in-theory        76430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am 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-76430.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-157, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76431
in-theory        76431
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76431.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-147, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76432
in-theory        76432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76432.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-134, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76433
in-theory        76433
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76433.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-125, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76434
in-theory        76434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76434.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G and H) -> H))), M:tm-113, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76435
in-theory        76435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76435.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-105, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76436
in-theory        76436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76436.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E and F) -> F))), M:tm-95, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76437
in-theory        76437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76437.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-83, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76438
in-theory        76438
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76438.        (((not (not A)) -> A) and ((B or (B or C)) -> ((D and E) -> E))), M:tm-76, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76439
in-theory        76439
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-73 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76439.        (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C and D) -> D)), M:tm-73, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76440
in-theory        76440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76440.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E and F) -> F))), M:tm-69, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76441
in-theory        76441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76441.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-54, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76442
in-theory        76442
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-50 tm-865 ((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76442.        (((A or B) or (A or (A or B))) -> ((C and D) -> D)), M:tm-50, m:tm-865, u:((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76443
in-theory        76443
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-49 tm-865 ((A Am) (B (or Am Bm)) (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-4.            ((A 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-76443.        ((A or (A or (A or B))) -> ((C and D) -> D)), M:tm-49, m:tm-865, u:((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76444
in-theory        76444
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-47 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76444.        (((A and (B or (B or C))) or (B or (B or C))) -> ((D and E) -> E)), M:tm-47, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76445
in-theory        76445
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-46 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76445.        ((((A or (A or B)) and C) or (A or (A or B))) -> ((D and E) -> E)), M:tm-46, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76446
in-theory        76446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76446.        ((A -> (B or A)) and ((C or (C or D)) -> ((E and F) -> F))), M:tm-42, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76447
in-theory        76447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76447.        ((A -> (A or B)) and ((C or (C or D)) -> ((E and F) -> F))), M:tm-32, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76448
in-theory        76448
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-24 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76448.        ((A or (A or B)) -> ((A or (A or B)) and ((C and D) -> D))), M:tm-24, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76449
in-theory        76449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76449.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E and F) -> F))), M:tm-23, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76450
in-theory        76450
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76450.        (((A and B) -> B) and ((C or (C or D)) -> ((E and F) -> F))), M:tm-22, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76451
in-theory        76451
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76451.        (((A and B) -> A) and ((C or (C or D)) -> ((E and F) -> F))), M:tm-21, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76452
in-theory        76452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76452.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-20, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76453
in-theory        76453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76453.        ((A -> (B -> A)) and ((C or (C or D)) -> ((E and F) -> F))), M:tm-19, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76454
in-theory        76454
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not ((C and D) -> D))) -> (not (A or (A or B))))
theorem-size     19
proof            (modus-ponens tm-9 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76454.        (((A or (A or B)) -> (not ((C and D) -> D))) -> (not (A or (A or B)))), M:tm-9, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76455
in-theory        76455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (((D or (D or E)) or ((A and B) -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-865 ((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-76455.        ((((A and B) -> B) -> C) -> (((D or (D or E)) or ((A and B) -> B)) -> C)), M:tm-8, m:tm-865, u:((A (or Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-76456
in-theory        76456
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76456.        (A or ((B or (B or C)) -> ((D and E) -> E))), M:tm-7, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76457
in-theory        76457
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-865 ((A (-> (or Am (or Am Bm)) (-> (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-49.           (((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-76457.        (((A or (A or B)) -> ((C and D) -> D)) or E), M:tm-6, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76458
in-theory        76458
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76458.        (A -> (((B or (B or C)) -> ((D and E) -> E)) and A)), M:tm-5, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76459
in-theory        76459
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C and D)) -> ((A or (A or B)) -> D))
theorem-size     17
proof            (modus-ponens tm-2 tm-865 ((A (or Am (or Am Bm))) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76459.        (((A or (A or B)) -> (C and D)) -> ((A or (A or B)) -> D)), M:tm-2, m:tm-865, u:((A (or Am (or Am Bm))) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-76460
in-theory        76460
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76460.        (A -> ((B or (B or C)) -> ((D and E) -> E))), M:tm-1, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-76461
in-theory        76461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-855 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76461.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-855, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76462
in-theory        76462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-808 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76462.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-808, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76463
in-theory        76463
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-798 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76463.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B)))), M:tm-798, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76464
in-theory        76464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-757 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76464.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-757, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76465
in-theory        76465
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-747 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76465.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B)))), M:tm-747, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76466
in-theory        76466
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F))))
theorem-size     41
proof            (modus-ponens tm-708 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76466.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F)))), M:tm-708, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76467
in-theory        76467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-665 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76467.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-665, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76468
in-theory        76468
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((D -> (E -> D)) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-623 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76468.        ((A or (A or B)) -> (C or ((D -> (E -> D)) and (A or B)))), M:tm-623, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76469
in-theory        76469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-622 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76469.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-622, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76470
in-theory        76470
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76470.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (F or E))), M:tm-609, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76471
in-theory        76471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-605 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76471.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-605, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76472
in-theory        76472
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (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-76472.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))), M:tm-595, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76473
in-theory        76473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-550 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76473.        (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-550, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76474
in-theory        76474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-540 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76474.        ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-540, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76475
in-theory        76475
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-530 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76475.        ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-530, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76476
in-theory        76476
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-520 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76476.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-520, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76477
in-theory        76477
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-510 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76477.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-510, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76478
in-theory        76478
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-500 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76478.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-500, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76479
in-theory        76479
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-490 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76479.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F)))), M:tm-490, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76480
in-theory        76480
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-480 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76480.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-480, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76481
in-theory        76481
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D -> C)) and (A or B)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
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-49.           (((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-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-76481.        ((A or (A or B)) -> (((C -> (D -> C)) and (A or B)) or E)), M:tm-470, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76482
in-theory        76482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-469 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76482.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-469, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76483
in-theory        76483
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76483.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (E or F))), M:tm-456, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76484
in-theory        76484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-453 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76484.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-453, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76485
in-theory        76485
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76485.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))), M:tm-443, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76486
in-theory        76486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-409 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76486.        (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-409, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76487
in-theory        76487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-400 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76487.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-400, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76488
in-theory        76488
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-391 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76488.        ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-391, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76489
in-theory        76489
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-382 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76489.        ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-382, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76490
in-theory        76490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-373 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76490.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F)))), M:tm-373, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76491
in-theory        76491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-364 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76491.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-364, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76492
in-theory        76492
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D -> (E -> D)) and (A or B)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76492.        ((A or (A or B)) -> (C -> (((D -> (E -> D)) and (A or B)) and C))), M:tm-355, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76493
in-theory        76493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-354 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76493.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-354, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76494
in-theory        76494
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76494.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76495
in-theory        76495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D))))
theorem-size     25
proof            (modus-ponens tm-338 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76495.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D)))), M:tm-338, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76496
in-theory        76496
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76496.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> C)) and (A or B))))), M:tm-328, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76497
in-theory        76497
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (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-76497.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))), M:tm-327, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76498
in-theory        76498
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (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-76498.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))), M:tm-326, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76499
in-theory        76499
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (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-76499.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))), M:tm-325, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76500
in-theory        76500
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76500.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))), M:tm-324, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76501
in-theory        76501
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76501.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))), M:tm-323, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76502
in-theory        76502
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76502.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E and F) -> F)), M:tm-322, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76503
in-theory        76503
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76503.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E and F) -> E)), M:tm-320, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76504
in-theory        76504
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76504.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76505
in-theory        76505
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     27
proof            (modus-ponens tm-316 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76505.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76506
in-theory        76506
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76506.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (F -> E))), M:tm-315, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76507
in-theory        76507
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((A or (A or B)) -> (not ((C -> (D -> C)) and (A or B)))) -> (not (A or (A or B)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (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-76507.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((A or (A or B)) -> (not ((C -> (D -> C)) and (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76508
in-theory        76508
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((((C -> (D -> C)) and (A or B)) -> E) -> (((A or (A or B)) or ((C -> (D -> C)) and (A or B))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (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-76508.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((((C -> (D -> C)) and (A or B)) -> E) -> (((A or (A or B)) or ((C -> (D -> C)) and (A or B))) -> E))), M:tm-312, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76509
in-theory        76509
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E or ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-1.            (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-76509.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E or ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))), M:tm-311, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76510
in-theory        76510
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76510.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) or E)), M:tm-310, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76511
in-theory        76511
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (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-76511.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and E))), M:tm-309, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76512
in-theory        76512
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76512.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (E -> ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))), M:tm-305, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76513
in-theory        76513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-303 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76513.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-303, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76514
in-theory        76514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-270 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76514.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-270, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76515
in-theory        76515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-239 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76515.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-239, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76516
in-theory        76516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-210 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76516.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F)))), M:tm-210, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76517
in-theory        76517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-183 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76517.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-183, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76518
in-theory        76518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-157 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76518.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-157, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76519
in-theory        76519
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-147 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76519.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-147, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76520
in-theory        76520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-134 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76520.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-134, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76521
in-theory        76521
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-125 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76521.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-125, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76522
in-theory        76522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-113 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76522.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F)))), M:tm-113, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76523
in-theory        76523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-105 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76523.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-105, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76524
in-theory        76524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-95 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76524.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D)))), M:tm-95, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76525
in-theory        76525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (E -> D)) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-84 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76525.        ((A or (A or B)) -> (C -> ((D -> (E -> D)) and (A or B)))), M:tm-84, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76526
in-theory        76526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-83 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76526.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-83, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76527
in-theory        76527
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (E -> D)) and (B or C))))
theorem-size     21
proof            (modus-ponens tm-76 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76527.        (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (E -> D)) and (B or C)))), M:tm-76, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76528
in-theory        76528
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-73 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 tm-5 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76528.        (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B))), M:tm-73, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76529
in-theory        76529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D))))
theorem-size     27
proof            (modus-ponens tm-69 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76529.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D)))), M:tm-69, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76530
in-theory        76530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-54 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76530.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-54, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76531
in-theory        76531
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-866 ((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-7 tm-6 tm-5 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76531.        (((A or B) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B))), M:tm-50, m:tm-866, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76532
in-theory        76532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> ((C -> (D -> C)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-866 ((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (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-76532.        ((A or (A or (A or B))) -> ((C -> (D -> C)) and (A or B))), M:tm-49, m:tm-866, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76533
in-theory        76533
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (E -> D)) and (B or C)))
theorem-size     23
proof            (modus-ponens tm-47 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 tm-5 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76533.        (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (E -> D)) and (B or C))), M:tm-47, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76534
in-theory        76534
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (E -> D)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-46 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 tm-5 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76534.        ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (E -> D)) and (A or B))), M:tm-46, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76535
in-theory        76535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-42 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76535.        ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D)))), M:tm-42, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76536
in-theory        76536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-32 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-76536.        ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D)))), M:tm-32, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76537
in-theory        76537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> C)) and (A or B))))
theorem-size     21
proof            (modus-ponens tm-24 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76537.        ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> C)) and (A or B)))), M:tm-24, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76538
in-theory        76538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-23 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (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-76538.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D)))), M:tm-23, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76539
in-theory        76539
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-22 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76539.        (((A and B) -> B) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D)))), M:tm-22, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76540
in-theory        76540
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-21 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76540.        (((A and B) -> A) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D)))), M:tm-21, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76541
in-theory        76541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-20 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76541.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-20, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76542
in-theory        76542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-19 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76542.        ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (F -> E)) and (C or D)))), M:tm-19, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76543
in-theory        76543
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not ((C -> (D -> C)) and (A or B)))) -> (not (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-9 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 tm-5 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76543.        (((A or (A or B)) -> (not ((C -> (D -> C)) and (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76544
in-theory        76544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and (C or D)) -> E) -> (((C or (C or D)) or ((A -> (B -> A)) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-866 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
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-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-76544.        ((((A -> (B -> A)) and (C or D)) -> E) -> (((C or (C or D)) or ((A -> (B -> A)) and (C or D))) -> E)), M:tm-8, m:tm-866, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-76545
in-theory        76545
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> ((D -> (E -> D)) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-7 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-7 tm-8 tm-6 tm-5 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76545.        (A or ((B or (B or C)) -> ((D -> (E -> D)) and (B or C)))), M:tm-7, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76546
in-theory        76546
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-6 tm-8 tm-5 tm-1)
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-49.           (((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-76546.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) or E), M:tm-6, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76547
in-theory        76547
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> ((D -> (E -> D)) and (B or C))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76547.        (A -> (((B or (B or C)) -> ((D -> (E -> D)) and (B or C))) and A)), M:tm-5, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76548
in-theory        76548
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> ((D -> (E -> D)) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-1 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76548.        (A -> ((B or (B or C)) -> ((D -> (E -> D)) and (B or C)))), M:tm-1, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-76549
in-theory        76549
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     41
proof            (modus-ponens tm-855 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76549.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-855, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76550
in-theory        76550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-808 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76550.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-808, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76551
in-theory        76551
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((F and (A or (A or B))) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))
theorem-size     55
proof            (modus-ponens tm-798 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76551.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((F and (A or (A or B))) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))), M:tm-798, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76552
in-theory        76552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-757 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76552.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-757, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76553
in-theory        76553
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((((A or (A or B)) and F) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))
theorem-size     55
proof            (modus-ponens tm-747 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-20.           (A -> (((B -> (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-76553.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((((A or (A or B)) and F) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))), M:tm-747, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76554
in-theory        76554
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F))))
theorem-size     49
proof            (modus-ponens tm-708 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76554.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F)))), M:tm-708, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76555
in-theory        76555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-665 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76555.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-665, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76556
in-theory        76556
times-derived    1
----------------------------------------------------------------
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-623 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76556.        ((A or (A or B)) -> (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or B)))), M:tm-623, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76557
in-theory        76557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-622 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76557.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-622, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76558
in-theory        76558
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-20.           (A -> (((B -> (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-76558.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (G or F))), M:tm-609, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76559
in-theory        76559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-605 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76559.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-605, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76560
in-theory        76560
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (G or F)) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-20.           (A -> (((B -> (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-76560.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (G or F)) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-595, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76561
in-theory        76561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-550 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76561.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-550, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76562
in-theory        76562
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-540 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76562.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-540, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76563
in-theory        76563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-530 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76563.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-530, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76564
in-theory        76564
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-520 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76564.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-520, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76565
in-theory        76565
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-510 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76565.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-510, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76566
in-theory        76566
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-500 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76566.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-500, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76567
in-theory        76567
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-490 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76567.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F)))), M:tm-490, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76568
in-theory        76568
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-480 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76568.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-480, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76569
in-theory        76569
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)) or F))
theorem-size     25
proof            (modus-ponens tm-470 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
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-49.           (((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-20.           (A -> (((B -> (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-76569.        ((A or (A or B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)) or F)), M:tm-470, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76570
in-theory        76570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-469 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
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-49.           (((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-20.           (A -> (((B -> (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-76570.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-469, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76571
in-theory        76571
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76571.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (F or G))), M:tm-456, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76572
in-theory        76572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-453 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76572.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-453, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76573
in-theory        76573
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (F or G)) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-20.           (A -> (((B -> (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-76573.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (F or G)) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-443, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76574
in-theory        76574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-409 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76574.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-409, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76575
in-theory        76575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-400 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76575.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-400, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76576
in-theory        76576
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-391 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76576.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-391, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76577
in-theory        76577
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-382 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76577.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-382, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76578
in-theory        76578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-373 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 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-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-20.           (A -> (((B -> (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-76578.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F)))), M:tm-373, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76579
in-theory        76579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-364 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
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-49.           (((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-20.           (A -> (((B -> (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-76579.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-364, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76580
in-theory        76580
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or B)) and C)))
theorem-size     27
proof            (modus-ponens tm-355 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-20.           (A -> (((B -> (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-76580.        ((A or (A or B)) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or B)) and C))), M:tm-355, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76581
in-theory        76581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-354 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76581.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-354, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76582
in-theory        76582
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-20.           (A -> (((B -> (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-76582.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76583
in-theory        76583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D))))
theorem-size     33
proof            (modus-ponens tm-338 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76583.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D)))), M:tm-338, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76584
in-theory        76584
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-20.           (A -> (((B -> (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-76584.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-328, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76585
in-theory        76585
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (G -> (F and G))) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76585.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (G -> (F and G))) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-327, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76586
in-theory        76586
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((F and G) -> G) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-20.           (A -> (((B -> (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-76586.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((F and G) -> G) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-326, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76587
in-theory        76587
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((F and G) -> F) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-20.           (A -> (((B -> (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-76587.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((F and G) -> F) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-325, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76588
in-theory        76588
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76588.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-324, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76589
in-theory        76589
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (G -> F)) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-20.           (A -> (((B -> (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-76589.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (G -> F)) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-323, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76590
in-theory        76590
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-20.           (A -> (((B -> (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-76590.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F and G) -> G)), M:tm-322, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76591
in-theory        76591
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-20.           (A -> (((B -> (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-76591.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F and G) -> F)), M:tm-320, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76592
in-theory        76592
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-20.           (A -> (((B -> (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-76592.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76593
in-theory        76593
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     35
proof            (modus-ponens tm-316 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-20.           (A -> (((B -> (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-76593.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76594
in-theory        76594
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-20.           (A -> (((B -> (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-76594.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (G -> F))), M:tm-315, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76595
in-theory        76595
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((A or (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))) -> (not (A or (A or B)))))
theorem-size     55
proof            (modus-ponens tm-313 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-20.           (A -> (((B -> (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-76595.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((A or (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76596
in-theory        76596
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)) -> F) -> (((A or (A or B)) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) -> F)))
theorem-size     69
proof            (modus-ponens tm-312 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76596.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)) -> F) -> (((A or (A or B)) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) -> F))), M:tm-312, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76597
in-theory        76597
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F or ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-20.           (A -> (((B -> (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-76597.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F or ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-311, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76598
in-theory        76598
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
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-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-20.           (A -> (((B -> (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-76598.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) or F)), M:tm-310, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76599
in-theory        76599
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-20.           (A -> (((B -> (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-76599.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and F))), M:tm-309, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76600
in-theory        76600
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-20.           (A -> (((B -> (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-76600.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (F -> ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-305, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76601
in-theory        76601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-303 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76601.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-303, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76602
in-theory        76602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-270 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76602.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-270, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76603
in-theory        76603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-239 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76603.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-239, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76604
in-theory        76604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F))))
theorem-size     41
proof            (modus-ponens tm-210 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76604.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F)))), M:tm-210, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76605
in-theory        76605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-183 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76605.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-183, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76606
in-theory        76606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-157 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76606.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-157, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76607
in-theory        76607
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     39
proof            (modus-ponens tm-147 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-20.           (A -> (((B -> (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-76607.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-147, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76608
in-theory        76608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-134 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76608.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-134, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76609
in-theory        76609
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     39
proof            (modus-ponens tm-125 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-20.           (A -> (((B -> (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-76609.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-125, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76610
in-theory        76610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-113 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76610.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F)))), M:tm-113, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76611
in-theory        76611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     43
proof            (modus-ponens tm-105 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-20.           (A -> (((B -> (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-76611.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-105, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76612
in-theory        76612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D))))
theorem-size     31
proof            (modus-ponens tm-95 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-20.           (A -> (((B -> (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-76612.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D)))), M:tm-95, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76613
in-theory        76613
times-derived    1
----------------------------------------------------------------
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-84 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76613.        ((A or (A or B)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or B)))), M:tm-84, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76614
in-theory        76614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-83 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76614.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-83, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76615
in-theory        76615
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C))))
theorem-size     29
proof            (modus-ponens tm-76 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76615.        (((not (not A)) -> A) and ((B or (B or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C)))), M:tm-76, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76616
in-theory        76616
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))
theorem-size     31
proof            (modus-ponens tm-73 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76616.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))), M:tm-73, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76617
in-theory        76617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D))))
theorem-size     35
proof            (modus-ponens tm-69 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76617.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D)))), M:tm-69, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76618
in-theory        76618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-54 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76618.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-54, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76619
in-theory        76619
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))
theorem-size     27
proof            (modus-ponens tm-50 tm-867 ((A Am) (B (or Am Bm)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76619.        (((A or B) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))), M:tm-50, m:tm-867, u:((A Am) (B (or Am Bm)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76620
in-theory        76620
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-49 tm-867 ((A Am) (B (or Am Bm)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-6 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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76620.        ((A or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))), M:tm-49, m:tm-867, u:((A Am) (B (or Am Bm)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76621
in-theory        76621
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C)))
theorem-size     31
proof            (modus-ponens tm-47 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76621.        (((A and (B or (B or C))) or (B or (B or C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C))), M:tm-47, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76622
in-theory        76622
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or B)))
theorem-size     31
proof            (modus-ponens tm-46 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76622.        ((((A or (A or B)) and C) or (A or (A or B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or B))), M:tm-46, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76623
in-theory        76623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-42 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-42.           (A -> ((B -> (C or B)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76623.        ((A -> (B or A)) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D)))), M:tm-42, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76624
in-theory        76624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-32 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-20.           (A -> (((B -> (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-76624.        ((A -> (A or B)) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D)))), M:tm-32, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76625
in-theory        76625
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-24 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76625.        ((A or (A or B)) -> ((A or (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))), M:tm-24, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76626
in-theory        76626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D))))
theorem-size     31
proof            (modus-ponens tm-23 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76626.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D)))), M:tm-23, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76627
in-theory        76627
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-22 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76627.        (((A and B) -> B) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D)))), M:tm-22, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76628
in-theory        76628
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-21 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76628.        (((A and B) -> A) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D)))), M:tm-21, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76629
in-theory        76629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-20 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76629.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-20, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76630
in-theory        76630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-19 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-76630.        ((A -> (B -> A)) and ((C or (C or D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (C or D)))), M:tm-19, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76631
in-theory        76631
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))) -> (not (A or (A or B))))
theorem-size     31
proof            (modus-ponens tm-9 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76631.        (((A or (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76632
in-theory        76632
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or E)) -> F) -> (((D or (D or E)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or E))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-867 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       149
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-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-76632.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or E)) -> F) -> (((D or (D or E)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or E))) -> F)), M:tm-8, m:tm-867, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-76633
in-theory        76633
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C))))
theorem-size     25
proof            (modus-ponens tm-7 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76633.        (A or ((B or (B or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C)))), M:tm-7, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76634
in-theory        76634
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-6 tm-8 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-49.           (((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-76634.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) or F), M:tm-6, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76635
in-theory        76635
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-76635.        (A -> (((B or (B or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C))) and A)), M:tm-5, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76636
in-theory        76636
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C))))
theorem-size     25
proof            (modus-ponens tm-1 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76636.        (A -> ((B or (B or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or C)))), M:tm-1, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-76637
in-theory        76637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-855 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76637.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-855, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76638
in-theory        76638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-808 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76638.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-808, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76639
in-theory        76639
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> (((C and D) -> C) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-798 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76639.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> (((C and D) -> C) and (A or B)))), M:tm-798, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76640
in-theory        76640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-757 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-76640.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-757, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76641
in-theory        76641
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (((C and D) -> C) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-747 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76641.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (((C and D) -> C) and (A or B)))), M:tm-747, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76642
in-theory        76642
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (((G and H) -> G) and (E or F))))
theorem-size     41
proof            (modus-ponens tm-708 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76642.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (((G and H) -> G) and (E or F)))), M:tm-708, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76643
in-theory        76643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-665 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76643.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-665, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76644
in-theory        76644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (((D and E) -> D) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-623 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76644.        ((A or (A or B)) -> (C or (((D and E) -> D) and (A or B)))), M:tm-623, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76645
in-theory        76645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-622 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76645.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-622, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76646
in-theory        76646
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76646.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (F or E))), M:tm-609, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76647
in-theory        76647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-605 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76647.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-605, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76648
in-theory        76648
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> (((C and D) -> C) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-3.            ((A and B) -> 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-76648.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> (((C and D) -> C) and (A or B))))), M:tm-595, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76649
in-theory        76649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-550 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-3.            ((A and B) -> 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-76649.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-550, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76650
in-theory        76650
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-540 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76650.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-540, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76651
in-theory        76651
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-530 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-3.            ((A and B) -> 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-76651.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-530, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76652
in-theory        76652
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-520 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76652.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-520, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76653
in-theory        76653
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-510 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76653.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-510, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76654
in-theory        76654
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-500 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-76654.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-500, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76655
in-theory        76655
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G and H) -> G) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-490 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76655.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G and H) -> G) and (E or F)))), M:tm-490, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76656
in-theory        76656
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-480 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76656.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-480, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76657
in-theory        76657
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C and D) -> C) and (A or B)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
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-49.           (((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-76657.        ((A or (A or B)) -> ((((C and D) -> C) and (A or B)) or E)), M:tm-470, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76658
in-theory        76658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-469 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
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-49.           (((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-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-76658.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-469, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76659
in-theory        76659
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
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-49.           (((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-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-76659.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (E or F))), M:tm-456, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76660
in-theory        76660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-453 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-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-76660.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-453, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76661
in-theory        76661
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> (((C and D) -> C) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-3.            ((A and B) -> 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-76661.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> (((C and D) -> C) and (A or B))))), M:tm-443, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76662
in-theory        76662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-409 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-3.            ((A and B) -> 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-76662.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-409, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76663
in-theory        76663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-400 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-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-76663.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-400, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76664
in-theory        76664
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-391 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-3.            ((A and B) -> 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-76664.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-391, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76665
in-theory        76665
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-382 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76665.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-382, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76666
in-theory        76666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (((G and H) -> G) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-373 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-49.           (((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-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-76666.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (((G and H) -> G) and (E or F)))), M:tm-373, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76667
in-theory        76667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-364 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
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-49.           (((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-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-76667.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-364, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76668
in-theory        76668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((((D and E) -> D) and (A or B)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76668.        ((A or (A or B)) -> (C -> ((((D and E) -> D) and (A or B)) and C))), M:tm-355, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76669
in-theory        76669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-354 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76669.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-354, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76670
in-theory        76670
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A and B) -> 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-76670.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76671
in-theory        76671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (((E and F) -> E) and (C or D))))
theorem-size     25
proof            (modus-ponens tm-338 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76671.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (((E and F) -> E) and (C or D)))), M:tm-338, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76672
in-theory        76672
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (((C and D) -> C) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76672.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (((C and D) -> C) and (A or B))))), M:tm-328, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76673
in-theory        76673
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (((C and D) -> C) and (A or B)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76673.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (((C and D) -> C) and (A or B))))), M:tm-327, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76674
in-theory        76674
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> (((C and D) -> C) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-3.            ((A and B) -> 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-76674.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> (((C and D) -> C) and (A or B))))), M:tm-326, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76675
in-theory        76675
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> (((C and D) -> C) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-76675.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> (((C and D) -> C) and (A or B))))), M:tm-325, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76676
in-theory        76676
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (((C and D) -> C) and (A or B)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76676.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (((C and D) -> C) and (A or B))))), M:tm-324, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76677
in-theory        76677
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> (((C and D) -> C) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A and B) -> 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-76677.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> (((C and D) -> C) and (A or B))))), M:tm-323, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76678
in-theory        76678
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76678.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E and F) -> F)), M:tm-322, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76679
in-theory        76679
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76679.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E and F) -> E)), M:tm-320, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76680
in-theory        76680
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76680.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76681
in-theory        76681
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     27
proof            (modus-ponens tm-316 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76681.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76682
in-theory        76682
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76682.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (F -> E))), M:tm-315, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76683
in-theory        76683
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((A or (A or B)) -> (not (((C and D) -> C) and (A or B)))) -> (not (A or (A or B)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-3.            ((A and B) -> 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-76683.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((A or (A or B)) -> (not (((C and D) -> C) and (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76684
in-theory        76684
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((((C and D) -> C) and (A or B)) -> E) -> (((A or (A or B)) or (((C and D) -> C) and (A or B))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-3.            ((A and B) -> 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-76684.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((((C and D) -> C) and (A or B)) -> E) -> (((A or (A or B)) or (((C and D) -> C) and (A or B))) -> E))), M:tm-312, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76685
in-theory        76685
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E or ((A or (A or B)) -> (((C and D) -> C) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-3.            ((A and B) -> 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-76685.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E or ((A or (A or B)) -> (((C and D) -> C) and (A or B))))), M:tm-311, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76686
in-theory        76686
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((A or (A or B)) -> (((C and D) -> C) and (A or B))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
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-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-3.            ((A and B) -> 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-76686.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((A or (A or B)) -> (((C and D) -> C) and (A or B))) or E)), M:tm-310, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76687
in-theory        76687
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-3.            ((A and B) -> 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-76687.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and E))), M:tm-309, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76688
in-theory        76688
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> ((A or (A or B)) -> (((C and D) -> C) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-3.            ((A and B) -> 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-76688.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (E -> ((A or (A or B)) -> (((C and D) -> C) and (A or B))))), M:tm-305, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76689
in-theory        76689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-303 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76689.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-303, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76690
in-theory        76690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-270 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76690.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-270, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76691
in-theory        76691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-239 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76691.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-239, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76692
in-theory        76692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (((G and H) -> G) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-210 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76692.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (((G and H) -> G) and (E or F)))), M:tm-210, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76693
in-theory        76693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-183 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76693.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-183, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76694
in-theory        76694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-157 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76694.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-157, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76695
in-theory        76695
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-147 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76695.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-147, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76696
in-theory        76696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-134 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76696.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-134, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76697
in-theory        76697
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-125 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-76697.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-125, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76698
in-theory        76698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G and H) -> G) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-113 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76698.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G and H) -> G) and (E or F)))), M:tm-113, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76699
in-theory        76699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-105 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76699.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-105, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76700
in-theory        76700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (((E and F) -> E) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-95 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76700.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (((E and F) -> E) and (C or D)))), M:tm-95, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76701
in-theory        76701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D and E) -> D) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-84 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76701.        ((A or (A or B)) -> (C -> (((D and E) -> D) and (A or B)))), M:tm-84, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76702
in-theory        76702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-83 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76702.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-83, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76703
in-theory        76703
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (((D and E) -> D) and (B or C))))
theorem-size     21
proof            (modus-ponens tm-76 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76703.        (((not (not A)) -> A) and ((B or (B or C)) -> (((D and E) -> D) and (B or C)))), M:tm-76, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76704
in-theory        76704
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (((C and D) -> C) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-73 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76704.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (((C and D) -> C) and (A or B))), M:tm-73, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76705
in-theory        76705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (((E and F) -> E) and (C or D))))
theorem-size     27
proof            (modus-ponens tm-69 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76705.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (((E and F) -> E) and (C or D)))), M:tm-69, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76706
in-theory        76706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-54 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76706.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-54, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76707
in-theory        76707
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (((C and D) -> C) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-868 ((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76707.        (((A or B) or (A or (A or B))) -> (((C and D) -> C) and (A or B))), M:tm-50, m:tm-868, u:((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76708
in-theory        76708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (((C and D) -> C) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-868 ((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-8 tm-6 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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-76708.        ((A or (A or (A or B))) -> (((C and D) -> C) and (A or B))), M:tm-49, m:tm-868, u:((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76709
in-theory        76709
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (((D and E) -> D) and (B or C)))
theorem-size     23
proof            (modus-ponens tm-47 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76709.        (((A and (B or (B or C))) or (B or (B or C))) -> (((D and E) -> D) and (B or C))), M:tm-47, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76710
in-theory        76710
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (((D and E) -> D) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-46 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76710.        ((((A or (A or B)) and C) or (A or (A or B))) -> (((D and E) -> D) and (A or B))), M:tm-46, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76711
in-theory        76711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (((E and F) -> E) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-42 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76711.        ((A -> (B or A)) and ((C or (C or D)) -> (((E and F) -> E) and (C or D)))), M:tm-42, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76712
in-theory        76712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (((E and F) -> E) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-32 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
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-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-3.            ((A and B) -> 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-76712.        ((A -> (A or B)) and ((C or (C or D)) -> (((E and F) -> E) and (C or D)))), M:tm-32, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76713
in-theory        76713
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (((C and D) -> C) and (A or B))))
theorem-size     21
proof            (modus-ponens tm-24 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76713.        ((A or (A or B)) -> ((A or (A or B)) and (((C and D) -> C) and (A or B)))), M:tm-24, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76714
in-theory        76714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (((E and F) -> E) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-23 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-3.            ((A and B) -> 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-76714.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (((E and F) -> E) and (C or D)))), M:tm-23, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76715
in-theory        76715
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (((E and F) -> E) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-22 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76715.        (((A and B) -> B) and ((C or (C or D)) -> (((E and F) -> E) and (C or D)))), M:tm-22, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76716
in-theory        76716
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (((E and F) -> E) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-21 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-76716.        (((A and B) -> A) and ((C or (C or D)) -> (((E and F) -> E) and (C or D)))), M:tm-21, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76717
in-theory        76717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-20 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76717.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-20, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76718
in-theory        76718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (((E and F) -> E) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-19 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76718.        ((A -> (B -> A)) and ((C or (C or D)) -> (((E and F) -> E) and (C or D)))), M:tm-19, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76719
in-theory        76719
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (((C and D) -> C) and (A or B)))) -> (not (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-9 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76719.        (((A or (A or B)) -> (not (((C and D) -> C) and (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76720
in-theory        76720
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and (C or D)) -> E) -> (((C or (C or D)) or (((A and B) -> A) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-868 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
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-3.            ((A and B) -> 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-76720.        (((((A and B) -> A) and (C or D)) -> E) -> (((C or (C or D)) or (((A and B) -> A) and (C or D))) -> E)), M:tm-8, m:tm-868, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-76721
in-theory        76721
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (((D and E) -> D) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-7 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76721.        (A or ((B or (B or C)) -> (((D and E) -> D) and (B or C)))), M:tm-7, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76722
in-theory        76722
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-6 tm-8 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-49.           (((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-76722.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) or E), M:tm-6, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76723
in-theory        76723
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (((D and E) -> D) and (B or C))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76723.        (A -> (((B or (B or C)) -> (((D and E) -> D) and (B or C))) and A)), M:tm-5, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76724
in-theory        76724
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (((D and E) -> D) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-1 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76724.        (A -> ((B or (B or C)) -> (((D and E) -> D) and (B or C)))), M:tm-1, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-76725
in-theory        76725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-855 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76725.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-855, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76726
in-theory        76726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-808 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76726.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-808, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76727
in-theory        76727
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> (((C and D) -> D) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-798 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76727.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> (((C and D) -> D) and (A or B)))), M:tm-798, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76728
in-theory        76728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-757 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76728.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-757, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76729
in-theory        76729
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (((C and D) -> D) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-747 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76729.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (((C and D) -> D) and (A or B)))), M:tm-747, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76730
in-theory        76730
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (((G and H) -> H) and (E or F))))
theorem-size     41
proof            (modus-ponens tm-708 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76730.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (((G and H) -> H) and (E or F)))), M:tm-708, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76731
in-theory        76731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-665 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76731.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-665, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76732
in-theory        76732
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (((D and E) -> E) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-623 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76732.        ((A or (A or B)) -> (C or (((D and E) -> E) and (A or B)))), M:tm-623, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76733
in-theory        76733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-622 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76733.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-622, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76734
in-theory        76734
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76734.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (F or E))), M:tm-609, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76735
in-theory        76735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-605 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76735.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-605, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76736
in-theory        76736
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> (((C and D) -> D) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> 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-76736.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> (((C and D) -> D) and (A or B))))), M:tm-595, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76737
in-theory        76737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-550 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-4.            ((A and B) -> 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-76737.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-550, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76738
in-theory        76738
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-540 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76738.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-540, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76739
in-theory        76739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-530 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-4.            ((A and B) -> 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-76739.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-530, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76740
in-theory        76740
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-520 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76740.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-520, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76741
in-theory        76741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-510 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-76741.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-510, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76742
in-theory        76742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-500 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76742.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-500, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76743
in-theory        76743
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G and H) -> H) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-490 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76743.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G and H) -> H) and (E or F)))), M:tm-490, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76744
in-theory        76744
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-480 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76744.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-480, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76745
in-theory        76745
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C and D) -> D) and (A or B)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
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-49.           (((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-76745.        ((A or (A or B)) -> ((((C and D) -> D) and (A or B)) or E)), M:tm-470, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76746
in-theory        76746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-469 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
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-49.           (((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-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-76746.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-469, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76747
in-theory        76747
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
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-49.           (((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-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-76747.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (E or F))), M:tm-456, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76748
in-theory        76748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-453 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-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-76748.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-453, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76749
in-theory        76749
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> (((C and D) -> D) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> 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-76749.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> (((C and D) -> D) and (A or B))))), M:tm-443, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76750
in-theory        76750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-409 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> 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-76750.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-409, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76751
in-theory        76751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-400 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-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-76751.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-400, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76752
in-theory        76752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-391 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76752.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-391, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76753
in-theory        76753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-382 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-4.            ((A and B) -> 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-76753.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-382, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76754
in-theory        76754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (((G and H) -> H) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-373 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-49.           (((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-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-76754.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (((G and H) -> H) and (E or F)))), M:tm-373, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76755
in-theory        76755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-364 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
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-49.           (((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-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-76755.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-364, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76756
in-theory        76756
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((((D and E) -> E) and (A or B)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76756.        ((A or (A or B)) -> (C -> ((((D and E) -> E) and (A or B)) and C))), M:tm-355, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76757
in-theory        76757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-354 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76757.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-354, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76758
in-theory        76758
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> 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-76758.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76759
in-theory        76759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (((E and F) -> F) and (C or D))))
theorem-size     25
proof            (modus-ponens tm-338 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76759.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (((E and F) -> F) and (C or D)))), M:tm-338, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76760
in-theory        76760
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (((C and D) -> D) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76760.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (((C and D) -> D) and (A or B))))), M:tm-328, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76761
in-theory        76761
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (((C and D) -> D) and (A or B)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76761.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (((C and D) -> D) and (A or B))))), M:tm-327, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76762
in-theory        76762
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> (((C and D) -> D) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-76762.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> (((C and D) -> D) and (A or B))))), M:tm-326, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76763
in-theory        76763
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> (((C and D) -> D) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> 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-76763.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> (((C and D) -> D) and (A or B))))), M:tm-325, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76764
in-theory        76764
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (((C and D) -> D) and (A or B)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76764.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (((C and D) -> D) and (A or B))))), M:tm-324, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76765
in-theory        76765
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> (((C and D) -> D) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> 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-76765.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> (((C and D) -> D) and (A or B))))), M:tm-323, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76766
in-theory        76766
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76766.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E and F) -> F)), M:tm-322, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76767
in-theory        76767
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76767.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E and F) -> E)), M:tm-320, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76768
in-theory        76768
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76768.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76769
in-theory        76769
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     27
proof            (modus-ponens tm-316 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76769.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76770
in-theory        76770
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76770.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (F -> E))), M:tm-315, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76771
in-theory        76771
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((A or (A or B)) -> (not (((C and D) -> D) and (A or B)))) -> (not (A or (A or B)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-4.            ((A and B) -> 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-76771.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((A or (A or B)) -> (not (((C and D) -> D) and (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76772
in-theory        76772
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((((C and D) -> D) and (A or B)) -> E) -> (((A or (A or B)) or (((C and D) -> D) and (A or B))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-4.            ((A and B) -> 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-76772.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((((C and D) -> D) and (A or B)) -> E) -> (((A or (A or B)) or (((C and D) -> D) and (A or B))) -> E))), M:tm-312, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76773
in-theory        76773
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E or ((A or (A or B)) -> (((C and D) -> D) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-4.            ((A and B) -> 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-76773.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E or ((A or (A or B)) -> (((C and D) -> D) and (A or B))))), M:tm-311, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76774
in-theory        76774
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((A or (A or B)) -> (((C and D) -> D) and (A or B))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-4.            ((A and B) -> 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-76774.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((A or (A or B)) -> (((C and D) -> D) and (A or B))) or E)), M:tm-310, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76775
in-theory        76775
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-4.            ((A and B) -> 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-76775.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and E))), M:tm-309, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76776
in-theory        76776
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> ((A or (A or B)) -> (((C and D) -> D) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-4.            ((A and B) -> 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-76776.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (E -> ((A or (A or B)) -> (((C and D) -> D) and (A or B))))), M:tm-305, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76777
in-theory        76777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-303 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76777.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-303, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76778
in-theory        76778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-270 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am 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-76778.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-270, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76779
in-theory        76779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-239 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76779.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-239, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76780
in-theory        76780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (((G and H) -> H) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-210 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76780.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (((G and H) -> H) and (E or F)))), M:tm-210, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76781
in-theory        76781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-183 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76781.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-183, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76782
in-theory        76782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-157 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76782.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-157, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76783
in-theory        76783
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-147 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-76783.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-147, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76784
in-theory        76784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-134 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76784.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-134, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76785
in-theory        76785
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-125 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76785.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-125, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76786
in-theory        76786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G and H) -> H) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-113 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76786.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G and H) -> H) and (E or F)))), M:tm-113, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76787
in-theory        76787
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-105 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76787.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-105, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76788
in-theory        76788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (((E and F) -> F) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-95 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76788.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (((E and F) -> F) and (C or D)))), M:tm-95, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76789
in-theory        76789
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D and E) -> E) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-84 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76789.        ((A or (A or B)) -> (C -> (((D and E) -> E) and (A or B)))), M:tm-84, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76790
in-theory        76790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-83 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76790.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-83, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76791
in-theory        76791
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (((D and E) -> E) and (B or C))))
theorem-size     21
proof            (modus-ponens tm-76 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76791.        (((not (not A)) -> A) and ((B or (B or C)) -> (((D and E) -> E) and (B or C)))), M:tm-76, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76792
in-theory        76792
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (((C and D) -> D) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-73 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76792.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (((C and D) -> D) and (A or B))), M:tm-73, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76793
in-theory        76793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (((E and F) -> F) and (C or D))))
theorem-size     27
proof            (modus-ponens tm-69 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76793.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (((E and F) -> F) and (C or D)))), M:tm-69, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76794
in-theory        76794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-54 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76794.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-54, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76795
in-theory        76795
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (((C and D) -> D) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-869 ((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76795.        (((A or B) or (A or (A or B))) -> (((C and D) -> D) and (A or B))), M:tm-50, m:tm-869, u:((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76796
in-theory        76796
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (((C and D) -> D) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-869 ((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-8 tm-6 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-76796.        ((A or (A or (A or B))) -> (((C and D) -> D) and (A or B))), M:tm-49, m:tm-869, u:((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76797
in-theory        76797
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (((D and E) -> E) and (B or C)))
theorem-size     23
proof            (modus-ponens tm-47 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76797.        (((A and (B or (B or C))) or (B or (B or C))) -> (((D and E) -> E) and (B or C))), M:tm-47, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76798
in-theory        76798
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (((D and E) -> E) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-46 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76798.        ((((A or (A or B)) and C) or (A or (A or B))) -> (((D and E) -> E) and (A or B))), M:tm-46, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76799
in-theory        76799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (((E and F) -> F) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-42 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76799.        ((A -> (B or A)) and ((C or (C or D)) -> (((E and F) -> F) and (C or D)))), M:tm-42, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76800
in-theory        76800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (((E and F) -> F) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-32 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
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-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-4.            ((A and B) -> 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-76800.        ((A -> (A or B)) and ((C or (C or D)) -> (((E and F) -> F) and (C or D)))), M:tm-32, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76801
in-theory        76801
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (((C and D) -> D) and (A or B))))
theorem-size     21
proof            (modus-ponens tm-24 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76801.        ((A or (A or B)) -> ((A or (A or B)) and (((C and D) -> D) and (A or B)))), M:tm-24, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76802
in-theory        76802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (((E and F) -> F) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-23 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-4.            ((A and B) -> 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-76802.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (((E and F) -> F) and (C or D)))), M:tm-23, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76803
in-theory        76803
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (((E and F) -> F) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-22 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am 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-76803.        (((A and B) -> B) and ((C or (C or D)) -> (((E and F) -> F) and (C or D)))), M:tm-22, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76804
in-theory        76804
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (((E and F) -> F) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-21 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76804.        (((A and B) -> A) and ((C or (C or D)) -> (((E and F) -> F) and (C or D)))), M:tm-21, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76805
in-theory        76805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-20 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76805.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-20, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76806
in-theory        76806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (((E and F) -> F) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-19 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76806.        ((A -> (B -> A)) and ((C or (C or D)) -> (((E and F) -> F) and (C or D)))), M:tm-19, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76807
in-theory        76807
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (((C and D) -> D) and (A or B)))) -> (not (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-9 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76807.        (((A or (A or B)) -> (not (((C and D) -> D) and (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76808
in-theory        76808
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and (C or D)) -> E) -> (((C or (C or D)) or (((A and B) -> B) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-869 ((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
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-4.            ((A and B) -> 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-76808.        (((((A and B) -> B) and (C or D)) -> E) -> (((C or (C or D)) or (((A and B) -> B) and (C or D))) -> E)), M:tm-8, m:tm-869, u:((A (or Am (or Am Bm))) (B (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-76809
in-theory        76809
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (((D and E) -> E) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-7 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76809.        (A or ((B or (B or C)) -> (((D and E) -> E) and (B or C)))), M:tm-7, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76810
in-theory        76810
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-6 tm-8 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-49.           (((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-76810.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) or E), M:tm-6, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76811
in-theory        76811
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (((D and E) -> E) and (B or C))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76811.        (A -> (((B or (B or C)) -> (((D and E) -> E) and (B or C))) and A)), M:tm-5, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76812
in-theory        76812
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (((D and E) -> E) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-1 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76812.        (A -> ((B or (B or C)) -> (((D and E) -> E) and (B or C)))), M:tm-1, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-76813
in-theory        76813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-855 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76813.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-855, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76814
in-theory        76814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-808 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76814.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-808, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76815
in-theory        76815
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B))))
theorem-size     43
proof            (modus-ponens tm-798 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76815.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B)))), M:tm-798, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76816
in-theory        76816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-757 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-76816.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-757, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76817
in-theory        76817
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B))))
theorem-size     43
proof            (modus-ponens tm-747 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-76817.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B)))), M:tm-747, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76818
in-theory        76818
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F))))
theorem-size     43
proof            (modus-ponens tm-708 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76818.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F)))), M:tm-708, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76819
in-theory        76819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-665 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76819.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-665, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76820
in-theory        76820
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((D -> (E -> (D and E))) and (A or B))))
theorem-size     19
proof            (modus-ponens tm-623 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76820.        ((A or (A or B)) -> (C or ((D -> (E -> (D and E))) and (A or B)))), M:tm-623, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76821
in-theory        76821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-622 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-76821.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-622, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76822
in-theory        76822
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-76822.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (F or E))), M:tm-609, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76823
in-theory        76823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-605 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76823.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-605, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76824
in-theory        76824
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-76824.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))), M:tm-595, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76825
in-theory        76825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-550 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-76825.        (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-550, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76826
in-theory        76826
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-540 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76826.        ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-540, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76827
in-theory        76827
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-530 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-76827.        ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-530, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76828
in-theory        76828
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-520 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76828.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-520, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76829
in-theory        76829
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-510 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76829.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-510, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76830
in-theory        76830
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-500 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76830.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-500, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76831
in-theory        76831
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-490 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76831.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F)))), M:tm-490, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76832
in-theory        76832
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-480 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76832.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-480, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76833
in-theory        76833
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D -> (C and D))) and (A or B)) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
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-49.           (((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-76833.        ((A or (A or B)) -> (((C -> (D -> (C and D))) and (A or B)) or E)), M:tm-470, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76834
in-theory        76834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-469 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76834.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-469, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76835
in-theory        76835
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76835.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (E or F))), M:tm-456, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76836
in-theory        76836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-453 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-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-76836.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-453, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76837
in-theory        76837
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-76837.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))), M:tm-443, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76838
in-theory        76838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-409 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-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-76838.        (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-409, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76839
in-theory        76839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-400 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-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-76839.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-400, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76840
in-theory        76840
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-391 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-76840.        ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-391, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76841
in-theory        76841
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-382 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-76841.        ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-382, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76842
in-theory        76842
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-373 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-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-76842.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F)))), M:tm-373, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76843
in-theory        76843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-364 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76843.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-364, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76844
in-theory        76844
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D -> (E -> (D and E))) and (A or B)) and C)))
theorem-size     21
proof            (modus-ponens tm-355 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76844.        ((A or (A or B)) -> (C -> (((D -> (E -> (D and E))) and (A or B)) and C))), M:tm-355, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76845
in-theory        76845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-354 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76845.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-354, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76846
in-theory        76846
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-76846.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76847
in-theory        76847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D))))
theorem-size     27
proof            (modus-ponens tm-338 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76847.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D)))), M:tm-338, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76848
in-theory        76848
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     41
proof            (modus-ponens tm-328 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-76848.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> (C and D))) and (A or B))))), M:tm-328, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76849
in-theory        76849
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-76849.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))), M:tm-327, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76850
in-theory        76850
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-76850.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))), M:tm-326, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76851
in-theory        76851
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-76851.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))), M:tm-325, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76852
in-theory        76852
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-76852.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))), M:tm-324, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76853
in-theory        76853
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-76853.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))), M:tm-323, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76854
in-theory        76854
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-76854.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E and F) -> F)), M:tm-322, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76855
in-theory        76855
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-76855.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E and F) -> E)), M:tm-320, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76856
in-theory        76856
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-76856.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76857
in-theory        76857
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     29
proof            (modus-ponens tm-316 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-76857.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76858
in-theory        76858
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-76858.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (F -> E))), M:tm-315, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76859
in-theory        76859
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((A or (A or B)) -> (not ((C -> (D -> (C and D))) and (A or B)))) -> (not (A or (A or B)))))
theorem-size     43
proof            (modus-ponens tm-313 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-76859.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((A or (A or B)) -> (not ((C -> (D -> (C and D))) and (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76860
in-theory        76860
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((((C -> (D -> (C and D))) and (A or B)) -> E) -> (((A or (A or B)) or ((C -> (D -> (C and D))) and (A or B))) -> E)))
theorem-size     51
proof            (modus-ponens tm-312 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-312.          ((A -> B) -> ((A -> B) and ((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-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-76860.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((((C -> (D -> (C and D))) and (A or B)) -> E) -> (((A or (A or B)) or ((C -> (D -> (C and D))) and (A or B))) -> E))), M:tm-312, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76861
in-theory        76861
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E or ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-76861.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E or ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))), M:tm-311, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76862
in-theory        76862
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-76862.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) or E)), M:tm-310, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76863
in-theory        76863
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-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-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-76863.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and E))), M:tm-309, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76864
in-theory        76864
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-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-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-76864.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (E -> ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))), M:tm-305, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76865
in-theory        76865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-303 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-76865.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-303, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76866
in-theory        76866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-270 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76866.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-270, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76867
in-theory        76867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-239 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76867.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-239, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76868
in-theory        76868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F))))
theorem-size     35
proof            (modus-ponens tm-210 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76868.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F)))), M:tm-210, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76869
in-theory        76869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-183 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76869.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-183, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76870
in-theory        76870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-157 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-76870.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-157, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76871
in-theory        76871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-147 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-76871.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-147, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76872
in-theory        76872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-134 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-76872.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-134, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76873
in-theory        76873
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-125 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-76873.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-125, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76874
in-theory        76874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-113 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76874.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F)))), M:tm-113, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76875
in-theory        76875
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-105 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-76875.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-105, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76876
in-theory        76876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D))))
theorem-size     25
proof            (modus-ponens tm-95 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-76876.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D)))), M:tm-95, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76877
in-theory        76877
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (E -> (D and E))) and (A or B))))
theorem-size     19
proof            (modus-ponens tm-84 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76877.        ((A or (A or B)) -> (C -> ((D -> (E -> (D and E))) and (A or B)))), M:tm-84, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76878
in-theory        76878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-83 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-76878.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-83, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76879
in-theory        76879
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (E -> (D and E))) and (B or C))))
theorem-size     23
proof            (modus-ponens tm-76 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76879.        (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (E -> (D and E))) and (B or C)))), M:tm-76, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76880
in-theory        76880
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-73 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76880.        (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B))), M:tm-73, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76881
in-theory        76881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-69 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76881.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D)))), M:tm-69, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76882
in-theory        76882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-54 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-76882.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-54, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76883
in-theory        76883
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-50 tm-870 ((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76883.        (((A or B) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B))), M:tm-50, m:tm-870, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76884
in-theory        76884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-870 ((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-8 tm-6 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-5.            (A -> (B -> (A and B))), axiom
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-76884.        ((A or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B))), M:tm-49, m:tm-870, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76885
in-theory        76885
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (E -> (D and E))) and (B or C)))
theorem-size     25
proof            (modus-ponens tm-47 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76885.        (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (E -> (D and E))) and (B or C))), M:tm-47, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76886
in-theory        76886
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (E -> (D and E))) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-46 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76886.        ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (E -> (D and E))) and (A or B))), M:tm-46, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76887
in-theory        76887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-42 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76887.        ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D)))), M:tm-42, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76888
in-theory        76888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-32 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-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-76888.        ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D)))), M:tm-32, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76889
in-theory        76889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> (C and D))) and (A or B))))
theorem-size     23
proof            (modus-ponens tm-24 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76889.        ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D -> (C and D))) and (A or B)))), M:tm-24, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76890
in-theory        76890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D))))
theorem-size     25
proof            (modus-ponens tm-23 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-76890.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D)))), M:tm-23, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76891
in-theory        76891
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-22 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76891.        (((A and B) -> B) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D)))), M:tm-22, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76892
in-theory        76892
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-21 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76892.        (((A and B) -> A) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D)))), M:tm-21, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76893
in-theory        76893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-20 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76893.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-20, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76894
in-theory        76894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-19 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76894.        ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (F -> (E and F))) and (C or D)))), M:tm-19, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76895
in-theory        76895
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not ((C -> (D -> (C and D))) and (A or B)))) -> (not (A or (A or B))))
theorem-size     25
proof            (modus-ponens tm-9 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76895.        (((A or (A or B)) -> (not ((C -> (D -> (C and D))) and (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76896
in-theory        76896
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and (C or D)) -> E) -> (((C or (C or D)) or ((A -> (B -> (A and B))) and (C or D))) -> E))
theorem-size     33
proof            (modus-ponens tm-8 tm-870 ((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       119
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-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-76896.        ((((A -> (B -> (A and B))) and (C or D)) -> E) -> (((C or (C or D)) or ((A -> (B -> (A and B))) and (C or D))) -> E)), M:tm-8, m:tm-870, u:((A (or Am (or Am Bm))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-76897
in-theory        76897
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> ((D -> (E -> (D and E))) and (B or C))))
theorem-size     19
proof            (modus-ponens tm-7 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76897.        (A or ((B or (B or C)) -> ((D -> (E -> (D and E))) and (B or C)))), M:tm-7, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76898
in-theory        76898
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-6 tm-8 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-49.           (((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-76898.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) or E), M:tm-6, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76899
in-theory        76899
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> ((D -> (E -> (D and E))) and (B or C))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76899.        (A -> (((B or (B or C)) -> ((D -> (E -> (D and E))) and (B or C))) and A)), M:tm-5, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76900
in-theory        76900
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> ((D -> (E -> (D and E))) and (B or C))))
theorem-size     19
proof            (modus-ponens tm-1 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76900.        (A -> ((B or (B or C)) -> ((D -> (E -> (D and E))) and (B or C)))), M:tm-1, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-76901
in-theory        76901
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76901.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-855, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76902
in-theory        76902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76902.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-808, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76903
in-theory        76903
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((E and (A or (A or B))) or (A or (A or B))) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-798 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76903.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((E and (A or (A or B))) or (A or (A or B))) -> (C -> (D -> (C and D))))), M:tm-798, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76904
in-theory        76904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76904.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-757, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76905
in-theory        76905
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-747 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), 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-76905.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (C -> (D -> (C and D))))), M:tm-747, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76906
in-theory        76906
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76906.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (H -> (G and H))))), M:tm-708, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76907
in-theory        76907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-76907.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-665, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76908
in-theory        76908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-76908.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-622, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76909
in-theory        76909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D or (A or (A or B))) and C)))
theorem-size     17
proof            (modus-ponens tm-617 tm-871 ((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (-> Dm (and (or B (or Am (or Am Bm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76909.        ((A or (A or B)) -> (C -> ((D or (A or (A or B))) and C))), M:tm-617, m:tm-871, u:((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (-> Dm (and (or B (or Am (or Am Bm))) Dm))))
================================================================
tm-name          tm-76910
in-theory        76910
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-76910.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76911
in-theory        76911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76911.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-605, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76912
in-theory        76912
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A or (A or B)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76912.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A or (A or B)) -> (C -> (D -> (C and D)))))), M:tm-595, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76913
in-theory        76913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76913.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-550, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76914
in-theory        76914
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76914.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-540, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76915
in-theory        76915
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76915.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-530, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76916
in-theory        76916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76916.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-520, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76917
in-theory        76917
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76917.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-510, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76918
in-theory        76918
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76918.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-500, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76919
in-theory        76919
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76919.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H -> (G and H))))), M:tm-490, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76920
in-theory        76920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76920.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-480, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76921
in-theory        76921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76921.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-469, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76922
in-theory        76922
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((A or (A or B)) or D) and C)))
theorem-size     17
proof            (modus-ponens tm-464 tm-871 ((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (-> Dm (and (or (or Am (or Am Bm)) 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-49.           (((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-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-76922.        ((A or (A or B)) -> (C -> (((A or (A or B)) or D) and C))), M:tm-464, m:tm-871, u:((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (-> Dm (and (or (or Am (or Am Bm)) B) Dm))))
================================================================
tm-name          tm-76923
in-theory        76923
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76923.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76924
in-theory        76924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76924.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-453, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76925
in-theory        76925
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A or (A or B)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76925.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A or (A or B)) -> (C -> (D -> (C and D)))))), M:tm-443, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76926
in-theory        76926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76926.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-409, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76927
in-theory        76927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76927.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-400, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76928
in-theory        76928
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76928.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-391, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76929
in-theory        76929
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76929.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-382, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76930
in-theory        76930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76930.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (H -> (G and H))))), M:tm-373, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76931
in-theory        76931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76931.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-364, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76932
in-theory        76932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-76932.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-354, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76933
in-theory        76933
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> ((A or (A or B)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-349 tm-871 ((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (-> Dm (and (-> B (and (or Am (or Am Bm)) B)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-76933.        ((A or (A or B)) -> (C -> ((D -> ((A or (A or B)) and D)) and C))), M:tm-349, m:tm-871, u:((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (-> Dm (and (-> B (and (or Am (or Am Bm)) B)) Dm))))
================================================================
tm-name          tm-76934
in-theory        76934
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-76934.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76935
in-theory        76935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76935.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (F -> (E and F))))), M:tm-338, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76936
in-theory        76936
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-328 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76936.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (D -> (C and D)))))), M:tm-328, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76937
in-theory        76937
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76937.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (C -> (D -> (C and D)))))), M:tm-327, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76938
in-theory        76938
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A or (A or B)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76938.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A or (A or B)) -> (C -> (D -> (C and D)))))), M:tm-326, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76939
in-theory        76939
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A or (A or B)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76939.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A or (A or B)) -> (C -> (D -> (C and D)))))), M:tm-325, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76940
in-theory        76940
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76940.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (C -> (D -> (C and D)))))), M:tm-324, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76941
in-theory        76941
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A or (A or B)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-76941.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A or (A or B)) -> (C -> (D -> (C and D)))))), M:tm-323, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76942
in-theory        76942
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-76942.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76943
in-theory        76943
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-76943.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76944
in-theory        76944
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-76944.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76945
in-theory        76945
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     25
proof            (modus-ponens tm-316 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-76945.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76946
in-theory        76946
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-76946.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76947
in-theory        76947
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((A or (A or B)) -> (not (C -> (D -> (C and D))))) -> (not (A or (A or B)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), 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-76947.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((A or (A or B)) -> (not (C -> (D -> (C and D))))) -> (not (A or (A or B))))), M:tm-313, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76948
in-theory        76948
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> (((A or (A or B)) or (C -> (D -> (C and D)))) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76948.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> (((A or (A or B)) or (C -> (D -> (C and D)))) -> E))), M:tm-312, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76949
in-theory        76949
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E or ((A or (A or B)) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), 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-76949.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E or ((A or (A or B)) -> (C -> (D -> (C and D)))))), M:tm-311, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76950
in-theory        76950
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((A or (A or B)) -> (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76950.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((A or (A or B)) -> (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76951
in-theory        76951
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (((A or (A or B)) -> (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), 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-76951.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> (((A or (A or B)) -> (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76952
in-theory        76952
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-306 tm-871 ((A (or Am (or Am Bm))) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), 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-76952.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D -> (C and D))))), M:tm-306, m:tm-871, u:((A (or Am (or Am Bm))) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-76953
in-theory        76953
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> ((A or (A or B)) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-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-76953.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (E -> ((A or (A or B)) -> (C -> (D -> (C and D)))))), M:tm-305, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76954
in-theory        76954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76954.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-303, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76955
in-theory        76955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76955.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-270, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76956
in-theory        76956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76956.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-239, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76957
in-theory        76957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76957.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (H -> (G and H))))), M:tm-210, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76958
in-theory        76958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76958.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-183, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76959
in-theory        76959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-76959.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-157, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76960
in-theory        76960
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76960.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-147, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76961
in-theory        76961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-76961.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-134, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76962
in-theory        76962
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76962.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-125, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76963
in-theory        76963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76963.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H -> (G and H))))), M:tm-113, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76964
in-theory        76964
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76964.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-105, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76965
in-theory        76965
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((A or (A or B)) and C)))
theorem-size     15
proof            (modus-ponens tm-99 tm-871 ((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (-> Dm (and (or Am (or Am Bm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76965.        ((A or (A or B)) -> (C -> ((A or (A or B)) and C))), M:tm-99, m:tm-871, u:((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (-> Dm (and (or Am (or Am Bm)) Dm))))
================================================================
tm-name          tm-76966
in-theory        76966
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (A or (A or B))) and C)))
theorem-size     17
proof            (modus-ponens tm-98 tm-871 ((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (-> Dm (and (-> B (or Am (or Am Bm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76966.        ((A or (A or B)) -> (C -> ((D -> (A or (A or B))) and C))), M:tm-98, m:tm-871, u:((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (-> Dm (and (-> B (or Am (or Am Bm))) Dm))))
================================================================
tm-name          tm-76967
in-theory        76967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-76967.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (F -> (E and F))))), M:tm-95, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76968
in-theory        76968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-76968.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-83, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76969
in-theory        76969
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76969.        (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (E -> (D and E))))), M:tm-76, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76970
in-theory        76970
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-73 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76970.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (D -> (C and D)))), M:tm-73, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76971
in-theory        76971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76971.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (F -> (E and F))))), M:tm-69, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76972
in-theory        76972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-1.            (A -> (B -> A)), 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-76972.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-54, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76973
in-theory        76973
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-50 tm-871 ((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76973.        (((A or B) or (A or (A or B))) -> (C -> (D -> (C and D)))), M:tm-50, m:tm-871, u:((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76974
in-theory        76974
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-49 tm-871 ((A Am) (B (or Am Bm)) (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-5.            (A -> (B -> (A and 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-76974.        ((A or (A or (A or B))) -> (C -> (D -> (C and D)))), M:tm-49, m:tm-871, u:((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76975
in-theory        76975
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-47 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76975.        (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (E -> (D and E)))), M:tm-47, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76976
in-theory        76976
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-46 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76976.        ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (E -> (D and E)))), M:tm-46, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76977
in-theory        76977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76977.        ((A -> (B or A)) and ((C or (C or D)) -> (E -> (F -> (E and F))))), M:tm-42, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76978
in-theory        76978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-76978.        ((A -> (A or B)) and ((C or (C or D)) -> (E -> (F -> (E and F))))), M:tm-32, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76979
in-theory        76979
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (C -> (D -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-24 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76979.        ((A or (A or B)) -> ((A or (A or B)) and (C -> (D -> (C and D))))), M:tm-24, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76980
in-theory        76980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76980.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (F -> (E and F))))), M:tm-23, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76981
in-theory        76981
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76981.        (((A and B) -> B) and ((C or (C or D)) -> (E -> (F -> (E and F))))), M:tm-22, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76982
in-theory        76982
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76982.        (((A and B) -> A) and ((C or (C or D)) -> (E -> (F -> (E and F))))), M:tm-21, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76983
in-theory        76983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76983.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-20, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76984
in-theory        76984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-76984.        ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (F -> (E and F))))), M:tm-19, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76985
in-theory        76985
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (C -> (D -> (C and D))))) -> (not (A or (A or B))))
theorem-size     21
proof            (modus-ponens tm-9 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76985.        (((A or (A or B)) -> (not (C -> (D -> (C and D))))) -> (not (A or (A or B)))), M:tm-9, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76986
in-theory        76986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (((D or (D or E)) or (A -> (B -> (A and B)))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 tm-871 ((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-76986.        (((A -> (B -> (A and B))) -> C) -> (((D or (D or E)) or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-871, u:((A (or Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-76987
in-theory        76987
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76987.        (A or ((B or (B or C)) -> (D -> (E -> (D and E))))), M:tm-7, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76988
in-theory        76988
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-871 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-76988.        (((A or (A or B)) -> (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76989
in-theory        76989
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76989.        (A -> (((B or (B or C)) -> (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76990
in-theory        76990
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-2 tm-871 ((A (or Am (or Am Bm))) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76990.        (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D -> (C and D)))), M:tm-2, m:tm-871, u:((A (or Am (or Am Bm))) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-76991
in-theory        76991
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-76991.        (A -> ((B or (B or C)) -> (D -> (E -> (D and E))))), M:tm-1, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-76992
in-theory        76992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-855 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76992.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-855, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-76993
in-theory        76993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-808 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76993.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-808, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-76994
in-theory        76994
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C -> (C or D)) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-798 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76994.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C -> (C or D)) and (A or B)))), M:tm-798, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-76995
in-theory        76995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-757 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-76995.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-757, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-76996
in-theory        76996
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C -> (C or D)) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-747 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76996.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C -> (C or D)) and (A or B)))), M:tm-747, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-76997
in-theory        76997
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F))))
theorem-size     41
proof            (modus-ponens tm-708 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-76997.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F)))), M:tm-708, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-76998
in-theory        76998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-665 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-76998.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-665, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-76999
in-theory        76999
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((D -> (D or E)) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-623 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-76999.        ((A or (A or B)) -> (C or ((D -> (D or E)) and (A or B)))), M:tm-623, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77000
in-theory        77000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-622 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77000.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-622, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77001
in-theory        77001
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77001.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (F or E))), M:tm-609, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77002
in-theory        77002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-605 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77002.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-605, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77003
in-theory        77003
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-77003.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))), M:tm-595, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77004
in-theory        77004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-550 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77004.        (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-550, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77005
in-theory        77005
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-540 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-77005.        ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-540, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77006
in-theory        77006
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-530 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77006.        ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-530, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77007
in-theory        77007
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-520 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77007.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-520, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77008
in-theory        77008
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-510 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-77008.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-510, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77009
in-theory        77009
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-500 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-77009.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-500, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77010
in-theory        77010
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-490 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77010.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F)))), M:tm-490, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77011
in-theory        77011
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-480 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77011.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-480, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77012
in-theory        77012
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (C or D)) and (A or B)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
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-49.           (((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-77012.        ((A or (A or B)) -> (((C -> (C or D)) and (A or B)) or E)), M:tm-470, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77013
in-theory        77013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-469 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77013.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-469, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77014
in-theory        77014
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77014.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (E or F))), M:tm-456, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77015
in-theory        77015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-453 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-77015.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-453, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77016
in-theory        77016
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-77016.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))), M:tm-443, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77017
in-theory        77017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-409 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77017.        (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-409, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77018
in-theory        77018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-400 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77018.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-400, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77019
in-theory        77019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-391 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77019.        ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-391, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77020
in-theory        77020
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-382 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77020.        ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-382, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77021
in-theory        77021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-373 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-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-77021.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F)))), M:tm-373, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77022
in-theory        77022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-364 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77022.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-364, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77023
in-theory        77023
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D -> (D or E)) and (A or B)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77023.        ((A or (A or B)) -> (C -> (((D -> (D or E)) and (A or B)) and C))), M:tm-355, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77024
in-theory        77024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-354 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77024.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-354, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77025
in-theory        77025
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77025.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77026
in-theory        77026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D))))
theorem-size     25
proof            (modus-ponens tm-338 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77026.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D)))), M:tm-338, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77027
in-theory        77027
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (C or D)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-77027.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (C or D)) and (A or B))))), M:tm-328, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77028
in-theory        77028
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77028.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))), M:tm-327, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77029
in-theory        77029
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-77029.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))), M:tm-326, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77030
in-theory        77030
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-77030.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))), M:tm-325, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77031
in-theory        77031
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77031.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))), M:tm-324, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77032
in-theory        77032
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77032.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))), M:tm-323, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77033
in-theory        77033
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77033.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E and F) -> F)), M:tm-322, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77034
in-theory        77034
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77034.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E and F) -> E)), M:tm-320, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77035
in-theory        77035
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77035.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77036
in-theory        77036
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     27
proof            (modus-ponens tm-316 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77036.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77037
in-theory        77037
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77037.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (F -> E))), M:tm-315, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77038
in-theory        77038
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((A or (A or B)) -> (not ((C -> (C or D)) and (A or B)))) -> (not (A or (A or B)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-77038.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((A or (A or B)) -> (not ((C -> (C or D)) and (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77039
in-theory        77039
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((((C -> (C or D)) and (A or B)) -> E) -> (((A or (A or B)) or ((C -> (C or D)) and (A or B))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-77039.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((((C -> (C or D)) and (A or B)) -> E) -> (((A or (A or B)) or ((C -> (C or D)) and (A or B))) -> E))), M:tm-312, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77040
in-theory        77040
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E or ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-77040.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E or ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))), M:tm-311, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77041
in-theory        77041
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-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-77041.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) or E)), M:tm-310, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77042
in-theory        77042
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77042.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and E))), M:tm-309, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77043
in-theory        77043
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77043.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (E -> ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))), M:tm-305, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77044
in-theory        77044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-303 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77044.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-303, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77045
in-theory        77045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-270 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77045.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-270, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77046
in-theory        77046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-239 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77046.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-239, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77047
in-theory        77047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-210 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77047.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F)))), M:tm-210, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77048
in-theory        77048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-183 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77048.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-183, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77049
in-theory        77049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-157 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77049.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-157, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77050
in-theory        77050
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-147 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-77050.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-147, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77051
in-theory        77051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-134 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77051.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-134, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77052
in-theory        77052
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-125 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-77052.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-125, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77053
in-theory        77053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-113 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77053.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F)))), M:tm-113, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77054
in-theory        77054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-105 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-77054.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-105, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77055
in-theory        77055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-95 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77055.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D)))), M:tm-95, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77056
in-theory        77056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (D or E)) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-84 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77056.        ((A or (A or B)) -> (C -> ((D -> (D or E)) and (A or B)))), M:tm-84, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77057
in-theory        77057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-83 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77057.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-83, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77058
in-theory        77058
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (D or E)) and (B or C))))
theorem-size     21
proof            (modus-ponens tm-76 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77058.        (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (D or E)) and (B or C)))), M:tm-76, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77059
in-theory        77059
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (C or D)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-73 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77059.        (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (C or D)) and (A or B))), M:tm-73, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77060
in-theory        77060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D))))
theorem-size     27
proof            (modus-ponens tm-69 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77060.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D)))), M:tm-69, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77061
in-theory        77061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-54 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77061.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-54, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77062
in-theory        77062
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> ((C -> (C or D)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-872 ((A Am) (B (or Am Bm)) (C (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77062.        (((A or B) or (A or (A or B))) -> ((C -> (C or D)) and (A or B))), M:tm-50, m:tm-872, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77063
in-theory        77063
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> ((C -> (C or D)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-872 ((A Am) (B (or Am Bm)) (C (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-8 tm-6 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-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-77063.        ((A or (A or (A or B))) -> ((C -> (C or D)) and (A or B))), M:tm-49, m:tm-872, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77064
in-theory        77064
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (D or E)) and (B or C)))
theorem-size     23
proof            (modus-ponens tm-47 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77064.        (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (D or E)) and (B or C))), M:tm-47, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77065
in-theory        77065
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (D or E)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-46 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77065.        ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (D or E)) and (A or B))), M:tm-46, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77066
in-theory        77066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-42 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77066.        ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D)))), M:tm-42, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77067
in-theory        77067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-32 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-77067.        ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D)))), M:tm-32, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77068
in-theory        77068
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and ((C -> (C or D)) and (A or B))))
theorem-size     21
proof            (modus-ponens tm-24 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77068.        ((A or (A or B)) -> ((A or (A or B)) and ((C -> (C or D)) and (A or B)))), M:tm-24, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77069
in-theory        77069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-23 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77069.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D)))), M:tm-23, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77070
in-theory        77070
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-22 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77070.        (((A and B) -> B) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D)))), M:tm-22, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77071
in-theory        77071
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-21 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77071.        (((A and B) -> A) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D)))), M:tm-21, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77072
in-theory        77072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-20 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77072.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-20, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77073
in-theory        77073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-19 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77073.        ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (E or F)) and (C or D)))), M:tm-19, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77074
in-theory        77074
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not ((C -> (C or D)) and (A or B)))) -> (not (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-9 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77074.        (((A or (A or B)) -> (not ((C -> (C or D)) and (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77075
in-theory        77075
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and (C or D)) -> E) -> (((C or (C or D)) or ((A -> (A or B)) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-872 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-77075.        ((((A -> (A or B)) and (C or D)) -> E) -> (((C or (C or D)) or ((A -> (A or B)) and (C or D))) -> E)), M:tm-8, m:tm-872, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-77076
in-theory        77076
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> ((D -> (D or E)) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-7 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77076.        (A or ((B or (B or C)) -> ((D -> (D or E)) and (B or C)))), M:tm-7, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77077
in-theory        77077
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-6 tm-8 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-49.           (((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-77077.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) or E), M:tm-6, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77078
in-theory        77078
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> ((D -> (D or E)) and (B or C))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-77078.        (A -> (((B or (B or C)) -> ((D -> (D or E)) and (B or C))) and A)), M:tm-5, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77079
in-theory        77079
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> ((D -> (D or E)) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-1 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77079.        (A -> ((B or (B or C)) -> ((D -> (D or E)) and (B or C)))), M:tm-1, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-77080
in-theory        77080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77080.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-855, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77081
in-theory        77081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77081.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-808, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77082
in-theory        77082
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (((E and (A or (A or B))) or (A or (A or B))) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-798 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77082.        (((A or (A or B)) -> (C -> (C or D))) and (((E and (A or (A or B))) or (A or (A or B))) -> (C -> (C or D)))), M:tm-798, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77083
in-theory        77083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77083.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-757, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77084
in-theory        77084
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-747 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (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-77084.        (((A or (A or B)) -> (C -> (C or D))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (C -> (C or D)))), M:tm-747, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77085
in-theory        77085
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77085.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (G or H)))), M:tm-708, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77086
in-theory        77086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77086.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-665, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77087
in-theory        77087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77087.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-622, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77088
in-theory        77088
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or (A or (A or B))) or D))
theorem-size     15
proof            (modus-ponens tm-617 tm-873 ((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (or (or B (or Am (or Am Bm))) 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77088.        ((A or (A or B)) -> ((C or (A or (A or B))) or D)), M:tm-617, m:tm-873, u:((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (or (or B (or Am (or Am Bm))) Dm)))
================================================================
tm-name          tm-77089
in-theory        77089
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77089.        (((A or (A or B)) -> (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77090
in-theory        77090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77090.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-605, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77091
in-theory        77091
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((E -> (F or E)) and ((A or (A or B)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77091.        (((A or (A or B)) -> (C -> (C or D))) and ((E -> (F or E)) and ((A or (A or B)) -> (C -> (C or D))))), M:tm-595, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77092
in-theory        77092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77092.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-550, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77093
in-theory        77093
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77093.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-540, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77094
in-theory        77094
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77094.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-530, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77095
in-theory        77095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77095.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-520, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77096
in-theory        77096
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77096.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-510, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77097
in-theory        77097
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77097.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-500, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77098
in-theory        77098
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77098.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (G or H)))), M:tm-490, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77099
in-theory        77099
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77099.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-480, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77100
in-theory        77100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-77100.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-469, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77101
in-theory        77101
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((A or (A or B)) or C) or D))
theorem-size     15
proof            (modus-ponens tm-464 tm-873 ((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (or (or (or Am (or Am Bm)) 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-77101.        ((A or (A or B)) -> (((A or (A or B)) or C) or D)), M:tm-464, m:tm-873, u:((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (or (or (or Am (or Am Bm)) B) Dm)))
================================================================
tm-name          tm-77102
in-theory        77102
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-77102.        (((A or (A or B)) -> (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77103
in-theory        77103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77103.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-453, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77104
in-theory        77104
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((E -> (E or F)) and ((A or (A or B)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77104.        (((A or (A or B)) -> (C -> (C or D))) and ((E -> (E or F)) and ((A or (A or B)) -> (C -> (C or D))))), M:tm-443, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77105
in-theory        77105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77105.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-409, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77106
in-theory        77106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77106.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-400, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77107
in-theory        77107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77107.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-391, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77108
in-theory        77108
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77108.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-382, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77109
in-theory        77109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77109.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (G or H)))), M:tm-373, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77110
in-theory        77110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77110.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-364, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77111
in-theory        77111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77111.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-354, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77112
in-theory        77112
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> ((A or (A or B)) and C)) or D))
theorem-size     17
proof            (modus-ponens tm-349 tm-873 ((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (or (-> B (and (or Am (or Am Bm)) 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77112.        ((A or (A or B)) -> ((C -> ((A or (A or B)) and C)) or D)), M:tm-349, m:tm-873, u:((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (or (-> B (and (or Am (or Am Bm)) B)) Dm)))
================================================================
tm-name          tm-77113
in-theory        77113
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77113.        (((A or (A or B)) -> (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77114
in-theory        77114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77114.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (E or F)))), M:tm-338, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77115
in-theory        77115
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77115.        (((A or (A or B)) -> (C -> (C or D))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (C or D))))), M:tm-328, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77116
in-theory        77116
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77116.        (((A or (A or B)) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (C -> (C or D))))), M:tm-327, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77117
in-theory        77117
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (((E and F) -> F) and ((A or (A or B)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77117.        (((A or (A or B)) -> (C -> (C or D))) and (((E and F) -> F) and ((A or (A or B)) -> (C -> (C or D))))), M:tm-326, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77118
in-theory        77118
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (((E and F) -> E) and ((A or (A or B)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77118.        (((A or (A or B)) -> (C -> (C or D))) and (((E and F) -> E) and ((A or (A or B)) -> (C -> (C or D))))), M:tm-325, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77119
in-theory        77119
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (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-77119.        (((A or (A or B)) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (C -> (C or D))))), M:tm-324, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77120
in-theory        77120
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((E -> (F -> E)) and ((A or (A or B)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77120.        (((A or (A or B)) -> (C -> (C or D))) and ((E -> (F -> E)) and ((A or (A or B)) -> (C -> (C or D))))), M:tm-323, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77121
in-theory        77121
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77121.        (((A or (A or B)) -> (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77122
in-theory        77122
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77122.        (((A or (A or B)) -> (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77123
in-theory        77123
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77123.        (((A or (A or B)) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77124
in-theory        77124
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-316 tm-873 ((A (or Am (or Am Bm))) (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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77124.        (((A or (A or B)) -> (C -> (C or D))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77125
in-theory        77125
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77125.        (((A or (A or B)) -> (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77126
in-theory        77126
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (((A or (A or B)) -> (not (C -> (C or D)))) -> (not (A or (A or B)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (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-77126.        (((A or (A or B)) -> (C -> (C or D))) and (((A or (A or B)) -> (not (C -> (C or D)))) -> (not (A or (A or B))))), M:tm-313, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77127
in-theory        77127
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> (((A or (A or B)) or (C -> (C or D))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77127.        (((A or (A or B)) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> (((A or (A or B)) or (C -> (C or D))) -> E))), M:tm-312, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77128
in-theory        77128
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (E or ((A or (A or B)) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-1.            (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-77128.        (((A or (A or B)) -> (C -> (C or D))) and (E or ((A or (A or B)) -> (C -> (C or D))))), M:tm-311, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77129
in-theory        77129
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (((A or (A or B)) -> (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77129.        (((A or (A or B)) -> (C -> (C or D))) and (((A or (A or B)) -> (C -> (C or D))) or E)), M:tm-310, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77130
in-theory        77130
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (E -> (((A or (A or B)) -> (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (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-77130.        (((A or (A or B)) -> (C -> (C or D))) and (E -> (((A or (A or B)) -> (C -> (C or D))) and E))), M:tm-309, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77131
in-theory        77131
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (C or D))))
theorem-size     29
proof            (modus-ponens tm-306 tm-873 ((A (or Am (or Am Bm))) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (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-77131.        (((A or (A or B)) -> (C -> (C or D))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (C or D)))), M:tm-306, m:tm-873, u:((A (or Am (or Am Bm))) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-77132
in-theory        77132
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (E -> ((A or (A or B)) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77132.        (((A or (A or B)) -> (C -> (C or D))) and (E -> ((A or (A or B)) -> (C -> (C or D))))), M:tm-305, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77133
in-theory        77133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77133.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-303, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77134
in-theory        77134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77134.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-270, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77135
in-theory        77135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77135.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-239, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77136
in-theory        77136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77136.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (G or H)))), M:tm-210, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77137
in-theory        77137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77137.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-183, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77138
in-theory        77138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77138.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-157, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77139
in-theory        77139
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77139.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-147, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77140
in-theory        77140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77140.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-134, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77141
in-theory        77141
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77141.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-125, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77142
in-theory        77142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77142.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (G or H)))), M:tm-113, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77143
in-theory        77143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77143.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-105, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77144
in-theory        77144
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) or C))
theorem-size     13
proof            (modus-ponens tm-99 tm-873 ((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (or (or Am (or Am Bm)) 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77144.        ((A or (A or B)) -> ((A or (A or B)) or C)), M:tm-99, m:tm-873, u:((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (or (or Am (or Am Bm)) Dm)))
================================================================
tm-name          tm-77145
in-theory        77145
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (A or (A or B))) or D))
theorem-size     15
proof            (modus-ponens tm-98 tm-873 ((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (or (-> B (or Am (or Am Bm))) 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77145.        ((A or (A or B)) -> ((C -> (A or (A or B))) or D)), M:tm-98, m:tm-873, u:((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (or (-> B (or Am (or Am Bm))) Dm)))
================================================================
tm-name          tm-77146
in-theory        77146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77146.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (E or F)))), M:tm-95, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77147
in-theory        77147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77147.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-83, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77148
in-theory        77148
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77148.        (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (D or E)))), M:tm-76, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77149
in-theory        77149
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-73 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77149.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (C or D))), M:tm-73, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77150
in-theory        77150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77150.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (E or F)))), M:tm-69, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77151
in-theory        77151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77151.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-54, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77152
in-theory        77152
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-50 tm-873 ((A Am) (B (or Am Bm)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77152.        (((A or B) or (A or (A or B))) -> (C -> (C or D))), M:tm-50, m:tm-873, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77153
in-theory        77153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-49 tm-873 ((A Am) (B (or Am Bm)) (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-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-77153.        ((A or (A or (A or B))) -> (C -> (C or D))), M:tm-49, m:tm-873, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77154
in-theory        77154
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-47 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77154.        (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (D or E))), M:tm-47, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77155
in-theory        77155
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-46 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77155.        ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (D or E))), M:tm-46, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77156
in-theory        77156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-77156.        ((A -> (B or A)) and ((C or (C or D)) -> (E -> (E or F)))), M:tm-42, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77157
in-theory        77157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77157.        ((A -> (A or B)) and ((C or (C or D)) -> (E -> (E or F)))), M:tm-32, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77158
in-theory        77158
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (C -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-24 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77158.        ((A or (A or B)) -> ((A or (A or B)) and (C -> (C or D)))), M:tm-24, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77159
in-theory        77159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77159.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (E or F)))), M:tm-23, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77160
in-theory        77160
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-77160.        (((A and B) -> B) and ((C or (C or D)) -> (E -> (E or F)))), M:tm-22, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77161
in-theory        77161
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-77161.        (((A and B) -> A) and ((C or (C or D)) -> (E -> (E or F)))), M:tm-21, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77162
in-theory        77162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (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-77162.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-20, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77163
in-theory        77163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77163.        ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (E or F)))), M:tm-19, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77164
in-theory        77164
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (C -> (C or D)))) -> (not (A or (A or B))))
theorem-size     19
proof            (modus-ponens tm-9 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77164.        (((A or (A or B)) -> (not (C -> (C or D)))) -> (not (A or (A or B)))), M:tm-9, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77165
in-theory        77165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (((D or (D or E)) or (A -> (A or B))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-873 ((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-6 tm-1)
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-1.            (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-77165.        (((A -> (A or B)) -> C) -> (((D or (D or E)) or (A -> (A or B))) -> C)), M:tm-8, m:tm-873, u:((A (or Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77166
in-theory        77166
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77166.        (A or ((B or (B or C)) -> (D -> (D or E)))), M:tm-7, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77167
in-theory        77167
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77167.        (((A or (A or B)) -> (C -> (C or D))) or E), M:tm-6, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77168
in-theory        77168
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77168.        (A -> (((B or (B or C)) -> (D -> (D or E))) and A)), M:tm-5, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77169
in-theory        77169
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> C) -> ((A or (A or B)) -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-2 tm-873 ((A (or Am (or Am Bm))) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77169.        (((A or (A or B)) -> C) -> ((A or (A or B)) -> (C or D))), M:tm-2, m:tm-873, u:((A (or Am (or Am Bm))) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-77170
in-theory        77170
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-873 ((A (-> (or Am (or Am Bm)) (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77170.        (A -> ((B or (B or C)) -> (D -> (D or E)))), M:tm-1, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77171
in-theory        77171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-855 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77171.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-855, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77172
in-theory        77172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-808 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77172.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-808, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77173
in-theory        77173
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C -> (D or C)) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-798 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77173.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((E and (A or (A or B))) or (A or (A or B))) -> ((C -> (D or C)) and (A or B)))), M:tm-798, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77174
in-theory        77174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-757 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77174.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-757, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77175
in-theory        77175
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C -> (D or C)) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-747 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77175.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((((A or (A or B)) and E) or (A or (A or B))) -> ((C -> (D or C)) and (A or B)))), M:tm-747, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77176
in-theory        77176
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F))))
theorem-size     41
proof            (modus-ponens tm-708 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77176.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F)))), M:tm-708, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77177
in-theory        77177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-665 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77177.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-665, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77178
in-theory        77178
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((D -> (E or D)) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-623 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77178.        ((A or (A or B)) -> (C or ((D -> (E or D)) and (A or B)))), M:tm-623, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77179
in-theory        77179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-622 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-77179.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-622, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77180
in-theory        77180
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-77180.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (F or E))), M:tm-609, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77181
in-theory        77181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-605 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77181.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-605, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77182
in-theory        77182
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-77182.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (F or E)) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))), M:tm-595, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77183
in-theory        77183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-550 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-77183.        (((A -> (B or A)) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-550, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77184
in-theory        77184
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-540 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-77184.        ((A or (B -> (C or B))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-540, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77185
in-theory        77185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-530 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-77185.        ((A or (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-530, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77186
in-theory        77186
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-520 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-77186.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-520, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77187
in-theory        77187
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-510 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-77187.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-510, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77188
in-theory        77188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-500 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-77188.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-500, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77189
in-theory        77189
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-490 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-77189.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F)))), M:tm-490, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77190
in-theory        77190
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-480 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-77190.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-480, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77191
in-theory        77191
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D or C)) and (A or B)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
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-49.           (((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-77191.        ((A or (A or B)) -> (((C -> (D or C)) and (A or B)) or E)), M:tm-470, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77192
in-theory        77192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-469 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-77192.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-469, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77193
in-theory        77193
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-77193.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (E or F))), M:tm-456, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77194
in-theory        77194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-453 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-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-77194.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-453, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77195
in-theory        77195
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or 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-77195.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (E or F)) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))), M:tm-443, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77196
in-theory        77196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-409 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-7.            (A -> (B or 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-77196.        (((A -> (A or B)) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-409, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77197
in-theory        77197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-400 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-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-77197.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-400, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77198
in-theory        77198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-391 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-7.            (A -> (B or 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-77198.        ((((A and B) -> B) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-391, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77199
in-theory        77199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-382 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-7.            (A -> (B or 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-77199.        ((((A and B) -> A) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-382, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77200
in-theory        77200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-373 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-49.           (((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-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-77200.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F)))), M:tm-373, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77201
in-theory        77201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-364 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
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-49.           (((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-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-77201.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-364, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77202
in-theory        77202
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D -> (E or D)) and (A or B)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77202.        ((A or (A or B)) -> (C -> (((D -> (E or D)) and (A or B)) and C))), M:tm-355, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77203
in-theory        77203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-354 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77203.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-354, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77204
in-theory        77204
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or 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-77204.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77205
in-theory        77205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D))))
theorem-size     25
proof            (modus-ponens tm-338 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77205.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D)))), M:tm-338, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77206
in-theory        77206
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D or C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77206.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D or C)) and (A or B))))), M:tm-328, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77207
in-theory        77207
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77207.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))), M:tm-327, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77208
in-theory        77208
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or 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-77208.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((E and F) -> F) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))), M:tm-326, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77209
in-theory        77209
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or 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-77209.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((E and F) -> E) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))), M:tm-325, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77210
in-theory        77210
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77210.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))), M:tm-324, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77211
in-theory        77211
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or 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-77211.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (F -> E)) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))), M:tm-323, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77212
in-theory        77212
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77212.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E and F) -> F)), M:tm-322, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77213
in-theory        77213
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77213.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E and F) -> E)), M:tm-320, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77214
in-theory        77214
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77214.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77215
in-theory        77215
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     27
proof            (modus-ponens tm-316 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77215.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77216
in-theory        77216
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77216.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (F -> E))), M:tm-315, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77217
in-theory        77217
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((A or (A or B)) -> (not ((C -> (D or C)) and (A or B)))) -> (not (A or (A or B)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-7.            (A -> (B or 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-77217.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((A or (A or B)) -> (not ((C -> (D or C)) and (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77218
in-theory        77218
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((((C -> (D or C)) and (A or B)) -> E) -> (((A or (A or B)) or ((C -> (D or C)) and (A or B))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-7.            (A -> (B or 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-77218.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((((C -> (D or C)) and (A or B)) -> E) -> (((A or (A or B)) or ((C -> (D or C)) and (A or B))) -> E))), M:tm-312, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77219
in-theory        77219
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E or ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-77219.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E or ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))), M:tm-311, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77220
in-theory        77220
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-7.            (A -> (B or 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-77220.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) or E)), M:tm-310, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77221
in-theory        77221
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or 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-77221.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and E))), M:tm-309, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77222
in-theory        77222
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-7.            (A -> (B or 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-77222.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (E -> ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))), M:tm-305, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77223
in-theory        77223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     27
proof            (modus-ponens tm-303 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77223.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-303, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77224
in-theory        77224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-270 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77224.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-270, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77225
in-theory        77225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-239 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77225.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-239, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77226
in-theory        77226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-210 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77226.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F)))), M:tm-210, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77227
in-theory        77227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     25
proof            (modus-ponens tm-183 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77227.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-183, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77228
in-theory        77228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-157 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77228.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-157, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77229
in-theory        77229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-147 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77229.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-147, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77230
in-theory        77230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-134 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77230.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-134, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77231
in-theory        77231
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-125 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77231.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-125, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77232
in-theory        77232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-113 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77232.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F)))), M:tm-113, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77233
in-theory        77233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-105 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77233.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-105, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77234
in-theory        77234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-95 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77234.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D)))), M:tm-95, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77235
in-theory        77235
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (E or D)) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-84 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77235.        ((A or (A or B)) -> (C -> ((D -> (E or D)) and (A or B)))), M:tm-84, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77236
in-theory        77236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     23
proof            (modus-ponens tm-83 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77236.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-83, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77237
in-theory        77237
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (E or D)) and (B or C))))
theorem-size     21
proof            (modus-ponens tm-76 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77237.        (((not (not A)) -> A) and ((B or (B or C)) -> ((D -> (E or D)) and (B or C)))), M:tm-76, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77238
in-theory        77238
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (D or C)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-73 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77238.        (((not (not (A or (A or B)))) or (A or (A or B))) -> ((C -> (D or C)) and (A or B))), M:tm-73, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77239
in-theory        77239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D))))
theorem-size     27
proof            (modus-ponens tm-69 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77239.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D)))), M:tm-69, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77240
in-theory        77240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-54 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77240.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-54, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77241
in-theory        77241
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> ((C -> (D or C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-874 ((A Am) (B (or Am Bm)) (C (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77241.        (((A or B) or (A or (A or B))) -> ((C -> (D or C)) and (A or B))), M:tm-50, m:tm-874, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77242
in-theory        77242
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> ((C -> (D or C)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-874 ((A Am) (B (or Am Bm)) (C (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-6 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-77242.        ((A or (A or (A or B))) -> ((C -> (D or C)) and (A or B))), M:tm-49, m:tm-874, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77243
in-theory        77243
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (E or D)) and (B or C)))
theorem-size     23
proof            (modus-ponens tm-47 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77243.        (((A and (B or (B or C))) or (B or (B or C))) -> ((D -> (E or D)) and (B or C))), M:tm-47, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77244
in-theory        77244
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (E or D)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-46 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77244.        ((((A or (A or B)) and C) or (A or (A or B))) -> ((D -> (E or D)) and (A or B))), M:tm-46, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77245
in-theory        77245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-42 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77245.        ((A -> (B or A)) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D)))), M:tm-42, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77246
in-theory        77246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-32 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-49.           (((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-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-77246.        ((A -> (A or B)) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D)))), M:tm-32, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77247
in-theory        77247
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D or C)) and (A or B))))
theorem-size     21
proof            (modus-ponens tm-24 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77247.        ((A or (A or B)) -> ((A or (A or B)) and ((C -> (D or C)) and (A or B)))), M:tm-24, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77248
in-theory        77248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D))))
theorem-size     23
proof            (modus-ponens tm-23 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-7.            (A -> (B or 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-77248.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D)))), M:tm-23, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77249
in-theory        77249
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-22 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77249.        (((A and B) -> B) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D)))), M:tm-22, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77250
in-theory        77250
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-21 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77250.        (((A and B) -> A) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D)))), M:tm-21, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77251
in-theory        77251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-20 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77251.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-20, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77252
in-theory        77252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D))))
theorem-size     21
proof            (modus-ponens tm-19 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77252.        ((A -> (B -> A)) and ((C or (C or D)) -> ((E -> (F or E)) and (C or D)))), M:tm-19, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77253
in-theory        77253
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not ((C -> (D or C)) and (A or B)))) -> (not (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-9 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77253.        (((A or (A or B)) -> (not ((C -> (D or C)) and (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77254
in-theory        77254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and (C or D)) -> E) -> (((C or (C or D)) or ((A -> (B or A)) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-874 ((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-7.            (A -> (B or 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-77254.        ((((A -> (B or A)) and (C or D)) -> E) -> (((C or (C or D)) or ((A -> (B or A)) and (C or D))) -> E)), M:tm-8, m:tm-874, u:((A (or Am (or Am Bm))) (B (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-77255
in-theory        77255
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> ((D -> (E or D)) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-7 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77255.        (A or ((B or (B or C)) -> ((D -> (E or D)) and (B or C)))), M:tm-7, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77256
in-theory        77256
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-6 tm-8 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-49.           (((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-77256.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) or E), M:tm-6, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77257
in-theory        77257
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> ((D -> (E or D)) and (B or C))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77257.        (A -> (((B or (B or C)) -> ((D -> (E or D)) and (B or C))) and A)), M:tm-5, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77258
in-theory        77258
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> ((D -> (E or D)) and (B or C))))
theorem-size     17
proof            (modus-ponens tm-1 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77258.        (A -> ((B or (B or C)) -> ((D -> (E or D)) and (B or C)))), M:tm-1, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-77259
in-theory        77259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77259.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-855, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77260
in-theory        77260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77260.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-808, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77261
in-theory        77261
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (((E and (A or (A or B))) or (A or (A or B))) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77261.        (((A or (A or B)) -> (C -> (D or C))) and (((E and (A or (A or B))) or (A or (A or B))) -> (C -> (D or C)))), M:tm-798, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77262
in-theory        77262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77262.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-757, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77263
in-theory        77263
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-77263.        (((A or (A or B)) -> (C -> (D or C))) and ((((A or (A or B)) and E) or (A or (A or B))) -> (C -> (D or C)))), M:tm-747, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77264
in-theory        77264
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77264.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (G -> (H or G)))), M:tm-708, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77265
in-theory        77265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77265.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-665, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77266
in-theory        77266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77266.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-622, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77267
in-theory        77267
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D or (A or (A or B)))))
theorem-size     15
proof            (modus-ponens tm-617 tm-875 ((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (or Dm (or B (or Am (or Am Bm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77267.        ((A or (A or B)) -> (C or (D or (A or (A or B))))), M:tm-617, m:tm-875, u:((A (or Am (or Am Bm))) (Cm (or B (or Am (or Am Bm)))) (C (or Dm (or B (or Am (or Am Bm))))))
================================================================
tm-name          tm-77268
in-theory        77268
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77268.        (((A or (A or B)) -> (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77269
in-theory        77269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77269.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-605, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77270
in-theory        77270
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((E -> (F or E)) and ((A or (A or B)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77270.        (((A or (A or B)) -> (C -> (D or C))) and ((E -> (F or E)) and ((A or (A or B)) -> (C -> (D or C))))), M:tm-595, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77271
in-theory        77271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-77271.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-550, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77272
in-theory        77272
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77272.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-540, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77273
in-theory        77273
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-77273.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-530, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77274
in-theory        77274
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77274.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-520, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77275
in-theory        77275
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77275.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-510, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77276
in-theory        77276
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77276.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-500, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77277
in-theory        77277
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77277.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H or G)))), M:tm-490, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77278
in-theory        77278
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-77278.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-480, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77279
in-theory        77279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-77279.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-469, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77280
in-theory        77280
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((A or (A or B)) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-875 ((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (or Dm (or (or Am (or Am Bm)) 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-49.           (((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-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-77280.        ((A or (A or B)) -> (C or ((A or (A or B)) or D))), M:tm-464, m:tm-875, u:((A (or Am (or Am Bm))) (Cm (or (or Am (or Am Bm)) B)) (C (or Dm (or (or Am (or Am Bm)) B))))
================================================================
tm-name          tm-77281
in-theory        77281
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-77281.        (((A or (A or B)) -> (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77282
in-theory        77282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77282.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-453, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77283
in-theory        77283
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((E -> (E or F)) and ((A or (A or B)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77283.        (((A or (A or B)) -> (C -> (D or C))) and ((E -> (E or F)) and ((A or (A or B)) -> (C -> (D or C))))), M:tm-443, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77284
in-theory        77284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77284.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-409, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77285
in-theory        77285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77285.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-400, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77286
in-theory        77286
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77286.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-391, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77287
in-theory        77287
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77287.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-382, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77288
in-theory        77288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77288.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (G -> (H or G)))), M:tm-373, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77289
in-theory        77289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-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-77289.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-364, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77290
in-theory        77290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77290.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-354, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77291
in-theory        77291
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D -> ((A or (A or B)) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-875 ((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (or Dm (-> B (and (or Am (or Am Bm)) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77291.        ((A or (A or B)) -> (C or (D -> ((A or (A or B)) and D)))), M:tm-349, m:tm-875, u:((A (or Am (or Am Bm))) (Cm (-> B (and (or Am (or Am Bm)) B))) (C (or Dm (-> B (and (or Am (or Am Bm)) B)))))
================================================================
tm-name          tm-77292
in-theory        77292
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77292.        (((A or (A or B)) -> (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77293
in-theory        77293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77293.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (E -> (F or E)))), M:tm-338, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77294
in-theory        77294
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77294.        (((A or (A or B)) -> (C -> (D or C))) and ((A or (A or B)) -> ((A or (A or B)) and (C -> (D or C))))), M:tm-328, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77295
in-theory        77295
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77295.        (((A or (A or B)) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A or (A or B)) -> (C -> (D or C))))), M:tm-327, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77296
in-theory        77296
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (((E and F) -> F) and ((A or (A or B)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77296.        (((A or (A or B)) -> (C -> (D or C))) and (((E and F) -> F) and ((A or (A or B)) -> (C -> (D or C))))), M:tm-326, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77297
in-theory        77297
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (((E and F) -> E) and ((A or (A or B)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77297.        (((A or (A or B)) -> (C -> (D or C))) and (((E and F) -> E) and ((A or (A or B)) -> (C -> (D or C))))), M:tm-325, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77298
in-theory        77298
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77298.        (((A or (A or B)) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (A or B)) -> (C -> (D or C))))), M:tm-324, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77299
in-theory        77299
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((E -> (F -> E)) and ((A or (A or B)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77299.        (((A or (A or B)) -> (C -> (D or C))) and ((E -> (F -> E)) and ((A or (A or B)) -> (C -> (D or C))))), M:tm-323, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77300
in-theory        77300
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77300.        (((A or (A or B)) -> (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77301
in-theory        77301
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77301.        (((A or (A or B)) -> (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77302
in-theory        77302
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (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-77302.        (((A or (A or B)) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77303
in-theory        77303
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-316 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77303.        (((A or (A or B)) -> (C -> (D or C))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77304
in-theory        77304
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77304.        (((A or (A or B)) -> (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77305
in-theory        77305
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (((A or (A or B)) -> (not (C -> (D or C)))) -> (not (A or (A or B)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77305.        (((A or (A or B)) -> (C -> (D or C))) and (((A or (A or B)) -> (not (C -> (D or C)))) -> (not (A or (A or B))))), M:tm-313, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77306
in-theory        77306
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> (((A or (A or B)) or (C -> (D or C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77306.        (((A or (A or B)) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> (((A or (A or B)) or (C -> (D or C))) -> E))), M:tm-312, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77307
in-theory        77307
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (E or ((A or (A or B)) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> 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-77307.        (((A or (A or B)) -> (C -> (D or C))) and (E or ((A or (A or B)) -> (C -> (D or C))))), M:tm-311, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77308
in-theory        77308
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (((A or (A or B)) -> (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77308.        (((A or (A or B)) -> (C -> (D or C))) and (((A or (A or B)) -> (C -> (D or C))) or E)), M:tm-310, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77309
in-theory        77309
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (E -> (((A or (A or B)) -> (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-77309.        (((A or (A or B)) -> (C -> (D or C))) and (E -> (((A or (A or B)) -> (C -> (D or C))) and E))), M:tm-309, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77310
in-theory        77310
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D or C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-875 ((A (or Am (or Am Bm))) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-77310.        (((A or (A or B)) -> (C -> (D or C))) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D or C)))), M:tm-306, m:tm-875, u:((A (or Am (or Am Bm))) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-77311
in-theory        77311
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (E -> ((A or (A or B)) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-7.            (A -> (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-77311.        (((A or (A or B)) -> (C -> (D or C))) and (E -> ((A or (A or B)) -> (C -> (D or C))))), M:tm-305, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77312
in-theory        77312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77312.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-303, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77313
in-theory        77313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77313.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-270, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77314
in-theory        77314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77314.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-239, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77315
in-theory        77315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77315.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (G -> (H or G)))), M:tm-210, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77316
in-theory        77316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77316.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-183, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77317
in-theory        77317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77317.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-157, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77318
in-theory        77318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77318.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-147, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77319
in-theory        77319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77319.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-134, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77320
in-theory        77320
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77320.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-125, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77321
in-theory        77321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77321.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (G -> (H or G)))), M:tm-113, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77322
in-theory        77322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77322.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-105, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77323
in-theory        77323
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (A or (A or B))))
theorem-size     13
proof            (modus-ponens tm-99 tm-875 ((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (or Dm (or Am (or Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77323.        ((A or (A or B)) -> (C or (A or (A or B)))), M:tm-99, m:tm-875, u:((Cm (or Am (or Am Bm))) (A (or Am (or Am Bm))) (B (or Dm (or Am (or Am Bm)))))
================================================================
tm-name          tm-77324
in-theory        77324
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D -> (A or (A or B)))))
theorem-size     15
proof            (modus-ponens tm-98 tm-875 ((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (or Dm (-> B (or Am (or Am Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77324.        ((A or (A or B)) -> (C or (D -> (A or (A or B))))), M:tm-98, m:tm-875, u:((A (or Am (or Am Bm))) (Cm (-> B (or Am (or Am Bm)))) (C (or Dm (-> B (or Am (or Am Bm))))))
================================================================
tm-name          tm-77325
in-theory        77325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77325.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (E -> (F or E)))), M:tm-95, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77326
in-theory        77326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77326.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-83, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77327
in-theory        77327
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77327.        (((not (not A)) -> A) and ((B or (B or C)) -> (D -> (E or D)))), M:tm-76, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77328
in-theory        77328
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77328.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (C -> (D or C))), M:tm-73, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77329
in-theory        77329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77329.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (E -> (F or E)))), M:tm-69, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77330
in-theory        77330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77330.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-54, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77331
in-theory        77331
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-875 ((A Am) (B (or Am Bm)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77331.        (((A or B) or (A or (A or B))) -> (C -> (D or C))), M:tm-50, m:tm-875, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77332
in-theory        77332
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-49 tm-875 ((A Am) (B (or Am Bm)) (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-7.            (A -> (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-77332.        ((A or (A or (A or B))) -> (C -> (D or C))), M:tm-49, m:tm-875, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77333
in-theory        77333
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77333.        (((A and (B or (B or C))) or (B or (B or C))) -> (D -> (E or D))), M:tm-47, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77334
in-theory        77334
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77334.        ((((A or (A or B)) and C) or (A or (A or B))) -> (D -> (E or D))), M:tm-46, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77335
in-theory        77335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77335.        ((A -> (B or A)) and ((C or (C or D)) -> (E -> (F or E)))), M:tm-42, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77336
in-theory        77336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77336.        ((A -> (A or B)) and ((C or (C or D)) -> (E -> (F or E)))), M:tm-32, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77337
in-theory        77337
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (C -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77337.        ((A or (A or B)) -> ((A or (A or B)) and (C -> (D or C)))), M:tm-24, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77338
in-theory        77338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77338.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (E -> (F or E)))), M:tm-23, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77339
in-theory        77339
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77339.        (((A and B) -> B) and ((C or (C or D)) -> (E -> (F or E)))), M:tm-22, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77340
in-theory        77340
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77340.        (((A and B) -> A) and ((C or (C or D)) -> (E -> (F or E)))), M:tm-21, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77341
in-theory        77341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77341.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-20, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77342
in-theory        77342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77342.        ((A -> (B -> A)) and ((C or (C or D)) -> (E -> (F or E)))), M:tm-19, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77343
in-theory        77343
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (C -> (D or C)))) -> (not (A or (A or B))))
theorem-size     19
proof            (modus-ponens tm-9 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77343.        (((A or (A or B)) -> (not (C -> (D or C)))) -> (not (A or (A or B)))), M:tm-9, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77344
in-theory        77344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (((D or (D or E)) or (A -> (B or A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-875 ((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-77344.        (((A -> (B or A)) -> C) -> (((D or (D or E)) or (A -> (B or A))) -> C)), M:tm-8, m:tm-875, u:((A (or Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77345
in-theory        77345
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77345.        (A or ((B or (B or C)) -> (D -> (E or D)))), M:tm-7, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77346
in-theory        77346
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-875 ((A (-> (or Am (or Am Bm)) (-> 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-49.           (((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-77346.        (((A or (A or B)) -> (C -> (D or C))) or E), M:tm-6, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77347
in-theory        77347
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77347.        (A -> (((B or (B or C)) -> (D -> (E or D))) and A)), M:tm-5, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77348
in-theory        77348
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-875 ((A (or Am (or Am Bm))) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77348.        (((A or (A or B)) -> C) -> ((A or (A or B)) -> (D or C))), M:tm-2, m:tm-875, u:((A (or Am (or Am Bm))) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-77349
in-theory        77349
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77349.        (A -> ((B or (B or C)) -> (D -> (E or D)))), M:tm-1, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77350
in-theory        77350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     41
proof            (modus-ponens tm-855 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77350.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-855, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77351
in-theory        77351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     35
proof            (modus-ponens tm-808 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-77351.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-808, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77352
in-theory        77352
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((D and (A or ((B or C) -> (A and (B or C))))) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C)))))
theorem-size     61
proof            (modus-ponens tm-798 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-77352.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((D and (A or ((B or C) -> (A and (B or C))))) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C))))), M:tm-798, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77353
in-theory        77353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     35
proof            (modus-ponens tm-757 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77353.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-757, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77354
in-theory        77354
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((((A or ((B or C) -> (A and (B or C)))) and D) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C)))))
theorem-size     61
proof            (modus-ponens tm-747 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77354.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((((A or ((B or C) -> (A and (B or C)))) and D) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C))))), M:tm-747, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77355
in-theory        77355
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G)))))
theorem-size     49
proof            (modus-ponens tm-708 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-48.           (((A -> (B and 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-77355.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G))))), M:tm-708, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77356
in-theory        77356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-665 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77356.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-665, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77357
in-theory        77357
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (D or ((B or (B or C)) -> (A and (B or C)))))
theorem-size     25
proof            (modus-ponens tm-623 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-6)
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-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-77357.        ((A or ((B or C) -> (A and (B or C)))) -> (D or ((B or (B or C)) -> (A and (B or C))))), M:tm-623, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77358
in-theory        77358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-622 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77358.        ((A -> (B -> (C or B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-622, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77359
in-theory        77359
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77359.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (E or D))), M:tm-609, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77360
in-theory        77360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-605 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-48.           (((A -> (B and 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-77360.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-605, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77361
in-theory        77361
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (E or D)) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77361.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (E or D)) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))))), M:tm-595, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77362
in-theory        77362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-550 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 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-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-49.           (((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-77362.        (((A -> (B or A)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-550, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77363
in-theory        77363
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-540 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-48.           (((A -> (B and 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-77363.        ((A or (B -> (C or B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-540, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77364
in-theory        77364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-530 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 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-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-49.           (((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-77364.        ((A or (B -> (B or C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-530, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77365
in-theory        77365
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-520 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-48.           (((A -> (B and 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-77365.        ((A or (B -> (C -> (B and C)))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-520, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77366
in-theory        77366
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-510 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-48.           (((A -> (B and 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-77366.        ((A or ((B and C) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-510, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77367
in-theory        77367
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-500 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-48.           (((A -> (B and 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-77367.        ((A or ((B and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-500, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77368
in-theory        77368
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-490 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-48.           (((A -> (B and 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-77368.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G))))), M:tm-490, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77369
in-theory        77369
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-480 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-48.           (((A -> (B and 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-77369.        ((A or (B -> (C -> B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-480, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77370
in-theory        77370
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (((B or (B or C)) -> (A and (B or C))) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
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-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-49.           (((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-77370.        ((A or ((B or C) -> (A and (B or C)))) -> (((B or (B or C)) -> (A and (B or C))) or D)), M:tm-470, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77371
in-theory        77371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-469 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 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-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-49.           (((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-77371.        ((A -> (B -> (B or C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-469, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77372
in-theory        77372
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-49.           (((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-77372.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (D or E))), M:tm-456, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77373
in-theory        77373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-453 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-77373.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-453, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77374
in-theory        77374
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (D or E)) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-77374.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (D or E)) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))))), M:tm-443, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77375
in-theory        77375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-409 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-77375.        (((A -> (A or B)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-409, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77376
in-theory        77376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-400 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-77376.        (((A -> (B -> (A and B))) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-400, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77377
in-theory        77377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-391 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 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-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-49.           (((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-77377.        ((((A and B) -> B) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-391, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77378
in-theory        77378
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-382 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 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-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-49.           (((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-77378.        ((((A and B) -> A) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-382, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77379
in-theory        77379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-373 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 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-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-49.           (((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-77379.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G))))), M:tm-373, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77380
in-theory        77380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-364 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-49.           (((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-77380.        (((A -> (B -> A)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-364, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77381
in-theory        77381
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (D -> (((B or (B or C)) -> (A and (B or C))) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77381.        ((A or ((B or C) -> (A and (B or C)))) -> (D -> (((B or (B or C)) -> (A and (B or C))) and D))), M:tm-355, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77382
in-theory        77382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-354 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-48.           (((A -> (B and 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-77382.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-354, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77383
in-theory        77383
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77383.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77384
in-theory        77384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E)))))
theorem-size     33
proof            (modus-ponens tm-338 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-48.           (((A -> (B and 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-77384.        (((A -> B) -> (A -> (A and B))) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E))))), M:tm-338, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77385
in-theory        77385
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((A or ((B or C) -> (A and (B or C)))) -> ((A or ((B or C) -> (A and (B or C)))) and ((B or (B or C)) -> (A and (B or C))))))
theorem-size     59
proof            (modus-ponens tm-328 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77385.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((A or ((B or C) -> (A and (B or C)))) -> ((A or ((B or C) -> (A and (B or C)))) and ((B or (B or C)) -> (A and (B or C)))))), M:tm-328, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77386
in-theory        77386
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (E -> (D and E))) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-77386.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (E -> (D and E))) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))))), M:tm-327, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77387
in-theory        77387
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((D and E) -> E) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77387.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((D and E) -> E) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))))), M:tm-326, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77388
in-theory        77388
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((D and E) -> D) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77388.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((D and E) -> D) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))))), M:tm-325, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77389
in-theory        77389
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-77389.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))))), M:tm-324, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77390
in-theory        77390
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (E -> D)) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77390.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (E -> D)) and ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))))), M:tm-323, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77391
in-theory        77391
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77391.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D and E) -> E)), M:tm-322, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77392
in-theory        77392
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77392.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D and E) -> D)), M:tm-320, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77393
in-theory        77393
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77393.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77394
in-theory        77394
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((A or ((B or C) -> (A and (B or C)))) -> (A or ((B or C) -> (A and (B or C))))))
theorem-size     47
proof            (modus-ponens tm-316 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77394.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((A or ((B or C) -> (A and (B or C)))) -> (A or ((B or C) -> (A and (B or C)))))), M:tm-316, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77395
in-theory        77395
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77395.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (E -> D))), M:tm-315, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77396
in-theory        77396
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> (not ((B or (B or C)) -> (A and (B or C))))) -> (not (A or ((B or C) -> (A and (B or C)))))))
theorem-size     61
proof            (modus-ponens tm-313 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77396.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> (not ((B or (B or C)) -> (A and (B or C))))) -> (not (A or ((B or C) -> (A and (B or C))))))), M:tm-313, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77397
in-theory        77397
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((((B or (B or C)) -> (A and (B or C))) -> D) -> (((A or ((B or C) -> (A and (B or C)))) or ((B or (B or C)) -> (A and (B or C)))) -> D)))
theorem-size     63
proof            (modus-ponens tm-312 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
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-312.          ((A -> B) -> ((A -> B) and ((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77397.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((((B or (B or C)) -> (A and (B or C))) -> D) -> (((A or ((B or C) -> (A and (B or C)))) or ((B or (B or C)) -> (A and (B or C)))) -> D))), M:tm-312, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77398
in-theory        77398
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D or ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77398.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D or ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))))), M:tm-311, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77399
in-theory        77399
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
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-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-49.           (((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-77399.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) or D)), M:tm-310, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77400
in-theory        77400
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77400.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and D))), M:tm-309, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77401
in-theory        77401
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> (B or (B or C))) -> ((A or ((B or C) -> (A and (B or C)))) -> (A and (B or C)))))
theorem-size     59
proof            (modus-ponens tm-306 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (or Bm (or Bm Cm))) (C (and Am (or Bm Cm)))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77401.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> (B or (B or C))) -> ((A or ((B or C) -> (A and (B or C)))) -> (A and (B or C))))), M:tm-306, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (or Bm (or Bm Cm))) (C (and Am (or Bm Cm))))
================================================================
tm-name          tm-77402
in-theory        77402
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77402.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and (D -> ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))))), M:tm-305, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77403
in-theory        77403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     35
proof            (modus-ponens tm-303 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-77403.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-303, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77404
in-theory        77404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-270 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-48.           (((A -> (B and 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-77404.        ((A -> (((B and C) -> C) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-270, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77405
in-theory        77405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-239 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-48.           (((A -> (B and 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-77405.        ((A -> (((B and C) -> B) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-239, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77406
in-theory        77406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G)))))
theorem-size     41
proof            (modus-ponens tm-210 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-48.           (((A -> (B and 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-77406.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G))))), M:tm-210, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77407
in-theory        77407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-183 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-48.           (((A -> (B and 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-77407.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-183, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77408
in-theory        77408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-157 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77408.        ((A -> ((B and C) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-157, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77409
in-theory        77409
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     39
proof            (modus-ponens tm-147 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77409.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-147, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77410
in-theory        77410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-134 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77410.        ((A -> ((B and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-134, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77411
in-theory        77411
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     39
proof            (modus-ponens tm-125 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77411.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-125, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77412
in-theory        77412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-113 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-48.           (((A -> (B and 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-77412.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G))))), M:tm-113, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77413
in-theory        77413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     43
proof            (modus-ponens tm-105 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77413.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-105, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77414
in-theory        77414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E)))))
theorem-size     31
proof            (modus-ponens tm-95 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77414.        (((A -> B) -> (A -> A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E))))), M:tm-95, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77415
in-theory        77415
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (D -> ((B or (B or C)) -> (A and (B or C)))))
theorem-size     25
proof            (modus-ponens tm-84 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-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-77415.        ((A or ((B or C) -> (A and (B or C)))) -> (D -> ((B or (B or C)) -> (A and (B or C))))), M:tm-84, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77416
in-theory        77416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-83 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77416.        ((A -> (B -> (C -> B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-83, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77417
in-theory        77417
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C or D) -> (B and (C or D)))) -> ((C or (C or D)) -> (B and (C or D)))))
theorem-size     29
proof            (modus-ponens tm-76 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-48.           (((A -> (B and 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-77417.        (((not (not A)) -> A) and ((B or ((C or D) -> (B and (C or D)))) -> ((C or (C or D)) -> (B and (C or D))))), M:tm-76, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77418
in-theory        77418
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or ((B or C) -> (A and (B or C)))))) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C))))
theorem-size     37
proof            (modus-ponens tm-73 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
proof-size       157
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-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-77418.        (((not (not (A or ((B or C) -> (A and (B or C)))))) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C)))), M:tm-73, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77419
in-theory        77419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E)))))
theorem-size     35
proof            (modus-ponens tm-69 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-48.           (((A -> (B and 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-77419.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E))))), M:tm-69, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77420
in-theory        77420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-54 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77420.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-54, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77421
in-theory        77421
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and (A or B))) or (C or ((A or B) -> (C and (A or B))))) -> ((A or (A or B)) -> (C and (A or B))))
theorem-size     33
proof            (modus-ponens tm-50 tm-876 ((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
proof-size       155
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-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-77421.        ((((A or B) -> (C and (A or B))) or (C or ((A or B) -> (C and (A or B))))) -> ((A or (A or B)) -> (C and (A or B)))), M:tm-50, m:tm-876, u:((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77422
in-theory        77422
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C))))
theorem-size     25
proof            (modus-ponens tm-49 tm-876 ((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-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-77422.        ((A or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C)))), M:tm-49, m:tm-876, u:((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77423
in-theory        77423
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or ((C or D) -> (B and (C or D))))) or (B or ((C or D) -> (B and (C or D))))) -> ((C or (C or D)) -> (B and (C or D))))
theorem-size     37
proof            (modus-ponens tm-47 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
proof-size       157
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-48.           (((A -> (B and 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-77423.        (((A and (B or ((C or D) -> (B and (C or D))))) or (B or ((C or D) -> (B and (C or D))))) -> ((C or (C or D)) -> (B and (C or D)))), M:tm-47, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77424
in-theory        77424
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B or C) -> (A and (B or C)))) and D) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C))))
theorem-size     37
proof            (modus-ponens tm-46 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
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-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-77424.        ((((A or ((B or C) -> (A and (B or C)))) and D) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C)))), M:tm-46, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77425
in-theory        77425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-42 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-48.           (((A -> (B and 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-77425.        ((A -> (B or A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E))))), M:tm-42, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77426
in-theory        77426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-32 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-77426.        ((A -> (A or B)) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E))))), M:tm-32, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77427
in-theory        77427
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> ((A or ((B or C) -> (A and (B or C)))) and ((B or (B or C)) -> (A and (B or C)))))
theorem-size     35
proof            (modus-ponens tm-24 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-77427.        ((A or ((B or C) -> (A and (B or C)))) -> ((A or ((B or C) -> (A and (B or C)))) and ((B or (B or C)) -> (A and (B or C))))), M:tm-24, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77428
in-theory        77428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E)))))
theorem-size     31
proof            (modus-ponens tm-23 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-77428.        ((A -> (B -> (A and B))) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E))))), M:tm-23, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77429
in-theory        77429
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-22 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-48.           (((A -> (B and 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-77429.        (((A and B) -> B) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E))))), M:tm-22, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77430
in-theory        77430
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-21 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-48.           (((A -> (B and 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-77430.        (((A and B) -> A) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E))))), M:tm-21, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77431
in-theory        77431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-20 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-48.           (((A -> (B and 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-77431.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-20, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77432
in-theory        77432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-19 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-48.           (((A -> (B and 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-77432.        ((A -> (B -> A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((D or (D or E)) -> (C and (D or E))))), M:tm-19, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77433
in-theory        77433
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (A or ((B or C) -> (A and (B or C)))))
theorem-size     23
proof            (modus-ponens tm-12 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77433.        ((A or ((B or C) -> (A and (B or C)))) -> (A or ((B or C) -> (A and (B or C))))), M:tm-12, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77434
in-theory        77434
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> (not ((B or (B or C)) -> (A and (B or C))))) -> (not (A or ((B or C) -> (A and (B or C))))))
theorem-size     37
proof            (modus-ponens tm-9 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-6)
proof-size       139
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-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-77434.        (((A or ((B or C) -> (A and (B or C)))) -> (not ((B or (B or C)) -> (A and (B or C))))) -> (not (A or ((B or C) -> (A and (B or C)))))), M:tm-9, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77435
in-theory        77435
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> (C and (A or B))) -> D) -> (((C or ((A or B) -> (C and (A or B)))) or ((A or (A or B)) -> (C and (A or B)))) -> D))
theorem-size     39
proof            (modus-ponens tm-8 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77435.        ((((A or (A or B)) -> (C and (A or B))) -> D) -> (((C or ((A or B) -> (C and (A or B)))) or ((A or (A or B)) -> (C and (A or B)))) -> D)), M:tm-8, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-77436
in-theory        77436
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or ((C or D) -> (B and (C or D)))) -> ((C or (C or D)) -> (B and (C or D)))))
theorem-size     25
proof            (modus-ponens tm-7 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-6)
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-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-77436.        (A or ((B or ((C or D) -> (B and (C or D)))) -> ((C or (C or D)) -> (B and (C or D))))), M:tm-7, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77437
in-theory        77437
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-6 tm-8 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-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-49.           (((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-77437.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) or D), M:tm-6, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77438
in-theory        77438
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C or D) -> (B and (C or D)))) -> ((C or (C or D)) -> (B and (C or D)))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-77438.        (A -> (((B or ((C or D) -> (B and (C or D)))) -> ((C or (C or D)) -> (B and (C or D)))) and A)), M:tm-5, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77439
in-theory        77439
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> (B or (B or C))) -> ((A or ((B or C) -> (A and (B or C)))) -> (A and (B or C))))
theorem-size     35
proof            (modus-ponens tm-2 tm-876 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (or Bm (or Bm Cm))) (C (and Am (or Bm Cm)))))
axioms-used      (tm-2 tm-8 tm-5 tm-6)
proof-size       139
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-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-77439.        (((A or ((B or C) -> (A and (B or C)))) -> (B or (B or C))) -> ((A or ((B or C) -> (A and (B or C)))) -> (A and (B or C)))), M:tm-2, m:tm-876, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (or Bm (or Bm Cm))) (C (and Am (or Bm Cm))))
================================================================
tm-name          tm-77440
in-theory        77440
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or ((C or D) -> (B and (C or D)))) -> ((C or (C or D)) -> (B and (C or D)))))
theorem-size     25
proof            (modus-ponens tm-1 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-6)
proof-size       121
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77440.        (A -> ((B or ((C or D) -> (B and (C or D)))) -> ((C or (C or D)) -> (B and (C or D))))), M:tm-1, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-77441
in-theory        77441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-855 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-77441.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-855, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77442
in-theory        77442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-808 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77442.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-808, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77443
in-theory        77443
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((E and ((A and ((B or C) -> D)) or ((B or C) -> D))) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D)))
theorem-size     59
proof            (modus-ponens tm-798 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77443.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((E and ((A and ((B or C) -> D)) or ((B or C) -> D))) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D))), M:tm-798, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77444
in-theory        77444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-757 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-49.           (((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-77444.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-757, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77445
in-theory        77445
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((((A and ((B or C) -> D)) or ((B or C) -> D)) and E) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D)))
theorem-size     59
proof            (modus-ponens tm-747 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77445.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((((A and ((B or C) -> D)) or ((B or C) -> D)) and E) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D))), M:tm-747, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77446
in-theory        77446
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-708 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77446.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H))), M:tm-708, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77447
in-theory        77447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-665 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77447.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-665, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77448
in-theory        77448
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E or ((B or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-623 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77448.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E or ((B or (B or C)) -> D))), M:tm-623, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77449
in-theory        77449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-622 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77449.        ((A -> (B -> (C or B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-622, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77450
in-theory        77450
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-49.           (((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-77450.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77451
in-theory        77451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-605 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77451.        ((A -> ((B -> (C or B)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-605, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77452
in-theory        77452
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (F or E)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-595 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-49.           (((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-77452.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (F or E)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))), M:tm-595, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77453
in-theory        77453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-550 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77453.        (((A -> (B or A)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-550, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77454
in-theory        77454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-540 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77454.        ((A or (B -> (C or B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-540, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77455
in-theory        77455
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-530 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77455.        ((A or (B -> (B or C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-530, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77456
in-theory        77456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-520 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77456.        ((A or (B -> (C -> (B and C)))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-520, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77457
in-theory        77457
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-510 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-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-77457.        ((A or ((B and C) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-510, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77458
in-theory        77458
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-500 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77458.        ((A or ((B and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-500, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77459
in-theory        77459
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-490 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77459.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H))), M:tm-490, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77460
in-theory        77460
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-480 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77460.        ((A or (B -> (C -> B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-480, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77461
in-theory        77461
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((B or (B or C)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77461.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((B or (B or C)) -> D) or E)), M:tm-470, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77462
in-theory        77462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-469 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-49.           (((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-77462.        ((A -> (B -> (B or C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-469, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77463
in-theory        77463
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-49.           (((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-77463.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77464
in-theory        77464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-453 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77464.        ((A -> ((B -> (B or C)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-453, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77465
in-theory        77465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (E or F)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-443 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-77465.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (E or F)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))), M:tm-443, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77466
in-theory        77466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-409 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77466.        (((A -> (A or B)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-409, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77467
in-theory        77467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-400 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77467.        (((A -> (B -> (A and B))) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-400, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77468
in-theory        77468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-391 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77468.        ((((A and B) -> B) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-391, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77469
in-theory        77469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-382 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77469.        ((((A and B) -> A) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-382, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77470
in-theory        77470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-373 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77470.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H))), M:tm-373, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77471
in-theory        77471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-364 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77471.        (((A -> (B -> A)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-364, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77472
in-theory        77472
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E -> (((B or (B or C)) -> D) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-49.           (((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-77472.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E -> (((B or (B or C)) -> D) and E))), M:tm-355, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77473
in-theory        77473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-354 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77473.        ((A -> (B -> (C -> (B and C)))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-354, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77474
in-theory        77474
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-49.           (((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-77474.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77475
in-theory        77475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-338 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77475.        (((A -> B) -> (A -> (A and B))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-338, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77476
in-theory        77476
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) and ((B or (B or C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-328 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-49.           (((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-77476.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) and ((B or (B or C)) -> D)))), M:tm-328, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77477
in-theory        77477
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))))
theorem-size     51
proof            (modus-ponens tm-327 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-49.           (((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-77477.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))), M:tm-327, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77478
in-theory        77478
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((E and F) -> F) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-326 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-49.           (((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-77478.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((E and F) -> F) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))), M:tm-326, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77479
in-theory        77479
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((E and F) -> E) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-325 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-49.           (((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-77479.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((E and F) -> E) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))), M:tm-325, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77480
in-theory        77480
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-324 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77480.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))), M:tm-324, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77481
in-theory        77481
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (F -> E)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-323 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-49.           (((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-77481.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (F -> E)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))), M:tm-323, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77482
in-theory        77482
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-49.           (((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-77482.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77483
in-theory        77483
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-49.           (((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-77483.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77484
in-theory        77484
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-49.           (((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-77484.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77485
in-theory        77485
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((A and ((B or C) -> D)) or ((B or C) -> D))))
theorem-size     49
proof            (modus-ponens tm-316 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-49.           (((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-77485.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((A and ((B or C) -> D)) or ((B or C) -> D)))), M:tm-316, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77486
in-theory        77486
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-49.           (((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-77486.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77487
in-theory        77487
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (not ((B or (B or C)) -> D))) -> (not ((A and ((B or C) -> D)) or ((B or C) -> D)))))
theorem-size     59
proof            (modus-ponens tm-313 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-49.           (((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-77487.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (not ((B or (B or C)) -> D))) -> (not ((A and ((B or C) -> D)) or ((B or C) -> D))))), M:tm-313, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77488
in-theory        77488
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((B or (B or C)) -> D) -> E) -> ((((A and ((B or C) -> D)) or ((B or C) -> D)) or ((B or (B or C)) -> D)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-77488.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((B or (B or C)) -> D) -> E) -> ((((A and ((B or C) -> D)) or ((B or C) -> D)) or ((B or (B or C)) -> D)) -> E))), M:tm-312, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77489
in-theory        77489
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E or (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-311 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-49.           (((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-77489.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E or (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))), M:tm-311, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77490
in-theory        77490
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (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-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-49.           (((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-77490.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) or E)), M:tm-310, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77491
in-theory        77491
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-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-49.           (((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-77491.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and E))), M:tm-309, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77492
in-theory        77492
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (B or (B or C))) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> D)))
theorem-size     57
proof            (modus-ponens tm-306 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (or Bm (or Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-306.          ((A -> (B -> C)) -> ((A -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77492.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (B or (B or C))) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> D))), M:tm-306, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (or Bm (or Bm Cm))) (C Dm))
================================================================
tm-name          tm-77493
in-theory        77493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-305 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-49.           (((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-77493.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (E -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))), M:tm-305, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77494
in-theory        77494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-303 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77494.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-303, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77495
in-theory        77495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-270 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-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-77495.        ((A -> (((B and C) -> C) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-270, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77496
in-theory        77496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-239 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77496.        ((A -> (((B and C) -> B) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-239, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77497
in-theory        77497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-210 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-49.           (((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-77497.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H))), M:tm-210, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77498
in-theory        77498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-183 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77498.        ((A -> ((B -> (C -> B)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-183, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77499
in-theory        77499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-157 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-49.           (((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-77499.        ((A -> ((B and C) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-157, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77500
in-theory        77500
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-147 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-49.           (((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-77500.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-147, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77501
in-theory        77501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-134 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77501.        ((A -> ((B and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-134, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77502
in-theory        77502
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-125 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-49.           (((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-77502.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-125, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77503
in-theory        77503
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> (D -> E))) or ((B or C) -> (D -> E))) -> (((B or (B or C)) -> D) -> ((B or (B or C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-114 tm-877 ((A (or (and Am (-> (or Bm Cm) (-> C D))) (-> (or Bm Cm) (-> C D)))) (B (or Bm (or Bm Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77503.        (((A and ((B or C) -> (D -> E))) or ((B or C) -> (D -> E))) -> (((B or (B or C)) -> D) -> ((B or (B or C)) -> E))), M:tm-114, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) (-> C D))) (-> (or Bm Cm) (-> C D)))) (B (or Bm (or Bm Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-77504
in-theory        77504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-113 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77504.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H))), M:tm-113, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77505
in-theory        77505
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-105 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77505.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-105, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77506
in-theory        77506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-95 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-49.           (((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-77506.        (((A -> B) -> (A -> A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-95, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77507
in-theory        77507
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E -> ((B or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-84 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77507.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E -> ((B or (B or C)) -> D))), M:tm-84, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77508
in-theory        77508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-83 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77508.        ((A -> (B -> (C -> B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-83, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77509
in-theory        77509
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-76 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77509.        (((not (not A)) -> A) and (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-76, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77510
in-theory        77510
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and ((B or C) -> D)) or ((B or C) -> D)))) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D))
theorem-size     37
proof            (modus-ponens tm-73 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77510.        (((not (not ((A and ((B or C) -> D)) or ((B or C) -> D)))) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D)), M:tm-73, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77511
in-theory        77511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-69 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77511.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-69, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77512
in-theory        77512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-54 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-77512.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-54, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77513
in-theory        77513
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((D and ((A or B) -> C)) or ((A or B) -> C))) -> ((A or (A or B)) -> C))
theorem-size     27
proof            (modus-ponens tm-50 tm-877 ((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-7 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77513.        ((((A or B) -> C) or ((D and ((A or B) -> C)) or ((A or B) -> C))) -> ((A or (A or B)) -> C)), M:tm-50, m:tm-877, u:((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77514
in-theory        77514
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D))
theorem-size     29
proof            (modus-ponens tm-49 tm-877 ((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-6 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-77514.        (((A and ((B or C) -> D)) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D)), M:tm-49, m:tm-877, u:((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77515
in-theory        77515
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and ((C or D) -> E)) or ((C or D) -> E))) or ((B and ((C or D) -> E)) or ((C or D) -> E))) -> ((C or (C or D)) -> E))
theorem-size     37
proof            (modus-ponens tm-47 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77515.        (((A and ((B and ((C or D) -> E)) or ((C or D) -> E))) or ((B and ((C or D) -> E)) or ((C or D) -> E))) -> ((C or (C or D)) -> E)), M:tm-47, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77516
in-theory        77516
times-derived    1
----------------------------------------------------------------
theorem          (((((A and ((B or C) -> D)) or ((B or C) -> D)) and E) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D))
theorem-size     37
proof            (modus-ponens tm-46 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77516.        (((((A and ((B or C) -> D)) or ((B or C) -> D)) and E) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D)), M:tm-46, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77517
in-theory        77517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-42 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77517.        ((A -> (B or A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-42, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77518
in-theory        77518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-32 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77518.        ((A -> (A or B)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-32, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77519
in-theory        77519
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) and ((B or (B or C)) -> D)))
theorem-size     35
proof            (modus-ponens tm-24 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-77519.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) and ((B or (B or C)) -> D))), M:tm-24, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77520
in-theory        77520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-23 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-77520.        ((A -> (B -> (A and B))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-23, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77521
in-theory        77521
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-22 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-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-77521.        (((A and B) -> B) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-22, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77522
in-theory        77522
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-21 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77522.        (((A and B) -> A) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-21, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77523
in-theory        77523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-20 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-49.           (((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-77523.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-20, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77524
in-theory        77524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-19 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77524.        ((A -> (B -> A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-19, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77525
in-theory        77525
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((A and ((B or C) -> D)) or ((B or C) -> D)))
theorem-size     27
proof            (modus-ponens tm-12 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77525.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((A and ((B or C) -> D)) or ((B or C) -> D))), M:tm-12, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77526
in-theory        77526
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (not ((B or (B or C)) -> D))) -> (not ((A and ((B or C) -> D)) or ((B or C) -> D))))
theorem-size     37
proof            (modus-ponens tm-9 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77526.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (not ((B or (B or C)) -> D))) -> (not ((A and ((B or C) -> D)) or ((B or C) -> D)))), M:tm-9, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77527
in-theory        77527
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> ((((E and ((A or B) -> C)) or ((A or B) -> C)) or ((A or (A or B)) -> C)) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-6)
proof-size       127
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-49.           (((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-77527.        ((((A or (A or B)) -> C) -> D) -> ((((E and ((A or B) -> C)) or ((A or B) -> C)) or ((A or (A or B)) -> C)) -> D)), M:tm-8, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77528
in-theory        77528
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-7 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77528.        (A or (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-7, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77529
in-theory        77529
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-77529.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) or E), M:tm-6, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77530
in-theory        77530
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((C or (C or D)) -> E)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-77530.        (A -> ((((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((C or (C or D)) -> E)) and A)), M:tm-5, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77531
in-theory        77531
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (B or (B or C))) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> D))
theorem-size     35
proof            (modus-ponens tm-2 tm-877 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (or Bm (or Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-77531.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (B or (B or C))) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> D)), M:tm-2, m:tm-877, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (or Bm (or Bm Cm))) (C Dm))
================================================================
tm-name          tm-77532
in-theory        77532
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-1 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-6)
proof-size       109
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77532.        (A -> (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-1, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-77533
in-theory        77533
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     39
proof            (modus-ponens tm-855 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
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-77533.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-855, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77534
in-theory        77534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-808 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-77534.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-808, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77535
in-theory        77535
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((E and ((((A or B) -> C) and D) or ((A or B) -> C))) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C)))
theorem-size     59
proof            (modus-ponens tm-798 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3 tm-6)
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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-77535.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((E and ((((A or B) -> C) and D) or ((A or B) -> C))) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C))), M:tm-798, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77536
in-theory        77536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-757 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-77536.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-757, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77537
in-theory        77537
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((((((A or B) -> C) and D) or ((A or B) -> C)) and E) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C)))
theorem-size     59
proof            (modus-ponens tm-747 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77537.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((((((A or B) -> C) and D) or ((A or B) -> C)) and E) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C))), M:tm-747, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77538
in-theory        77538
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) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     47
proof            (modus-ponens tm-708 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77538.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-708, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77539
in-theory        77539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-665 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77539.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-665, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77540
in-theory        77540
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E or ((A or (A or B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-623 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77540.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E or ((A or (A or B)) -> C))), M:tm-623, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77541
in-theory        77541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-622 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77541.        ((A -> (B -> (C or B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-622, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77542
in-theory        77542
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-49.           (((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-77542.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (F or E))), M:tm-609, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77543
in-theory        77543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-605 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77543.        ((A -> ((B -> (C or B)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-605, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77544
in-theory        77544
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (F or E)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-595 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-49.           (((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-77544.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (F or E)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))), M:tm-595, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77545
in-theory        77545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-550 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-49.           (((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-77545.        (((A -> (B or A)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-550, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77546
in-theory        77546
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-540 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77546.        ((A or (B -> (C or B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-540, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77547
in-theory        77547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-530 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-49.           (((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-77547.        ((A or (B -> (B or C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-530, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77548
in-theory        77548
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-520 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77548.        ((A or (B -> (C -> (B and C)))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-520, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77549
in-theory        77549
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-510 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77549.        ((A or ((B and C) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-510, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77550
in-theory        77550
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-500 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77550.        ((A or ((B and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-500, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77551
in-theory        77551
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-490 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77551.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-490, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77552
in-theory        77552
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-480 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77552.        ((A or (B -> (C -> B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-480, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77553
in-theory        77553
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or (A or B)) -> C) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or 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-49.           (((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-77553.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or (A or B)) -> C) or E)), M:tm-470, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77554
in-theory        77554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-469 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or 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-49.           (((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-77554.        ((A -> (B -> (B or C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-469, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77555
in-theory        77555
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or 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-49.           (((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-77555.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (E or F))), M:tm-456, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77556
in-theory        77556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-453 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
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-49.           (((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-77556.        ((A -> ((B -> (B or C)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-453, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77557
in-theory        77557
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (E or F)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-443 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-77557.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (E or F)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))), M:tm-443, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77558
in-theory        77558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-409 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-49.           (((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-77558.        (((A -> (A or B)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-409, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77559
in-theory        77559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-400 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
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-49.           (((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-77559.        (((A -> (B -> (A and B))) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-400, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77560
in-theory        77560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-391 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-77560.        ((((A and B) -> B) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-391, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77561
in-theory        77561
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-382 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-49.           (((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-77561.        ((((A and B) -> A) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-382, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77562
in-theory        77562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-373 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
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-49.           (((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-77562.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-373, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77563
in-theory        77563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-364 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or 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-49.           (((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-77563.        (((A -> (B -> A)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-364, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77564
in-theory        77564
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E -> (((A or (A or B)) -> C) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-49.           (((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-77564.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E -> (((A or (A or B)) -> C) and E))), M:tm-355, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77565
in-theory        77565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-354 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77565.        ((A -> (B -> (C -> (B and C)))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-354, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77566
in-theory        77566
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-49.           (((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-77566.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77567
in-theory        77567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-338 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77567.        (((A -> B) -> (A -> (A and B))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-338, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77568
in-theory        77568
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((((A or B) -> C) and D) or ((A or B) -> C)) and ((A or (A or B)) -> C))))
theorem-size     57
proof            (modus-ponens tm-328 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77568.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((((A or B) -> C) and D) or ((A or B) -> C)) and ((A or (A or B)) -> C)))), M:tm-328, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77569
in-theory        77569
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (F -> (E and F))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))))
theorem-size     51
proof            (modus-ponens tm-327 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-49.           (((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-77569.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (F -> (E and F))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))), M:tm-327, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77570
in-theory        77570
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((E and F) -> F) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-326 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-49.           (((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-77570.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((E and F) -> F) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))), M:tm-326, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77571
in-theory        77571
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((E and F) -> E) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-325 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-49.           (((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-77571.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((E and F) -> E) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))), M:tm-325, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77572
in-theory        77572
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))))
theorem-size     57
proof            (modus-ponens tm-324 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77572.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))), M:tm-324, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77573
in-theory        77573
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (F -> E)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-323 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-49.           (((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-77573.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (F -> E)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))), M:tm-323, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77574
in-theory        77574
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-49.           (((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-77574.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77575
in-theory        77575
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77575.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77576
in-theory        77576
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-49.           (((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-77576.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77577
in-theory        77577
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((((A or B) -> C) and D) or ((A or B) -> C))))
theorem-size     49
proof            (modus-ponens tm-316 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-49.           (((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-77577.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((((A or B) -> C) and D) or ((A or B) -> C)))), M:tm-316, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77578
in-theory        77578
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-49.           (((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-77578.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77579
in-theory        77579
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (not ((A or (A or B)) -> C))) -> (not ((((A or B) -> C) and D) or ((A or B) -> C)))))
theorem-size     59
proof            (modus-ponens tm-313 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-49.           (((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-77579.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (not ((A or (A or B)) -> C))) -> (not ((((A or B) -> C) and D) or ((A or B) -> C))))), M:tm-313, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77580
in-theory        77580
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((((A or (A or B)) -> C) -> E) -> ((((((A or B) -> C) and D) or ((A or B) -> C)) or ((A or (A or B)) -> C)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77580.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((((A or (A or B)) -> C) -> E) -> ((((((A or B) -> C) and D) or ((A or B) -> C)) or ((A or (A or B)) -> C)) -> E))), M:tm-312, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77581
in-theory        77581
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E or (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-311 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-49.           (((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-77581.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E or (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))), M:tm-311, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77582
in-theory        77582
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((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)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
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-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-49.           (((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-77582.        ((((((A or B) -> C) and D) or ((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)) or E)), M:tm-310, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77583
in-theory        77583
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-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-49.           (((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-77583.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and E))), M:tm-309, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77584
in-theory        77584
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((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))) -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> C)))
theorem-size     57
proof            (modus-ponens tm-306 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (or Am (or Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-306.          ((A -> (B -> C)) -> ((A -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77584.        ((((((A or B) -> C) and D) or ((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))) -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> C))), M:tm-306, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (or Am (or Am Bm))) (C Cm))
================================================================
tm-name          tm-77585
in-theory        77585
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-305 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-49.           (((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-77585.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (E -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))), M:tm-305, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77586
in-theory        77586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-303 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77586.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-303, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77587
in-theory        77587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-270 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77587.        ((A -> (((B and C) -> C) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-270, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77588
in-theory        77588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-239 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77588.        ((A -> (((B and C) -> B) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-239, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77589
in-theory        77589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-210 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-49.           (((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-77589.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-210, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77590
in-theory        77590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-183 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77590.        ((A -> ((B -> (C -> B)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-183, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77591
in-theory        77591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-157 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77591.        ((A -> ((B and C) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-157, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77592
in-theory        77592
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-147 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-49.           (((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-77592.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-147, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77593
in-theory        77593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-134 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-49.           (((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-77593.        ((A -> ((B and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-134, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77594
in-theory        77594
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-125 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-49.           (((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-77594.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-125, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77595
in-theory        77595
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> (C -> D)) and E) or ((A or B) -> (C -> D))) -> (((A or (A or B)) -> C) -> ((A or (A or B)) -> D)))
theorem-size     33
proof            (modus-ponens tm-114 tm-878 ((A (or (and (-> (or Am Bm) (-> C D)) Dm) (-> (or Am Bm) (-> C D)))) (B (or Am (or Am Bm))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77595.        (((((A or B) -> (C -> D)) and E) or ((A or B) -> (C -> D))) -> (((A or (A or B)) -> C) -> ((A or (A or B)) -> D))), M:tm-114, m:tm-878, u:((A (or (and (-> (or Am Bm) (-> C D)) Dm) (-> (or Am Bm) (-> C D)))) (B (or Am (or Am Bm))) (Cm (-> C D)))
================================================================
tm-name          tm-77596
in-theory        77596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-113 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77596.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-113, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77597
in-theory        77597
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-105 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77597.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-105, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77598
in-theory        77598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-95 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-49.           (((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-77598.        (((A -> B) -> (A -> A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-95, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77599
in-theory        77599
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E -> ((A or (A or B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-84 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77599.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E -> ((A or (A or B)) -> C))), M:tm-84, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77600
in-theory        77600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-83 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77600.        ((A -> (B -> (C -> B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-83, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77601
in-theory        77601
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-76 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77601.        (((not (not A)) -> A) and (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((B or (B or C)) -> D))), M:tm-76, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77602
in-theory        77602
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A or B) -> C) and D) or ((A or B) -> C)))) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C))
theorem-size     37
proof            (modus-ponens tm-73 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-10 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77602.        (((not (not ((((A or B) -> C) and D) or ((A or B) -> C)))) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C)), M:tm-73, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77603
in-theory        77603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-69 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77603.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-69, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77604
in-theory        77604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-54 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-77604.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-54, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77605
in-theory        77605
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C))
theorem-size     27
proof            (modus-ponens tm-50 tm-878 ((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-7 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77605.        ((((A or B) -> C) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C)), M:tm-50, m:tm-878, u:((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77606
in-theory        77606
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) 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-49 tm-878 ((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-6 tm-3)
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-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-77606.        (((((A or B) -> C) and D) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C)), M:tm-49, m:tm-878, u:((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77607
in-theory        77607
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B or C) -> D) and E) or ((B or C) -> D))) or ((((B or C) -> D) and E) or ((B or C) -> D))) -> ((B or (B or C)) -> D))
theorem-size     37
proof            (modus-ponens tm-47 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77607.        (((A and ((((B or C) -> D) and E) or ((B or C) -> D))) or ((((B or C) -> D) and E) or ((B or C) -> D))) -> ((B or (B or C)) -> D)), M:tm-47, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77608
in-theory        77608
times-derived    1
----------------------------------------------------------------
theorem          (((((((A or B) -> C) and D) or ((A or B) -> C)) and E) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C))
theorem-size     37
proof            (modus-ponens tm-46 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77608.        (((((((A or B) -> C) and D) or ((A or B) -> C)) and E) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C)), M:tm-46, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77609
in-theory        77609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-42 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77609.        ((A -> (B or A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-42, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77610
in-theory        77610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-32 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-49.           (((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-77610.        ((A -> (A or B)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-32, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77611
in-theory        77611
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((((A or B) -> C) and D) or ((A or B) -> C)) and ((A or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-24 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77611.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((((A or B) -> C) and D) or ((A or B) -> C)) and ((A or (A or B)) -> C))), M:tm-24, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77612
in-theory        77612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-23 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-49.           (((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-77612.        ((A -> (B -> (A and B))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-23, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77613
in-theory        77613
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-22 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77613.        (((A and B) -> B) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-22, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77614
in-theory        77614
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-21 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77614.        (((A and B) -> A) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-21, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77615
in-theory        77615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-20 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-49.           (((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-77615.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-20, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77616
in-theory        77616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-19 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77616.        ((A -> (B -> A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((C or (C or D)) -> E))), M:tm-19, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77617
in-theory        77617
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((((A or B) -> C) and D) or ((A or B) -> C)))
theorem-size     27
proof            (modus-ponens tm-12 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77617.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((((A or B) -> C) and D) or ((A or B) -> C))), M:tm-12, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77618
in-theory        77618
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (not ((A or (A or B)) -> C))) -> (not ((((A or B) -> C) and D) or ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-9 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-9 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77618.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (not ((A or (A or B)) -> C))) -> (not ((((A or B) -> C) and D) or ((A or B) -> C)))), M:tm-9, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77619
in-theory        77619
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> ((((((A or B) -> C) and E) or ((A or B) -> C)) or ((A or (A or B)) -> C)) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77619.        ((((A or (A or B)) -> C) -> D) -> ((((((A or B) -> C) and E) or ((A or B) -> C)) or ((A or (A or B)) -> C)) -> D)), M:tm-8, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-77620
in-theory        77620
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-7 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77620.        (A or (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((B or (B or C)) -> D))), M:tm-7, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77621
in-theory        77621
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-6 tm-8 tm-3)
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-49.           (((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-77621.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) or E), M:tm-6, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77622
in-theory        77622
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B or C) -> D) and E) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
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-77622.        (A -> ((((((B or C) -> D) and E) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and A)), M:tm-5, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77623
in-theory        77623
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (A or (A or B))) -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> C))
theorem-size     35
proof            (modus-ponens tm-2 tm-878 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (or Am (or Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77623.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (A or (A or B))) -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> C)), M:tm-2, m:tm-878, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (or Am (or Am Bm))) (C Cm))
================================================================
tm-name          tm-77624
in-theory        77624
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((B or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-1 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-1 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77624.        (A -> (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((B or (B or C)) -> D))), M:tm-1, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-77625
in-theory        77625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     33
proof            (modus-ponens tm-855 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-77625.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-855, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77626
in-theory        77626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-6)
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-77626.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-808, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77627
in-theory        77627
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((D and (A or ((B or C) -> A))) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A)))
theorem-size     41
proof            (modus-ponens tm-798 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-77627.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((D and (A or ((B or C) -> A))) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A))), M:tm-798, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77628
in-theory        77628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77628.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-757, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77629
in-theory        77629
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((((A or ((B or C) -> A)) and D) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A)))
theorem-size     41
proof            (modus-ponens tm-747 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-49.           (((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-77629.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((((A or ((B or C) -> A)) and D) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A))), M:tm-747, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77630
in-theory        77630
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77630.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E))), M:tm-708, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77631
in-theory        77631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77631.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-665, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77632
in-theory        77632
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (D or ((B or (B or C)) -> A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-49.           (((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-77632.        ((A or ((B or C) -> A)) -> (D or ((B or (B or C)) -> A))), M:tm-623, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77633
in-theory        77633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77633.        ((A -> (B -> (C or B))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-622, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77634
in-theory        77634
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-49.           (((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-77634.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (E or D))), M:tm-609, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77635
in-theory        77635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-49.           (((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-77635.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-605, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77636
in-theory        77636
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (E or D)) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-49.           (((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-77636.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (E or D)) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)))), M:tm-595, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77637
in-theory        77637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77637.        (((A -> (B or A)) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-550, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77638
in-theory        77638
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-49.           (((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-77638.        ((A or (B -> (C or B))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-540, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77639
in-theory        77639
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77639.        ((A or (B -> (B or C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-530, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77640
in-theory        77640
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-49.           (((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-77640.        ((A or (B -> (C -> (B and C)))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-520, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77641
in-theory        77641
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-49.           (((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-77641.        ((A or ((B and C) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-510, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77642
in-theory        77642
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-49.           (((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-77642.        ((A or ((B and C) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-500, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77643
in-theory        77643
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77643.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E))), M:tm-490, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77644
in-theory        77644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77644.        ((A or (B -> (C -> B))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-480, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77645
in-theory        77645
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (((B or (B or C)) -> A) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or 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-49.           (((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-77645.        ((A or ((B or C) -> A)) -> (((B or (B or C)) -> A) or D)), M:tm-470, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77646
in-theory        77646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77646.        ((A -> (B -> (B or C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-469, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77647
in-theory        77647
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77647.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (D or E))), M:tm-456, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77648
in-theory        77648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77648.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-453, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77649
in-theory        77649
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (D or E)) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77649.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (D or E)) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)))), M:tm-443, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77650
in-theory        77650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77650.        (((A -> (A or B)) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-409, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77651
in-theory        77651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77651.        (((A -> (B -> (A and B))) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-400, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77652
in-theory        77652
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77652.        ((((A and B) -> B) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-391, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77653
in-theory        77653
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77653.        ((((A and B) -> A) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-382, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77654
in-theory        77654
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77654.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E))), M:tm-373, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77655
in-theory        77655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77655.        (((A -> (B -> A)) or C) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-364, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77656
in-theory        77656
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (D -> (((B or (B or C)) -> A) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-49.           (((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-77656.        ((A or ((B or C) -> A)) -> (D -> (((B or (B or C)) -> A) and D))), M:tm-355, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77657
in-theory        77657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77657.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-354, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77658
in-theory        77658
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-49.           (((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-77658.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77659
in-theory        77659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-49.           (((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-77659.        (((A -> B) -> (A -> (A and B))) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C))), M:tm-338, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77660
in-theory        77660
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((A or ((B or C) -> A)) -> ((A or ((B or C) -> A)) and ((B or (B or C)) -> A))))
theorem-size     39
proof            (modus-ponens tm-328 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-49.           (((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-77660.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((A or ((B or C) -> A)) -> ((A or ((B or C) -> A)) and ((B or (B or C)) -> A)))), M:tm-328, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77661
in-theory        77661
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (E -> (D and E))) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-49.           (((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-77661.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (E -> (D and E))) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)))), M:tm-327, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77662
in-theory        77662
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((D and E) -> E) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-49.           (((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-77662.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((D and E) -> E) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)))), M:tm-326, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77663
in-theory        77663
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((D and E) -> D) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-49.           (((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-77663.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((D and E) -> D) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)))), M:tm-325, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77664
in-theory        77664
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-49.           (((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-77664.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)))), M:tm-324, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77665
in-theory        77665
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (E -> D)) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-49.           (((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-77665.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (E -> D)) and ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)))), M:tm-323, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77666
in-theory        77666
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-49.           (((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-77666.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D and E) -> E)), M:tm-322, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77667
in-theory        77667
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-49.           (((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-77667.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D and E) -> D)), M:tm-320, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77668
in-theory        77668
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-49.           (((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-77668.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77669
in-theory        77669
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((A or ((B or C) -> A)) -> (A or ((B or C) -> A))))
theorem-size     31
proof            (modus-ponens tm-316 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-49.           (((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-77669.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((A or ((B or C) -> A)) -> (A or ((B or C) -> A)))), M:tm-316, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77670
in-theory        77670
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-49.           (((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-77670.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (E -> D))), M:tm-315, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77671
in-theory        77671
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> (not ((B or (B or C)) -> A))) -> (not (A or ((B or C) -> A)))))
theorem-size     41
proof            (modus-ponens tm-313 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-49.           (((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-77671.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> (not ((B or (B or C)) -> A))) -> (not (A or ((B or C) -> A))))), M:tm-313, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77672
in-theory        77672
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((((B or (B or C)) -> A) -> D) -> (((A or ((B or C) -> A)) or ((B or (B or C)) -> A)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
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-312.          ((A -> B) -> ((A -> B) and ((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-49.           (((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-77672.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((((B or (B or C)) -> A) -> D) -> (((A or ((B or C) -> A)) or ((B or (B or C)) -> A)) -> D))), M:tm-312, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77673
in-theory        77673
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D or ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-49.           (((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-77673.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D or ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)))), M:tm-311, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77674
in-theory        77674
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77674.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) or D)), M:tm-310, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77675
in-theory        77675
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
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-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-49.           (((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-77675.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and D))), M:tm-309, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77676
in-theory        77676
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> (B or (B or C))) -> ((A or ((B or C) -> A)) -> A)))
theorem-size     39
proof            (modus-ponens tm-306 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (or Bm (or Bm Cm))) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-49.           (((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-77676.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> (B or (B or C))) -> ((A or ((B or C) -> A)) -> A))), M:tm-306, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (or Bm (or Bm Cm))) (C Am))
================================================================
tm-name          tm-77677
in-theory        77677
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
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-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-49.           (((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-77677.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and (D -> ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)))), M:tm-305, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77678
in-theory        77678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-49.           (((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-77678.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-303, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77679
in-theory        77679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77679.        ((A -> (((B and C) -> C) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-270, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77680
in-theory        77680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77680.        ((A -> (((B and C) -> B) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-239, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77681
in-theory        77681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-49.           (((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-77681.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E))), M:tm-210, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77682
in-theory        77682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77682.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-183, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77683
in-theory        77683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77683.        ((A -> ((B and C) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-157, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77684
in-theory        77684
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-49.           (((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-77684.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-147, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77685
in-theory        77685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77685.        ((A -> ((B and C) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-134, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77686
in-theory        77686
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-49.           (((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-77686.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-125, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77687
in-theory        77687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C or D) -> (A -> B))) -> (((C or (C or D)) -> A) -> ((C or (C or D)) -> B)))
theorem-size     27
proof            (modus-ponens tm-114 tm-879 ((A (or (-> C D) (-> (or Bm Cm) (-> C D)))) (B (or Bm (or Bm Cm))) (Am (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 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-14.           (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77687.        (((A -> B) or ((C or D) -> (A -> B))) -> (((C or (C or D)) -> A) -> ((C or (C or D)) -> B))), M:tm-114, m:tm-879, u:((A (or (-> C D) (-> (or Bm Cm) (-> C D)))) (B (or Bm (or Bm Cm))) (Am (-> C D)))
================================================================
tm-name          tm-77688
in-theory        77688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77688.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E))), M:tm-113, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77689
in-theory        77689
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-49.           (((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-77689.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-105, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77690
in-theory        77690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-49.           (((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-77690.        (((A -> B) -> (A -> A)) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C))), M:tm-95, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77691
in-theory        77691
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (D -> ((B or (B or C)) -> A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-49.           (((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-77691.        ((A or ((B or C) -> A)) -> (D -> ((B or (B or C)) -> A))), M:tm-84, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77692
in-theory        77692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77692.        ((A -> (B -> (C -> B))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-83, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77693
in-theory        77693
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C or D) -> B)) -> ((C or (C or D)) -> B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77693.        (((not (not A)) -> A) and ((B or ((C or D) -> B)) -> ((C or (C or D)) -> B))), M:tm-76, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77694
in-theory        77694
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or ((B or C) -> A)))) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A))
theorem-size     25
proof            (modus-ponens tm-73 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77694.        (((not (not (A or ((B or C) -> A)))) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A)), M:tm-73, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77695
in-theory        77695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77695.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C))), M:tm-69, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77696
in-theory        77696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-77696.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-54, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77697
in-theory        77697
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or (C or ((A or B) -> C))) -> ((A or (A or B)) -> C))
theorem-size     21
proof            (modus-ponens tm-50 tm-879 ((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77697.        ((((A or B) -> C) or (C or ((A or B) -> C))) -> ((A or (A or B)) -> C)), M:tm-50, m:tm-879, u:((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77698
in-theory        77698
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A))
theorem-size     17
proof            (modus-ponens tm-49 tm-879 ((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Bm (or 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-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-77698.        ((A or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A)), M:tm-49, m:tm-879, u:((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77699
in-theory        77699
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or ((C or D) -> B))) or (B or ((C or D) -> B))) -> ((C or (C or D)) -> B))
theorem-size     25
proof            (modus-ponens tm-47 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77699.        (((A and (B or ((C or D) -> B))) or (B or ((C or D) -> B))) -> ((C or (C or D)) -> B)), M:tm-47, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77700
in-theory        77700
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B or C) -> A)) and D) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A))
theorem-size     25
proof            (modus-ponens tm-46 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77700.        ((((A or ((B or C) -> A)) and D) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A)), M:tm-46, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77701
in-theory        77701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77701.        ((A -> (B or A)) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C))), M:tm-42, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77702
in-theory        77702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77702.        ((A -> (A or B)) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C))), M:tm-32, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77703
in-theory        77703
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> ((A or ((B or C) -> A)) and ((B or (B or C)) -> A)))
theorem-size     23
proof            (modus-ponens tm-24 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77703.        ((A or ((B or C) -> A)) -> ((A or ((B or C) -> A)) and ((B or (B or C)) -> A))), M:tm-24, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77704
in-theory        77704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-49.           (((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-77704.        ((A -> (B -> (A and B))) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C))), M:tm-23, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77705
in-theory        77705
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77705.        (((A and B) -> B) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C))), M:tm-22, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77706
in-theory        77706
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77706.        (((A and B) -> A) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C))), M:tm-21, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77707
in-theory        77707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-49.           (((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-77707.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-20, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77708
in-theory        77708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
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-19.           (A -> ((B -> (C -> B)) and 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-49.           (((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-77708.        ((A -> (B -> A)) and ((C or ((D or E) -> C)) -> ((D or (D or E)) -> C))), M:tm-19, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77709
in-theory        77709
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (A or ((B or C) -> A)))
theorem-size     15
proof            (modus-ponens tm-12 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77709.        ((A or ((B or C) -> A)) -> (A or ((B or C) -> A))), M:tm-12, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77710
in-theory        77710
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> (not ((B or (B or C)) -> A))) -> (not (A or ((B or C) -> A))))
theorem-size     25
proof            (modus-ponens tm-9 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-9 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77710.        (((A or ((B or C) -> A)) -> (not ((B or (B or C)) -> A))) -> (not (A or ((B or C) -> A)))), M:tm-9, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77711
in-theory        77711
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> (((C or ((A or B) -> C)) or ((A or (A or B)) -> C)) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77711.        ((((A or (A or B)) -> C) -> D) -> (((C or ((A or B) -> C)) or ((A or (A or B)) -> C)) -> D)), M:tm-8, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-77712
in-theory        77712
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or ((C or D) -> B)) -> ((C or (C or D)) -> B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-7 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77712.        (A or ((B or ((C or D) -> B)) -> ((C or (C or D)) -> B))), M:tm-7, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77713
in-theory        77713
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or 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-49.           (((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-77713.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) or D), M:tm-6, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77714
in-theory        77714
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C or D) -> B)) -> ((C or (C or D)) -> B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77714.        (A -> (((B or ((C or D) -> B)) -> ((C or (C or D)) -> B)) and A)), M:tm-5, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77715
in-theory        77715
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> (B or (B or C))) -> ((A or ((B or C) -> A)) -> A))
theorem-size     23
proof            (modus-ponens tm-2 tm-879 ((A (or Am (-> (or Bm Cm) Am))) (B (or Bm (or Bm Cm))) (C Am)))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77715.        (((A or ((B or C) -> A)) -> (B or (B or C))) -> ((A or ((B or C) -> A)) -> A)), M:tm-2, m:tm-879, u:((A (or Am (-> (or Bm Cm) Am))) (B (or Bm (or Bm Cm))) (C Am))
================================================================
tm-name          tm-77716
in-theory        77716
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or ((C or D) -> B)) -> ((C or (C or D)) -> B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77716.        (A -> ((B or ((C or D) -> B)) -> ((C or (C or D)) -> B))), M:tm-1, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-77717
in-theory        77717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-77717.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-855, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77718
in-theory        77718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-77718.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-808, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77719
in-theory        77719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-49.           (((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-77719.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-757, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77720
in-theory        77720
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) -> ((G or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77720.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-708, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77721
in-theory        77721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-49.           (((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-77721.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-665, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77722
in-theory        77722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77722.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-622, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77723
in-theory        77723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77723.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77724
in-theory        77724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77724.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-605, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77725
in-theory        77725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-77725.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-595, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77726
in-theory        77726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-49.           (((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-77726.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-550, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77727
in-theory        77727
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77727.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-540, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77728
in-theory        77728
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-49.           (((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-77728.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-530, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77729
in-theory        77729
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77729.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-520, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77730
in-theory        77730
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77730.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-510, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77731
in-theory        77731
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77731.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-500, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77732
in-theory        77732
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77732.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-490, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77733
in-theory        77733
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77733.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-480, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77734
in-theory        77734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77734.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-469, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77735
in-theory        77735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77735.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77736
in-theory        77736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm 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-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-77736.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-453, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77737
in-theory        77737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-77737.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-443, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77738
in-theory        77738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-49.           (((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-77738.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-409, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77739
in-theory        77739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm 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-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-77739.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-400, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77740
in-theory        77740
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-77740.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-391, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77741
in-theory        77741
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-49.           (((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-77741.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-382, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77742
in-theory        77742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm 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-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-77742.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-373, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77743
in-theory        77743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77743.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-364, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77744
in-theory        77744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77744.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-354, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77745
in-theory        77745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77745.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77746
in-theory        77746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77746.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-338, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77747
in-theory        77747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77747.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-327, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77748
in-theory        77748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77748.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-326, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77749
in-theory        77749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77749.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-325, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77750
in-theory        77750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77750.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-324, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77751
in-theory        77751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77751.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-323, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77752
in-theory        77752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77752.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77753
in-theory        77753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77753.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77754
in-theory        77754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77754.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77755
in-theory        77755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77755.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77756
in-theory        77756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77756.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-311, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77757
in-theory        77757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-49.           (((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-77757.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)), M:tm-310, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77758
in-theory        77758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77758.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F))), M:tm-309, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77759
in-theory        77759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-880 ((A (-> Am (or Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-77759.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-308, m:tm-880, u:((A (-> Am (or Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-77760
in-theory        77760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (A -> (B or A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-880 ((A (-> Am (or Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77760.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (A -> (B or A))), M:tm-307, m:tm-880, u:((A (-> Am (or Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-77761
in-theory        77761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77761.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-305, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77762
in-theory        77762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77762.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-303, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77763
in-theory        77763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77763.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-270, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77764
in-theory        77764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77764.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-239, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77765
in-theory        77765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77765.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-210, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77766
in-theory        77766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77766.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-183, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77767
in-theory        77767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77767.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-157, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77768
in-theory        77768
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77768.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-147, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77769
in-theory        77769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77769.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-134, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77770
in-theory        77770
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77770.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-125, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77771
in-theory        77771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77771.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-113, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77772
in-theory        77772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77772.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-105, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77773
in-theory        77773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77773.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-95, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77774
in-theory        77774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77774.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-83, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77775
in-theory        77775
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77775.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-76, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77776
in-theory        77776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77776.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-69, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77777
in-theory        77777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-77777.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-54, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77778
in-theory        77778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77778.        ((A -> (B or A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-42, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77779
in-theory        77779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm 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-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-77779.        ((A -> (A or B)) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-32, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77780
in-theory        77780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-77780.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-23, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77781
in-theory        77781
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77781.        (((A and B) -> B) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-22, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77782
in-theory        77782
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77782.        (((A and B) -> A) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-21, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77783
in-theory        77783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-77783.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-20, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77784
in-theory        77784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77784.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-19, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77785
in-theory        77785
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-7 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77785.        (A or ((B -> (C or B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-7, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77786
in-theory        77786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8)
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-49.           (((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-77786.        (((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F), M:tm-6, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77787
in-theory        77787
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77787.        (A -> (((B -> (C or B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A)), M:tm-5, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77788
in-theory        77788
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-1 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77788.        (A -> ((B -> (C or B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-1, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77789
in-theory        77789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-49.           (((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-77789.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-855, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77790
in-theory        77790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-49.           (((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-77790.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-808, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77791
in-theory        77791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-49.           (((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-77791.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-757, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77792
in-theory        77792
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) -> ((G or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-49.           (((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-77792.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-708, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77793
in-theory        77793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77793.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-665, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77794
in-theory        77794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77794.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-622, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77795
in-theory        77795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77795.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77796
in-theory        77796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77796.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-605, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77797
in-theory        77797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-49.           (((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-77797.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-595, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77798
in-theory        77798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-49.           (((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-77798.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-550, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77799
in-theory        77799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-49.           (((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-77799.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-540, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77800
in-theory        77800
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-49.           (((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-77800.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-530, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77801
in-theory        77801
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77801.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-520, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77802
in-theory        77802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-49.           (((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-77802.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-510, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77803
in-theory        77803
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-49.           (((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-77803.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-500, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77804
in-theory        77804
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77804.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-490, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77805
in-theory        77805
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77805.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-480, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77806
in-theory        77806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77806.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-469, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77807
in-theory        77807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77807.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77808
in-theory        77808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-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-77808.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-453, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77809
in-theory        77809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-77809.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-443, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77810
in-theory        77810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-77810.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-409, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77811
in-theory        77811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-77811.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-400, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77812
in-theory        77812
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-77812.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-391, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77813
in-theory        77813
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-49.           (((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-77813.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-382, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77814
in-theory        77814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-49.           (((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-77814.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-373, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77815
in-theory        77815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77815.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-364, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77816
in-theory        77816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77816.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-354, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77817
in-theory        77817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77817.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77818
in-theory        77818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77818.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-338, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77819
in-theory        77819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77819.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-327, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77820
in-theory        77820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-49.           (((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-77820.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-326, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77821
in-theory        77821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-49.           (((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-77821.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-325, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77822
in-theory        77822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77822.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-324, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77823
in-theory        77823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77823.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-323, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77824
in-theory        77824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77824.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77825
in-theory        77825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77825.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77826
in-theory        77826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77826.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77827
in-theory        77827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77827.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77828
in-theory        77828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-49.           (((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-77828.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-311, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77829
in-theory        77829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-49.           (((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-77829.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)), M:tm-310, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77830
in-theory        77830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (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-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-49.           (((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-77830.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F))), M:tm-309, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77831
in-theory        77831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-881 ((A (-> Am (or Am Bm))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77831.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-308, m:tm-881, u:((A (-> Am (or Am Bm))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-77832
in-theory        77832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (A -> (A or B)))
theorem-size     25
proof            (modus-ponens tm-307 tm-881 ((A (-> Am (or Am Bm))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-49.           (((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-77832.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (A -> (A or B))), M:tm-307, m:tm-881, u:((A (-> Am (or Am Bm))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-77833
in-theory        77833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77833.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-305, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77834
in-theory        77834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77834.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-303, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77835
in-theory        77835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77835.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-270, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77836
in-theory        77836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77836.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-239, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77837
in-theory        77837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77837.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-210, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77838
in-theory        77838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77838.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-183, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77839
in-theory        77839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77839.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-157, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77840
in-theory        77840
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77840.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-147, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77841
in-theory        77841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77841.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-134, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77842
in-theory        77842
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77842.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-125, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77843
in-theory        77843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77843.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-113, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77844
in-theory        77844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-49.           (((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-77844.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-105, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77845
in-theory        77845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77845.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-95, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77846
in-theory        77846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77846.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-83, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77847
in-theory        77847
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77847.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-76, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77848
in-theory        77848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77848.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-69, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77849
in-theory        77849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-77849.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-54, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77850
in-theory        77850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77850.        ((A -> (B or A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-42, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77851
in-theory        77851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-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-77851.        ((A -> (A or B)) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-32, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77852
in-theory        77852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (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-23.           (A -> ((B -> (C -> (B and 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-49.           (((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-77852.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-23, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77853
in-theory        77853
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77853.        (((A and B) -> B) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-22, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77854
in-theory        77854
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77854.        (((A and B) -> A) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-21, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77855
in-theory        77855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-77855.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-20, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77856
in-theory        77856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77856.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-19, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77857
in-theory        77857
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-7 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8)
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-49.           (((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-77857.        (A or ((B -> (B or C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-7, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77858
in-theory        77858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-8)
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-49.           (((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-77858.        (((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F), M:tm-6, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77859
in-theory        77859
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-77859.        (A -> (((B -> (B or C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A)), M:tm-5, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77860
in-theory        77860
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-1 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-77860.        (A -> ((B -> (B or C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-1, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-77861
in-theory        77861
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (A or B))) and ((A or (A or B)) -> (C -> (A or B))))
theorem-size     21
proof            (modus-ponens tm-882 tm-1 ((Am (or A B)) (C (-> Bm (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-77861.        (((A or B) -> (C -> (A or B))) and ((A or (A or B)) -> (C -> (A or B)))), M:tm-882, m:tm-1, u:((Am (or A B)) (C (-> Bm (or A B))))
================================================================
tm-name          tm-77862
in-theory        77862
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((A or B) and C))) and ((A or (A or B)) -> (C -> ((A or B) and C))))
theorem-size     25
proof            (modus-ponens tm-882 tm-5 ((Am (or A B)) (C (-> Bm (and (or A B) Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77862.        (((A or B) -> (C -> ((A or B) and C))) and ((A or (A or B)) -> (C -> ((A or B) and C)))), M:tm-882, m:tm-5, u:((Am (or A B)) (C (-> Bm (and (or A B) Bm))))
================================================================
tm-name          tm-77863
in-theory        77863
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) or C)) and ((A or (A or B)) -> ((A or B) or C)))
theorem-size     21
proof            (modus-ponens tm-882 tm-6 ((Am (or A B)) (C (or (or A B) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-77863.        (((A or B) -> ((A or B) or C)) and ((A or (A or B)) -> ((A or B) or C))), M:tm-882, m:tm-6, u:((Am (or A B)) (C (or (or A B) Bm)))
================================================================
tm-name          tm-77864
in-theory        77864
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (A or B))) and ((A or (A or B)) -> (C or (A or B))))
theorem-size     21
proof            (modus-ponens tm-882 tm-7 ((Am (or A B)) (C (or Bm (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-77864.        (((A or B) -> (C or (A or B))) and ((A or (A or B)) -> (C or (A or B)))), M:tm-882, m:tm-7, u:((Am (or A B)) (C (or Bm (or A B))))
================================================================
tm-name          tm-77865
in-theory        77865
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> C))) and ((A or (A or B)) -> (C -> (D -> C))))
theorem-size     21
proof            (modus-ponens tm-882 tm-11 ((Am (or A B)) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-77865.        (((A or B) -> (C -> (D -> C))) and ((A or (A or B)) -> (C -> (D -> C)))), M:tm-882, m:tm-11, u:((Am (or A B)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-77866
in-theory        77866
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-882 tm-14 ((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-77866.        (((A or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-882, m:tm-14, u:((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-77867
in-theory        77867
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C and D) -> C)) and ((A or (A or B)) -> ((C and D) -> C)))
theorem-size     21
proof            (modus-ponens tm-882 tm-16 ((Am (or A B)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-77867.        (((A or B) -> ((C and D) -> C)) and ((A or (A or B)) -> ((C and D) -> C))), M:tm-882, m:tm-16, u:((Am (or A B)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-77868
in-theory        77868
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C and D) -> D)) and ((A or (A or B)) -> ((C and D) -> D)))
theorem-size     21
proof            (modus-ponens tm-882 tm-18 ((Am (or A B)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-77868.        (((A or B) -> ((C and D) -> D)) and ((A or (A or B)) -> ((C and D) -> D))), M:tm-882, m:tm-18, u:((Am (or A B)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-77869
in-theory        77869
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> C)) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-882 tm-19 ((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-77869.        (((A or B) -> ((C -> (D -> C)) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))), M:tm-882, m:tm-19, u:((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B))))
================================================================
tm-name          tm-77870
in-theory        77870
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-882 tm-20 ((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-77870.        (((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))), M:tm-882, m:tm-20, u:((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B))))
================================================================
tm-name          tm-77871
in-theory        77871
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and D) -> C) and (A or B))) and ((A or (A or B)) -> (((C and D) -> C) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-882 tm-21 ((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-77871.        (((A or B) -> (((C and D) -> C) and (A or B))) and ((A or (A or B)) -> (((C and D) -> C) and (A or B)))), M:tm-882, m:tm-21, u:((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B))))
================================================================
tm-name          tm-77872
in-theory        77872
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and D) -> D) and (A or B))) and ((A or (A or B)) -> (((C and D) -> D) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-882 tm-22 ((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-77872.        (((A or B) -> (((C and D) -> D) and (A or B))) and ((A or (A or B)) -> (((C and D) -> D) and (A or B)))), M:tm-882, m:tm-22, u:((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B))))
================================================================
tm-name          tm-77873
in-theory        77873
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (C and D))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-23 ((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-77873.        (((A or B) -> ((C -> (D -> (C and D))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))), M:tm-882, m:tm-23, u:((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-77874
in-theory        77874
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (C and D)))) and ((A or (A or B)) -> (C -> (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-882 tm-25 ((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-77874.        (((A or B) -> (C -> (D -> (C and D)))) and ((A or (A or B)) -> (C -> (D -> (C and D))))), M:tm-882, m:tm-25, u:((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-77875
in-theory        77875
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (C or D)) and (A or B))) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-882 tm-32 ((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-77875.        (((A or B) -> ((C -> (C or D)) and (A or B))) and ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))), M:tm-882, m:tm-32, u:((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B))))
================================================================
tm-name          tm-77876
in-theory        77876
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (C or D))) and ((A or (A or B)) -> (C -> (C or D))))
theorem-size     21
proof            (modus-ponens tm-882 tm-33 ((Am (or A B)) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-77876.        (((A or B) -> (C -> (C or D))) and ((A or (A or B)) -> (C -> (C or D)))), M:tm-882, m:tm-33, u:((Am (or A B)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-77877
in-theory        77877
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D or C)) and (A or B))) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-882 tm-42 ((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-77877.        (((A or B) -> ((C -> (D or C)) and (A or B))) and ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))), M:tm-882, m:tm-42, u:((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B))))
================================================================
tm-name          tm-77878
in-theory        77878
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D or C))) and ((A or (A or B)) -> (C -> (D or C))))
theorem-size     21
proof            (modus-ponens tm-882 tm-43 ((Am (or A B)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-77878.        (((A or B) -> (C -> (D or C))) and ((A or (A or B)) -> (C -> (D or C)))), M:tm-882, m:tm-43, u:((Am (or A B)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-77879
in-theory        77879
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-882 tm-54 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-77879.        (((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))), M:tm-882, m:tm-54, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B))))
================================================================
tm-name          tm-77880
in-theory        77880
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((A or (A or B)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-882 tm-56 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77880.        (((A or B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((A or (A or B)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-882, m:tm-56, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-77881
in-theory        77881
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B))))
theorem-size     41
proof            (modus-ponens tm-882 tm-69 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-77881.        (((A or B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B)))), M:tm-882, m:tm-69, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B))))
================================================================
tm-name          tm-77882
in-theory        77882
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((A or (A or B)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     33
proof            (modus-ponens tm-882 tm-71 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77882.        (((A or B) -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((A or (A or B)) -> ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-882, m:tm-71, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-77883
in-theory        77883
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((not (not C)) -> C) and (A or B))) and ((A or (A or B)) -> (((not (not C)) -> C) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-882 tm-76 ((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-77883.        (((A or B) -> (((not (not C)) -> C) and (A or B))) and ((A or (A or B)) -> (((not (not C)) -> C) and (A or B)))), M:tm-882, m:tm-76, u:((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B))))
================================================================
tm-name          tm-77884
in-theory        77884
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((not (not C)) -> C)) and ((A or (A or B)) -> ((not (not C)) -> C)))
theorem-size     21
proof            (modus-ponens tm-882 tm-78 ((Am (or A B)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77884.        (((A or B) -> ((not (not C)) -> C)) and ((A or (A or B)) -> ((not (not C)) -> C))), M:tm-882, m:tm-78, u:((Am (or A B)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-77885
in-theory        77885
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (E -> D))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (E -> D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-83 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-77885.        (((A or B) -> ((C -> (D -> (E -> D))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (E -> D))) and (A or B)))), M:tm-882, m:tm-83, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-77886
in-theory        77886
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (E -> D)))) and ((A or (A or B)) -> (C -> (D -> (E -> D)))))
theorem-size     25
proof            (modus-ponens tm-882 tm-85 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77886.        (((A or B) -> (C -> (D -> (E -> D)))) and ((A or (A or B)) -> (C -> (D -> (E -> D))))), M:tm-882, m:tm-85, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-77887
in-theory        77887
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (A or B)) and ((A or (A or B)) -> (A or B)))
theorem-size     17
proof            (modus-ponens tm-882 tm-86 ((Am (or A B)) (C (or A B))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-77887.        (((A or B) -> (A or B)) and ((A or (A or B)) -> (A or B))), M:tm-882, m:tm-86, u:((Am (or A B)) (C (or A B)))
================================================================
tm-name          tm-77888
in-theory        77888
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> (C -> C)) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> (C -> C)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-95 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-77888.        (((A or B) -> (((C -> D) -> (C -> C)) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> (C -> C)) and (A or B)))), M:tm-882, m:tm-95, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B))))
================================================================
tm-name          tm-77889
in-theory        77889
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> (C -> C))) and ((A or (A or B)) -> ((C -> D) -> (C -> C))))
theorem-size     25
proof            (modus-ponens tm-882 tm-97 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-77889.        (((A or B) -> ((C -> D) -> (C -> C))) and ((A or (A or B)) -> ((C -> D) -> (C -> C)))), M:tm-882, m:tm-97, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-77890
in-theory        77890
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B))) and ((A or (A or B)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B))))
theorem-size     57
proof            (modus-ponens tm-882 tm-105 ((Am (or A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (or A B)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-77890.        (((A or B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B))) and ((A or (A or B)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B)))), M:tm-882, 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-77891
in-theory        77891
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((A or (A or B)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     49
proof            (modus-ponens tm-882 tm-107 ((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77891.        (((A or B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((A or (A or B)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-882, m:tm-107, u:((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-77892
in-theory        77892
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-113 ((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-77892.        (((A or B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B)))), M:tm-882, m:tm-113, u:((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B))))
================================================================
tm-name          tm-77893
in-theory        77893
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A or (A or B)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     41
proof            (modus-ponens tm-882 tm-115 ((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (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-77893.        (((A or B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A or (A or B)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-882, m:tm-115, u:((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-77894
in-theory        77894
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B))) and ((A or (A or B)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-125 ((Am (or A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-77894.        (((A or B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B))) and ((A or (A or B)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B)))), M:tm-882, 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-77895
in-theory        77895
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((A or (A or B)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-882 tm-127 ((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77895.        (((A or B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((A or (A or B)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-882, m:tm-127, u:((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-77896
in-theory        77896
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D and E) -> D)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D and E) -> D)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-134 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-77896.        (((A or B) -> ((C -> ((D and E) -> D)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D and E) -> D)) and (A or B)))), M:tm-882, m:tm-134, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-77897
in-theory        77897
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D and E) -> D))) and ((A or (A or B)) -> (C -> ((D and E) -> D))))
theorem-size     25
proof            (modus-ponens tm-882 tm-136 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-77897.        (((A or B) -> (C -> ((D and E) -> D))) and ((A or (A or B)) -> (C -> ((D and E) -> D)))), M:tm-882, m:tm-136, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-77898
in-theory        77898
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-147 ((Am (or A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-77898.        (((A or B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B)))), M:tm-882, 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-77899
in-theory        77899
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((A or (A or B)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     41
proof            (modus-ponens tm-882 tm-149 ((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77899.        (((A or B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((A or (A or B)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-882, m:tm-149, u:((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-77900
in-theory        77900
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D and E) -> E)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D and E) -> E)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-157 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-77900.        (((A or B) -> ((C -> ((D and E) -> E)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D and E) -> E)) and (A or B)))), M:tm-882, m:tm-157, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-77901
in-theory        77901
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D and E) -> E))) and ((A or (A or B)) -> (C -> ((D and E) -> E))))
theorem-size     25
proof            (modus-ponens tm-882 tm-159 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-77901.        (((A or B) -> (C -> ((D and E) -> E))) and ((A or (A or B)) -> (C -> ((D and E) -> E)))), M:tm-882, m:tm-159, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-77902
in-theory        77902
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (E -> D)) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (E -> D)) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-183 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-77902.        (((A or B) -> ((C -> ((D -> (E -> D)) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (E -> D)) and C)) and (A or B)))), M:tm-882, m:tm-183, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-77903
in-theory        77903
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (E -> D)) and C))) and ((A or (A or B)) -> (C -> ((D -> (E -> D)) and C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-184 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-77903.        (((A or B) -> (C -> ((D -> (E -> D)) and C))) and ((A or (A or B)) -> (C -> ((D -> (E -> D)) and C)))), M:tm-882, m:tm-184, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-77904
in-theory        77904
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B))))
theorem-size     53
proof            (modus-ponens tm-882 tm-210 ((Am (or A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (or A B)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-77904.        (((A or B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B)))), M:tm-882, 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-77905
in-theory        77905
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((A or (A or B)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     45
proof            (modus-ponens tm-882 tm-211 ((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77905.        (((A or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((A or (A or B)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-882, m:tm-211, u:((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-77906
in-theory        77906
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (((D and E) -> D) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> (((D and E) -> D) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-239 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-77906.        (((A or B) -> ((C -> (((D and E) -> D) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> (((D and E) -> D) and C)) and (A or B)))), M:tm-882, m:tm-239, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B))))
================================================================
tm-name          tm-77907
in-theory        77907
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (((D and E) -> D) and C))) and ((A or (A or B)) -> (C -> (((D and E) -> D) and C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-240 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77907.        (((A or B) -> (C -> (((D and E) -> D) and C))) and ((A or (A or B)) -> (C -> (((D and E) -> D) and C)))), M:tm-882, m:tm-240, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-77908
in-theory        77908
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (((D and E) -> E) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> (((D and E) -> E) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-270 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-77908.        (((A or B) -> ((C -> (((D and E) -> E) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> (((D and E) -> E) and C)) and (A or B)))), M:tm-882, m:tm-270, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B))))
================================================================
tm-name          tm-77909
in-theory        77909
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (((D and E) -> E) and C))) and ((A or (A or B)) -> (C -> (((D and E) -> E) and C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-271 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77909.        (((A or B) -> (C -> (((D and E) -> E) and C))) and ((A or (A or B)) -> (C -> (((D and E) -> E) and C)))), M:tm-882, m:tm-271, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-77910
in-theory        77910
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B))))
theorem-size     41
proof            (modus-ponens tm-882 tm-303 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-77910.        (((A or B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B)))), M:tm-882, m:tm-303, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B))))
================================================================
tm-name          tm-77911
in-theory        77911
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (E -> (D and E))) and C))) and ((A or (A or B)) -> (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     33
proof            (modus-ponens tm-882 tm-304 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77911.        (((A or B) -> (C -> ((D -> (E -> (D and E))) and C))) and ((A or (A or B)) -> (C -> ((D -> (E -> (D and E))) and C)))), M:tm-882, m:tm-304, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-77912
in-theory        77912
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (A or B)))) and ((A or (A or B)) -> ((A or B) and (C -> (A or B)))))
theorem-size     29
proof            (modus-ponens tm-882 tm-305 ((Am (or A B)) (C (and (or A B) (-> Bm (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-77912.        (((A or B) -> ((A or B) and (C -> (A or B)))) and ((A or (A or B)) -> ((A or B) and (C -> (A or B))))), M:tm-882, m:tm-305, u:((Am (or A B)) (C (and (or A B) (-> Bm (or A B)))))
================================================================
tm-name          tm-77913
in-theory        77913
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> ((A or B) and C)))) and ((A or (A or B)) -> ((A or B) and (C -> ((A or B) and C)))))
theorem-size     33
proof            (modus-ponens tm-882 tm-309 ((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-77913.        (((A or B) -> ((A or B) and (C -> ((A or B) and C)))) and ((A or (A or B)) -> ((A or B) and (C -> ((A or B) and C))))), M:tm-882, m:tm-309, u:((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm)))))
================================================================
tm-name          tm-77914
in-theory        77914
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((A or B) or C))) and ((A or (A or B)) -> ((A or B) and ((A or B) or C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-310 ((Am (or A B)) (C (and (or A B) (or (or A B) Bm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-77914.        (((A or B) -> ((A or B) and ((A or B) or C))) and ((A or (A or B)) -> ((A or B) and ((A or B) or C)))), M:tm-882, m:tm-310, u:((Am (or A B)) (C (and (or A B) (or (or A B) Bm))))
================================================================
tm-name          tm-77915
in-theory        77915
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C or (A or B)))) and ((A or (A or B)) -> ((A or B) and (C or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-882 tm-311 ((Am (or A B)) (C (and (or A B) (or Bm (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-77915.        (((A or B) -> ((A or B) and (C or (A or B)))) and ((A or (A or B)) -> ((A or B) and (C or (A or B))))), M:tm-882, m:tm-311, u:((Am (or A B)) (C (and (or A B) (or Bm (or A B)))))
================================================================
tm-name          tm-77916
in-theory        77916
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (D -> C)))) and ((A or (A or B)) -> ((A or B) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-882 tm-315 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-77916.        (((A or B) -> ((A or B) and (C -> (D -> C)))) and ((A or (A or B)) -> ((A or B) and (C -> (D -> C))))), M:tm-882, m:tm-315, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-77917
in-theory        77917
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A or (A or B)) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-882 tm-318 ((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-77917.        (((A or B) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A or (A or B)) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-882, m:tm-318, u:((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-77918
in-theory        77918
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C and D) -> C))) and ((A or (A or B)) -> ((A or B) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-320 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-77918.        (((A or B) -> ((A or B) and ((C and D) -> C))) and ((A or (A or B)) -> ((A or B) and ((C and D) -> C)))), M:tm-882, m:tm-320, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-77919
in-theory        77919
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C and D) -> D))) and ((A or (A or B)) -> ((A or B) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-882 tm-322 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-77919.        (((A or B) -> ((A or B) and ((C and D) -> D))) and ((A or (A or B)) -> ((A or B) and ((C and D) -> D)))), M:tm-882, m:tm-322, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-77920
in-theory        77920
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (D -> C)) and (A or B)))) and ((A or (A or B)) -> ((A or B) and ((C -> (D -> C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-882 tm-323 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-77920.        (((A or B) -> ((A or B) and ((C -> (D -> C)) and (A or B)))) and ((A or (A or B)) -> ((A or B) and ((C -> (D -> C)) and (A or B))))), M:tm-882, m:tm-323, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B)))))
================================================================
tm-name          tm-77921
in-theory        77921
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))) and ((A or (A or B)) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-77921.        (((A or B) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))) and ((A or (A or B)) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-882, 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-77922
in-theory        77922
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (((C and D) -> C) and (A or B)))) and ((A or (A or B)) -> ((A or B) and (((C and D) -> C) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-882 tm-325 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-77922.        (((A or B) -> ((A or B) and (((C and D) -> C) and (A or B)))) and ((A or (A or B)) -> ((A or B) and (((C and D) -> C) and (A or B))))), M:tm-882, m:tm-325, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B)))))
================================================================
tm-name          tm-77923
in-theory        77923
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (((C and D) -> D) and (A or B)))) and ((A or (A or B)) -> ((A or B) and (((C and D) -> D) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-882 tm-326 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-77923.        (((A or B) -> ((A or B) and (((C and D) -> D) and (A or B)))) and ((A or (A or B)) -> ((A or B) and (((C and D) -> D) and (A or B))))), M:tm-882, m:tm-326, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B)))))
================================================================
tm-name          tm-77924
in-theory        77924
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B)))) and ((A or (A or B)) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     41
proof            (modus-ponens tm-882 tm-327 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-77924.        (((A or B) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B)))) and ((A or (A or B)) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B))))), M:tm-882, 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-77925
in-theory        77925
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> (C -> (C and D))) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> (C -> (C and D))) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-338 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-77925.        (((A or B) -> (((C -> D) -> (C -> (C and D))) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> (C -> (C and D))) and (A or B)))), M:tm-882, m:tm-338, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-77926
in-theory        77926
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> (C -> (C and D)))) and ((A or (A or B)) -> ((C -> D) -> (C -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-882 tm-340 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77926.        (((A or B) -> ((C -> D) -> (C -> (C and D)))) and ((A or (A or B)) -> ((C -> D) -> (C -> (C and D))))), M:tm-882, m:tm-340, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-77927
in-theory        77927
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (D -> (C and D))))) and ((A or (A or B)) -> ((A or B) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-882 tm-341 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-77927.        (((A or B) -> ((A or B) and (C -> (D -> (C and D))))) and ((A or (A or B)) -> ((A or B) and (C -> (D -> (C and D)))))), M:tm-882, m:tm-341, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-77928
in-theory        77928
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (E -> (D and E)))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (E -> (D and E)))) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-354 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-77928.        (((A or B) -> ((C -> (D -> (E -> (D and E)))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (E -> (D and E)))) and (A or B)))), M:tm-882, m:tm-354, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-77929
in-theory        77929
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (E -> (D and E))))) and ((A or (A or B)) -> (C -> (D -> (E -> (D and E))))))
theorem-size     29
proof            (modus-ponens tm-882 tm-356 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> 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-77929.        (((A or B) -> (C -> (D -> (E -> (D and E))))) and ((A or (A or B)) -> (C -> (D -> (E -> (D and E)))))), M:tm-882, m:tm-356, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-77930
in-theory        77930
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> C)) or E) and (A or B))) and ((A or (A or B)) -> (((C -> (D -> C)) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-364 ((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-77930.        (((A or B) -> (((C -> (D -> C)) or E) and (A or B))) and ((A or (A or B)) -> (((C -> (D -> C)) or E) and (A or B)))), M:tm-882, m:tm-364, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-77931
in-theory        77931
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> C)) or E)) and ((A or (A or B)) -> ((C -> (D -> C)) or E)))
theorem-size     25
proof            (modus-ponens tm-882 tm-365 ((Am (or A B)) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77931.        (((A or B) -> ((C -> (D -> C)) or E)) and ((A or (A or B)) -> ((C -> (D -> C)) or E))), M:tm-882, m:tm-365, u:((Am (or A B)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-77932
in-theory        77932
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B))) and ((A or (A or B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-373 ((Am (or A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-77932.        (((A or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B))) and ((A or (A or B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B)))), M:tm-882, 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-77933
in-theory        77933
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     41
proof            (modus-ponens tm-882 tm-374 ((Am (or A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77933.        (((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-882, m:tm-374, u:((Am (or A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-77934
in-theory        77934
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C and D) -> C) or E) and (A or B))) and ((A or (A or B)) -> ((((C and D) -> C) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-382 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-77934.        (((A or B) -> ((((C and D) -> C) or E) and (A or B))) and ((A or (A or B)) -> ((((C and D) -> C) or E) and (A or B)))), M:tm-882, m:tm-382, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B))))
================================================================
tm-name          tm-77935
in-theory        77935
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and D) -> C) or E)) and ((A or (A or B)) -> (((C and D) -> C) or E)))
theorem-size     25
proof            (modus-ponens tm-882 tm-383 ((Am (or A B)) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77935.        (((A or B) -> (((C and D) -> C) or E)) and ((A or (A or B)) -> (((C and D) -> C) or E))), M:tm-882, m:tm-383, u:((Am (or A B)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-77936
in-theory        77936
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C and D) -> D) or E) and (A or B))) and ((A or (A or B)) -> ((((C and D) -> D) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-391 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-77936.        (((A or B) -> ((((C and D) -> D) or E) and (A or B))) and ((A or (A or B)) -> ((((C and D) -> D) or E) and (A or B)))), M:tm-882, m:tm-391, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B))))
================================================================
tm-name          tm-77937
in-theory        77937
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and D) -> D) or E)) and ((A or (A or B)) -> (((C and D) -> D) or E)))
theorem-size     25
proof            (modus-ponens tm-882 tm-392 ((Am (or A B)) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77937.        (((A or B) -> (((C and D) -> D) or E)) and ((A or (A or B)) -> (((C and D) -> D) or E))), M:tm-882, m:tm-392, u:((Am (or A B)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-77938
in-theory        77938
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> (C and D))) or E) and (A or B))) and ((A or (A or B)) -> (((C -> (D -> (C and D))) or E) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-400 ((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-77938.        (((A or B) -> (((C -> (D -> (C and D))) or E) and (A or B))) and ((A or (A or B)) -> (((C -> (D -> (C and D))) or E) and (A or B)))), M:tm-882, m:tm-400, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B))))
================================================================
tm-name          tm-77939
in-theory        77939
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (C and D))) or E)) and ((A or (A or B)) -> ((C -> (D -> (C and D))) or E)))
theorem-size     29
proof            (modus-ponens tm-882 tm-401 ((Am (or A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77939.        (((A or B) -> ((C -> (D -> (C and D))) or E)) and ((A or (A or B)) -> ((C -> (D -> (C and D))) or E))), M:tm-882, m:tm-401, u:((Am (or A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-77940
in-theory        77940
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (C or D)) or E) and (A or B))) and ((A or (A or B)) -> (((C -> (C or D)) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-409 ((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-77940.        (((A or B) -> (((C -> (C or D)) or E) and (A or B))) and ((A or (A or B)) -> (((C -> (C or D)) or E) and (A or B)))), M:tm-882, m:tm-409, u:((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B))))
================================================================
tm-name          tm-77941
in-theory        77941
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (C or D)) or E)) and ((A or (A or B)) -> ((C -> (C or D)) or E)))
theorem-size     25
proof            (modus-ponens tm-882 tm-410 ((Am (or A B)) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77941.        (((A or B) -> ((C -> (C or D)) or E)) and ((A or (A or B)) -> ((C -> (C or D)) or E))), M:tm-882, m:tm-410, u:((Am (or A B)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-77942
in-theory        77942
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (C or D)) and (A or B)))) and ((A or (A or B)) -> ((A or B) and ((C -> (C or D)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-882 tm-443 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-77942.        (((A or B) -> ((A or B) and ((C -> (C or D)) and (A or B)))) and ((A or (A or B)) -> ((A or B) and ((C -> (C or D)) and (A or B))))), M:tm-882, m:tm-443, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B)))))
================================================================
tm-name          tm-77943
in-theory        77943
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (D or E)) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (D or E)) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-453 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-77943.        (((A or B) -> ((C -> ((D -> (D or E)) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (D or E)) and C)) and (A or B)))), M:tm-882, m:tm-453, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B))))
================================================================
tm-name          tm-77944
in-theory        77944
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (D or E)) and C))) and ((A or (A or B)) -> (C -> ((D -> (D or E)) and C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-454 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77944.        (((A or B) -> (C -> ((D -> (D or E)) and C))) and ((A or (A or B)) -> (C -> ((D -> (D or E)) and C)))), M:tm-882, m:tm-454, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-77945
in-theory        77945
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (C or D)))) and ((A or (A or B)) -> ((A or B) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-882 tm-456 ((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-77945.        (((A or B) -> ((A or B) and (C -> (C or D)))) and ((A or (A or B)) -> ((A or B) and (C -> (C or D))))), M:tm-882, m:tm-456, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-77946
in-theory        77946
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (D or E))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (D or E))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-469 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-77946.        (((A or B) -> ((C -> (D -> (D or E))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (D or E))) and (A or B)))), M:tm-882, m:tm-469, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-77947
in-theory        77947
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (D or E)))) and ((A or (A or B)) -> (C -> (D -> (D or E)))))
theorem-size     25
proof            (modus-ponens tm-882 tm-471 ((Am (or A B)) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-77947.        (((A or B) -> (C -> (D -> (D or E)))) and ((A or (A or B)) -> (C -> (D -> (D or E))))), M:tm-882, m:tm-471, u:((Am (or A B)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77948
in-theory        77948
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or (D -> (E -> D))) and (A or B))) and ((A or (A or B)) -> ((C or (D -> (E -> D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-480 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-77948.        (((A or B) -> ((C or (D -> (E -> D))) and (A or B))) and ((A or (A or B)) -> ((C or (D -> (E -> D))) and (A or B)))), M:tm-882, m:tm-480, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-77949
in-theory        77949
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (D -> (E -> D)))) and ((A or (A or B)) -> (C or (D -> (E -> D)))))
theorem-size     25
proof            (modus-ponens tm-882 tm-481 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77949.        (((A or B) -> (C or (D -> (E -> D)))) and ((A or (A or B)) -> (C or (D -> (E -> D))))), M:tm-882, m:tm-481, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-77950
in-theory        77950
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))) and ((A or (A or B)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-490 ((Am (or A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-77950.        (((A or B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))) and ((A or (A or B)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B)))), M:tm-882, 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-77951
in-theory        77951
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A or (A or B)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     41
proof            (modus-ponens tm-882 tm-491 ((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77951.        (((A or B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A or (A or B)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-882, m:tm-491, u:((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-77952
in-theory        77952
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or ((D and E) -> D)) and (A or B))) and ((A or (A or B)) -> ((C or ((D and E) -> D)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-500 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-77952.        (((A or B) -> ((C or ((D and E) -> D)) and (A or B))) and ((A or (A or B)) -> ((C or ((D and E) -> D)) and (A or B)))), M:tm-882, m:tm-500, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-77953
in-theory        77953
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or ((D and E) -> D))) and ((A or (A or B)) -> (C or ((D and E) -> D))))
theorem-size     25
proof            (modus-ponens tm-882 tm-501 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77953.        (((A or B) -> (C or ((D and E) -> D))) and ((A or (A or B)) -> (C or ((D and E) -> D)))), M:tm-882, m:tm-501, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-77954
in-theory        77954
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or ((D and E) -> E)) and (A or B))) and ((A or (A or B)) -> ((C or ((D and E) -> E)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-510 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-77954.        (((A or B) -> ((C or ((D and E) -> E)) and (A or B))) and ((A or (A or B)) -> ((C or ((D and E) -> E)) and (A or B)))), M:tm-882, m:tm-510, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-77955
in-theory        77955
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or ((D and E) -> E))) and ((A or (A or B)) -> (C or ((D and E) -> E))))
theorem-size     25
proof            (modus-ponens tm-882 tm-511 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77955.        (((A or B) -> (C or ((D and E) -> E))) and ((A or (A or B)) -> (C or ((D and E) -> E)))), M:tm-882, m:tm-511, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-77956
in-theory        77956
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or (D -> (E -> (D and E)))) and (A or B))) and ((A or (A or B)) -> ((C or (D -> (E -> (D and E)))) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-520 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-77956.        (((A or B) -> ((C or (D -> (E -> (D and E)))) and (A or B))) and ((A or (A or B)) -> ((C or (D -> (E -> (D and E)))) and (A or B)))), M:tm-882, m:tm-520, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-77957
in-theory        77957
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (D -> (E -> (D and E))))) and ((A or (A or B)) -> (C or (D -> (E -> (D and E))))))
theorem-size     29
proof            (modus-ponens tm-882 tm-521 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77957.        (((A or B) -> (C or (D -> (E -> (D and E))))) and ((A or (A or B)) -> (C or (D -> (E -> (D and E)))))), M:tm-882, m:tm-521, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-77958
in-theory        77958
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or (D -> (D or E))) and (A or B))) and ((A or (A or B)) -> ((C or (D -> (D or E))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-530 ((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77958.        (((A or B) -> ((C or (D -> (D or E))) and (A or B))) and ((A or (A or B)) -> ((C or (D -> (D or E))) and (A or B)))), M:tm-882, m:tm-530, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-77959
in-theory        77959
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (D -> (D or E)))) and ((A or (A or B)) -> (C or (D -> (D or E)))))
theorem-size     25
proof            (modus-ponens tm-882 tm-531 ((Am (or A B)) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77959.        (((A or B) -> (C or (D -> (D or E)))) and ((A or (A or B)) -> (C or (D -> (D or E))))), M:tm-882, m:tm-531, u:((Am (or A B)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-77960
in-theory        77960
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or (D -> (E or D))) and (A or B))) and ((A or (A or B)) -> ((C or (D -> (E or D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-540 ((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-77960.        (((A or B) -> ((C or (D -> (E or D))) and (A or B))) and ((A or (A or B)) -> ((C or (D -> (E or D))) and (A or B)))), M:tm-882, m:tm-540, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-77961
in-theory        77961
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (D -> (E or D)))) and ((A or (A or B)) -> (C or (D -> (E or D)))))
theorem-size     25
proof            (modus-ponens tm-882 tm-541 ((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77961.        (((A or B) -> (C or (D -> (E or D)))) and ((A or (A or B)) -> (C or (D -> (E or D))))), M:tm-882, m:tm-541, u:((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77962
in-theory        77962
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D or C)) or E) and (A or B))) and ((A or (A or B)) -> (((C -> (D or C)) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-550 ((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-77962.        (((A or B) -> (((C -> (D or C)) or E) and (A or B))) and ((A or (A or B)) -> (((C -> (D or C)) or E) and (A or B)))), M:tm-882, m:tm-550, u:((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-77963
in-theory        77963
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D or C)) or E)) and ((A or (A or B)) -> ((C -> (D or C)) or E)))
theorem-size     25
proof            (modus-ponens tm-882 tm-551 ((Am (or A B)) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77963.        (((A or B) -> ((C -> (D or C)) or E)) and ((A or (A or B)) -> ((C -> (D or C)) or E))), M:tm-882, m:tm-551, u:((Am (or A B)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-77964
in-theory        77964
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (D or C)) and (A or B)))) and ((A or (A or B)) -> ((A or B) and ((C -> (D or C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-882 tm-595 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-77964.        (((A or B) -> ((A or B) and ((C -> (D or C)) and (A or B)))) and ((A or (A or B)) -> ((A or B) and ((C -> (D or C)) and (A or B))))), M:tm-882, m:tm-595, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B)))))
================================================================
tm-name          tm-77965
in-theory        77965
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (E or D)) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (E or D)) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-605 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-77965.        (((A or B) -> ((C -> ((D -> (E or D)) and C)) and (A or B))) and ((A or (A or B)) -> ((C -> ((D -> (E or D)) and C)) and (A or B)))), M:tm-882, m:tm-605, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-77966
in-theory        77966
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (E or D)) and C))) and ((A or (A or B)) -> (C -> ((D -> (E or D)) and C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-606 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-77966.        (((A or B) -> (C -> ((D -> (E or D)) and C))) and ((A or (A or B)) -> (C -> ((D -> (E or D)) and C)))), M:tm-882, m:tm-606, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-77967
in-theory        77967
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (D or C)))) and ((A or (A or B)) -> ((A or B) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-882 tm-609 ((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-77967.        (((A or B) -> ((A or B) and (C -> (D or C)))) and ((A or (A or B)) -> ((A or B) and (C -> (D or C))))), M:tm-882, m:tm-609, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-77968
in-theory        77968
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (E or D))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (E or D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-622 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-77968.        (((A or B) -> ((C -> (D -> (E or D))) and (A or B))) and ((A or (A or B)) -> ((C -> (D -> (E or D))) and (A or B)))), M:tm-882, m:tm-622, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-77969
in-theory        77969
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (E or D)))) and ((A or (A or B)) -> (C -> (D -> (E or D)))))
theorem-size     25
proof            (modus-ponens tm-882 tm-624 ((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-77969.        (((A or B) -> (C -> (D -> (E or D)))) and ((A or (A or B)) -> (C -> (D -> (E or D))))), M:tm-882, m:tm-624, u:((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-77970
in-theory        77970
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((A or (A or (B -> A))) -> (C -> (B -> A))))
theorem-size     25
proof            (modus-ponens tm-882 tm-625 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77970.        (((A or (B -> A)) -> (C -> (B -> A))) and ((A or (A or (B -> A))) -> (C -> (B -> A)))), M:tm-882, m:tm-625, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-77971
in-theory        77971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((A -> B) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B))))
theorem-size     39
proof            (modus-ponens tm-882 tm-626 ((A (-> Am Bm)) (B (-> Cm (-> Am Bm))) (C (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77971.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((A -> B) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B)))), M:tm-882, m:tm-626, u:((A (-> Am Bm)) (B (-> Cm (-> Am Bm))) (C (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-77972
in-theory        77972
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((A or (A or (B -> A))) -> (C -> ((B -> A) and C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-627 ((A Am) (B (-> Bm Am)) (C (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77972.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((A or (A or (B -> A))) -> (C -> ((B -> A) and C)))), M:tm-882, m:tm-627, u:((A Am) (B (-> Bm Am)) (C (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-77973
in-theory        77973
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((A or (A or (B -> A))) -> ((B -> A) or C)))
theorem-size     25
proof            (modus-ponens tm-882 tm-628 ((A Am) (B (-> Bm Am)) (C (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77973.        (((A or (B -> A)) -> ((B -> A) or C)) and ((A or (A or (B -> A))) -> ((B -> A) or C))), M:tm-882, m:tm-628, u:((A Am) (B (-> Bm Am)) (C (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-77974
in-theory        77974
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((A or (A or (B -> A))) -> (C or (B -> A))))
theorem-size     25
proof            (modus-ponens tm-882 tm-629 ((A Am) (B (-> Bm Am)) (C (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77974.        (((A or (B -> A)) -> (C or (B -> A))) and ((A or (A or (B -> A))) -> (C or (B -> A)))), M:tm-882, m:tm-629, u:((A Am) (B (-> Bm Am)) (C (or Cm (-> Bm Am))))
================================================================
tm-name          tm-77975
in-theory        77975
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((A or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C))))
theorem-size     33
proof            (modus-ponens tm-882 tm-630 ((A Am) (B (-> Bm Am)) (C (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77975.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((A or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C)))), M:tm-882, m:tm-630, u:((A Am) (B (-> Bm Am)) (C (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-77976
in-theory        77976
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((A or (A or (B -> A))) -> ((B -> (not A)) -> (not B))))
theorem-size     29
proof            (modus-ponens tm-882 tm-631 ((A Am) (B (-> Bm Am)) (C (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77976.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((A or (A or (B -> A))) -> ((B -> (not A)) -> (not B)))), M:tm-882, m:tm-631, u:((A Am) (B (-> Bm Am)) (C (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-77977
in-theory        77977
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((A or (A or (B -> A))) -> (C -> (D -> C))))
theorem-size     25
proof            (modus-ponens tm-882 tm-632 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77977.        (((A or (B -> A)) -> (C -> (D -> C))) and ((A or (A or (B -> A))) -> (C -> (D -> C)))), M:tm-882, m:tm-632, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-77978
in-theory        77978
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((A or (A or (B -> A))) -> (B -> B)))
theorem-size     21
proof            (modus-ponens tm-882 tm-633 ((A Am) (B (-> Bm Am)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77978.        (((A or (B -> A)) -> (B -> B)) and ((A or (A or (B -> A))) -> (B -> B))), M:tm-882, m:tm-633, u:((A Am) (B (-> Bm Am)) (C (-> Bm Bm)))
================================================================
tm-name          tm-77979
in-theory        77979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> B) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-882 tm-634 ((A (-> Am Bm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77979.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> B) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-882, m:tm-634, u:((A (-> Am Bm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-77980
in-theory        77980
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-882 tm-635 ((A Am) (B (-> Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77980.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-882, m:tm-635, u:((A Am) (B (-> Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-77981
in-theory        77981
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((A or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)))
theorem-size     37
proof            (modus-ponens tm-882 tm-636 ((A Am) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77981.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((A or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))), M:tm-882, m:tm-636, u:((A Am) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-77982
in-theory        77982
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((A or (A or (B -> A))) -> ((C and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-882 tm-637 ((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77982.        (((A or (B -> A)) -> ((C and D) -> C)) and ((A or (A or (B -> A))) -> ((C and D) -> C))), M:tm-882, m:tm-637, u:((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-77983
in-theory        77983
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((A or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C)))
theorem-size     37
proof            (modus-ponens tm-882 tm-638 ((A Am) (B (-> (and Bm (-> Am Cm)) Am)) (C (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77983.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((A or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C))), M:tm-882, m:tm-638, u:((A Am) (B (-> (and Bm (-> Am Cm)) Am)) (C (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-77984
in-theory        77984
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((A or (A or (B -> A))) -> ((C and D) -> D)))
theorem-size     25
proof            (modus-ponens tm-882 tm-639 ((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77984.        (((A or (B -> A)) -> ((C and D) -> D)) and ((A or (A or (B -> A))) -> ((C and D) -> D))), M:tm-882, m:tm-639, u:((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-77985
in-theory        77985
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((A or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-640 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77985.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((A or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A)))), M:tm-882, m:tm-640, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-77986
in-theory        77986
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((A or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))
theorem-size     49
proof            (modus-ponens tm-882 tm-641 ((A Am) (B (-> Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77986.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((A or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))), M:tm-882, m:tm-641, u:((A Am) (B (-> Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-77987
in-theory        77987
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((A or (A or (B -> A))) -> (((C and D) -> C) and (B -> A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-642 ((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77987.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((A or (A or (B -> A))) -> (((C and D) -> C) and (B -> A)))), M:tm-882, m:tm-642, u:((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-77988
in-theory        77988
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((A or (A or (B -> A))) -> (((C and D) -> D) and (B -> A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-643 ((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77988.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((A or (A or (B -> A))) -> (((C and D) -> D) and (B -> A)))), M:tm-882, m:tm-643, u:((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-77989
in-theory        77989
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((A or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A))))
theorem-size     37
proof            (modus-ponens tm-882 tm-644 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77989.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((A or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A)))), M:tm-882, m:tm-644, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-77990
in-theory        77990
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((A or (A or (B -> A))) -> (B -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-882 tm-645 ((A Am) (B (-> Bm Am)) (C (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77990.        (((A or (B -> A)) -> (B -> (B and A))) and ((A or (A or (B -> A))) -> (B -> (B and A)))), M:tm-882, m:tm-645, u:((A Am) (B (-> Bm Am)) (C (-> Bm (and Bm Am))))
================================================================
tm-name          tm-77991
in-theory        77991
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((A or (A or (B -> A))) -> (C -> (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-882 tm-646 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77991.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((A or (A or (B -> A))) -> (C -> (D -> (C and D))))), M:tm-882, m:tm-646, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-77992
in-theory        77992
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((A or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-647 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77992.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((A or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A)))), M:tm-882, m:tm-647, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-77993
in-theory        77993
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((A or (A or (B -> A))) -> (C -> (C or D))))
theorem-size     25
proof            (modus-ponens tm-882 tm-648 ((A Am) (B (-> Bm Am)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77993.        (((A or (B -> A)) -> (C -> (C or D))) and ((A or (A or (B -> A))) -> (C -> (C or D)))), M:tm-882, m:tm-648, u:((A Am) (B (-> Bm Am)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-77994
in-theory        77994
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((A or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-649 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77994.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((A or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A)))), M:tm-882, m:tm-649, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-77995
in-theory        77995
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((A or (A or (B -> A))) -> (C -> (D or C))))
theorem-size     25
proof            (modus-ponens tm-882 tm-650 ((A Am) (B (-> Bm Am)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77995.        (((A or (B -> A)) -> (C -> (D or C))) and ((A or (A or (B -> A))) -> (C -> (D or C)))), M:tm-882, m:tm-650, u:((A Am) (B (-> Bm Am)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-77996
in-theory        77996
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((A or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A)))
theorem-size     33
proof            (modus-ponens tm-882 tm-651 ((A Am) (B (-> (-> Bm Cm) Am)) (C (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77996.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((A or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A))), M:tm-882, m:tm-651, u:((A Am) (B (-> (-> Bm Cm) Am)) (C (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-77997
in-theory        77997
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-882 tm-665 ((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-77997.        (((A or B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B)))), M:tm-882, m:tm-665, u:((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-77998
in-theory        77998
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((A or (A or B)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     37
proof            (modus-ponens tm-882 tm-667 ((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-77998.        (((A or B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((A or (A or B)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-882, m:tm-667, u:((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-77999
in-theory        77999
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-882 tm-668 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-77999.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C))))), M:tm-882, m:tm-668, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-78000
in-theory        78000
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 -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C))))
theorem-size     57
proof            (modus-ponens tm-882 tm-669 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78000.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C)))), M:tm-882, m:tm-669, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-78001
in-theory        78001
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 -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D))))
theorem-size     57
proof            (modus-ponens tm-882 tm-670 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78001.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D)))), M:tm-882, m:tm-670, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-78002
in-theory        78002
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 -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D)))
theorem-size     53
proof            (modus-ponens tm-882 tm-671 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78002.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D))), M:tm-882, m:tm-671, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-78003
in-theory        78003
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 -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-882 tm-672 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78003.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C))))), M:tm-882, m:tm-672, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-78004
in-theory        78004
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 -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))
theorem-size     65
proof            (modus-ponens tm-882 tm-673 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78004.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))), M:tm-882, 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-78005
in-theory        78005
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 -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))
theorem-size     61
proof            (modus-ponens tm-882 tm-674 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78005.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))), M:tm-882, 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-78006
in-theory        78006
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D))))
theorem-size     45
proof            (modus-ponens tm-882 tm-675 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78006.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D)))), M:tm-882, m:tm-675, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-78007
in-theory        78007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-676 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78007.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B)))), M:tm-882, m:tm-676, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-78008
in-theory        78008
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) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     63
proof            (modus-ponens tm-882 tm-677 ((A (-> Am (-> (-> Bm Cm) Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78008.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> ((B -> C) -> B)) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-882, m:tm-677, u:((A (-> Am (-> (-> Bm Cm) Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-78009
in-theory        78009
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 -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     61
proof            (modus-ponens tm-882 tm-678 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78009.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-882, m:tm-678, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-78010
in-theory        78010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D)))
theorem-size     45
proof            (modus-ponens tm-882 tm-679 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78010.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D))), M:tm-882, m:tm-679, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-78011
in-theory        78011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E)))
theorem-size     45
proof            (modus-ponens tm-882 tm-680 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78011.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E))), M:tm-882, m:tm-680, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Em)))
================================================================
tm-name          tm-78012
in-theory        78012
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 -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-882 tm-681 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78012.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))), M:tm-882, 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-78013
in-theory        78013
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 -> 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-882 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-2 tm-5 tm-8 tm-6)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78013.        ((((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 -> C)) or ((A -> B) -> (A -> C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))), M:tm-882, 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-78014
in-theory        78014
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 -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-882 tm-683 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78014.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))), M:tm-882, 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-78015
in-theory        78015
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 -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-882 tm-684 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78015.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))), M:tm-882, 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-78016
in-theory        78016
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 -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78016.        ((((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 -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))), M:tm-882, 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-78017
in-theory        78017
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 -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-882 tm-686 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78017.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C))))), M:tm-882, m:tm-686, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-78018
in-theory        78018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E)))))
theorem-size     49
proof            (modus-ponens tm-882 tm-687 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78018.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E))))), M:tm-882, m:tm-687, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-78019
in-theory        78019
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 -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-882 tm-688 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78019.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))), M:tm-882, 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-78020
in-theory        78020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E))))
theorem-size     45
proof            (modus-ponens tm-882 tm-689 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78020.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E)))), M:tm-882, m:tm-689, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Dm Em))))
================================================================
tm-name          tm-78021
in-theory        78021
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 -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-882 tm-690 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78021.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))), M:tm-882, 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-78022
in-theory        78022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D))))
theorem-size     45
proof            (modus-ponens tm-882 tm-691 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78022.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D)))), M:tm-882, m:tm-691, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Em Dm))))
================================================================
tm-name          tm-78023
in-theory        78023
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 -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C))))
theorem-size     53
proof            (modus-ponens tm-882 tm-692 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-78023.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C)))), M:tm-882, m:tm-692, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-78024
in-theory        78024
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) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))
theorem-size     97
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 tm-6)
proof-size       321
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78024.        (((((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) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))), M:tm-882, 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-78025
in-theory        78025
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((A or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))
theorem-size     57
proof            (modus-ponens tm-882 tm-694 ((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-78025.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((A or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))), M:tm-882, 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-78026
in-theory        78026
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B))) and ((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     69
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-78026.        (((A or B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B))) and ((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-882, 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-78027
in-theory        78027
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((A or (A or B)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     61
proof            (modus-ponens tm-882 tm-710 ((Am (or 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78027.        (((A or B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((A or (A or B)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-882, 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-78028
in-theory        78028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (((A and B) or ((A and B) or A)) -> (C -> A)))
theorem-size     23
proof            (modus-ponens tm-882 tm-711 ((A (and Am Bm)) (B Am) (C (-> Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78028.        ((((A and B) or A) -> (C -> A)) and (((A and B) or ((A and B) or A)) -> (C -> A))), M:tm-882, m:tm-711, u:((A (and Am Bm)) (B Am) (C (-> Cm Am)))
================================================================
tm-name          tm-78029
in-theory        78029
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 D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-882 tm-712 ((A (and (-> Am (-> Bm Cm)) Dm)) (B (-> Am (-> Bm Cm))) (C (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78029.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((((A -> (B -> C)) and D) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))), M:tm-882, m:tm-712, u:((A (and (-> Am (-> Bm Cm)) Dm)) (B (-> Am (-> Bm Cm))) (C (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-78030
in-theory        78030
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 C) or (A and B))) -> A))
theorem-size     29
proof            (modus-ponens tm-882 tm-713 ((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78030.        (((((A and B) and C) or (A and B)) -> A) and ((((A and B) and C) or (((A and B) and C) or (A and B))) -> A)), M:tm-882, m:tm-713, u:((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Am))
================================================================
tm-name          tm-78031
in-theory        78031
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 C) or (A and B))) -> B))
theorem-size     29
proof            (modus-ponens tm-882 tm-714 ((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78031.        (((((A and B) and C) or (A and B)) -> B) and ((((A and B) and C) or (((A and B) and C) or (A and B))) -> B)), M:tm-882, m:tm-714, u:((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Bm))
================================================================
tm-name          tm-78032
in-theory        78032
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (((A and B) or ((A and B) or A)) -> (C -> (A and C))))
theorem-size     27
proof            (modus-ponens tm-882 tm-715 ((A (and Am Bm)) (B Am) (C (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78032.        ((((A and B) or A) -> (C -> (A and C))) and (((A and B) or ((A and B) or A)) -> (C -> (A and C)))), M:tm-882, m:tm-715, u:((A (and Am Bm)) (B Am) (C (-> Cm (and Am Cm))))
================================================================
tm-name          tm-78033
in-theory        78033
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (((A and B) or ((A and B) or A)) -> (A or C)))
theorem-size     23
proof            (modus-ponens tm-882 tm-716 ((A (and Am Bm)) (B Am) (C (or Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78033.        ((((A and B) or A) -> (A or C)) and (((A and B) or ((A and B) or A)) -> (A or C))), M:tm-882, m:tm-716, u:((A (and Am Bm)) (B Am) (C (or Am Cm)))
================================================================
tm-name          tm-78034
in-theory        78034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (((A and B) or ((A and B) or A)) -> (C or A)))
theorem-size     23
proof            (modus-ponens tm-882 tm-717 ((A (and Am Bm)) (B Am) (C (or Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78034.        ((((A and B) or A) -> (C or A)) and (((A and B) or ((A and B) or A)) -> (C or A))), M:tm-882, m:tm-717, u:((A (and Am Bm)) (B Am) (C (or Cm Am)))
================================================================
tm-name          tm-78035
in-theory        78035
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 C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D))))
theorem-size     45
proof            (modus-ponens tm-882 tm-718 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78035.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D)))), M:tm-882, m:tm-718, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-78036
in-theory        78036
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 C) or (A -> B))) -> ((A -> (not B)) -> (not A))))
theorem-size     41
proof            (modus-ponens tm-882 tm-719 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78036.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A)))), M:tm-882, m:tm-719, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-78037
in-theory        78037
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 B) or (not (not A)))) -> A))
theorem-size     29
proof            (modus-ponens tm-882 tm-720 ((A (and (not (not Am)) Bm)) (B (not (not Am))) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78037.        (((((not (not A)) and B) or (not (not A))) -> A) and ((((not (not A)) and B) or (((not (not A)) and B) or (not (not A)))) -> A)), M:tm-882, m:tm-720, u:((A (and (not (not Am)) Bm)) (B (not (not Am))) (C Am))
================================================================
tm-name          tm-78038
in-theory        78038
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (((A and B) or ((A and B) or A)) -> (C -> (D -> C))))
theorem-size     27
proof            (modus-ponens tm-882 tm-721 ((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78038.        ((((A and B) or A) -> (C -> (D -> C))) and (((A and B) or ((A and B) or A)) -> (C -> (D -> C)))), M:tm-882, m:tm-721, u:((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-78039
in-theory        78039
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (A -> A)))
theorem-size     33
proof            (modus-ponens tm-882 tm-722 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78039.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (A -> A))), M:tm-882, m:tm-722, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am Am)))
================================================================
tm-name          tm-78040
in-theory        78040
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 D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     75
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78040.        ((((((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 D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-882, 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-78041
in-theory        78041
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     43
proof            (modus-ponens tm-882 tm-724 ((A (and Am Bm)) (B Am) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78041.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-882, m:tm-724, u:((A (and Am Bm)) (B Am) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-78042
in-theory        78042
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 D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)))
theorem-size     61
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78042.        (((((((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 D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))), M:tm-882, 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-78043
in-theory        78043
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (((A and B) or ((A and B) or A)) -> ((C and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-882 tm-726 ((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78043.        ((((A and B) or A) -> ((C and D) -> C)) and (((A and B) or ((A and B) or A)) -> ((C and D) -> C))), M:tm-882, m:tm-726, u:((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-78044
in-theory        78044
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 D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C)))
theorem-size     61
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78044.        ((((((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 D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C))), M:tm-882, 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-78045
in-theory        78045
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (((A and B) or ((A and B) or A)) -> ((C and D) -> D)))
theorem-size     27
proof            (modus-ponens tm-882 tm-728 ((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78045.        ((((A and B) or A) -> ((C and D) -> D)) and (((A and B) or ((A and B) or A)) -> ((C and D) -> D))), M:tm-882, m:tm-728, u:((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-78046
in-theory        78046
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((A and B) or ((A and B) or A)) -> ((C -> (D -> C)) and A)))
theorem-size     31
proof            (modus-ponens tm-882 tm-729 ((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78046.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((A and B) or ((A and B) or A)) -> ((C -> (D -> C)) and A))), M:tm-882, m:tm-729, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-78047
in-theory        78047
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 B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))
theorem-size     47
proof            (modus-ponens tm-882 tm-730 ((A (and Am Bm)) (B Am) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78047.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((A and B) or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))), M:tm-882, m:tm-730, u:((A (and Am Bm)) (B Am) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-78048
in-theory        78048
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (((A and B) or ((A and B) or A)) -> (((C and D) -> C) and A)))
theorem-size     31
proof            (modus-ponens tm-882 tm-731 ((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78048.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (((A and B) or ((A and B) or A)) -> (((C and D) -> C) and A))), M:tm-882, m:tm-731, u:((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-78049
in-theory        78049
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (((A and B) or ((A and B) or A)) -> (((C and D) -> D) and A)))
theorem-size     31
proof            (modus-ponens tm-882 tm-732 ((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78049.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (((A and B) or ((A and B) or A)) -> (((C and D) -> D) and A))), M:tm-882, m:tm-732, u:((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-78050
in-theory        78050
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((A and B) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A)))
theorem-size     35
proof            (modus-ponens tm-882 tm-733 ((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78050.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((A and B) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A))), M:tm-882, m:tm-733, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-78051
in-theory        78051
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-734 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78051.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B)))), M:tm-882, m:tm-734, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am (and Am Bm))))
================================================================
tm-name          tm-78052
in-theory        78052
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((A and B) or ((A and B) or A)) -> (C -> (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-882 tm-735 ((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78052.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((A and B) or ((A and B) or A)) -> (C -> (D -> (C and D))))), M:tm-882, m:tm-735, u:((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-78053
in-theory        78053
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((A and B) or ((A and B) or A)) -> ((C -> (C or D)) and A)))
theorem-size     31
proof            (modus-ponens tm-882 tm-736 ((A (and Am Bm)) (B Am) (C (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78053.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((A and B) or ((A and B) or A)) -> ((C -> (C or D)) and A))), M:tm-882, m:tm-736, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-78054
in-theory        78054
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (((A and B) or ((A and B) or A)) -> (C -> (C or D))))
theorem-size     27
proof            (modus-ponens tm-882 tm-737 ((A (and Am Bm)) (B Am) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78054.        ((((A and B) or A) -> (C -> (C or D))) and (((A and B) or ((A and B) or A)) -> (C -> (C or D)))), M:tm-882, m:tm-737, u:((A (and Am Bm)) (B Am) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-78055
in-theory        78055
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((A and B) or ((A and B) or A)) -> ((C -> (D or C)) and A)))
theorem-size     31
proof            (modus-ponens tm-882 tm-738 ((A (and Am Bm)) (B Am) (C (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78055.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((A and B) or ((A and B) or A)) -> ((C -> (D or C)) and A))), M:tm-882, m:tm-738, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-78056
in-theory        78056
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (((A and B) or ((A and B) or A)) -> (C -> (D or C))))
theorem-size     27
proof            (modus-ponens tm-882 tm-739 ((A (and Am Bm)) (B Am) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78056.        ((((A and B) or A) -> (C -> (D or C))) and (((A and B) or ((A and B) or A)) -> (C -> (D or C)))), M:tm-882, m:tm-739, u:((A (and Am Bm)) (B Am) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-78057
in-theory        78057
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 D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C)))
theorem-size     51
proof            (modus-ponens tm-882 tm-740 ((A (and (-> (-> Am Bm) Cm) Dm)) (B (-> (-> Am Bm) Cm)) (C (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-78057.        ((((((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 D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C))), M:tm-882, m:tm-740, u:((A (and (-> (-> Am Bm) Cm) Dm)) (B (-> (-> Am Bm) Cm)) (C (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-78058
in-theory        78058
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 E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     87
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78058.        (((((((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 E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-882, 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-78059
in-theory        78059
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 C) or (A -> B))) -> (((A and D) or A) -> B)))
theorem-size     41
proof            (modus-ponens tm-882 tm-742 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78059.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B))), M:tm-882, m:tm-742, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-78060
in-theory        78060
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 -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))
theorem-size     61
proof            (modus-ponens tm-882 tm-743 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78060.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))), M:tm-882, 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-78061
in-theory        78061
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((A or (A or (B -> A))) -> (((B and C) or B) -> A)))
theorem-size     29
proof            (modus-ponens tm-882 tm-744 ((A Am) (B (-> Bm Am)) (C (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-78061.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((A or (A or (B -> A))) -> (((B and C) or B) -> A))), M:tm-882, m:tm-744, u:((A Am) (B (-> Bm Am)) (C (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-78062
in-theory        78062
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B))))
theorem-size     41
proof            (modus-ponens tm-882 tm-757 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-78062.        (((A or B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B)))), M:tm-882, m:tm-757, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-78063
in-theory        78063
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> (((C and E) or C) -> D))) and ((A or (A or B)) -> ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     33
proof            (modus-ponens tm-882 tm-759 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78063.        (((A or B) -> ((C -> D) -> (((C and E) or C) -> D))) and ((A or (A or B)) -> ((C -> D) -> (((C and E) or C) -> D)))), M:tm-882, m:tm-759, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-78064
in-theory        78064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (((A and B) or ((A and B) or B)) -> (C -> B)))
theorem-size     23
proof            (modus-ponens tm-882 tm-760 ((A (and Am Bm)) (B Bm) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-78064.        ((((A and B) or B) -> (C -> B)) and (((A and B) or ((A and B) or B)) -> (C -> B))), M:tm-882, m:tm-760, u:((A (and Am Bm)) (B Bm) (C (-> Cm Bm)))
================================================================
tm-name          tm-78065
in-theory        78065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((A and (B -> (C -> D))) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D))))
theorem-size     51
proof            (modus-ponens tm-882 tm-761 ((A (and Am (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78065.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((A and (B -> (C -> D))) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))), M:tm-882, m:tm-761, u:((A (and Am (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-78066
in-theory        78066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (((A and (B and C)) or ((A and (B and C)) or (B and C))) -> B))
theorem-size     29
proof            (modus-ponens tm-882 tm-762 ((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78066.        ((((A and (B and C)) or (B and C)) -> B) and (((A and (B and C)) or ((A and (B and C)) or (B and C))) -> B)), M:tm-882, m:tm-762, u:((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-78067
in-theory        78067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (((A and (B and C)) or ((A and (B and C)) or (B and C))) -> C))
theorem-size     29
proof            (modus-ponens tm-882 tm-763 ((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78067.        ((((A and (B and C)) or (B and C)) -> C) and (((A and (B and C)) or ((A and (B and C)) or (B and C))) -> C)), M:tm-882, m:tm-763, u:((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-78068
in-theory        78068
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (((A and B) or ((A and B) or B)) -> (C -> (B and C))))
theorem-size     27
proof            (modus-ponens tm-882 tm-764 ((A (and Am Bm)) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78068.        ((((A and B) or B) -> (C -> (B and C))) and (((A and B) or ((A and B) or B)) -> (C -> (B and C)))), M:tm-882, m:tm-764, u:((A (and Am Bm)) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-78069
in-theory        78069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (((A and B) or ((A and B) or B)) -> (B or C)))
theorem-size     23
proof            (modus-ponens tm-882 tm-765 ((A (and Am Bm)) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78069.        ((((A and B) or B) -> (B or C)) and (((A and B) or ((A and B) or B)) -> (B or C))), M:tm-882, m:tm-765, u:((A (and Am Bm)) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-78070
in-theory        78070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (((A and B) or ((A and B) or B)) -> (C or B)))
theorem-size     23
proof            (modus-ponens tm-882 tm-766 ((A (and Am Bm)) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78070.        ((((A and B) or B) -> (C or B)) and (((A and B) or ((A and B) or B)) -> (C or B))), M:tm-882, m:tm-766, u:((A (and Am Bm)) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-78071
in-theory        78071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     45
proof            (modus-ponens tm-882 tm-767 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78071.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D)))), M:tm-882, m:tm-767, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-78072
in-theory        78072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B))))
theorem-size     41
proof            (modus-ponens tm-882 tm-768 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78072.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B)))), M:tm-882, m:tm-768, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-78073
in-theory        78073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (((A and (not (not B))) or ((A and (not (not B))) or (not (not B)))) -> B))
theorem-size     29
proof            (modus-ponens tm-882 tm-769 ((A (and Am (not (not Bm)))) (B (not (not Bm))) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78073.        ((((A and (not (not B))) or (not (not B))) -> B) and (((A and (not (not B))) or ((A and (not (not B))) or (not (not B)))) -> B)), M:tm-882, m:tm-769, u:((A (and Am (not (not Bm)))) (B (not (not Bm))) (C Bm))
================================================================
tm-name          tm-78074
in-theory        78074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (((A and B) or ((A and B) or B)) -> (C -> (D -> C))))
theorem-size     27
proof            (modus-ponens tm-882 tm-770 ((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-78074.        ((((A and B) or B) -> (C -> (D -> C))) and (((A and B) or ((A and B) or B)) -> (C -> (D -> C)))), M:tm-882, m:tm-770, u:((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-78075
in-theory        78075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (B -> B)))
theorem-size     33
proof            (modus-ponens tm-882 tm-771 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-78075.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (B -> B))), M:tm-882, m:tm-771, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-78076
in-theory        78076
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 ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     75
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 tm-6 tm-4)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78076.        ((((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 ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-882, 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-78077
in-theory        78077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     43
proof            (modus-ponens tm-882 tm-773 ((A (and Am Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-78077.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-882, m:tm-773, u:((A (and Am Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-78078
in-theory        78078
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 ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C)))
theorem-size     61
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78078.        ((((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 ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C))), M:tm-882, 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-78079
in-theory        78079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (((A and B) or ((A and B) or B)) -> ((C and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-882 tm-775 ((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-78079.        ((((A and B) or B) -> ((C and D) -> C)) and (((A and B) or ((A and B) or B)) -> ((C and D) -> C))), M:tm-882, m:tm-775, u:((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-78080
in-theory        78080
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 ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D)))
theorem-size     61
proof            (modus-ponens tm-882 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-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78080.        ((((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 ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D))), M:tm-882, 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-78081
in-theory        78081
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (((A and B) or ((A and B) or B)) -> ((C and D) -> D)))
theorem-size     27
proof            (modus-ponens tm-882 tm-777 ((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-78081.        ((((A and B) or B) -> ((C and D) -> D)) and (((A and B) or ((A and B) or B)) -> ((C and D) -> D))), M:tm-882, m:tm-777, u:((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-78082
in-theory        78082
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((A and B) or ((A and B) or B)) -> ((C -> (D -> C)) and B)))
theorem-size     31
proof            (modus-ponens tm-882 tm-778 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-78082.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((A and B) or ((A and B) or B)) -> ((C -> (D -> C)) and B))), M:tm-882, m:tm-778, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-78083
in-theory        78083
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((A and B) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     47
proof            (modus-ponens tm-882 tm-779 ((A (and Am Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78083.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((A and B) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-882, m:tm-779, u:((A (and Am Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-78084
in-theory        78084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (((A and B) or ((A and B) or B)) -> (((C and D) -> C) and B)))
theorem-size     31
proof            (modus-ponens tm-882 tm-780 ((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78084.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (((A and B) or ((A and B) or B)) -> (((C and D) -> C) and B))), M:tm-882, m:tm-780, u:((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-78085
in-theory        78085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (((A and B) or ((A and B) or B)) -> (((C and D) -> D) and B)))
theorem-size     31
proof            (modus-ponens tm-882 tm-781 ((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78085.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (((A and B) or ((A and B) or B)) -> (((C and D) -> D) and B))), M:tm-882, m:tm-781, u:((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-78086
in-theory        78086
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((A and B) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B)))
theorem-size     35
proof            (modus-ponens tm-882 tm-782 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78086.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((A and B) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B))), M:tm-882, m:tm-782, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-78087
in-theory        78087
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C))))
theorem-size     37
proof            (modus-ponens tm-882 tm-783 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78087.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C)))), M:tm-882, m:tm-783, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-78088
in-theory        78088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((A and B) or ((A and B) or B)) -> (C -> (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-882 tm-784 ((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), 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-78088.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and (((A and B) or ((A and B) or B)) -> (C -> (D -> (C and D))))), M:tm-882, m:tm-784, u:((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-78089
in-theory        78089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((A and B) or ((A and B) or B)) -> ((C -> (C or D)) and B)))
theorem-size     31
proof            (modus-ponens tm-882 tm-785 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-78089.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and (((A and B) or ((A and B) or B)) -> ((C -> (C or D)) and B))), M:tm-882, m:tm-785, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-78090
in-theory        78090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and (((A and B) or ((A and B) or B)) -> (C -> (C or D))))
theorem-size     27
proof            (modus-ponens tm-882 tm-786 ((A (and Am Bm)) (B Bm) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-78090.        ((((A and B) or B) -> (C -> (C or D))) and (((A and B) or ((A and B) or B)) -> (C -> (C or D)))), M:tm-882, m:tm-786, u:((A (and Am Bm)) (B Bm) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-78091
in-theory        78091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((A and B) or ((A and B) or B)) -> ((C -> (D or C)) and B)))
theorem-size     31
proof            (modus-ponens tm-882 tm-787 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-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-78091.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and (((A and B) or ((A and B) or B)) -> ((C -> (D or C)) and B))), M:tm-882, m:tm-787, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-78092
in-theory        78092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and (((A and B) or ((A and B) or B)) -> (C -> (D or C))))
theorem-size     27
proof            (modus-ponens tm-882 tm-788 ((A (and Am Bm)) (B Bm) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-78092.        ((((A and B) or B) -> (C -> (D or C))) and (((A and B) or ((A and B) or B)) -> (C -> (D or C)))), M:tm-882, m:tm-788, u:((A (and Am Bm)) (B Bm) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-78093
in-theory        78093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((A and ((B -> C) -> D)) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D)))
theorem-size     51
proof            (modus-ponens tm-882 tm-789 ((A (and Am (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-78093.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and (((A and ((B -> C) -> D)) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D))), M:tm-882, m:tm-789, u:((A (and Am (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-78094
in-theory        78094
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((A and (((B -> C) -> (B -> D)) -> E)) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     87
proof            (modus-ponens tm-882 tm-790 ((A (and Am (-> (-> (-> 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-5 tm-8 tm-6 tm-4)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-78094.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((A and (((B -> C) -> (B -> D)) -> E)) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-882, m:tm-790, u:((A (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-78095
in-theory        78095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C)))
theorem-size     41
proof            (modus-ponens tm-882 tm-791 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78095.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C))), M:tm-882, m:tm-791, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-78096
in-theory        78096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C)))
theorem-size     41
proof            (modus-ponens tm-882 tm-792 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78096.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C))), M:tm-882, m:tm-792, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-78097
in-theory        78097
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B)))
theorem-size     41
proof            (modus-ponens tm-882 tm-793 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-78097.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B))), M:tm-882, m:tm-793, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-78098
in-theory        78098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     61
proof            (modus-ponens tm-882 tm-794 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-4)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78098.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-882, m:tm-794, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-78099
in-theory        78099
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((A or (A or (B -> A))) -> (((C and B) or B) -> A)))
theorem-size     29
proof            (modus-ponens tm-882 tm-795 ((A Am) (B (-> Bm Am)) (C (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-78099.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and ((A or (A or (B -> A))) -> (((C and B) or B) -> A))), M:tm-882, m:tm-795, u:((A Am) (B (-> Bm Am)) (C (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-78100
in-theory        78100
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B))))
theorem-size     41
proof            (modus-ponens tm-882 tm-808 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-78100.        (((A or B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B))) and ((A or (A or B)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B)))), M:tm-882, m:tm-808, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-78101
in-theory        78101
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> (((E and C) or C) -> D))) and ((A or (A or B)) -> ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     33
proof            (modus-ponens tm-882 tm-810 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-78101.        (((A or B) -> ((C -> D) -> (((E and C) or C) -> D))) and ((A or (A or B)) -> ((C -> D) -> (((E and C) or C) -> D)))), M:tm-882, m:tm-810, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-78102
in-theory        78102
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (C -> (B -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-882 tm-811 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78102.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (C -> (B -> (A and B))))), M:tm-882, m:tm-811, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-78103
in-theory        78103
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((A or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C))))
theorem-size     37
proof            (modus-ponens tm-882 tm-812 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78103.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and ((A or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C)))), M:tm-882, m:tm-812, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-78104
in-theory        78104
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((A or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C)))
theorem-size     33
proof            (modus-ponens tm-882 tm-813 ((A Am) (B (-> Bm (and Am Bm))) (C (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-78104.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and ((A or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C))), M:tm-882, m:tm-813, u:((A Am) (B (-> Bm (and Am Bm))) (C (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-78105
in-theory        78105
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (C or (B -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-882 tm-814 ((A Am) (B (-> Bm (and Am Bm))) (C (or Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78105.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (C or (B -> (A and B))))), M:tm-882, m:tm-814, u:((A Am) (B (-> Bm (and Am Bm))) (C (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-78106
in-theory        78106
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((A or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-882 tm-815 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78106.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and ((A or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))), M:tm-882, m:tm-815, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-78107
in-theory        78107
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((A or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-816 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78107.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and ((A or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B)))), M:tm-882, m:tm-816, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-78108
in-theory        78108
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((A or (A or (B -> (A and B)))) -> (C -> (D -> C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-817 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78108.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and ((A or (A or (B -> (A and B)))) -> (C -> (D -> C)))), M:tm-882, m:tm-817, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-78109
in-theory        78109
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and ((A or (A or (B -> (A and B)))) -> (B -> B)))
theorem-size     25
proof            (modus-ponens tm-882 tm-818 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-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-78109.        (((A or (B -> (A and B))) -> (B -> B)) and ((A or (A or (B -> (A and B)))) -> (B -> B))), M:tm-882, m:tm-818, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm Bm)))
================================================================
tm-name          tm-78110
in-theory        78110
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     45
proof            (modus-ponens tm-882 tm-819 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-14.           (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-78110.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-882, m:tm-819, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-78111
in-theory        78111
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((A or (A or (B -> (A and B)))) -> ((C and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-882 tm-820 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78111.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and ((A or (A or (B -> (A and B)))) -> ((C and D) -> C))), M:tm-882, m:tm-820, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-78112
in-theory        78112
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((A or (A or (B -> (A and B)))) -> ((C and D) -> D)))
theorem-size     29
proof            (modus-ponens tm-882 tm-821 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78112.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and ((A or (A or (B -> (A and B)))) -> ((C and D) -> D))), M:tm-882, m:tm-821, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-78113
in-theory        78113
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-882 tm-822 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78113.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B))))), M:tm-882, m:tm-822, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-78114
in-theory        78114
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))
theorem-size     57
proof            (modus-ponens tm-882 tm-823 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-78114.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))), M:tm-882, m:tm-823, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-78115
in-theory        78115
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-882 tm-824 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78115.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B))))), M:tm-882, m:tm-824, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-78116
in-theory        78116
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-882 tm-825 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78116.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B))))), M:tm-882, m:tm-825, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-78117
in-theory        78117
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))
theorem-size     45
proof            (modus-ponens tm-882 tm-826 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78117.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))), M:tm-882, m:tm-826, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-78118
in-theory        78118
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((A or (A or (B -> (A and B)))) -> (B -> (B and (A and B)))))
theorem-size     33
proof            (modus-ponens tm-882 tm-827 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-78118.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and ((A or (A or (B -> (A and B)))) -> (B -> (B and (A and B))))), M:tm-882, m:tm-827, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-78119
in-theory        78119
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((A or (A or (B -> (A and B)))) -> (C -> (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-882 tm-828 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78119.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and ((A or (A or (B -> (A and B)))) -> (C -> (D -> (C and D))))), M:tm-882, m:tm-828, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-78120
in-theory        78120
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-882 tm-829 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-78120.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B))))), M:tm-882, m:tm-829, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-78121
in-theory        78121
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and ((A or (A or (B -> (A and B)))) -> (C -> (C or D))))
theorem-size     29
proof            (modus-ponens tm-882 tm-830 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-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-78121.        (((A or (B -> (A and B))) -> (C -> (C or D))) and ((A or (A or (B -> (A and B)))) -> (C -> (C or D)))), M:tm-882, m:tm-830, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-78122
in-theory        78122
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-882 tm-831 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78122.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B))))), M:tm-882, m:tm-831, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-78123
in-theory        78123
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and ((A or (A or (B -> (A and B)))) -> (C -> (D or C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-832 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78123.        (((A or (B -> (A and B))) -> (C -> (D or C))) and ((A or (A or (B -> (A and B)))) -> (C -> (D or C)))), M:tm-882, m:tm-832, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-78124
in-theory        78124
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((A or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C)))))
theorem-size     49
proof            (modus-ponens tm-882 tm-833 ((A Am) (B (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78124.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((A or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C))))), M:tm-882, m:tm-833, u:((A Am) (B (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-78125
in-theory        78125
times-derived    1
----------------------------------------------------------------
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))))) and ((A or (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     89
proof            (modus-ponens tm-882 tm-834 ((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (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-5 tm-8 tm-6)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-78125.        (((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))))) and ((A or (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-882, m:tm-834, u:((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-78126
in-theory        78126
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((A or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-835 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78126.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and ((A or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B)))), M:tm-882, m:tm-835, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-78127
in-theory        78127
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((A or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-836 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78127.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and ((A or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B)))), M:tm-882, m:tm-836, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-78128
in-theory        78128
times-derived    1
----------------------------------------------------------------
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))))) and ((A or (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     65
proof            (modus-ponens tm-882 tm-837 ((A Am) (B (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78128.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((A or (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-882, m:tm-837, u:((A Am) (B (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-78129
in-theory        78129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((A and ((B -> (C and B)) -> D)) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D)))
theorem-size     65
proof            (modus-ponens tm-882 tm-838 ((A (and Am (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-78129.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and (((A and ((B -> (C and B)) -> D)) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D))), M:tm-882, m:tm-838, u:((A (and Am (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-78130
in-theory        78130
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((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) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C)))
theorem-size     65
proof            (modus-ponens tm-882 tm-839 ((A (and (-> (-> Am (and Bm Am)) Cm) Dm)) (B (-> (-> Am (and Bm Am)) Cm)) (C (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-78130.        ((((((A -> (B and A)) -> C) and D) or ((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) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C))), M:tm-882, m:tm-839, u:((A (and (-> (-> Am (and Bm Am)) Cm) Dm)) (B (-> (-> Am (and Bm Am)) Cm)) (C (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-78131
in-theory        78131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((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) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     67
proof            (modus-ponens tm-882 tm-840 ((A (-> Am (-> (and Bm Am) Cm))) (B (-> (-> Am (and Bm Am)) (-> Am Cm))) (C (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-78131.        ((((A -> ((B and A) -> C)) or ((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) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C)))), M:tm-882, m:tm-840, u:((A (-> Am (-> (and Bm Am) Cm))) (B (-> (-> Am (and Bm Am)) (-> Am Cm))) (C (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-78132
in-theory        78132
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((A or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A)))
theorem-size     41
proof            (modus-ponens tm-882 tm-841 ((A Am) (B (-> (-> Bm (and Cm Bm)) Am)) (C (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-78132.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((A or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A))), M:tm-882, m:tm-841, u:((A Am) (B (-> (-> Bm (and Cm Bm)) Am)) (C (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-78133
in-theory        78133
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B))))
theorem-size     53
proof            (modus-ponens tm-882 tm-855 ((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-78133.        (((A or B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B)))), M:tm-882, m:tm-855, u:((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B))))
================================================================
tm-name          tm-78134
in-theory        78134
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((A or (A or B)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     45
proof            (modus-ponens tm-882 tm-857 ((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-78134.        (((A or B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((A or (A or B)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-882, m:tm-857, u:((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-78135
in-theory        78135
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and ((A or (A or (A or B))) -> (C -> (A or B))))
theorem-size     25
proof            (modus-ponens tm-882 tm-858 ((A Am) (B (or Am Bm)) (C (-> Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78135.        (((A or (A or B)) -> (C -> (A or B))) and ((A or (A or (A or B))) -> (C -> (A or B)))), M:tm-882, m:tm-858, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Am Bm))))
================================================================
tm-name          tm-78136
in-theory        78136
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and ((A or (A or (A or B))) -> (C -> ((A or B) and C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-859 ((A Am) (B (or Am Bm)) (C (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78136.        (((A or (A or B)) -> (C -> ((A or B) and C))) and ((A or (A or (A or B))) -> (C -> ((A or B) and C)))), M:tm-882, m:tm-859, u:((A Am) (B (or Am Bm)) (C (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-78137
in-theory        78137
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and ((A or (A or (A or B))) -> ((A or B) or C)))
theorem-size     25
proof            (modus-ponens tm-882 tm-860 ((A Am) (B (or Am Bm)) (C (or (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78137.        (((A or (A or B)) -> ((A or B) or C)) and ((A or (A or (A or B))) -> ((A or B) or C))), M:tm-882, m:tm-860, u:((A Am) (B (or Am Bm)) (C (or (or Am Bm) Cm)))
================================================================
tm-name          tm-78138
in-theory        78138
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and ((A or (A or (A or B))) -> (C or (A or B))))
theorem-size     25
proof            (modus-ponens tm-882 tm-861 ((A Am) (B (or Am Bm)) (C (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78138.        (((A or (A or B)) -> (C or (A or B))) and ((A or (A or (A or B))) -> (C or (A or B)))), M:tm-882, m:tm-861, u:((A Am) (B (or Am Bm)) (C (or Cm (or Am Bm))))
================================================================
tm-name          tm-78139
in-theory        78139
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and ((A or (A or (A or B))) -> (C -> (D -> C))))
theorem-size     25
proof            (modus-ponens tm-882 tm-862 ((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78139.        (((A or (A or B)) -> (C -> (D -> C))) and ((A or (A or (A or B))) -> (C -> (D -> C)))), M:tm-882, m:tm-862, u:((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-78140
in-theory        78140
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-882 tm-863 ((A Am) (B (or Am Bm)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (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-78140.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-882, m:tm-863, u:((A Am) (B (or Am Bm)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-78141
in-theory        78141
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and ((A or (A or (A or B))) -> ((C and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-882 tm-864 ((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-78141.        (((A or (A or B)) -> ((C and D) -> C)) and ((A or (A or (A or B))) -> ((C and D) -> C))), M:tm-882, m:tm-864, u:((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-78142
in-theory        78142
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and ((A or (A or (A or B))) -> ((C and D) -> D)))
theorem-size     25
proof            (modus-ponens tm-882 tm-865 ((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-78142.        (((A or (A or B)) -> ((C and D) -> D)) and ((A or (A or (A or B))) -> ((C and D) -> D))), M:tm-882, m:tm-865, u:((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-78143
in-theory        78143
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((A or (A or (A or B))) -> ((C -> (D -> C)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-866 ((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-78143.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and ((A or (A or (A or B))) -> ((C -> (D -> C)) and (A or B)))), M:tm-882, m:tm-866, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-78144
in-theory        78144
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((A or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-867 ((A Am) (B (or Am Bm)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-78144.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((A or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))), M:tm-882, m:tm-867, u:((A Am) (B (or Am Bm)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-78145
in-theory        78145
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((A or (A or (A or B))) -> (((C and D) -> C) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-868 ((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-78145.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and ((A or (A or (A or B))) -> (((C and D) -> C) and (A or B)))), M:tm-882, m:tm-868, u:((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-78146
in-theory        78146
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((A or (A or (A or B))) -> (((C and D) -> D) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-869 ((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-78146.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and ((A or (A or (A or B))) -> (((C and D) -> D) and (A or B)))), M:tm-882, m:tm-869, u:((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-78147
in-theory        78147
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((A or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-882 tm-870 ((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78147.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and ((A or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B)))), M:tm-882, m:tm-870, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-78148
in-theory        78148
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((A or (A or (A or B))) -> (C -> (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-882 tm-871 ((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-78148.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and ((A or (A or (A or B))) -> (C -> (D -> (C and D))))), M:tm-882, m:tm-871, u:((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-78149
in-theory        78149
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((A or (A or (A or B))) -> ((C -> (C or D)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-872 ((A Am) (B (or Am Bm)) (C (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78149.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and ((A or (A or (A or B))) -> ((C -> (C or D)) and (A or B)))), M:tm-882, m:tm-872, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-78150
in-theory        78150
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and ((A or (A or (A or B))) -> (C -> (C or D))))
theorem-size     25
proof            (modus-ponens tm-882 tm-873 ((A Am) (B (or Am Bm)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-78150.        (((A or (A or B)) -> (C -> (C or D))) and ((A or (A or (A or B))) -> (C -> (C or D)))), M:tm-882, m:tm-873, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-78151
in-theory        78151
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((A or (A or (A or B))) -> ((C -> (D or C)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-882 tm-874 ((A Am) (B (or Am Bm)) (C (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-78151.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and ((A or (A or (A or B))) -> ((C -> (D or C)) and (A or B)))), M:tm-882, m:tm-874, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-78152
in-theory        78152
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and ((A or (A or (A or B))) -> (C -> (D or C))))
theorem-size     25
proof            (modus-ponens tm-882 tm-875 ((A Am) (B (or Am Bm)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-78152.        (((A or (A or B)) -> (C -> (D or C))) and ((A or (A or (A or B))) -> (C -> (D or C)))), M:tm-882, m:tm-875, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-78153
in-theory        78153
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((A or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C)))))
theorem-size     49
proof            (modus-ponens tm-882 tm-876 ((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and 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-78153.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((A or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C))))), M:tm-882, m:tm-876, u:((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-78154
in-theory        78154
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D)))
theorem-size     51
proof            (modus-ponens tm-882 tm-877 ((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-78154.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D))), M:tm-882, m:tm-877, u:((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-78155
in-theory        78155
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C)))
theorem-size     51
proof            (modus-ponens tm-882 tm-878 ((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
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-78155.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C))), M:tm-882, m:tm-878, u:((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-78156
in-theory        78156
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((A or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A)))
theorem-size     33
proof            (modus-ponens tm-882 tm-879 ((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
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-78156.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((A or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A))), M:tm-882, m:tm-879, u:((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-78157
in-theory        78157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     37
proof            (modus-ponens tm-855 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78157.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-855, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78158
in-theory        78158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((B or (B or (A -> (B and A)))) -> C)))
theorem-size     39
proof            (modus-ponens tm-852 tm-882 ((A Am) (Bm (-> B (and Am B))) (C Cm) (D (and (-> (or Am (-> B (and Am B))) Cm) (-> (or Am (or Am (-> B (and Am B)))) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78158.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and ((B or (B or (A -> (B and A)))) -> C))), M:tm-852, m:tm-882, u:((A Am) (Bm (-> B (and Am B))) (C Cm) (D (and (-> (or Am (-> B (and Am B))) Cm) (-> (or Am (or Am (-> B (and Am B)))) Cm))))
================================================================
tm-name          tm-78159
in-theory        78159
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C and (A or B))) -> (((A or B) -> (C and (A or B))) and ((A or (A or B)) -> (C and (A or B)))))
theorem-size     31
proof            (modus-ponens tm-850 tm-882 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Am (or Am Bm)) (and B (or Am Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       187
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78159.        (((A or B) -> (C and (A or B))) -> (((A or B) -> (C and (A or B))) and ((A or (A or B)) -> (C and (A or B))))), M:tm-850, m:tm-882, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Am (or Am Bm)) (and B (or Am Bm))))))
================================================================
tm-name          tm-78160
in-theory        78160
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and (A or B))) -> (((A or B) -> (C and (A or B))) and ((A or (A or B)) -> (C and (A or B))))) and ((C or ((A or B) -> (C and (A or B)))) -> (((A or B) -> (C and (A or B))) and ((A or (A or B)) -> (C and (A or B))))))
theorem-size     65
proof            (modus-ponens tm-844 tm-882 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Am (or Am Bm)) (and B (or Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78160.        ((((A or B) -> (C and (A or B))) -> (((A or B) -> (C and (A or B))) and ((A or (A or B)) -> (C and (A or B))))) and ((C or ((A or B) -> (C and (A or B)))) -> (((A or B) -> (C and (A or B))) and ((A or (A or B)) -> (C and (A or B)))))), M:tm-844, m:tm-882, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Am (or Am Bm)) (and B (or Am Bm))))))
================================================================
tm-name          tm-78161
in-theory        78161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-808 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-6)
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78161.        (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-808, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78162
in-theory        78162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((C and A) or ((C and A) or A)) -> B)))
theorem-size     31
proof            (modus-ponens tm-805 tm-882 ((Am (and A Bm)) (B Bm) (C Cm) (D (and (-> (or (and A Bm) Bm) Cm) (-> (or (and A Bm) (or (and A Bm) Bm)) Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78162.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and (((C and A) or ((C and A) or A)) -> B))), M:tm-805, m:tm-882, u:((Am (and A Bm)) (B Bm) (C Cm) (D (and (-> (or (and A Bm) Bm) Cm) (-> (or (and A Bm) (or (and A Bm) Bm)) Cm))))
================================================================
tm-name          tm-78163
in-theory        78163
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C))))
theorem-size     47
proof            (modus-ponens tm-798 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78163.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C)))), M:tm-798, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78164
in-theory        78164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-757 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78164.        (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-757, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78165
in-theory        78165
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 C) or A)) -> B)))
theorem-size     31
proof            (modus-ponens tm-754 tm-882 ((Am (and Bm B)) (A Bm) (C Cm) (D (and (-> (or (and Bm B) Bm) Cm) (-> (or (and Bm B) (or (and Bm B) Bm)) Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-6)
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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78165.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((A and C) or ((A and C) or A)) -> B))), M:tm-754, m:tm-882, u:((Am (and Bm B)) (A Bm) (C Cm) (D (and (-> (or (and Bm B) Bm) Cm) (-> (or (and Bm B) (or (and Bm B) Bm)) Cm))))
================================================================
tm-name          tm-78166
in-theory        78166
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C))))
theorem-size     47
proof            (modus-ponens tm-747 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-78166.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C)))), M:tm-747, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78167
in-theory        78167
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 F) -> G) and ((E or (E or F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-708 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78167.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G)))), M:tm-708, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78168
in-theory        78168
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 -> C)) or ((A -> B) -> (A -> C)))) -> D)))
theorem-size     63
proof            (modus-ponens tm-705 tm-882 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D Cm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm) (-> (or (-> A (-> B C)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78168.        (((((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 -> C)) or ((A -> B) -> (A -> C)))) -> D))), M:tm-705, m:tm-882, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D Cm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm) (-> (or (-> A (-> B C)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm))))
================================================================
tm-name          tm-78169
in-theory        78169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-665 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-49.           (((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-78169.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-665, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78170
in-theory        78170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((B or (B or (A -> B))) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-882 ((A Am) (Bm (-> B Am)) (C Cm) (D (and (-> (or Am (-> B Am)) Cm) (-> (or Am (or Am (-> B Am))) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78170.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((B or (B or (A -> B))) -> C))), M:tm-662, m:tm-882, u:((A Am) (Bm (-> B Am)) (C Cm) (D (and (-> (or Am (-> B Am)) Cm) (-> (or Am (or Am (-> B Am))) Cm))))
================================================================
tm-name          tm-78171
in-theory        78171
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((C or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-654 tm-882 ((A (or Am Bm)) (B Cm) (C (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-78171.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((C or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C)))), M:tm-654, m:tm-882, u:((A (or Am Bm)) (B Cm) (C (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78172
in-theory        78172
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D or (((A or B) -> C) and ((A or (A or B)) -> C))))
theorem-size     21
proof            (modus-ponens tm-623 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78172.        (((A or B) -> C) -> (D or (((A or B) -> C) and ((A or (A or B)) -> C)))), M:tm-623, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78173
in-theory        78173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-622 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78173.        ((A -> (B -> (C or B))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-622, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78174
in-theory        78174
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D or (B or C)))) -> (((B or C) -> (D or (B or C))) and ((B or (B or C)) -> (D or (B or C)))))
theorem-size     33
proof            (modus-ponens tm-619 tm-882 ((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (and (-> (or Am Bm) (or B (or Am Bm))) (-> (or Am (or Am Bm)) (or B (or Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78174.        ((A or ((B or C) -> (D or (B or C)))) -> (((B or C) -> (D or (B or C))) and ((B or (B or C)) -> (D or (B or C))))), M:tm-619, m:tm-882, u:((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (and (-> (or Am Bm) (or B (or Am Bm))) (-> (or Am (or Am Bm)) (or B (or Am Bm))))))
================================================================
tm-name          tm-78175
in-theory        78175
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78175.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (E or D))), M:tm-609, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78176
in-theory        78176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-605 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78176.        ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-605, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78177
in-theory        78177
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (E or D)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78177.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (E or D)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-595, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78178
in-theory        78178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-550 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-49.           (((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-78178.        (((A -> (B or A)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-550, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78179
in-theory        78179
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-540 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78179.        ((A or (B -> (C or B))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-540, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78180
in-theory        78180
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-530 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-49.           (((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-78180.        ((A or (B -> (B or C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-530, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78181
in-theory        78181
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-520 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78181.        ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-520, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78182
in-theory        78182
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-510 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78182.        ((A or ((B and C) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-510, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78183
in-theory        78183
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-500 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78183.        ((A or ((B and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-500, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78184
in-theory        78184
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-490 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78184.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G)))), M:tm-490, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78185
in-theory        78185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-480 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78185.        ((A or (B -> (C -> B))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-480, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78186
in-theory        78186
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> ((((A or B) -> C) and ((A or (A or B)) -> C)) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-78186.        (((A or B) -> C) -> ((((A or B) -> C) and ((A or (A or B)) -> C)) or D)), M:tm-470, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78187
in-theory        78187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-469 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-78187.        ((A -> (B -> (B or C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-469, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78188
in-theory        78188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> ((B or C) or D))) -> (((B or C) -> ((B or C) or D)) and ((B or (B or C)) -> ((B or C) or D))))
theorem-size     33
proof            (modus-ponens tm-466 tm-882 ((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (and (-> (or Am Bm) (or (or Am Bm) B)) (-> (or Am (or Am Bm)) (or (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-49.           (((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-78188.        ((A or ((B or C) -> ((B or C) or D))) -> (((B or C) -> ((B or C) or D)) and ((B or (B or C)) -> ((B or C) or D)))), M:tm-466, m:tm-882, u:((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (and (-> (or Am Bm) (or (or Am Bm) B)) (-> (or Am (or Am Bm)) (or (or Am Bm) B)))))
================================================================
tm-name          tm-78189
in-theory        78189
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-78189.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (D or E))), M:tm-456, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78190
in-theory        78190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-453 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-78190.        ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-453, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78191
in-theory        78191
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (D or E)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-78191.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (D or E)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-443, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78192
in-theory        78192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-409 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-49.           (((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-78192.        (((A -> (A or B)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-409, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78193
in-theory        78193
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-400 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-78193.        (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-400, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78194
in-theory        78194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-391 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-78194.        ((((A and B) -> B) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-391, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78195
in-theory        78195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-382 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-49.           (((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-78195.        ((((A and B) -> A) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-382, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78196
in-theory        78196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-373 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-78196.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G)))), M:tm-373, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78197
in-theory        78197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-364 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-78197.        (((A -> (B -> A)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-364, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78198
in-theory        78198
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> ((((A or B) -> C) and ((A or (A or B)) -> C)) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78198.        (((A or B) -> C) -> (D -> ((((A or B) -> C) and ((A or (A or B)) -> C)) and D))), M:tm-355, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78199
in-theory        78199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-354 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78199.        ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-354, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78200
in-theory        78200
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> ((B or C) and D)))) -> (((B or C) -> (D -> ((B or C) and D))) and ((B or (B or C)) -> (D -> ((B or C) and D)))))
theorem-size     39
proof            (modus-ponens tm-351 tm-882 ((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (and (-> (or Am Bm) (-> B (and (or Am Bm) B))) (-> (or Am (or Am Bm)) (-> B (and (or Am Bm) B)))))))
axioms-used      (tm-8 tm-1 tm-5 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-5.            (A -> (B -> (A and 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-49.           (((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-78200.        ((A or ((B or C) -> (D -> ((B or C) and D)))) -> (((B or C) -> (D -> ((B or C) and D))) and ((B or (B or C)) -> (D -> ((B or C) and D))))), M:tm-351, m:tm-882, u:((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (and (-> (or Am Bm) (-> B (and (or Am Bm) B))) (-> (or Am (or Am Bm)) (-> B (and (or Am Bm) B))))))
================================================================
tm-name          tm-78201
in-theory        78201
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-78201.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78202
in-theory        78202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E))))
theorem-size     29
proof            (modus-ponens tm-338 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-78202.        (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E)))), M:tm-338, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78203
in-theory        78203
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> (((A or B) -> ((A or B) and C)) and ((A or (A or B)) -> ((A or B) and C))))
theorem-size     37
proof            (modus-ponens tm-335 tm-882 ((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (and (-> (or Am Bm) (and (or Am Bm) B)) (-> (or Am (or Am Bm)) (and (or Am Bm) B))))))
axioms-used      (tm-8 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
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-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-78203.        ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> (((A or B) -> ((A or B) and C)) and ((A or (A or B)) -> ((A or B) and C)))), M:tm-335, m:tm-882, u:((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (and (-> (or Am Bm) (and (or Am Bm) B)) (-> (or Am (or Am Bm)) (and (or Am Bm) B)))))
================================================================
tm-name          tm-78204
in-theory        78204
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((A or B) -> C) -> (((A or B) -> C) and (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-328 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-78204.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((A or B) -> C) -> (((A or B) -> C) and (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-328, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78205
in-theory        78205
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-78205.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-327, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78206
in-theory        78206
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((D and E) -> E) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78206.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((D and E) -> E) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-326, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78207
in-theory        78207
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((D and E) -> D) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78207.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((D and E) -> D) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-325, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78208
in-theory        78208
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78208.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-324, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78209
in-theory        78209
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (E -> D)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78209.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (E -> D)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-323, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78210
in-theory        78210
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78210.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78211
in-theory        78211
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78211.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78212
in-theory        78212
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-78212.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78213
in-theory        78213
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((A or B) -> C) -> ((A or B) -> C)))
theorem-size     31
proof            (modus-ponens tm-316 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-78213.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((A or B) -> C) -> ((A or B) -> C))), M:tm-316, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78214
in-theory        78214
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-78214.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78215
in-theory        78215
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((((A or B) -> C) -> (not (((A or B) -> C) and ((A or (A or B)) -> C)))) -> (not ((A or B) -> C))))
theorem-size     47
proof            (modus-ponens tm-313 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-78215.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((((A or B) -> C) -> (not (((A or B) -> C) and ((A or (A or B)) -> C)))) -> (not ((A or B) -> C)))), M:tm-313, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78216
in-theory        78216
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((((A or B) -> C) and ((A or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or (((A or B) -> C) and ((A or (A or B)) -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-312 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-78216.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (((((A or B) -> C) and ((A or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or (((A or B) -> C) and ((A or (A or B)) -> C))) -> D))), M:tm-312, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78217
in-theory        78217
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D or (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-78217.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D or (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-311, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78218
in-theory        78218
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (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-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-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-78218.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) or D)), M:tm-310, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78219
in-theory        78219
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78219.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and D))), M:tm-309, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78220
in-theory        78220
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
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-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-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-78220.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) and (D -> (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))), M:tm-305, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78221
in-theory        78221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-303 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78221.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-303, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78222
in-theory        78222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-270 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78222.        ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-270, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78223
in-theory        78223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-239 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78223.        ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-239, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78224
in-theory        78224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-210 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78224.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G)))), M:tm-210, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78225
in-theory        78225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-183 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78225.        ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-183, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78226
in-theory        78226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-157 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78226.        ((A -> ((B and C) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-157, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78227
in-theory        78227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-147 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78227.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-147, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78228
in-theory        78228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-134 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78228.        ((A -> ((B and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-134, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78229
in-theory        78229
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-125 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78229.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-125, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78230
in-theory        78230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-113 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78230.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G)))), M:tm-113, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78231
in-theory        78231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-105 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78231.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-105, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78232
in-theory        78232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-95 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78232.        (((A -> B) -> (A -> A)) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E)))), M:tm-95, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78233
in-theory        78233
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> (A or B))) -> (((A or B) -> (A or B)) and ((A or (A or B)) -> (A or B))))
theorem-size     31
proof            (modus-ponens tm-92 tm-882 ((Cm (or Am Bm)) (A (or Am Bm)) (B (and (-> (or Am Bm) (or Am Bm)) (-> (or Am (or Am Bm)) (or Am Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78233.        ((((A or B) -> C) or ((A or B) -> (A or B))) -> (((A or B) -> (A or B)) and ((A or (A or B)) -> (A or B)))), M:tm-92, m:tm-882, u:((Cm (or Am Bm)) (A (or Am Bm)) (B (and (-> (or Am Bm) (or Am Bm)) (-> (or Am (or Am Bm)) (or Am Bm)))))
================================================================
tm-name          tm-78234
in-theory        78234
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> (((A or B) -> C) and ((A or (A or B)) -> C))))
theorem-size     21
proof            (modus-ponens tm-84 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78234.        (((A or B) -> C) -> (D -> (((A or B) -> C) and ((A or (A or B)) -> C)))), M:tm-84, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78235
in-theory        78235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-83 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78235.        ((A -> (B -> (C -> B))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-83, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78236
in-theory        78236
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> (B or C)))) -> (((B or C) -> (D -> (B or C))) and ((B or (B or C)) -> (D -> (B or C)))))
theorem-size     33
proof            (modus-ponens tm-80 tm-882 ((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (and (-> (or Am Bm) (-> B (or Am Bm))) (-> (or Am (or Am Bm)) (-> B (or Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78236.        ((A or ((B or C) -> (D -> (B or C)))) -> (((B or C) -> (D -> (B or C))) and ((B or (B or C)) -> (D -> (B or C))))), M:tm-80, m:tm-882, u:((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (and (-> (or Am Bm) (-> B (or Am Bm))) (-> (or Am (or Am Bm)) (-> B (or Am Bm))))))
================================================================
tm-name          tm-78237
in-theory        78237
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B or C) -> D) -> (((B or C) -> D) and ((B or (B or C)) -> D))))
theorem-size     25
proof            (modus-ponens tm-76 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78237.        (((not (not A)) -> A) and (((B or C) -> D) -> (((B or C) -> D) and ((B or (B or C)) -> D)))), M:tm-76, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78238
in-theory        78238
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-73 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78238.        (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C))), M:tm-73, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78239
in-theory        78239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E))))
theorem-size     31
proof            (modus-ponens tm-69 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78239.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E)))), M:tm-69, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78240
in-theory        78240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-54 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-78240.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-54, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78241
in-theory        78241
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (((B or C) -> (A and (B or C))) and ((B or (B or C)) -> (A and (B or C)))))
theorem-size     33
proof            (modus-ponens tm-48 tm-882 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Am (or Am Bm)) (and B (or Am Bm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78241.        ((A or ((B or C) -> (A and (B or C)))) -> (((B or C) -> (A and (B or C))) and ((B or (B or C)) -> (A and (B or C))))), M:tm-48, m:tm-882, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Am (or Am Bm)) (and B (or Am Bm))))))
================================================================
tm-name          tm-78242
in-theory        78242
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((B or C) -> D) and ((B or (B or C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-47 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78242.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((B or C) -> D) and ((B or (B or C)) -> D))), M:tm-47, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78243
in-theory        78243
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-46 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78243.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or B) -> C) and ((A or (A or B)) -> C))), M:tm-46, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78244
in-theory        78244
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (((B or C) -> A) and ((B or (B or C)) -> A)))
theorem-size     21
proof            (modus-ponens tm-44 tm-882 ((A (or Am Bm)) (B Cm) (C (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78244.        ((A or ((B or C) -> A)) -> (((B or C) -> A) and ((B or (B or C)) -> A))), M:tm-44, m:tm-882, u:((A (or Am Bm)) (B Cm) (C (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78245
in-theory        78245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-42 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78245.        ((A -> (B or A)) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E)))), M:tm-42, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78246
in-theory        78246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-32 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and 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-49.           (((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-78246.        ((A -> (A or B)) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E)))), M:tm-32, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78247
in-theory        78247
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (((A or B) -> C) and (((A or B) -> C) and ((A or (A or B)) -> C))))
theorem-size     25
proof            (modus-ponens tm-24 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78247.        (((A or B) -> C) -> (((A or B) -> C) and (((A or B) -> C) and ((A or (A or B)) -> C)))), M:tm-24, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78248
in-theory        78248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-23 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78248.        ((A -> (B -> (A and B))) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E)))), M:tm-23, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78249
in-theory        78249
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-22 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78249.        (((A and B) -> B) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E)))), M:tm-22, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78250
in-theory        78250
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-21 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78250.        (((A and B) -> A) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E)))), M:tm-21, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78251
in-theory        78251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-20 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78251.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-20, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78252
in-theory        78252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-19 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78252.        ((A -> (B -> A)) and (((C or D) -> E) -> (((C or D) -> E) and ((C or (C or D)) -> E)))), M:tm-19, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78253
in-theory        78253
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not (((A or B) -> C) and ((A or (A or B)) -> C)))) -> (not ((A or B) -> C)))
theorem-size     27
proof            (modus-ponens tm-9 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78253.        ((((A or B) -> C) -> (not (((A or B) -> C) and ((A or (A or B)) -> C)))) -> (not ((A or B) -> C))), M:tm-9, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78254
in-theory        78254
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and ((A or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or (((A or B) -> C) and ((A or (A or B)) -> C))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-882 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-78254.        (((((A or B) -> C) and ((A or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or (((A or B) -> C) and ((A or (A or B)) -> C))) -> D)), M:tm-8, m:tm-882, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-78255
in-theory        78255
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B or C) -> D) -> (((B or C) -> D) and ((B or (B or C)) -> D))))
theorem-size     21
proof            (modus-ponens tm-7 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78255.        (A or (((B or C) -> D) -> (((B or C) -> D) and ((B or (B or C)) -> D)))), M:tm-7, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78256
in-theory        78256
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-8)
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-49.           (((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-78256.        ((((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))) or D), M:tm-6, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78257
in-theory        78257
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> (((B or C) -> D) and ((B or (B or C)) -> D))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-78257.        (A -> ((((B or C) -> D) -> (((B or C) -> D) and ((B or (B or C)) -> D))) and A)), M:tm-5, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78258
in-theory        78258
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or C) -> D) -> (((B or C) -> D) and ((B or (B or C)) -> D))))
theorem-size     21
proof            (modus-ponens tm-1 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78258.        (A -> (((B or C) -> D) -> (((B or C) -> D) and ((B or (B or C)) -> D)))), M:tm-1, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-78259
in-theory        78259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-78259.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-855, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78260
in-theory        78260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-808 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-78260.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-808, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78261
in-theory        78261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78261.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-757, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78262
in-theory        78262
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) -> ((G or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78262.        (((((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) -> ((G or (G or H)) -> I)))), M:tm-708, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78263
in-theory        78263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-49.           (((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-78263.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-665, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78264
in-theory        78264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78264.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-622, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78265
in-theory        78265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78265.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78266
in-theory        78266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78266.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-605, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78267
in-theory        78267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78267.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-595, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78268
in-theory        78268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-49.           (((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-78268.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-550, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78269
in-theory        78269
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78269.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-540, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78270
in-theory        78270
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-49.           (((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-78270.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-530, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78271
in-theory        78271
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78271.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-520, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78272
in-theory        78272
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78272.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-510, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78273
in-theory        78273
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78273.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-500, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78274
in-theory        78274
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78274.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-490, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78275
in-theory        78275
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78275.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-480, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78276
in-theory        78276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78276.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-469, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78277
in-theory        78277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78277.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78278
in-theory        78278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-78278.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-453, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78279
in-theory        78279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-78279.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-443, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78280
in-theory        78280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-78280.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-409, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78281
in-theory        78281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-78281.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-400, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78282
in-theory        78282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-49.           (((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-78282.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-391, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78283
in-theory        78283
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-49.           (((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-78283.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-382, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78284
in-theory        78284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-78284.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-373, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78285
in-theory        78285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78285.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-364, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78286
in-theory        78286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78286.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-354, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78287
in-theory        78287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78287.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78288
in-theory        78288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78288.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-338, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78289
in-theory        78289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-78289.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-327, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78290
in-theory        78290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78290.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-326, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78291
in-theory        78291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78291.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-325, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78292
in-theory        78292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78292.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-324, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78293
in-theory        78293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78293.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-323, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78294
in-theory        78294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78294.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78295
in-theory        78295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78295.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78296
in-theory        78296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78296.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78297
in-theory        78297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78297.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78298
in-theory        78298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78298.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-311, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78299
in-theory        78299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-49.           (((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-78299.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)), M:tm-310, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78300
in-theory        78300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78300.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F))), M:tm-309, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78301
in-theory        78301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     35
proof            (modus-ponens tm-308 tm-883 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-78301.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-308, m:tm-883, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-78302
in-theory        78302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (A -> (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-307 tm-883 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78302.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-883, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-78303
in-theory        78303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78303.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-305, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78304
in-theory        78304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78304.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-303, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78305
in-theory        78305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78305.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-270, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78306
in-theory        78306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78306.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-239, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78307
in-theory        78307
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) -> ((G or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78307.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-210, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78308
in-theory        78308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78308.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-183, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78309
in-theory        78309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78309.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-157, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78310
in-theory        78310
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) -> ((F or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78310.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-147, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78311
in-theory        78311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78311.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-134, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78312
in-theory        78312
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) -> ((F or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78312.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-125, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78313
in-theory        78313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78313.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-113, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78314
in-theory        78314
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) -> ((F or (F or G)) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78314.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-105, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78315
in-theory        78315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78315.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-95, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78316
in-theory        78316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78316.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-83, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78317
in-theory        78317
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78317.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-76, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78318
in-theory        78318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78318.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-69, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78319
in-theory        78319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-78319.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-54, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78320
in-theory        78320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78320.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-42, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78321
in-theory        78321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-78321.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-32, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78322
in-theory        78322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-78322.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-23, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78323
in-theory        78323
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78323.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-22, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78324
in-theory        78324
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78324.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-21, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78325
in-theory        78325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78325.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-20, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78326
in-theory        78326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78326.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-19, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78327
in-theory        78327
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-7 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78327.        (A or ((B -> (C -> (B and C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-7, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78328
in-theory        78328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-8)
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-49.           (((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-78328.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F), M:tm-6, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78329
in-theory        78329
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
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-49.           (((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-78329.        (A -> (((B -> (C -> (B and C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A)), M:tm-5, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78330
in-theory        78330
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-1 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78330.        (A -> ((B -> (C -> (B and C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-1, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78331
in-theory        78331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-78331.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-855, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78332
in-theory        78332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-78332.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-808, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78333
in-theory        78333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-49.           (((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-78333.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-757, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78334
in-theory        78334
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) -> ((G or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78334.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-708, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78335
in-theory        78335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-78335.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-665, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78336
in-theory        78336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78336.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-622, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78337
in-theory        78337
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78337.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78338
in-theory        78338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78338.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-605, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78339
in-theory        78339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78339.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-595, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78340
in-theory        78340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-49.           (((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-78340.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-550, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78341
in-theory        78341
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78341.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-540, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78342
in-theory        78342
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-49.           (((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-78342.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-530, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78343
in-theory        78343
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78343.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-520, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78344
in-theory        78344
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78344.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-510, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78345
in-theory        78345
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78345.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-500, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78346
in-theory        78346
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78346.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-490, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78347
in-theory        78347
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78347.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-480, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78348
in-theory        78348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78348.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-469, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78349
in-theory        78349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78349.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78350
in-theory        78350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-78350.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-453, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78351
in-theory        78351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-78351.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-443, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78352
in-theory        78352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-49.           (((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-78352.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-409, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78353
in-theory        78353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-78353.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-400, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78354
in-theory        78354
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-78354.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-391, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78355
in-theory        78355
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-49.           (((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-78355.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-382, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78356
in-theory        78356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-78356.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-373, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78357
in-theory        78357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78357.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-364, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78358
in-theory        78358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78358.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-354, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78359
in-theory        78359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78359.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78360
in-theory        78360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78360.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-338, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78361
in-theory        78361
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78361.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-327, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78362
in-theory        78362
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-78362.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-326, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78363
in-theory        78363
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78363.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-325, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78364
in-theory        78364
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78364.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-324, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78365
in-theory        78365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78365.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-323, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78366
in-theory        78366
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78366.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78367
in-theory        78367
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78367.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78368
in-theory        78368
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78368.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78369
in-theory        78369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78369.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78370
in-theory        78370
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8 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-7.            (A -> (B or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78370.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-311, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78371
in-theory        78371
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-49.           (((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-78371.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)), M:tm-310, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78372
in-theory        78372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78372.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F))), M:tm-309, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78373
in-theory        78373
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-884 ((A (-> (and Am Bm) Bm)) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-22.           (A -> (((B and C) -> C) and A)), 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-78373.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-308, m:tm-884, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-78374
in-theory        78374
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((A and B) -> B))
theorem-size     25
proof            (modus-ponens tm-307 tm-884 ((A (-> (and Am Bm) Bm)) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78374.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((A and B) -> B)), M:tm-307, m:tm-884, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-78375
in-theory        78375
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78375.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-305, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78376
in-theory        78376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78376.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-303, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78377
in-theory        78377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78377.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-270, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78378
in-theory        78378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78378.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-239, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78379
in-theory        78379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78379.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-210, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78380
in-theory        78380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78380.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-183, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78381
in-theory        78381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78381.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-157, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78382
in-theory        78382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78382.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-147, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78383
in-theory        78383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78383.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-134, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78384
in-theory        78384
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78384.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-125, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78385
in-theory        78385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78385.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-113, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78386
in-theory        78386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78386.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-105, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78387
in-theory        78387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78387.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-95, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78388
in-theory        78388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78388.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-83, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78389
in-theory        78389
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78389.        (((not (not A)) -> A) and (((B and C) -> C) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-76, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78390
in-theory        78390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78390.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-69, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78391
in-theory        78391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-78391.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-54, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78392
in-theory        78392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78392.        ((A -> (B or A)) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-42, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78393
in-theory        78393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-78393.        ((A -> (A or B)) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-32, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78394
in-theory        78394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-78394.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-23, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78395
in-theory        78395
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78395.        (((A and B) -> B) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-22, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78396
in-theory        78396
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78396.        (((A and B) -> A) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-21, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78397
in-theory        78397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-78397.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-20, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78398
in-theory        78398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78398.        ((A -> (B -> A)) and (((C and D) -> D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-19, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78399
in-theory        78399
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-7 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78399.        (A or (((B and C) -> C) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-7, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78400
in-theory        78400
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-4 tm-8)
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-49.           (((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-78400.        ((((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F), M:tm-6, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78401
in-theory        78401
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78401.        (A -> ((((B and C) -> C) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A)), M:tm-5, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78402
in-theory        78402
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-1 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78402.        (A -> (((B and C) -> C) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-1, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78403
in-theory        78403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-78403.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-855, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78404
in-theory        78404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-78404.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-808, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78405
in-theory        78405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-49.           (((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-78405.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-757, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78406
in-theory        78406
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) -> ((G or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78406.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-708, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78407
in-theory        78407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-78407.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-665, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78408
in-theory        78408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78408.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-622, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78409
in-theory        78409
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78409.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78410
in-theory        78410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78410.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-605, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78411
in-theory        78411
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78411.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-595, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78412
in-theory        78412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-49.           (((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-78412.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-550, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78413
in-theory        78413
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78413.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-540, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78414
in-theory        78414
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-49.           (((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-78414.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-530, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78415
in-theory        78415
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78415.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-520, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78416
in-theory        78416
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78416.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-510, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78417
in-theory        78417
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78417.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-500, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78418
in-theory        78418
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78418.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-490, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78419
in-theory        78419
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78419.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-480, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78420
in-theory        78420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78420.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-469, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78421
in-theory        78421
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78421.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78422
in-theory        78422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) 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-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-78422.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-453, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78423
in-theory        78423
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-78423.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-443, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78424
in-theory        78424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-49.           (((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-78424.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-409, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78425
in-theory        78425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) 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-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-78425.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-400, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78426
in-theory        78426
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-78426.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-391, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78427
in-theory        78427
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-49.           (((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-78427.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-382, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78428
in-theory        78428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) 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-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-78428.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-373, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78429
in-theory        78429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78429.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-364, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78430
in-theory        78430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78430.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-354, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78431
in-theory        78431
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78431.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78432
in-theory        78432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78432.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-338, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78433
in-theory        78433
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78433.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-327, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78434
in-theory        78434
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78434.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-326, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78435
in-theory        78435
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-78435.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-325, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78436
in-theory        78436
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78436.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-324, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78437
in-theory        78437
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78437.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-323, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78438
in-theory        78438
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78438.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78439
in-theory        78439
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78439.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78440
in-theory        78440
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78440.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78441
in-theory        78441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78441.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78442
in-theory        78442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8 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-7.            (A -> (B or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78442.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-311, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78443
in-theory        78443
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-49.           (((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-78443.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)), M:tm-310, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78444
in-theory        78444
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78444.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F))), M:tm-309, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78445
in-theory        78445
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-885 ((A (-> (and Am Bm) Am)) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-78445.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-308, m:tm-885, u:((A (-> (and Am Bm) Am)) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-78446
in-theory        78446
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((A and B) -> A))
theorem-size     25
proof            (modus-ponens tm-307 tm-885 ((A (-> (and Am Bm) Am)) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78446.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((A and B) -> A)), M:tm-307, m:tm-885, u:((A (-> (and Am Bm) Am)) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-78447
in-theory        78447
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78447.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-305, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78448
in-theory        78448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78448.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-303, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78449
in-theory        78449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78449.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-270, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78450
in-theory        78450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78450.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-239, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78451
in-theory        78451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78451.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-210, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78452
in-theory        78452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78452.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-183, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78453
in-theory        78453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78453.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-157, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78454
in-theory        78454
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78454.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-147, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78455
in-theory        78455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78455.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-134, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78456
in-theory        78456
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78456.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-125, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78457
in-theory        78457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78457.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-113, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78458
in-theory        78458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78458.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-105, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78459
in-theory        78459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78459.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-95, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78460
in-theory        78460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78460.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-83, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78461
in-theory        78461
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78461.        (((not (not A)) -> A) and (((B and C) -> B) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-76, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78462
in-theory        78462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78462.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-69, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78463
in-theory        78463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-78463.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-54, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78464
in-theory        78464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78464.        ((A -> (B or A)) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-42, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78465
in-theory        78465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) 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-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-78465.        ((A -> (A or B)) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-32, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78466
in-theory        78466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-78466.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-23, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78467
in-theory        78467
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78467.        (((A and B) -> B) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-22, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78468
in-theory        78468
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78468.        (((A and B) -> A) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-21, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78469
in-theory        78469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-78469.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-20, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78470
in-theory        78470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78470.        ((A -> (B -> A)) and (((C and D) -> C) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-19, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78471
in-theory        78471
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-7 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78471.        (A or (((B and C) -> B) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-7, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78472
in-theory        78472
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-3 tm-8)
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-49.           (((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-78472.        ((((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F), M:tm-6, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78473
in-theory        78473
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78473.        (A -> ((((B and C) -> B) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A)), M:tm-5, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78474
in-theory        78474
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-1 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78474.        (A -> (((B and C) -> B) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-1, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78475
in-theory        78475
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 (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-855 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-78475.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-855, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78476
in-theory        78476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-808 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-78476.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-808, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78477
in-theory        78477
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) -> ((G or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-757 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-49.           (((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-78477.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-757, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78478
in-theory        78478
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) -> ((H or (H or I)) -> J))))
theorem-size     53
proof            (modus-ponens tm-708 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78478.        (((((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) -> ((H or (H or I)) -> J)))), M:tm-708, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78479
in-theory        78479
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) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-665 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-49.           (((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-78479.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-665, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78480
in-theory        78480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-622 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78480.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-622, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78481
in-theory        78481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78481.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H or G))), M:tm-609, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78482
in-theory        78482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-605 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78482.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-605, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78483
in-theory        78483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78483.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-595, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78484
in-theory        78484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-550 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-49.           (((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-78484.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-550, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78485
in-theory        78485
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-540 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78485.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-540, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78486
in-theory        78486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-530 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-49.           (((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-78486.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-530, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78487
in-theory        78487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-520 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78487.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-520, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78488
in-theory        78488
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-510 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78488.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-510, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78489
in-theory        78489
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-500 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78489.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-500, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78490
in-theory        78490
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) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-490 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78490.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-490, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78491
in-theory        78491
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-480 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78491.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-480, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78492
in-theory        78492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-469 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or 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-49.           (((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-78492.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-469, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78493
in-theory        78493
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or 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-49.           (((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-78493.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (G or H))), M:tm-456, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78494
in-theory        78494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-453 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-78494.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-453, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78495
in-theory        78495
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-78495.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-443, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78496
in-theory        78496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-409 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-49.           (((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-78496.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-409, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78497
in-theory        78497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-400 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-78497.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-400, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78498
in-theory        78498
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-391 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-78498.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-391, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78499
in-theory        78499
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-382 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-49.           (((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-78499.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-382, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78500
in-theory        78500
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) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-373 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-78500.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-373, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78501
in-theory        78501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-364 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or 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-49.           (((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-78501.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-364, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78502
in-theory        78502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-354 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78502.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-354, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78503
in-theory        78503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H -> (G and H))))
theorem-size     35
proof            (modus-ponens tm-341 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78503.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78504
in-theory        78504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-338 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78504.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-338, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78505
in-theory        78505
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78505.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-327, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78506
in-theory        78506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78506.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-326, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78507
in-theory        78507
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78507.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-325, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78508
in-theory        78508
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-78508.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-324, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78509
in-theory        78509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78509.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-323, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78510
in-theory        78510
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78510.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78511
in-theory        78511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78511.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78512
in-theory        78512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     41
proof            (modus-ponens tm-318 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78512.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78513
in-theory        78513
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78513.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78514
in-theory        78514
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78514.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-311, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78515
in-theory        78515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
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-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-49.           (((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-78515.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) or G)), M:tm-310, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78516
in-theory        78516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78516.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and G))), M:tm-309, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78517
in-theory        78517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-308 tm-886 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78517.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-308, m:tm-886, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-78518
in-theory        78518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-307 tm-886 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78518.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-886, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-78519
in-theory        78519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78519.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-305, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78520
in-theory        78520
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) -> ((G or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-303 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78520.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-303, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78521
in-theory        78521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-270 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78521.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-270, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78522
in-theory        78522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-239 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78522.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-239, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78523
in-theory        78523
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) -> ((H or (H or I)) -> J))))
theorem-size     45
proof            (modus-ponens tm-210 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78523.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-210, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78524
in-theory        78524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-183 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78524.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-183, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78525
in-theory        78525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-157 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78525.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-157, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78526
in-theory        78526
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) -> ((G or (G or H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-147 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78526.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-147, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78527
in-theory        78527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-134 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78527.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-134, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78528
in-theory        78528
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) -> ((G or (G or H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-125 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78528.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-125, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78529
in-theory        78529
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) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-113 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78529.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-113, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78530
in-theory        78530
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) -> ((G or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-105 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78530.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-105, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78531
in-theory        78531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-95 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78531.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-95, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78532
in-theory        78532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-83 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78532.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-83, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78533
in-theory        78533
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-76 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78533.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-76, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78534
in-theory        78534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-69 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78534.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-69, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78535
in-theory        78535
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) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-54 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78535.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-54, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78536
in-theory        78536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-42 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78536.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-42, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78537
in-theory        78537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-32 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-78537.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-32, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78538
in-theory        78538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-23 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78538.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-23, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78539
in-theory        78539
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-22 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78539.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-22, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78540
in-theory        78540
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-21 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78540.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-21, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78541
in-theory        78541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-20 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-78541.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-20, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78542
in-theory        78542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-19 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78542.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-19, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78543
in-theory        78543
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-7 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78543.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-7, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78544
in-theory        78544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) or G)
theorem-size     29
proof            (modus-ponens tm-6 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-8)
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-49.           (((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-78544.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) or G), M:tm-6, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78545
in-theory        78545
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78545.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))) and A)), M:tm-5, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78546
in-theory        78546
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-1 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78546.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-1, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-78547
in-theory        78547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-78547.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-855, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78548
in-theory        78548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-78548.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-808, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78549
in-theory        78549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-49.           (((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-78549.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-757, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78550
in-theory        78550
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) -> ((G or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78550.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-708, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78551
in-theory        78551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-78551.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-665, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78552
in-theory        78552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78552.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-622, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78553
in-theory        78553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78553.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78554
in-theory        78554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78554.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-605, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78555
in-theory        78555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78555.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-595, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78556
in-theory        78556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78556.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-550, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78557
in-theory        78557
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78557.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-540, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78558
in-theory        78558
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78558.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-530, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78559
in-theory        78559
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78559.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-520, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78560
in-theory        78560
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78560.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-510, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78561
in-theory        78561
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78561.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-500, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78562
in-theory        78562
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78562.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-490, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78563
in-theory        78563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78563.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-480, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78564
in-theory        78564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78564.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-469, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78565
in-theory        78565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78565.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78566
in-theory        78566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78566.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-453, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78567
in-theory        78567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78567.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-443, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78568
in-theory        78568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78568.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-409, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78569
in-theory        78569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78569.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-400, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78570
in-theory        78570
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78570.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-391, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78571
in-theory        78571
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78571.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-382, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78572
in-theory        78572
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78572.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-373, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78573
in-theory        78573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78573.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-364, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78574
in-theory        78574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78574.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-354, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78575
in-theory        78575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78575.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78576
in-theory        78576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78576.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-338, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78577
in-theory        78577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78577.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-327, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78578
in-theory        78578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78578.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-326, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78579
in-theory        78579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78579.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-325, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78580
in-theory        78580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78580.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-324, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78581
in-theory        78581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-78581.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-323, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78582
in-theory        78582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78582.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78583
in-theory        78583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78583.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78584
in-theory        78584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78584.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78585
in-theory        78585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78585.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78586
in-theory        78586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8 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-7.            (A -> (B or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78586.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F or ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-311, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78587
in-theory        78587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78587.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)), M:tm-310, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78588
in-theory        78588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78588.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and F))), M:tm-309, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78589
in-theory        78589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-887 ((A (-> Am (-> Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-78589.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-308, m:tm-887, u:((A (-> Am (-> Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-78590
in-theory        78590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (A -> (B -> A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-887 ((A (-> Am (-> Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78590.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (A -> (B -> A))), M:tm-307, m:tm-887, u:((A (-> Am (-> Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-78591
in-theory        78591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78591.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) and (F -> ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))))), M:tm-305, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78592
in-theory        78592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78592.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-303, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78593
in-theory        78593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78593.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-270, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78594
in-theory        78594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78594.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-239, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78595
in-theory        78595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78595.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-210, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78596
in-theory        78596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78596.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-183, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78597
in-theory        78597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78597.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-157, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78598
in-theory        78598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78598.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-147, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78599
in-theory        78599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78599.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-134, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78600
in-theory        78600
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78600.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-125, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78601
in-theory        78601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78601.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-113, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78602
in-theory        78602
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78602.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-105, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78603
in-theory        78603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78603.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-95, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78604
in-theory        78604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78604.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-83, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78605
in-theory        78605
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78605.        (((not (not A)) -> A) and ((B -> (C -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-76, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78606
in-theory        78606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78606.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-69, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78607
in-theory        78607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-78607.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-54, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78608
in-theory        78608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78608.        ((A -> (B or A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-42, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78609
in-theory        78609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78609.        ((A -> (A or B)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-32, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78610
in-theory        78610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-78610.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-23, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78611
in-theory        78611
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78611.        (((A and B) -> B) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-22, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78612
in-theory        78612
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78612.        (((A and B) -> A) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-21, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78613
in-theory        78613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-78613.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-20, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78614
in-theory        78614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78614.        ((A -> (B -> A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-19, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78615
in-theory        78615
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-7 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78615.        (A or ((B -> (C -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-7, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78616
in-theory        78616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or 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-49.           (((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-78616.        (((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))) or F), M:tm-6, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78617
in-theory        78617
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78617.        (A -> (((B -> (C -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and A)), M:tm-5, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78618
in-theory        78618
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-1 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78618.        (A -> ((B -> (C -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-1, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-78619
in-theory        78619
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (A or B)))
theorem-size     9
proof            (modus-ponens tm-888 tm-1 ((Am (or A B)) (C (-> Bm (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78619.        ((A or B) -> (C -> (A or B))), M:tm-888, m:tm-1, u:((Am (or A B)) (C (-> Bm (or A B))))
================================================================
tm-name          tm-78620
in-theory        78620
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> ((A or B) and C)))
theorem-size     11
proof            (modus-ponens tm-888 tm-5 ((Am (or A B)) (C (-> Bm (and (or A B) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-78620.        ((A or B) -> (C -> ((A or B) and C))), M:tm-888, m:tm-5, u:((Am (or A B)) (C (-> Bm (and (or A B) Bm))))
================================================================
tm-name          tm-78621
in-theory        78621
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) or C))
theorem-size     9
proof            (modus-ponens tm-888 tm-6 ((Am (or A B)) (C (or (or A B) Bm))))
axioms-used      (tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78621.        ((A or B) -> ((A or B) or C)), M:tm-888, m:tm-6, u:((Am (or A B)) (C (or (or A B) Bm)))
================================================================
tm-name          tm-78622
in-theory        78622
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C or (A or B)))
theorem-size     9
proof            (modus-ponens tm-888 tm-7 ((Am (or A B)) (C (or Bm (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-78622.        ((A or B) -> (C or (A or B))), M:tm-888, m:tm-7, u:((Am (or A B)) (C (or Bm (or A B))))
================================================================
tm-name          tm-78623
in-theory        78623
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (D -> C)))
theorem-size     9
proof            (modus-ponens tm-888 tm-11 ((Am (or A B)) (C (-> Bm (-> Cm Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-78623.        ((A or B) -> (C -> (D -> C))), M:tm-888, m:tm-11, u:((Am (or A B)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-78624
in-theory        78624
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     17
proof            (modus-ponens tm-888 tm-14 ((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-78624.        ((A or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-888, m:tm-14, u:((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-78625
in-theory        78625
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C and D) -> C))
theorem-size     9
proof            (modus-ponens tm-888 tm-16 ((Am (or A B)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-78625.        ((A or B) -> ((C and D) -> C)), M:tm-888, m:tm-16, u:((Am (or A B)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-78626
in-theory        78626
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C and D) -> D))
theorem-size     9
proof            (modus-ponens tm-888 tm-18 ((Am (or A B)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-78626.        ((A or B) -> ((C and D) -> D)), M:tm-888, m:tm-18, u:((Am (or A B)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-78627
in-theory        78627
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D -> C)) and (A or B)))
theorem-size     13
proof            (modus-ponens tm-888 tm-19 ((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78627.        ((A or B) -> ((C -> (D -> C)) and (A or B))), M:tm-888, m:tm-19, u:((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B))))
================================================================
tm-name          tm-78628
in-theory        78628
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-888 tm-20 ((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78628.        ((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))), M:tm-888, m:tm-20, u:((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B))))
================================================================
tm-name          tm-78629
in-theory        78629
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C and D) -> C) and (A or B)))
theorem-size     13
proof            (modus-ponens tm-888 tm-21 ((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-78629.        ((A or B) -> (((C and D) -> C) and (A or B))), M:tm-888, m:tm-21, u:((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B))))
================================================================
tm-name          tm-78630
in-theory        78630
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C and D) -> D) and (A or B)))
theorem-size     13
proof            (modus-ponens tm-888 tm-22 ((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-78630.        ((A or B) -> (((C and D) -> D) and (A or B))), M:tm-888, m:tm-22, u:((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B))))
================================================================
tm-name          tm-78631
in-theory        78631
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D -> (C and D))) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-23 ((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-78631.        ((A or B) -> ((C -> (D -> (C and D))) and (A or B))), M:tm-888, m:tm-23, u:((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-78632
in-theory        78632
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (D -> (C and D))))
theorem-size     11
proof            (modus-ponens tm-888 tm-25 ((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-78632.        ((A or B) -> (C -> (D -> (C and D)))), M:tm-888, m:tm-25, u:((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-78633
in-theory        78633
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (C or D)) and (A or B)))
theorem-size     13
proof            (modus-ponens tm-888 tm-32 ((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78633.        ((A or B) -> ((C -> (C or D)) and (A or B))), M:tm-888, m:tm-32, u:((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B))))
================================================================
tm-name          tm-78634
in-theory        78634
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (C or D)))
theorem-size     9
proof            (modus-ponens tm-888 tm-33 ((Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-78634.        ((A or B) -> (C -> (C or D))), M:tm-888, m:tm-33, u:((Am (or A B)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-78635
in-theory        78635
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D or C)) and (A or B)))
theorem-size     13
proof            (modus-ponens tm-888 tm-42 ((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-78635.        ((A or B) -> ((C -> (D or C)) and (A or B))), M:tm-888, m:tm-42, u:((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B))))
================================================================
tm-name          tm-78636
in-theory        78636
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (D or C)))
theorem-size     9
proof            (modus-ponens tm-888 tm-43 ((Am (or A B)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-78636.        ((A or B) -> (C -> (D or C))), M:tm-888, m:tm-43, u:((Am (or A B)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-78637
in-theory        78637
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-888 tm-54 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78637.        ((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))), M:tm-888, m:tm-54, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B))))
================================================================
tm-name          tm-78638
in-theory        78638
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     17
proof            (modus-ponens tm-888 tm-56 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-78638.        ((A or B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-888, m:tm-56, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-78639
in-theory        78639
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-888 tm-69 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-78639.        ((A or B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B))), M:tm-888, m:tm-69, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B))))
================================================================
tm-name          tm-78640
in-theory        78640
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     15
proof            (modus-ponens tm-888 tm-71 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78640.        ((A or B) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-888, m:tm-71, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-78641
in-theory        78641
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((not (not C)) -> C) and (A or B)))
theorem-size     13
proof            (modus-ponens tm-888 tm-76 ((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-78641.        ((A or B) -> (((not (not C)) -> C) and (A or B))), M:tm-888, m:tm-76, u:((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B))))
================================================================
tm-name          tm-78642
in-theory        78642
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((not (not C)) -> C))
theorem-size     9
proof            (modus-ponens tm-888 tm-78 ((Am (or A B)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78642.        ((A or B) -> ((not (not C)) -> C)), M:tm-888, m:tm-78, u:((Am (or A B)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-78643
in-theory        78643
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D -> (E -> D))) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-83 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78643.        ((A or B) -> ((C -> (D -> (E -> D))) and (A or B))), M:tm-888, m:tm-83, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-78644
in-theory        78644
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (D -> (E -> D))))
theorem-size     11
proof            (modus-ponens tm-888 tm-85 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78644.        ((A or B) -> (C -> (D -> (E -> D)))), M:tm-888, m:tm-85, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-78645
in-theory        78645
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (A or B))
theorem-size     7
proof            (modus-ponens tm-888 tm-86 ((Am (or A B)) (C (or A B))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-78645.        ((A or B) -> (A or B)), M:tm-888, m:tm-86, u:((Am (or A B)) (C (or A B)))
================================================================
tm-name          tm-78646
in-theory        78646
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> D) -> (C -> C)) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-95 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-78646.        ((A or B) -> (((C -> D) -> (C -> C)) and (A or B))), M:tm-888, m:tm-95, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B))))
================================================================
tm-name          tm-78647
in-theory        78647
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> D) -> (C -> C)))
theorem-size     11
proof            (modus-ponens tm-888 tm-97 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-78647.        ((A or B) -> ((C -> D) -> (C -> C))), M:tm-888, m:tm-97, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-78648
in-theory        78648
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B)))
theorem-size     27
proof            (modus-ponens tm-888 tm-105 ((Am (or A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78648.        ((A or B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B))), M:tm-888, 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-78649
in-theory        78649
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-888 tm-107 ((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-13.           (((A -> (B -> C)) -> (A -> 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-78649.        ((A or B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-888, m:tm-107, u:((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-78650
in-theory        78650
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-888 tm-113 ((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78650.        ((A or B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))), M:tm-888, m:tm-113, u:((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B))))
================================================================
tm-name          tm-78651
in-theory        78651
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     19
proof            (modus-ponens tm-888 tm-115 ((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-78651.        ((A or B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-888, m:tm-115, u:((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-78652
in-theory        78652
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-888 tm-125 ((Am (or A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-78652.        ((A or B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B))), M:tm-888, 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-78653
in-theory        78653
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-888 tm-127 ((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-78653.        ((A or B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-888, m:tm-127, u:((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-78654
in-theory        78654
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> ((D and E) -> D)) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-134 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78654.        ((A or B) -> ((C -> ((D and E) -> D)) and (A or B))), M:tm-888, m:tm-134, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-78655
in-theory        78655
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> ((D and E) -> D)))
theorem-size     11
proof            (modus-ponens tm-888 tm-136 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A 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-78655.        ((A or B) -> (C -> ((D and E) -> D))), M:tm-888, m:tm-136, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-78656
in-theory        78656
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-888 tm-147 ((Am (or A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-78656.        ((A or B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B))), M:tm-888, 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-78657
in-theory        78657
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-888 tm-149 ((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-78657.        ((A or B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-888, m:tm-149, u:((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-78658
in-theory        78658
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> ((D and E) -> E)) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-157 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78658.        ((A or B) -> ((C -> ((D and E) -> E)) and (A or B))), M:tm-888, m:tm-157, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-78659
in-theory        78659
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> ((D and E) -> E)))
theorem-size     11
proof            (modus-ponens tm-888 tm-159 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A 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-78659.        ((A or B) -> (C -> ((D and E) -> E))), M:tm-888, m:tm-159, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-78660
in-theory        78660
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> ((D -> (E -> D)) and C)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-888 tm-183 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-78660.        ((A or B) -> ((C -> ((D -> (E -> D)) and C)) and (A or B))), M:tm-888, m:tm-183, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-78661
in-theory        78661
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     13
proof            (modus-ponens tm-888 tm-184 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78661.        ((A or B) -> (C -> ((D -> (E -> D)) and C))), M:tm-888, m:tm-184, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-78662
in-theory        78662
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-888 tm-210 ((Am (or A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78662.        ((A or B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B))), M:tm-888, 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-78663
in-theory        78663
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     21
proof            (modus-ponens tm-888 tm-211 ((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78663.        ((A or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-888, m:tm-211, u:((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-78664
in-theory        78664
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (((D and E) -> D) and C)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-888 tm-239 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-78664.        ((A or B) -> ((C -> (((D and E) -> D) and C)) and (A or B))), M:tm-888, m:tm-239, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B))))
================================================================
tm-name          tm-78665
in-theory        78665
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (((D and E) -> D) and C)))
theorem-size     13
proof            (modus-ponens tm-888 tm-240 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-78665.        ((A or B) -> (C -> (((D and E) -> D) and C))), M:tm-888, m:tm-240, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-78666
in-theory        78666
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (((D and E) -> E) and C)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-888 tm-270 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-78666.        ((A or B) -> ((C -> (((D and E) -> E) and C)) and (A or B))), M:tm-888, m:tm-270, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B))))
================================================================
tm-name          tm-78667
in-theory        78667
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (((D and E) -> E) and C)))
theorem-size     13
proof            (modus-ponens tm-888 tm-271 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-78667.        ((A or B) -> (C -> (((D and E) -> E) and C))), M:tm-888, m:tm-271, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-78668
in-theory        78668
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-888 tm-303 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-78668.        ((A or B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B))), M:tm-888, m:tm-303, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B))))
================================================================
tm-name          tm-78669
in-theory        78669
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     15
proof            (modus-ponens tm-888 tm-304 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
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-78669.        ((A or B) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-888, m:tm-304, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-78670
in-theory        78670
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (C -> (A or B))))
theorem-size     13
proof            (modus-ponens tm-888 tm-305 ((Am (or A B)) (C (and (or A B) (-> Bm (or A B))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
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-78670.        ((A or B) -> ((A or B) and (C -> (A or B)))), M:tm-888, m:tm-305, u:((Am (or A B)) (C (and (or A B) (-> Bm (or A B)))))
================================================================
tm-name          tm-78671
in-theory        78671
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (C -> ((A or B) and C))))
theorem-size     15
proof            (modus-ponens tm-888 tm-309 ((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-78671.        ((A or B) -> ((A or B) and (C -> ((A or B) and C)))), M:tm-888, m:tm-309, u:((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm)))))
================================================================
tm-name          tm-78672
in-theory        78672
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and ((A or B) or C)))
theorem-size     13
proof            (modus-ponens tm-888 tm-310 ((Am (or A B)) (C (and (or A B) (or (or A B) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
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-78672.        ((A or B) -> ((A or B) and ((A or B) or C))), M:tm-888, m:tm-310, u:((Am (or A B)) (C (and (or A B) (or (or A B) Bm))))
================================================================
tm-name          tm-78673
in-theory        78673
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (C or (A or B))))
theorem-size     13
proof            (modus-ponens tm-888 tm-311 ((Am (or A B)) (C (and (or A B) (or Bm (or A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-78673.        ((A or B) -> ((A or B) and (C or (A or B)))), M:tm-888, m:tm-311, u:((Am (or A B)) (C (and (or A B) (or Bm (or A B)))))
================================================================
tm-name          tm-78674
in-theory        78674
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (C -> (D -> C))))
theorem-size     13
proof            (modus-ponens tm-888 tm-315 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
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-78674.        ((A or B) -> ((A or B) and (C -> (D -> C)))), M:tm-888, m:tm-315, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-78675
in-theory        78675
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     21
proof            (modus-ponens tm-888 tm-318 ((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
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-78675.        ((A or B) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-888, m:tm-318, u:((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-78676
in-theory        78676
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and ((C and D) -> C)))
theorem-size     13
proof            (modus-ponens tm-888 tm-320 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-78676.        ((A or B) -> ((A or B) and ((C and D) -> C))), M:tm-888, m:tm-320, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-78677
in-theory        78677
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and ((C and D) -> D)))
theorem-size     13
proof            (modus-ponens tm-888 tm-322 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-78677.        ((A or B) -> ((A or B) and ((C and D) -> D))), M:tm-888, m:tm-322, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-78678
in-theory        78678
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and ((C -> (D -> C)) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-888 tm-323 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
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-78678.        ((A or B) -> ((A or B) and ((C -> (D -> C)) and (A or B)))), M:tm-888, m:tm-323, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B)))))
================================================================
tm-name          tm-78679
in-theory        78679
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))
theorem-size     25
proof            (modus-ponens tm-888 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-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-78679.        ((A or B) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))), M:tm-888, 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-78680
in-theory        78680
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (((C and D) -> C) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-888 tm-325 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-78680.        ((A or B) -> ((A or B) and (((C and D) -> C) and (A or B)))), M:tm-888, m:tm-325, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B)))))
================================================================
tm-name          tm-78681
in-theory        78681
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (((C and D) -> D) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-888 tm-326 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-78681.        ((A or B) -> ((A or B) and (((C and D) -> D) and (A or B)))), M:tm-888, m:tm-326, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B)))))
================================================================
tm-name          tm-78682
in-theory        78682
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B))))
theorem-size     19
proof            (modus-ponens tm-888 tm-327 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-78682.        ((A or B) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B)))), M:tm-888, 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-78683
in-theory        78683
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> D) -> (C -> (C and D))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-888 tm-338 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-78683.        ((A or B) -> (((C -> D) -> (C -> (C and D))) and (A or B))), M:tm-888, m:tm-338, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-78684
in-theory        78684
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> D) -> (C -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-888 tm-340 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
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-78684.        ((A or B) -> ((C -> D) -> (C -> (C and D)))), M:tm-888, m:tm-340, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-78685
in-theory        78685
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (C -> (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-888 tm-341 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
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-78685.        ((A or B) -> ((A or B) and (C -> (D -> (C and D))))), M:tm-888, m:tm-341, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-78686
in-theory        78686
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D -> (E -> (D and E)))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-888 tm-354 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and 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-78686.        ((A or B) -> ((C -> (D -> (E -> (D and E)))) and (A or B))), M:tm-888, m:tm-354, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-78687
in-theory        78687
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (D -> (E -> (D and E)))))
theorem-size     13
proof            (modus-ponens tm-888 tm-356 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and 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-78687.        ((A or B) -> (C -> (D -> (E -> (D and E))))), M:tm-888, m:tm-356, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-78688
in-theory        78688
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> (D -> C)) or E) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-364 ((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78688.        ((A or B) -> (((C -> (D -> C)) or E) and (A or B))), M:tm-888, m:tm-364, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-78689
in-theory        78689
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D -> C)) or E))
theorem-size     11
proof            (modus-ponens tm-888 tm-365 ((Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78689.        ((A or B) -> ((C -> (D -> C)) or E)), M:tm-888, m:tm-365, u:((Am (or A B)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-78690
in-theory        78690
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-888 tm-373 ((Am (or A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78690.        ((A or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B))), M:tm-888, 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-78691
in-theory        78691
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     19
proof            (modus-ponens tm-888 tm-374 ((Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-27.           (((A -> (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-78691.        ((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-888, m:tm-374, u:((Am (or A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-78692
in-theory        78692
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C and D) -> C) or E) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-382 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78692.        ((A or B) -> ((((C and D) -> C) or E) and (A or B))), M:tm-888, m:tm-382, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B))))
================================================================
tm-name          tm-78693
in-theory        78693
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C and D) -> C) or E))
theorem-size     11
proof            (modus-ponens tm-888 tm-383 ((Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and 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-78693.        ((A or B) -> (((C and D) -> C) or E)), M:tm-888, m:tm-383, u:((Am (or A B)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-78694
in-theory        78694
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C and D) -> D) or E) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-391 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78694.        ((A or B) -> ((((C and D) -> D) or E) and (A or B))), M:tm-888, m:tm-391, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B))))
================================================================
tm-name          tm-78695
in-theory        78695
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C and D) -> D) or E))
theorem-size     11
proof            (modus-ponens tm-888 tm-392 ((Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and 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-78695.        ((A or B) -> (((C and D) -> D) or E)), M:tm-888, m:tm-392, u:((Am (or A B)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-78696
in-theory        78696
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> (D -> (C and D))) or E) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-888 tm-400 ((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-78696.        ((A or B) -> (((C -> (D -> (C and D))) or E) and (A or B))), M:tm-888, m:tm-400, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B))))
================================================================
tm-name          tm-78697
in-theory        78697
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D -> (C and D))) or E))
theorem-size     13
proof            (modus-ponens tm-888 tm-401 ((Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78697.        ((A or B) -> ((C -> (D -> (C and D))) or E)), M:tm-888, m:tm-401, u:((Am (or A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-78698
in-theory        78698
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> (C or D)) or E) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-409 ((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78698.        ((A or B) -> (((C -> (C or D)) or E) and (A or B))), M:tm-888, m:tm-409, u:((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B))))
================================================================
tm-name          tm-78699
in-theory        78699
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (C or D)) or E))
theorem-size     11
proof            (modus-ponens tm-888 tm-410 ((Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78699.        ((A or B) -> ((C -> (C or D)) or E)), M:tm-888, m:tm-410, u:((Am (or A B)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-78700
in-theory        78700
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and ((C -> (C or D)) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-888 tm-443 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
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-78700.        ((A or B) -> ((A or B) and ((C -> (C or D)) and (A or B)))), M:tm-888, m:tm-443, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B)))))
================================================================
tm-name          tm-78701
in-theory        78701
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> ((D -> (D or E)) and C)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-888 tm-453 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-78701.        ((A or B) -> ((C -> ((D -> (D or E)) and C)) and (A or B))), M:tm-888, m:tm-453, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B))))
================================================================
tm-name          tm-78702
in-theory        78702
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> ((D -> (D or E)) and C)))
theorem-size     13
proof            (modus-ponens tm-888 tm-454 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78702.        ((A or B) -> (C -> ((D -> (D or E)) and C))), M:tm-888, m:tm-454, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-78703
in-theory        78703
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (C -> (C or D))))
theorem-size     13
proof            (modus-ponens tm-888 tm-456 ((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
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-78703.        ((A or B) -> ((A or B) and (C -> (C or D)))), M:tm-888, m:tm-456, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-78704
in-theory        78704
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D -> (D or E))) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-469 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-78704.        ((A or B) -> ((C -> (D -> (D or E))) and (A or B))), M:tm-888, m:tm-469, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-78705
in-theory        78705
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (D -> (D or E))))
theorem-size     11
proof            (modus-ponens tm-888 tm-471 ((Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78705.        ((A or B) -> (C -> (D -> (D or E)))), M:tm-888, m:tm-471, u:((Am (or A B)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-78706
in-theory        78706
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C or (D -> (E -> D))) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-480 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78706.        ((A or B) -> ((C or (D -> (E -> D))) and (A or B))), M:tm-888, m:tm-480, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-78707
in-theory        78707
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C or (D -> (E -> D))))
theorem-size     11
proof            (modus-ponens tm-888 tm-481 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (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-78707.        ((A or B) -> (C or (D -> (E -> D)))), M:tm-888, m:tm-481, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-78708
in-theory        78708
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-888 tm-490 ((Am (or A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78708.        ((A or B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))), M:tm-888, 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-78709
in-theory        78709
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     19
proof            (modus-ponens tm-888 tm-491 ((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-35.           (A 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-78709.        ((A or B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-888, m:tm-491, u:((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-78710
in-theory        78710
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C or ((D and E) -> D)) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-500 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-78710.        ((A or B) -> ((C or ((D and E) -> D)) and (A or B))), M:tm-888, m:tm-500, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-78711
in-theory        78711
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C or ((D and E) -> D)))
theorem-size     11
proof            (modus-ponens tm-888 tm-501 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-78711.        ((A or B) -> (C or ((D and E) -> D))), M:tm-888, m:tm-501, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-78712
in-theory        78712
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C or ((D and E) -> E)) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-510 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-78712.        ((A or B) -> ((C or ((D and E) -> E)) and (A or B))), M:tm-888, m:tm-510, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-78713
in-theory        78713
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C or ((D and E) -> E)))
theorem-size     11
proof            (modus-ponens tm-888 tm-511 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-78713.        ((A or B) -> (C or ((D and E) -> E))), M:tm-888, m:tm-511, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-78714
in-theory        78714
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C or (D -> (E -> (D and E)))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-888 tm-520 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-78714.        ((A or B) -> ((C or (D -> (E -> (D and E)))) and (A or B))), M:tm-888, m:tm-520, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-78715
in-theory        78715
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C or (D -> (E -> (D and E)))))
theorem-size     13
proof            (modus-ponens tm-888 tm-521 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78715.        ((A or B) -> (C or (D -> (E -> (D and E))))), M:tm-888, m:tm-521, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-78716
in-theory        78716
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C or (D -> (D or E))) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-530 ((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78716.        ((A or B) -> ((C or (D -> (D or E))) and (A or B))), M:tm-888, m:tm-530, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-78717
in-theory        78717
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C or (D -> (D or E))))
theorem-size     11
proof            (modus-ponens tm-888 tm-531 ((Am (or A B)) (C (or Bm (-> Cm (or Cm 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78717.        ((A or B) -> (C or (D -> (D or E)))), M:tm-888, m:tm-531, u:((Am (or A B)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-78718
in-theory        78718
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C or (D -> (E or D))) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-540 ((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-78718.        ((A or B) -> ((C or (D -> (E or D))) and (A or B))), M:tm-888, m:tm-540, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-78719
in-theory        78719
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C or (D -> (E or D))))
theorem-size     11
proof            (modus-ponens tm-888 tm-541 ((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B 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-78719.        ((A or B) -> (C or (D -> (E or D)))), M:tm-888, m:tm-541, u:((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-78720
in-theory        78720
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> (D or C)) or E) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-550 ((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78720.        ((A or B) -> (((C -> (D or C)) or E) and (A or B))), M:tm-888, m:tm-550, u:((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-78721
in-theory        78721
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D or C)) or E))
theorem-size     11
proof            (modus-ponens tm-888 tm-551 ((Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B 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-78721.        ((A or B) -> ((C -> (D or C)) or E)), M:tm-888, m:tm-551, u:((Am (or A B)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-78722
in-theory        78722
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and ((C -> (D or C)) and (A or B))))
theorem-size     17
proof            (modus-ponens tm-888 tm-595 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-78722.        ((A or B) -> ((A or B) and ((C -> (D or C)) and (A or B)))), M:tm-888, m:tm-595, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B)))))
================================================================
tm-name          tm-78723
in-theory        78723
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> ((D -> (E or D)) and C)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-888 tm-605 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-78723.        ((A or B) -> ((C -> ((D -> (E or D)) and C)) and (A or B))), M:tm-888, m:tm-605, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-78724
in-theory        78724
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> ((D -> (E or D)) and C)))
theorem-size     13
proof            (modus-ponens tm-888 tm-606 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-78724.        ((A or B) -> (C -> ((D -> (E or D)) and C))), M:tm-888, m:tm-606, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-78725
in-theory        78725
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((A or B) and (C -> (D or C))))
theorem-size     13
proof            (modus-ponens tm-888 tm-609 ((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-78725.        ((A or B) -> ((A or B) and (C -> (D or C)))), M:tm-888, m:tm-609, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-78726
in-theory        78726
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> (D -> (E or D))) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-888 tm-622 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78726.        ((A or B) -> ((C -> (D -> (E or D))) and (A or B))), M:tm-888, m:tm-622, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-78727
in-theory        78727
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C -> (D -> (E or D))))
theorem-size     11
proof            (modus-ponens tm-888 tm-624 ((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (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-78727.        ((A or B) -> (C -> (D -> (E or D)))), M:tm-888, m:tm-624, u:((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-78728
in-theory        78728
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-888 tm-665 ((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78728.        ((A or B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B))), M:tm-888, m:tm-665, u:((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-78729
in-theory        78729
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     17
proof            (modus-ponens tm-888 tm-667 ((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78729.        ((A or B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-888, m:tm-667, u:((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-78730
in-theory        78730
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B)))
theorem-size     33
proof            (modus-ponens tm-888 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-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78730.        ((A or B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B))), M:tm-888, 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-78731
in-theory        78731
times-derived    1
----------------------------------------------------------------
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-888 tm-710 ((Am (or 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 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-78731.        ((A or B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-888, 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-78732
in-theory        78732
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-888 tm-757 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78732.        ((A or B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B))), M:tm-888, m:tm-757, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-78733
in-theory        78733
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     15
proof            (modus-ponens tm-888 tm-759 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A and B) -> A), axiom
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-78733.        ((A or B) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-888, m:tm-759, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-78734
in-theory        78734
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-888 tm-808 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-78734.        ((A or B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B))), M:tm-888, m:tm-808, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-78735
in-theory        78735
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     15
proof            (modus-ponens tm-888 tm-810 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A and B) -> B), axiom
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-78735.        ((A or B) -> ((C -> D) -> (((E and C) or C) -> D))), M:tm-888, m:tm-810, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-78736
in-theory        78736
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-888 tm-855 ((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-78736.        ((A or B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B))), M:tm-888, m:tm-855, u:((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B))))
================================================================
tm-name          tm-78737
in-theory        78737
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     21
proof            (modus-ponens tm-888 tm-857 ((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-78737.        ((A or B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-888, m:tm-857, u:((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-78738
in-theory        78738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-78738.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-855, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78739
in-theory        78739
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C and (A or B))) -> ((A or B) -> (C and (A or B))))
theorem-size     19
proof            (modus-ponens tm-850 tm-888 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Am Bm) (and B (or Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       163
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78739.        (((A or B) -> (C and (A or B))) -> ((A or B) -> (C and (A or B)))), M:tm-850, m:tm-888, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Am Bm) (and B (or Am Bm)))))
================================================================
tm-name          tm-78740
in-theory        78740
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and (A or B))) -> ((A or B) -> (C and (A or B)))) and ((C or ((A or B) -> (C and (A or B)))) -> ((A or B) -> (C and (A or B)))))
theorem-size     41
proof            (modus-ponens tm-844 tm-888 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Am Bm) (and B (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-78740.        ((((A or B) -> (C and (A or B))) -> ((A or B) -> (C and (A or B)))) and ((C or ((A or B) -> (C and (A or B)))) -> ((A or B) -> (C and (A or B))))), M:tm-844, m:tm-888, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Am Bm) (and B (or Am Bm)))))
================================================================
tm-name          tm-78741
in-theory        78741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-78741.        (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-808, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78742
in-theory        78742
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> ((A or B) -> C)))
theorem-size     31
proof            (modus-ponens tm-798 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-78742.        ((((A or B) -> C) -> ((A or B) -> C)) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> ((A or B) -> C))), M:tm-798, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78743
in-theory        78743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78743.        (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-757, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78744
in-theory        78744
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or B) -> C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78744.        ((((A or B) -> C) -> ((A or B) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or B) -> C))), M:tm-747, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78745
in-theory        78745
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 F) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78745.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E or F) -> G) -> ((E or F) -> G))), M:tm-708, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78746
in-theory        78746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78746.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-665, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78747
in-theory        78747
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((C or ((A or B) -> C)) -> ((A or B) -> C)))
theorem-size     25
proof            (modus-ponens tm-654 tm-888 ((A (or Am Bm)) (B Cm) (C (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78747.        ((((A or B) -> C) -> ((A or B) -> C)) and ((C or ((A or B) -> C)) -> ((A or B) -> C))), M:tm-654, m:tm-888, u:((A (or Am Bm)) (B Cm) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78748
in-theory        78748
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D or ((A or B) -> C)))
theorem-size     13
proof            (modus-ponens tm-623 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-2 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78748.        (((A or B) -> C) -> (D or ((A or B) -> C))), M:tm-623, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78749
in-theory        78749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78749.        ((A -> (B -> (C or B))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-622, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78750
in-theory        78750
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D or (B or C)))) -> ((B or C) -> (D or (B or C))))
theorem-size     21
proof            (modus-ponens tm-619 tm-888 ((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (-> (or Am Bm) (or B (or Am Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78750.        ((A or ((B or C) -> (D or (B or C)))) -> ((B or C) -> (D or (B or C)))), M:tm-619, m:tm-888, u:((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (-> (or Am Bm) (or B (or Am Bm)))))
================================================================
tm-name          tm-78751
in-theory        78751
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78751.        ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (E or D))), M:tm-609, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78752
in-theory        78752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78752.        ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-605, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78753
in-theory        78753
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (E or D)) and (((A or B) -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78753.        ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (E or D)) and (((A or B) -> C) -> ((A or B) -> C)))), M:tm-595, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78754
in-theory        78754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78754.        (((A -> (B or A)) or C) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-550, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78755
in-theory        78755
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78755.        ((A or (B -> (C or B))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-540, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78756
in-theory        78756
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78756.        ((A or (B -> (B or C))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-530, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78757
in-theory        78757
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78757.        ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-520, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78758
in-theory        78758
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78758.        ((A or ((B and C) -> C)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-510, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78759
in-theory        78759
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78759.        ((A or ((B and C) -> B)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-500, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78760
in-theory        78760
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((E or F) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78760.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((E or F) -> G))), M:tm-490, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78761
in-theory        78761
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78761.        ((A or (B -> (C -> B))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-480, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78762
in-theory        78762
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (((A or B) -> C) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or 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-49.           (((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-78762.        (((A or B) -> C) -> (((A or B) -> C) or D)), M:tm-470, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78763
in-theory        78763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78763.        ((A -> (B -> (B or C))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-469, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78764
in-theory        78764
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> ((B or C) or D))) -> ((B or C) -> ((B or C) or D)))
theorem-size     21
proof            (modus-ponens tm-466 tm-888 ((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (-> (or Am Bm) (or (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-49.           (((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-78764.        ((A or ((B or C) -> ((B or C) or D))) -> ((B or C) -> ((B or C) or D))), M:tm-466, m:tm-888, u:((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (-> (or Am Bm) (or (or Am Bm) B))))
================================================================
tm-name          tm-78765
in-theory        78765
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78765.        ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (D or E))), M:tm-456, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78766
in-theory        78766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78766.        ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-453, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78767
in-theory        78767
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (D or E)) and (((A or B) -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78767.        ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (D or E)) and (((A or B) -> C) -> ((A or B) -> C)))), M:tm-443, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78768
in-theory        78768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78768.        (((A -> (A or B)) or C) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-409, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78769
in-theory        78769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78769.        (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-400, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78770
in-theory        78770
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78770.        ((((A and B) -> B) or C) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-391, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78771
in-theory        78771
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78771.        ((((A and B) -> A) or C) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-382, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78772
in-theory        78772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> ((E or F) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78772.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> ((E or F) -> G))), M:tm-373, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78773
in-theory        78773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78773.        (((A -> (B -> A)) or C) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-364, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78774
in-theory        78774
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> (((A or B) -> C) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78774.        (((A or B) -> C) -> (D -> (((A or B) -> C) and D))), M:tm-355, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78775
in-theory        78775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78775.        ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-354, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78776
in-theory        78776
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> ((B or C) and D)))) -> ((B or C) -> (D -> ((B or C) and D))))
theorem-size     25
proof            (modus-ponens tm-351 tm-888 ((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (-> (or Am Bm) (-> B (and (or Am Bm) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-78776.        ((A or ((B or C) -> (D -> ((B or C) and D)))) -> ((B or C) -> (D -> ((B or C) and D)))), M:tm-351, m:tm-888, u:((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (-> (or Am Bm) (-> B (and (or Am Bm) B)))))
================================================================
tm-name          tm-78777
in-theory        78777
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78777.        ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78778
in-theory        78778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> ((C or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78778.        (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> ((C or D) -> E))), M:tm-338, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78779
in-theory        78779
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> ((A or B) -> ((A or B) and C)))
theorem-size     25
proof            (modus-ponens tm-335 tm-888 ((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (-> (or Am Bm) (and (or Am Bm) B)))))
axioms-used      (tm-8 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78779.        ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> ((A or B) -> ((A or B) and C))), M:tm-335, m:tm-888, u:((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (-> (or Am Bm) (and (or Am Bm) B))))
================================================================
tm-name          tm-78780
in-theory        78780
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
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-328.          ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78780.        ((((A or B) -> C) -> ((A or B) -> C)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or B) -> C)))), M:tm-328, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78781
in-theory        78781
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78781.        ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> ((A or B) -> C)))), M:tm-327, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78782
in-theory        78782
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (((D and E) -> E) and (((A or B) -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78782.        ((((A or B) -> C) -> ((A or B) -> C)) and (((D and E) -> E) and (((A or B) -> C) -> ((A or B) -> C)))), M:tm-326, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78783
in-theory        78783
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (((D and E) -> D) and (((A or B) -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78783.        ((((A or B) -> C) -> ((A or B) -> C)) and (((D and E) -> D) and (((A or B) -> C) -> ((A or B) -> C)))), M:tm-325, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78784
in-theory        78784
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78784.        ((((A or B) -> C) -> ((A or B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> ((A or B) -> C)))), M:tm-324, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78785
in-theory        78785
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (E -> D)) and (((A or B) -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78785.        ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (E -> D)) and (((A or B) -> C) -> ((A or B) -> C)))), M:tm-323, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78786
in-theory        78786
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78786.        ((((A or B) -> C) -> ((A or B) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78787
in-theory        78787
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78787.        ((((A or B) -> C) -> ((A or B) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78788
in-theory        78788
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78788.        ((((A or B) -> C) -> ((A or B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78789
in-theory        78789
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (((A or B) -> C) -> ((A or B) -> C)))
theorem-size     23
proof            (modus-ponens tm-316 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-78789.        ((((A or B) -> C) -> ((A or B) -> C)) and (((A or B) -> C) -> ((A or B) -> C))), M:tm-316, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78790
in-theory        78790
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78790.        ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78791
in-theory        78791
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> (not ((A or B) -> C))) -> (not ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-313 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78791.        ((((A or B) -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> (not ((A or B) -> C))) -> (not ((A or B) -> C)))), M:tm-313, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78792
in-theory        78792
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> D) -> ((((A or B) -> C) or ((A or B) -> C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78792.        ((((A or B) -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> D) -> ((((A or B) -> C) or ((A or B) -> C)) -> D))), M:tm-312, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78793
in-theory        78793
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (D or (((A or B) -> C) -> ((A or B) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78793.        ((((A or B) -> C) -> ((A or B) -> C)) and (D or (((A or B) -> C) -> ((A or B) -> C)))), M:tm-311, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78794
in-theory        78794
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> ((A or B) -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78794.        ((((A or B) -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> ((A or B) -> C)) or D)), M:tm-310, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78795
in-theory        78795
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (D -> ((((A or B) -> C) -> ((A or B) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78795.        ((((A or B) -> C) -> ((A or B) -> C)) and (D -> ((((A or B) -> C) -> ((A or B) -> C)) and D))), M:tm-309, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78796
in-theory        78796
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> (A or B)) -> (((A or B) -> C) -> C)))
theorem-size     29
proof            (modus-ponens tm-306 tm-888 ((A (-> (or Am Bm) Cm)) (B (or Am Bm)) (C 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-306.          ((A -> (B -> C)) -> ((A -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78796.        ((((A or B) -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> (A or B)) -> (((A or B) -> C) -> C))), M:tm-306, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (or Am Bm)) (C Cm))
================================================================
tm-name          tm-78797
in-theory        78797
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (((A or B) -> C) -> ((A or B) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78797.        ((((A or B) -> C) -> ((A or B) -> C)) and (D -> (((A or B) -> C) -> ((A or B) -> C)))), M:tm-305, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78798
in-theory        78798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78798.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-303, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78799
in-theory        78799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78799.        ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-270, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78800
in-theory        78800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78800.        ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-239, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78801
in-theory        78801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> ((E or F) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78801.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> ((E or F) -> G))), M:tm-210, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78802
in-theory        78802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78802.        ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-183, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78803
in-theory        78803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78803.        ((A -> ((B and C) -> C)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-157, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78804
in-theory        78804
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78804.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-147, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78805
in-theory        78805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78805.        ((A -> ((B and C) -> B)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-134, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78806
in-theory        78806
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78806.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-125, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78807
in-theory        78807
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> D)) -> (((A or B) -> C) -> ((A or B) -> D)))
theorem-size     19
proof            (modus-ponens tm-114 tm-888 ((A (-> (or Am Bm) (-> C D))) (B (or Am Bm)) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 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-14.           (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78807.        (((A or B) -> (C -> D)) -> (((A or B) -> C) -> ((A or B) -> D))), M:tm-114, m:tm-888, u:((A (-> (or Am Bm) (-> C D))) (B (or Am Bm)) (Cm (-> C D)))
================================================================
tm-name          tm-78808
in-theory        78808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((E or F) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78808.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((E or F) -> G))), M:tm-113, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78809
in-theory        78809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78809.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-105, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78810
in-theory        78810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C or D) -> E) -> ((C or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-78810.        (((A -> B) -> (A -> A)) and (((C or D) -> E) -> ((C or D) -> E))), M:tm-95, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78811
in-theory        78811
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> (A or B))) -> ((A or B) -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-92 tm-888 ((Cm (or Am Bm)) (A (or Am Bm)) (B (-> (or Am Bm) (or Am Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78811.        ((((A or B) -> C) or ((A or B) -> (A or B))) -> ((A or B) -> (A or B))), M:tm-92, m:tm-888, u:((Cm (or Am Bm)) (A (or Am Bm)) (B (-> (or Am Bm) (or Am Bm))))
================================================================
tm-name          tm-78812
in-theory        78812
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> ((A or B) -> C)))
theorem-size     13
proof            (modus-ponens tm-84 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78812.        (((A or B) -> C) -> (D -> ((A or B) -> C))), M:tm-84, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78813
in-theory        78813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78813.        ((A -> (B -> (C -> B))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-83, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78814
in-theory        78814
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> (B or C)))) -> ((B or C) -> (D -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-80 tm-888 ((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (-> (or Am Bm) (-> B (or Am Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78814.        ((A or ((B or C) -> (D -> (B or C)))) -> ((B or C) -> (D -> (B or C)))), M:tm-80, m:tm-888, u:((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (-> (or Am Bm) (-> B (or Am Bm)))))
================================================================
tm-name          tm-78815
in-theory        78815
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B or C) -> D) -> ((B or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78815.        (((not (not A)) -> A) and (((B or C) -> D) -> ((B or C) -> D))), M:tm-76, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78816
in-theory        78816
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> ((A or B) -> C))
theorem-size     19
proof            (modus-ponens tm-73 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78816.        (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> ((A or B) -> C)), M:tm-73, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78817
in-theory        78817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> ((C or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78817.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> ((C or D) -> E))), M:tm-69, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78818
in-theory        78818
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (A or B)) -> (((A or B) or (A or B)) -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-55 tm-888 ((A (or Am Bm)) (Cm (or Am Bm)) (B (or Am Bm)) (C (or Am Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       129
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78818.        (((A or B) -> (A or B)) -> (((A or B) or (A or B)) -> (A or B))), M:tm-55, m:tm-888, u:((A (or Am Bm)) (Cm (or Am Bm)) (B (or Am Bm)) (C (or Am Bm)))
================================================================
tm-name          tm-78819
in-theory        78819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78819.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-54, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78820
in-theory        78820
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> ((B or C) -> (A and (B or C))))
theorem-size     21
proof            (modus-ponens tm-48 tm-888 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Am Bm) (and B (or Am Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78820.        ((A or ((B or C) -> (A and (B or C)))) -> ((B or C) -> (A and (B or C)))), M:tm-48, m:tm-888, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Am Bm) (and B (or Am Bm)))))
================================================================
tm-name          tm-78821
in-theory        78821
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or C) -> D))
theorem-size     19
proof            (modus-ponens tm-47 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78821.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or C) -> D)), M:tm-47, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78822
in-theory        78822
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or B) -> C))
theorem-size     19
proof            (modus-ponens tm-46 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-8 tm-3 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-78822.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or B) -> C)), M:tm-46, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78823
in-theory        78823
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> ((B or C) -> A))
theorem-size     13
proof            (modus-ponens tm-44 tm-888 ((A (or Am Bm)) (B Cm) (C (-> (or Am Bm) Cm))))
axioms-used      (tm-8 tm-1 tm-2 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-78823.        ((A or ((B or C) -> A)) -> ((B or C) -> A)), M:tm-44, m:tm-888, u:((A (or Am Bm)) (B Cm) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78824
in-theory        78824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C or D) -> E) -> ((C or D) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78824.        ((A -> (B or A)) and (((C or D) -> E) -> ((C or D) -> E))), M:tm-42, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78825
in-theory        78825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C or D) -> E) -> ((C or D) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78825.        ((A -> (A or B)) and (((C or D) -> E) -> ((C or D) -> E))), M:tm-32, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78826
in-theory        78826
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (((A or B) -> C) and ((A or B) -> C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (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-12.           ((A -> B) -> (A -> A)), M: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-78826.        (((A or B) -> C) -> (((A or B) -> C) and ((A or B) -> C))), M:tm-24, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78827
in-theory        78827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78827.        ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or D) -> E))), M:tm-23, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78828
in-theory        78828
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C or D) -> E) -> ((C or D) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78828.        (((A and B) -> B) and (((C or D) -> E) -> ((C or D) -> E))), M:tm-22, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78829
in-theory        78829
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C or D) -> E) -> ((C or D) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78829.        (((A and B) -> A) and (((C or D) -> E) -> ((C or D) -> E))), M:tm-21, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78830
in-theory        78830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78830.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-20, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78831
in-theory        78831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C or D) -> E) -> ((C or D) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78831.        ((A -> (B -> A)) and (((C or D) -> E) -> ((C or D) -> E))), M:tm-19, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78832
in-theory        78832
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((A or B) -> C))) -> (not ((A or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-9 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-9 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78832.        ((((A or B) -> C) -> (not ((A or B) -> C))) -> (not ((A or B) -> C))), M:tm-9, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78833
in-theory        78833
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> D) -> ((((A or B) -> C) or ((A or B) -> C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-888 ((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78833.        ((((A or B) -> C) -> D) -> ((((A or B) -> C) or ((A or B) -> C)) -> D)), M:tm-8, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-78834
in-theory        78834
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B or C) -> D) -> ((B or C) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78834.        (A or (((B or C) -> D) -> ((B or C) -> D))), M:tm-7, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78835
in-theory        78835
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or B) -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or 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-49.           (((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-78835.        ((((A or B) -> C) -> ((A or B) -> C)) or D), M:tm-6, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78836
in-theory        78836
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> ((B or C) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-78836.        (A -> ((((B or C) -> D) -> ((B or C) -> D)) and A)), M:tm-5, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78837
in-theory        78837
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (A or B)) -> (((A or B) -> C) -> C))
theorem-size     17
proof            (modus-ponens tm-2 tm-888 ((A (-> (or Am Bm) Cm)) (B (or Am Bm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78837.        ((((A or B) -> C) -> (A or B)) -> (((A or B) -> C) -> C)), M:tm-2, m:tm-888, u:((A (-> (or Am Bm) Cm)) (B (or Am Bm)) (C Cm))
================================================================
tm-name          tm-78838
in-theory        78838
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or C) -> D) -> ((B or C) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78838.        (A -> (((B or C) -> D) -> ((B or C) -> D))), M:tm-1, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78839
in-theory        78839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-855 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-9 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-48.           (((A -> (B and 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78839.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-855, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78840
in-theory        78840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-808 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78840.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-808, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78841
in-theory        78841
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C))))
theorem-size     60
proof            (modus-ponens tm-798 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9 tm-6)
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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-78841.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C)))), M:tm-798, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78842
in-theory        78842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-757 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-49.           (((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-78842.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-757, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78843
in-theory        78843
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((((A or B) -> C) -> (not ((A or (A or B)) -> C))) and D) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C))))
theorem-size     60
proof            (modus-ponens tm-747 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78843.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((((A or B) -> C) -> (not ((A or (A or B)) -> C))) and D) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C)))), M:tm-747, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78844
in-theory        78844
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     47
proof            (modus-ponens tm-708 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78844.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-708, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78845
in-theory        78845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-665 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-49.           (((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-78845.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-665, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78846
in-theory        78846
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((not ((A or (A or B)) -> C)) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C))))
theorem-size     52
proof            (modus-ponens tm-654 tm-889 ((A (-> (or Am Bm) Cm)) (B (not (-> (or Am (or Am Bm)) Cm))) (C (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78846.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((not ((A or (A or B)) -> C)) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C)))), M:tm-654, m:tm-889, u:((A (-> (or Am Bm) Cm)) (B (not (-> (or Am (or Am Bm)) Cm))) (C (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78847
in-theory        78847
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (D or (not ((A or B) -> C))))
theorem-size     23
proof            (modus-ponens tm-623 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78847.        ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (D or (not ((A or B) -> C)))), M:tm-623, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78848
in-theory        78848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-622 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78848.        ((A -> (B -> (C or B))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-622, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78849
in-theory        78849
times-derived    1
----------------------------------------------------------------
theorem          (not (((A or B) -> (C or (A or B))) -> (not ((A or (A or B)) -> (C or (A or B))))))
theorem-size     23
proof            (modus-ponens tm-618 tm-889 ((A (-> (-> (or Am Bm) (or C (or Am Bm))) (not (-> (or Am (or Am Bm)) (or C (or Am Bm)))))) (B (or Am Bm)) (Cm (or C (or Am Bm)))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78849.        (not (((A or B) -> (C or (A or B))) -> (not ((A or (A or B)) -> (C or (A or B)))))), M:tm-618, m:tm-889, u:((A (-> (-> (or Am Bm) (or C (or Am Bm))) (not (-> (or Am (or Am Bm)) (or C (or Am Bm)))))) (B (or Am Bm)) (Cm (or C (or Am Bm))))
================================================================
tm-name          tm-78850
in-theory        78850
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-609 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78850.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E or D))), M:tm-609, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78851
in-theory        78851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-605 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78851.        ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-605, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78852
in-theory        78852
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E or D)) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78852.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E or D)) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-595, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78853
in-theory        78853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-550 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-49.           (((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-78853.        (((A -> (B or A)) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-550, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78854
in-theory        78854
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-540 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78854.        ((A or (B -> (C or B))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-540, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78855
in-theory        78855
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-530 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-49.           (((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-78855.        ((A or (B -> (B or C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-530, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78856
in-theory        78856
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-520 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78856.        ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-520, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78857
in-theory        78857
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-510 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78857.        ((A or ((B and C) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-510, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78858
in-theory        78858
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-500 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78858.        ((A or ((B and C) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-500, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78859
in-theory        78859
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-490 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78859.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-490, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78860
in-theory        78860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-480 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78860.        ((A or (B -> (C -> B))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-480, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78861
in-theory        78861
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> ((not ((A or B) -> C)) or D))
theorem-size     23
proof            (modus-ponens tm-470 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or 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-49.           (((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-78861.        ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> ((not ((A or B) -> C)) or D)), M:tm-470, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78862
in-theory        78862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-469 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or 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-49.           (((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-78862.        ((A -> (B -> (B or C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-469, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78863
in-theory        78863
times-derived    1
----------------------------------------------------------------
theorem          (not (((A or B) -> ((A or B) or C)) -> (not ((A or (A or B)) -> ((A or B) or C)))))
theorem-size     23
proof            (modus-ponens tm-465 tm-889 ((A (-> (-> (or Am Bm) (or (or Am Bm) C)) (not (-> (or Am (or Am Bm)) (or (or Am Bm) C))))) (B (or Am Bm)) (Cm (or (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-49.           (((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-78863.        (not (((A or B) -> ((A or B) or C)) -> (not ((A or (A or B)) -> ((A or B) or C))))), M:tm-465, m:tm-889, u:((A (-> (-> (or Am Bm) (or (or Am Bm) C)) (not (-> (or Am (or Am Bm)) (or (or Am Bm) C))))) (B (or Am Bm)) (Cm (or (or Am Bm) C)))
================================================================
tm-name          tm-78864
in-theory        78864
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-456 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or 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-49.           (((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-78864.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (D or E))), M:tm-456, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78865
in-theory        78865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-453 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
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-49.           (((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-78865.        ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-453, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78866
in-theory        78866
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (D or E)) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-78866.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (D or E)) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-443, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78867
in-theory        78867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-409 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-49.           (((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-78867.        (((A -> (A or B)) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-409, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78868
in-theory        78868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-400 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
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-49.           (((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-78868.        (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-400, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78869
in-theory        78869
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-391 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-78869.        ((((A and B) -> B) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-391, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78870
in-theory        78870
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-382 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-49.           (((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-78870.        ((((A and B) -> A) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-382, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78871
in-theory        78871
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-373 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-8)
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-49.           (((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-78871.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-373, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78872
in-theory        78872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-364 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or 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-49.           (((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-78872.        (((A -> (B -> A)) or C) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-364, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78873
in-theory        78873
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (D -> ((not ((A or B) -> C)) and D)))
theorem-size     25
proof            (modus-ponens tm-355 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78873.        ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (D -> ((not ((A or B) -> C)) and D))), M:tm-355, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78874
in-theory        78874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-354 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78874.        ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-354, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78875
in-theory        78875
times-derived    1
----------------------------------------------------------------
theorem          (not (((A or B) -> (C -> ((A or B) and C))) -> (not ((A or (A or B)) -> (C -> ((A or B) and C))))))
theorem-size     27
proof            (modus-ponens tm-350 tm-889 ((A (-> (-> (or Am Bm) (-> C (and (or Am Bm) C))) (not (-> (or Am (or Am Bm)) (-> C (and (or Am Bm) C)))))) (B (or Am Bm)) (Cm (-> C (and (or Am Bm) C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78875.        (not (((A or B) -> (C -> ((A or B) and C))) -> (not ((A or (A or B)) -> (C -> ((A or B) and C)))))), M:tm-350, m:tm-889, u:((A (-> (-> (or Am Bm) (-> C (and (or Am Bm) C))) (not (-> (or Am (or Am Bm)) (-> C (and (or Am Bm) C)))))) (B (or Am Bm)) (Cm (-> C (and (or Am Bm) C))))
================================================================
tm-name          tm-78876
in-theory        78876
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-341 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78876.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78877
in-theory        78877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-338 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78877.        (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-338, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78878
in-theory        78878
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) and (not ((A or B) -> C)))))
theorem-size     58
proof            (modus-ponens tm-328 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78878.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) and (not ((A or B) -> C))))), M:tm-328, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78879
in-theory        78879
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78879.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-327, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78880
in-theory        78880
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and E) -> E) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78880.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and E) -> E) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-326, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78881
in-theory        78881
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and E) -> D) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78881.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and E) -> D) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-325, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78882
in-theory        78882
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78882.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-324, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78883
in-theory        78883
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> D)) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78883.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> D)) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-323, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78884
in-theory        78884
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-322 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78884.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78885
in-theory        78885
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-320 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78885.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78886
in-theory        78886
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-318 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78886.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78887
in-theory        78887
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (((A or B) -> C) -> (not ((A or (A or B)) -> C)))))
theorem-size     51
proof            (modus-ponens tm-316 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78887.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (((A or B) -> C) -> (not ((A or (A or B)) -> C))))), M:tm-316, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78888
in-theory        78888
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-315 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78888.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78889
in-theory        78889
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not (not ((A or B) -> C)))) -> (not (((A or B) -> C) -> (not ((A or (A or B)) -> C))))))
theorem-size     60
proof            (modus-ponens tm-313 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78889.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not (not ((A or B) -> C)))) -> (not (((A or B) -> C) -> (not ((A or (A or B)) -> C)))))), M:tm-313, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78890
in-theory        78890
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((not ((A or B) -> C)) -> D) -> (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) or (not ((A or B) -> C))) -> D)))
theorem-size     54
proof            (modus-ponens tm-312 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78890.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((not ((A or B) -> C)) -> D) -> (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) or (not ((A or B) -> C))) -> D))), M:tm-312, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78891
in-theory        78891
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D or ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-8 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-7.            (A -> (B or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78891.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D or ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-311, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78892
in-theory        78892
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) or D))
theorem-size     45
proof            (modus-ponens tm-310 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
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-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-49.           (((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-78892.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) or D)), M:tm-310, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78893
in-theory        78893
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and D)))
theorem-size     47
proof            (modus-ponens tm-309 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78893.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and D))), M:tm-309, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78894
in-theory        78894
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 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-1.            (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78894.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-305, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78895
in-theory        78895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-303 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78895.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-303, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78896
in-theory        78896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-270 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78896.        ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-270, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78897
in-theory        78897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-239 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78897.        ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-239, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78898
in-theory        78898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-210 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 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-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78898.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-210, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78899
in-theory        78899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-183 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78899.        ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-183, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78900
in-theory        78900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-157 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78900.        ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-157, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78901
in-theory        78901
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-147 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78901.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-147, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78902
in-theory        78902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-134 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78902.        ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-134, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78903
in-theory        78903
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-125 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78903.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-125, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78904
in-theory        78904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-113 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78904.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-113, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78905
in-theory        78905
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-105 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78905.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-105, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78906
in-theory        78906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-95 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78906.        (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-95, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78907
in-theory        78907
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (D -> (not ((A or B) -> C))))
theorem-size     23
proof            (modus-ponens tm-84 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-9 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78907.        ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (D -> (not ((A or B) -> C)))), M:tm-84, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78908
in-theory        78908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-83 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78908.        ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-83, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78909
in-theory        78909
times-derived    1
----------------------------------------------------------------
theorem          (not (((A or B) -> (C -> (A or B))) -> (not ((A or (A or B)) -> (C -> (A or B))))))
theorem-size     23
proof            (modus-ponens tm-79 tm-889 ((A (-> (-> (or Am Bm) (-> C (or Am Bm))) (not (-> (or Am (or Am Bm)) (-> C (or Am Bm)))))) (B (or Am Bm)) (Cm (-> C (or Am Bm)))))
axioms-used      (tm-9 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78909.        (not (((A or B) -> (C -> (A or B))) -> (not ((A or (A or B)) -> (C -> (A or B)))))), M:tm-79, m:tm-889, u:((A (-> (-> (or Am Bm) (-> C (or Am Bm))) (not (-> (or Am (or Am Bm)) (-> C (or Am Bm)))))) (B (or Am Bm)) (Cm (-> C (or Am Bm))))
================================================================
tm-name          tm-78910
in-theory        78910
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or C) -> D) -> (not ((B or (B or C)) -> D))) -> (not ((B or C) -> D))))
theorem-size     27
proof            (modus-ponens tm-76 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78910.        (((not (not A)) -> A) and ((((B or C) -> D) -> (not ((B or (B or C)) -> D))) -> (not ((B or C) -> D)))), M:tm-76, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78911
in-theory        78911
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A or B) -> C) -> (not ((A or (A or B)) -> C))))) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C)))
theorem-size     38
proof            (modus-ponens tm-73 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78911.        (((not (not (((A or B) -> C) -> (not ((A or (A or B)) -> C))))) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C))), M:tm-73, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78912
in-theory        78912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-69 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78912.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-69, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78913
in-theory        78913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-54 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78913.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-54, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78914
in-theory        78914
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B or C) -> D) -> (not ((B or (B or C)) -> D)))) or (((B or C) -> D) -> (not ((B or (B or C)) -> D)))) -> (not ((B or C) -> D)))
theorem-size     38
proof            (modus-ponens tm-47 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78914.        (((A and (((B or C) -> D) -> (not ((B or (B or C)) -> D)))) or (((B or C) -> D) -> (not ((B or (B or C)) -> D)))) -> (not ((B or C) -> D))), M:tm-47, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78915
in-theory        78915
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> (not ((A or (A or B)) -> C))) and D) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C)))
theorem-size     38
proof            (modus-ponens tm-46 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78915.        ((((((A or B) -> C) -> (not ((A or (A or B)) -> C))) and D) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C))), M:tm-46, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78916
in-theory        78916
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A or (A or B)) -> C)) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C)))
theorem-size     30
proof            (modus-ponens tm-44 tm-889 ((A (-> (or Am Bm) Cm)) (B (not (-> (or Am (or Am Bm)) Cm))) (C (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78916.        (((not ((A or (A or B)) -> C)) or (((A or B) -> C) -> (not ((A or (A or B)) -> C)))) -> (not ((A or B) -> C))), M:tm-44, m:tm-889, u:((A (-> (or Am Bm) Cm)) (B (not (-> (or Am (or Am Bm)) Cm))) (C (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78917
in-theory        78917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-42 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78917.        ((A -> (B or A)) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-42, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78918
in-theory        78918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-32 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-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-78918.        ((A -> (A or B)) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-32, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78919
in-theory        78919
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) and (not ((A or B) -> C))))
theorem-size     36
proof            (modus-ponens tm-24 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78919.        ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) and (not ((A or B) -> C)))), M:tm-24, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78920
in-theory        78920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-23 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78920.        ((A -> (B -> (A and B))) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-23, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78921
in-theory        78921
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-22 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78921.        (((A and B) -> B) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-22, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78922
in-theory        78922
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-21 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78922.        (((A and B) -> A) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-21, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78923
in-theory        78923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-20 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78923.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-20, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78924
in-theory        78924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-19 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78924.        ((A -> (B -> A)) and ((((C or D) -> E) -> (not ((C or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-19, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78925
in-theory        78925
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (((A or B) -> C) -> (not ((A or (A or B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-12 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-9 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-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-78925.        ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (((A or B) -> C) -> (not ((A or (A or B)) -> C)))), M:tm-12, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78926
in-theory        78926
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not (not ((A or B) -> C)))) -> (not (((A or B) -> C) -> (not ((A or (A or B)) -> C)))))
theorem-size     38
proof            (modus-ponens tm-9 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78926.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not (not ((A or B) -> C)))) -> (not (((A or B) -> C) -> (not ((A or (A or B)) -> C))))), M:tm-9, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78927
in-theory        78927
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A or B) -> C)) -> D) -> (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) or (not ((A or B) -> C))) -> D))
theorem-size     32
proof            (modus-ponens tm-8 tm-889 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78927.        (((not ((A or B) -> C)) -> D) -> (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) or (not ((A or B) -> C))) -> D)), M:tm-8, m:tm-889, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-78928
in-theory        78928
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B or C) -> D) -> (not ((B or (B or C)) -> D))) -> (not ((B or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-7 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-7 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78928.        (A or ((((B or C) -> D) -> (not ((B or (B or C)) -> D))) -> (not ((B or C) -> D)))), M:tm-7, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78929
in-theory        78929
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) or D)
theorem-size     23
proof            (modus-ponens tm-6 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-6 tm-9 tm-8)
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-49.           (((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-78929.        (((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))) or D), M:tm-6, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78930
in-theory        78930
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) -> (not ((B or (B or C)) -> D))) -> (not ((B or C) -> D))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78930.        (A -> (((((B or C) -> D) -> (not ((B or (B or C)) -> D))) -> (not ((B or C) -> D))) and A)), M:tm-5, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78931
in-theory        78931
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> (not ((B or (B or C)) -> D))) -> (not ((B or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-1 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-1 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-78931.        (A -> ((((B or C) -> D) -> (not ((B or (B or C)) -> D))) -> (not ((B or C) -> D)))), M:tm-1, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-78932
in-theory        78932
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((A or (A or B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-890 tm-1 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       97
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-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-1.            (A -> (B -> A)), axiom
tm-78932.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((A or (A or B)) -> C))), M:tm-890, m:tm-1, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78933
in-theory        78933
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> D)) or ((A or (A or B)) -> (C -> D))) -> (((A or (A or B)) -> C) -> ((A or (A or B)) -> D)))
theorem-size     33
proof            (modus-ponens tm-890 tm-2 ((Am (or A (or A B))) (C (-> Bm Cm)) (D (-> (-> (or A (or A B)) Bm) (-> (or A (or A B)) Cm)))))
axioms-used      (tm-8 tm-6 tm-2)
proof-size       115
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-78933.        ((((A or B) -> (C -> D)) or ((A or (A or B)) -> (C -> D))) -> (((A or (A or B)) -> C) -> ((A or (A or B)) -> D))), M:tm-890, m:tm-2, u:((Am (or A (or A B))) (C (-> Bm Cm)) (D (-> (-> (or A (or A B)) Bm) (-> (or A (or A B)) Cm))))
================================================================
tm-name          tm-78934
in-theory        78934
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (((A or (A or B)) -> C) and D)))
theorem-size     25
proof            (modus-ponens tm-890 tm-5 ((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> (or A (or A B)) C) Bm)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       101
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-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-5.            (A -> (B -> (A and B))), axiom
tm-78934.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (((A or (A or B)) -> C) and D))), M:tm-890, m:tm-5, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> (or A (or A B)) C) Bm))))
================================================================
tm-name          tm-78935
in-theory        78935
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) or D))
theorem-size     23
proof            (modus-ponens tm-890 tm-6 ((Am (-> (or A (or A B)) C)) (D (or (-> (or A (or A B)) C) Bm))))
axioms-used      (tm-8 tm-6)
proof-size       97
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-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-78935.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) or D)), M:tm-890, m:tm-6, u:((Am (-> (or A (or A B)) C)) (D (or (-> (or A (or A B)) C) Bm)))
================================================================
tm-name          tm-78936
in-theory        78936
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((A or (A or B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-890 tm-7 ((Am (-> (or A (or A B)) C)) (D (or Bm (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-7)
proof-size       97
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-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-7.            (A -> (B or A)), axiom
tm-78936.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((A or (A or B)) -> C))), M:tm-890, m:tm-7, u:((Am (-> (or A (or A B)) C)) (D (or Bm (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78937
in-theory        78937
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((C -> D) -> (((A or (A or B)) or C) -> D)))
theorem-size     27
proof            (modus-ponens tm-890 tm-8 ((Am (or A (or A B))) (C Bm) (D (-> (-> Bm Cm) (-> (or (or A (or A B)) Bm) Cm)))))
axioms-used      (tm-8 tm-6)
proof-size       109
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-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-78937.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((C -> D) -> (((A or (A or B)) or C) -> D))), M:tm-890, m:tm-8, u:((Am (or A (or A B))) (C Bm) (D (-> (-> Bm Cm) (-> (or (or A (or A B)) Bm) Cm))))
================================================================
tm-name          tm-78938
in-theory        78938
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> (not C)) -> (not (A or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-890 tm-9 ((Am (or A (or A B))) (C Bm) (D (-> (-> (or A (or A B)) (not Bm)) (not (or A (or A B)))))))
axioms-used      (tm-8 tm-6 tm-9)
proof-size       109
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-78938.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> (not C)) -> (not (A or (A or B))))), M:tm-890, m:tm-9, u:((Am (or A (or A B))) (C Bm) (D (-> (-> (or A (or A B)) (not Bm)) (not (or A (or A B))))))
================================================================
tm-name          tm-78939
in-theory        78939
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-890 tm-11 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-78939.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> D))), M:tm-890, m:tm-11, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-78940
in-theory        78940
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (A or (A or B))))
theorem-size     25
proof            (modus-ponens tm-890 tm-12 ((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       119
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-78940.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (A or (A or B)))), M:tm-890, m:tm-12, u:((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (or A (or A B)))))
================================================================
tm-name          tm-78941
in-theory        78941
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-890 tm-14 ((Am (-> (or A (or A B)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       129
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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-78941.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-890, m:tm-14, u:((Am (-> (or A (or A B)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-78942
in-theory        78942
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-890 tm-16 ((Am (-> (or A (or A B)) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-78942.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D and E) -> D)), M:tm-890, m:tm-16, u:((Am (-> (or A (or A B)) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-78943
in-theory        78943
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-890 tm-18 ((Am (-> (or A (or A B)) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-78943.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D and E) -> E)), M:tm-890, m:tm-18, u:((Am (-> (or A (or A B)) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-78944
in-theory        78944
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> D)) and ((A or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-890 tm-19 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-78944.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-19, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78945
in-theory        78945
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-890 tm-20 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       141
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-78945.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-20, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78946
in-theory        78946
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and E) -> D) and ((A or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-890 tm-21 ((Am (-> (or A (or A B)) C)) (D (and (-> (and Bm Cm) Bm) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-78946.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and E) -> D) and ((A or (A or B)) -> C))), M:tm-890, m:tm-21, u:((Am (-> (or A (or A B)) C)) (D (and (-> (and Bm Cm) Bm) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78947
in-theory        78947
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and E) -> E) and ((A or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-890 tm-22 ((Am (-> (or A (or A B)) C)) (D (and (-> (and Bm Cm) Cm) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-78947.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and E) -> E) and ((A or (A or B)) -> C))), M:tm-890, m:tm-22, u:((Am (-> (or A (or A B)) C)) (D (and (-> (and Bm Cm) Cm) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78948
in-theory        78948
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (D and E))) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-23 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-78948.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (D and E))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-23, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78949
in-theory        78949
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> ((A or (A or B)) and C)))
theorem-size     27
proof            (modus-ponens tm-890 tm-24 ((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (and (or A (or A B)) Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       125
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-78949.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> ((A or (A or B)) and C))), M:tm-890, m:tm-24, u:((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (and (or A (or A B)) Bm))))
================================================================
tm-name          tm-78950
in-theory        78950
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-890 tm-25 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
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-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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-78950.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (D and E)))), M:tm-890, m:tm-25, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-78951
in-theory        78951
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (D or E)) and ((A or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-890 tm-32 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (or Bm Cm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-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-78951.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (D or E)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-32, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (or Bm Cm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78952
in-theory        78952
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-890 tm-33 ((Am (-> (or A (or A B)) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-78952.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (D or E))), M:tm-890, m:tm-33, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-78953
in-theory        78953
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E or D)) and ((A or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-890 tm-42 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (or Cm Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-78953.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E or D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-42, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (or Cm Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78954
in-theory        78954
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-890 tm-43 ((Am (-> (or A (or A B)) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-78954.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E or D))), M:tm-890, m:tm-43, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-78955
in-theory        78955
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((A or (A or B)) and D) or (A or (A or B))) -> C))
theorem-size     29
proof            (modus-ponens tm-890 tm-46 ((Am (or A (or A B))) (C Bm) (D (-> (or (and (or A (or A B)) Cm) (or A (or A B))) Bm))))
axioms-used      (tm-8 tm-6 tm-3)
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-78955.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((A or (A or B)) and D) or (A or (A or B))) -> C)), M:tm-890, m:tm-46, u:((Am (or A (or A B))) (C Bm) (D (-> (or (and (or A (or A B)) Cm) (or A (or A B))) Bm)))
================================================================
tm-name          tm-78956
in-theory        78956
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and (A or (A or B))) or (A or (A or B))) -> C))
theorem-size     29
proof            (modus-ponens tm-890 tm-47 ((Am (or A (or A B))) (C Bm) (D (-> (or (and Cm (or A (or A B))) (or A (or A B))) Bm))))
axioms-used      (tm-8 tm-6 tm-4)
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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-78956.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and (A or (A or B))) or (A or (A or B))) -> C)), M:tm-890, m:tm-47, u:((Am (or A (or A B))) (C Bm) (D (-> (or (and Cm (or A (or A B))) (or A (or A B))) Bm)))
================================================================
tm-name          tm-78957
in-theory        78957
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or (A or B))) -> C))
theorem-size     23
proof            (modus-ponens tm-890 tm-49 ((A Am) (Bm (or Am B)) (C Cm) (D (-> (or Am (or Am (or Am B))) Cm))))
axioms-used      (tm-8 tm-6)
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-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-78957.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or (A or B))) -> C)), M:tm-890, m:tm-49, u:((A Am) (Bm (or Am B)) (C Cm) (D (-> (or Am (or Am (or Am B))) Cm)))
================================================================
tm-name          tm-78958
in-theory        78958
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or B) or (A or (A or B))) -> C))
theorem-size     25
proof            (modus-ponens tm-890 tm-50 ((A Am) (Bm (or Am B)) (C Cm) (D (-> (or (or Am B) (or Am (or Am B))) Cm))))
axioms-used      (tm-8 tm-6 tm-7)
proof-size       125
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-78958.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or B) or (A or (A or B))) -> C)), M:tm-890, m:tm-50, u:((A Am) (Bm (or Am B)) (C Cm) (D (-> (or (or Am B) (or Am (or Am B))) Cm)))
================================================================
tm-name          tm-78959
in-theory        78959
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-890 tm-54 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       141
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-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-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-78959.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-54, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78960
in-theory        78960
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-890 tm-56 ((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       129
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-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-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-78960.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-890, m:tm-56, u:((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-78961
in-theory        78961
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (A or (A or B))))) or ((A or (A or B)) -> (not (C -> (A or (A or B)))))) -> (not (A or (A or B))))
theorem-size     34
proof            (modus-ponens tm-890 tm-57 ((Am (or A (or A B))) (C (not (-> Bm (or A (or A B))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-1)
proof-size       128
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-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-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-78961.        ((((A or B) -> (not (C -> (A or (A or B))))) or ((A or (A or B)) -> (not (C -> (A or (A or B)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-57, u:((Am (or A (or A B))) (C (not (-> Bm (or A (or A B))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-78962
in-theory        78962
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> ((A or (A or B)) and C)))) or ((A or (A or B)) -> (not (C -> ((A or (A or B)) and C))))) -> (not (A or (A or B))))
theorem-size     38
proof            (modus-ponens tm-890 tm-61 ((Am (or A (or A B))) (C (not (-> Bm (and (or A (or A B)) Bm)))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-5)
proof-size       136
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-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-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-78962.        ((((A or B) -> (not (C -> ((A or (A or B)) and C)))) or ((A or (A or B)) -> (not (C -> ((A or (A or B)) and C))))) -> (not (A or (A or B)))), M:tm-890, m:tm-61, u:((Am (or A (or A B))) (C (not (-> Bm (and (or A (or A B)) Bm)))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-78963
in-theory        78963
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((A or (A or B)) or C))) or ((A or (A or B)) -> (not ((A or (A or B)) or C)))) -> (not (A or (A or B))))
theorem-size     34
proof            (modus-ponens tm-890 tm-62 ((Am (or A (or A B))) (C (not (or (or A (or A B)) Bm))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9)
proof-size       128
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-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-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-78963.        ((((A or B) -> (not ((A or (A or B)) or C))) or ((A or (A or B)) -> (not ((A or (A or B)) or C)))) -> (not (A or (A or B)))), M:tm-890, m:tm-62, u:((Am (or A (or A B))) (C (not (or (or A (or A B)) Bm))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-78964
in-theory        78964
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C or (A or (A or B))))) or ((A or (A or B)) -> (not (C or (A or (A or B)))))) -> (not (A or (A or B))))
theorem-size     34
proof            (modus-ponens tm-890 tm-63 ((Am (or A (or A B))) (C (not (or Bm (or A (or A B))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-7)
proof-size       128
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-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-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-78964.        ((((A or B) -> (not (C or (A or (A or B))))) or ((A or (A or B)) -> (not (C or (A or (A or B)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-63, u:((Am (or A (or A B))) (C (not (or Bm (or A (or A B))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-78965
in-theory        78965
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A or (A or B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-890 tm-69 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-9)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-78965.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-69, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78966
in-theory        78966
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-890 tm-71 ((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-9)
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-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-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-78966.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-890, m:tm-71, u:((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-78967
in-theory        78967
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((not (not (A or (A or B)))) or (A or (A or B))) -> C))
theorem-size     29
proof            (modus-ponens tm-890 tm-73 ((Am (or A (or A B))) (C Bm) (D (-> (or (not (not (or A (or A B)))) (or A (or A B))) Bm))))
axioms-used      (tm-8 tm-6 tm-10)
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-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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-78967.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((not (not (A or (A or B)))) or (A or (A or B))) -> C)), M:tm-890, m:tm-73, u:((Am (or A (or A B))) (C Bm) (D (-> (or (not (not (or A (or A B)))) (or A (or A B))) Bm)))
================================================================
tm-name          tm-78968
in-theory        78968
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((not (not D)) -> D) and ((A or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-890 tm-76 ((Am (-> (or A (or A B)) C)) (D (and (-> (not (not Bm)) Bm) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-10)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-78968.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((not (not D)) -> D) and ((A or (A or B)) -> C))), M:tm-890, m:tm-76, u:((Am (-> (or A (or A B)) C)) (D (and (-> (not (not Bm)) Bm) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78969
in-theory        78969
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-890 tm-78 ((Am (-> (or A (or A B)) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-6 tm-1 tm-10)
proof-size       105
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-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-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-78969.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((not (not D)) -> D)), M:tm-890, m:tm-78, u:((Am (-> (or A (or A B)) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-78970
in-theory        78970
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (D -> C)))) or ((A or (A or B)) -> (not (C -> (D -> C))))) -> (not (A or (A or B))))
theorem-size     30
proof            (modus-ponens tm-890 tm-79 ((Am (or A (or A B))) (C (not (-> Bm (-> Cm Bm)))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-1)
proof-size       138
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-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-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-78970.        ((((A or B) -> (not (C -> (D -> C)))) or ((A or (A or B)) -> (not (C -> (D -> C))))) -> (not (A or (A or B)))), M:tm-890, m:tm-79, u:((Am (or A (or A B))) (C (not (-> Bm (-> Cm Bm)))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-78971
in-theory        78971
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (F -> E))) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-83 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-78971.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (F -> E))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-83, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78972
in-theory        78972
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (D -> C)))
theorem-size     23
proof            (modus-ponens tm-890 tm-84 ((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (-> Cm Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-78972.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (D -> C))), M:tm-890, m:tm-84, u:((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (-> Cm Bm))))
================================================================
tm-name          tm-78973
in-theory        78973
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-890 tm-85 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       121
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-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-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-78973.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (F -> E)))), M:tm-890, m:tm-85, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-78974
in-theory        78974
times-derived    3
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> C))
theorem-size     21
proof            (modus-ponens tm-890 tm-86 ((Am (-> (or A (or A B)) C)) (D (-> (or A (or A B)) C))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-78974.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> C)), M:tm-890, m:tm-86, u:((Am (-> (or A (or A B)) C)) (D (-> (or A (or A B)) C)))
================================================================
tm-name          tm-78975
in-theory        78975
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> D)) or ((A or (A or B)) -> (C -> D))) -> ((A or (A or B)) -> (C -> D)))
theorem-size     27
proof            (modus-ponens tm-890 tm-87 ((Am (or A (or A B))) (C (-> Bm Cm)) (D (-> (or A (or A B)) (-> Bm Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       145
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-78975.        ((((A or B) -> (C -> D)) or ((A or (A or B)) -> (C -> D))) -> ((A or (A or B)) -> (C -> D))), M:tm-890, m:tm-87, u:((Am (or A (or A B))) (C (-> Bm Cm)) (D (-> (or A (or A B)) (-> Bm Cm))))
================================================================
tm-name          tm-78976
in-theory        78976
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> (D -> D)) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-95 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2 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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-78976.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> (D -> D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-95, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78977
in-theory        78977
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-890 tm-97 ((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
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-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-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-78977.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> (D -> D))), M:tm-890, m:tm-97, u:((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-78978
in-theory        78978
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> ((C -> (A or (A or B))) -> D)) or ((A or (A or B)) -> ((C -> (A or (A or B))) -> D))) -> ((A or (A or B)) -> D))
theorem-size     37
proof            (modus-ponens tm-890 tm-98 ((Am (or A (or A B))) (C (-> (-> Bm (or A (or A B))) Cm)) (D (-> (or A (or A B)) Cm))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-78978.        ((((A or B) -> ((C -> (A or (A or B))) -> D)) or ((A or (A or B)) -> ((C -> (A or (A or B))) -> D))) -> ((A or (A or B)) -> D)), M:tm-890, m:tm-98, u:((Am (or A (or A B))) (C (-> (-> Bm (or A (or A B))) Cm)) (D (-> (or A (or A B)) Cm)))
================================================================
tm-name          tm-78979
in-theory        78979
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> ((A or (A or B)) -> C)) or ((A or (A or B)) -> ((A or (A or B)) -> C))) -> ((A or (A or B)) -> C))
theorem-size     33
proof            (modus-ponens tm-890 tm-99 ((Am (or A (or A B))) (C (-> (or A (or A B)) Bm)) (D (-> (or A (or A B)) Bm))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-78979.        ((((A or B) -> ((A or (A or B)) -> C)) or ((A or (A or B)) -> ((A or (A or B)) -> C))) -> ((A or (A or B)) -> C)), M:tm-890, m:tm-99, u:((Am (or A (or A B))) (C (-> (or A (or A B)) Bm)) (D (-> (or A (or A B)) Bm)))
================================================================
tm-name          tm-78980
in-theory        78980
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A or (A or B)) -> C)))
theorem-size     41
proof            (modus-ponens tm-890 tm-105 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       185
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-78980.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-105, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78981
in-theory        78981
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-890 tm-107 ((Am (-> (or A (or A B)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       173
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-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-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-78981.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-890, m:tm-107, u:((Am (-> (or A (or A B)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-78982
in-theory        78982
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or ((A or (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (A or (A or B))))
theorem-size     46
proof            (modus-ponens tm-890 tm-109 ((Am (or A (or A B))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-1 tm-2)
proof-size       178
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-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-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-78982.        ((((A or B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or ((A or (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-109, u:((Am (or A (or A B))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-78983
in-theory        78983
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-890 tm-113 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-2)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-78983.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-113, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78984
in-theory        78984
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> (D -> E))) or ((A or (A or B)) -> (C -> (D -> E)))) -> ((A or (A or B)) -> ((C -> D) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-890 tm-114 ((Am (or A (or A B))) (C (-> Bm (-> Cm Dm))) (D (-> (or A (or A B)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
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-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-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-78984.        ((((A or B) -> (C -> (D -> E))) or ((A or (A or B)) -> (C -> (D -> E)))) -> ((A or (A or B)) -> ((C -> D) -> (C -> E)))), M:tm-890, m:tm-114, u:((Am (or A (or A B))) (C (-> Bm (-> Cm Dm))) (D (-> (or A (or A B)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-78985
in-theory        78985
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-890 tm-115 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-6 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-78985.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-890, m:tm-115, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-78986
in-theory        78986
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-890 tm-125 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2 tm-3)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-78986.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-125, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78987
in-theory        78987
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-890 tm-127 ((Am (-> (or A (or A B)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 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-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-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-78987.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-890, m:tm-127, u:((Am (-> (or A (or A B)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-78988
in-theory        78988
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C and D) -> C))) or ((A or (A or B)) -> (not ((C and D) -> C)))) -> (not (A or (A or B))))
theorem-size     30
proof            (modus-ponens tm-890 tm-130 ((Am (or A (or A B))) (C (not (-> (and Bm Cm) Bm))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-1 tm-3)
proof-size       138
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-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-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-78988.        ((((A or B) -> (not ((C and D) -> C))) or ((A or (A or B)) -> (not ((C and D) -> C)))) -> (not (A or (A or B)))), M:tm-890, m:tm-130, u:((Am (or A (or A B))) (C (not (-> (and Bm Cm) Bm))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-78989
in-theory        78989
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E and F) -> E)) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-134 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-3)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-78989.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E and F) -> E)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-134, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78990
in-theory        78990
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and D)) or ((A or (A or B)) -> (C and D))) -> ((A or (A or B)) -> C))
theorem-size     25
proof            (modus-ponens tm-890 tm-135 ((Am (or A (or A B))) (C (and Bm Cm)) (D (-> (or A (or A B)) Bm))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-3)
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-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-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-78990.        ((((A or B) -> (C and D)) or ((A or (A or B)) -> (C and D))) -> ((A or (A or B)) -> C)), M:tm-890, m:tm-135, u:((Am (or A (or A B))) (C (and Bm Cm)) (D (-> (or A (or A B)) Bm)))
================================================================
tm-name          tm-78991
in-theory        78991
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-890 tm-136 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
proof-size       121
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-78991.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E and F) -> E))), M:tm-890, m:tm-136, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-78992
in-theory        78992
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-890 tm-147 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2 tm-4)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-78992.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-147, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78993
in-theory        78993
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-890 tm-149 ((Am (-> (or A (or A B)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-6 tm-1 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-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-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-78993.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-890, m:tm-149, u:((Am (-> (or A (or A B)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-78994
in-theory        78994
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C and D) -> D))) or ((A or (A or B)) -> (not ((C and D) -> D)))) -> (not (A or (A or B))))
theorem-size     30
proof            (modus-ponens tm-890 tm-153 ((Am (or A (or A B))) (C (not (-> (and Bm Cm) Cm))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-1 tm-4)
proof-size       138
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-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-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-78994.        ((((A or B) -> (not ((C and D) -> D))) or ((A or (A or B)) -> (not ((C and D) -> D)))) -> (not (A or (A or B)))), M:tm-890, m:tm-153, u:((Am (or A (or A B))) (C (not (-> (and Bm Cm) Cm))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-78995
in-theory        78995
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E and F) -> F)) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-157 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-4)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-78995.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E and F) -> F)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-157, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-78996
in-theory        78996
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and D)) or ((A or (A or B)) -> (C and D))) -> ((A or (A or B)) -> D))
theorem-size     25
proof            (modus-ponens tm-890 tm-158 ((Am (or A (or A B))) (C (and Bm Cm)) (D (-> (or A (or A B)) Cm))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-4)
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-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-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-78996.        ((((A or B) -> (C and D)) or ((A or (A or B)) -> (C and D))) -> ((A or (A or B)) -> D)), M:tm-890, m:tm-158, u:((Am (or A (or A B))) (C (and Bm Cm)) (D (-> (or A (or A B)) Cm)))
================================================================
tm-name          tm-78997
in-theory        78997
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-890 tm-159 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
proof-size       121
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-78997.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E and F) -> F))), M:tm-890, m:tm-159, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-78998
in-theory        78998
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (D -> C)) and (A or (A or B))))) or ((A or (A or B)) -> (not ((C -> (D -> C)) and (A or (A or B)))))) -> (not (A or (A or B))))
theorem-size     42
proof            (modus-ponens tm-890 tm-179 ((Am (or A (or A B))) (C (not (and (-> Bm (-> Cm Bm)) (or A (or A B))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-5 tm-1)
proof-size       156
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-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-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-78998.        ((((A or B) -> (not ((C -> (D -> C)) and (A or (A or B))))) or ((A or (A or B)) -> (not ((C -> (D -> C)) and (A or (A or B)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-179, u:((Am (or A (or A B))) (C (not (and (-> Bm (-> Cm Bm)) (or A (or A B))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-78999
in-theory        78999
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-183 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-78999.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-183, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79000
in-theory        79000
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-890 tm-184 ((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
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-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-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-79000.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (F -> E)) and D))), M:tm-890, m:tm-184, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-79001
in-theory        79001
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or (A or B))))) or ((A or (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or (A or B)))))) -> (not (A or (A or B))))
theorem-size     58
proof            (modus-ponens tm-890 tm-206 ((Am (or A (or A B))) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A (or A B))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-5 tm-2)
proof-size       196
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-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-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-79001.        ((((A or B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or (A or B))))) or ((A or (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or (A or B)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-206, u:((Am (or A (or A B))) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A (or A B))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-79002
in-theory        79002
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A or (A or B)) -> C)))
theorem-size     39
proof            (modus-ponens tm-890 tm-210 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       173
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-79002.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-210, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79003
in-theory        79003
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-890 tm-211 ((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-2)
proof-size       161
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-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-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-79003.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-890, m:tm-211, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-79004
in-theory        79004
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (((C and D) -> C) and (A or (A or B))))) or ((A or (A or B)) -> (not (((C and D) -> C) and (A or (A or B)))))) -> (not (A or (A or B))))
theorem-size     42
proof            (modus-ponens tm-890 tm-235 ((Am (or A (or A B))) (C (not (and (-> (and Bm Cm) Bm) (or A (or A B))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-5 tm-3)
proof-size       156
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-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-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-79004.        ((((A or B) -> (not (((C and D) -> C) and (A or (A or B))))) or ((A or (A or B)) -> (not (((C and D) -> C) and (A or (A or B)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-235, u:((Am (or A (or A B))) (C (not (and (-> (and Bm Cm) Bm) (or A (or A B))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-79005
in-theory        79005
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-239 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-79005.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-239, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79006
in-theory        79006
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-890 tm-240 ((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 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-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-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-79006.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (((E and F) -> E) and D))), M:tm-890, m:tm-240, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-79007
in-theory        79007
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (((C and D) -> D) and (A or (A or B))))) or ((A or (A or B)) -> (not (((C and D) -> D) and (A or (A or B)))))) -> (not (A or (A or B))))
theorem-size     42
proof            (modus-ponens tm-890 tm-266 ((Am (or A (or A B))) (C (not (and (-> (and Bm Cm) Cm) (or A (or A B))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-5 tm-4)
proof-size       156
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-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-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-79007.        ((((A or B) -> (not (((C and D) -> D) and (A or (A or B))))) or ((A or (A or B)) -> (not (((C and D) -> D) and (A or (A or B)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-266, u:((Am (or A (or A B))) (C (not (and (-> (and Bm Cm) Cm) (or A (or A B))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-79008
in-theory        79008
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-270 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-79008.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-270, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79009
in-theory        79009
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-890 tm-271 ((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-4)
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-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-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-79009.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (((E and F) -> F) and D))), M:tm-890, m:tm-271, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-79010
in-theory        79010
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (D -> (C and D))) and (A or (A or B))))) or ((A or (A or B)) -> (not ((C -> (D -> (C and D))) and (A or (A or B)))))) -> (not (A or (A or B))))
theorem-size     46
proof            (modus-ponens tm-890 tm-299 ((Am (or A (or A B))) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or A (or A B))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-5)
proof-size       166
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-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-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-79010.        ((((A or B) -> (not ((C -> (D -> (C and D))) and (A or (A or B))))) or ((A or (A or B)) -> (not ((C -> (D -> (C and D))) and (A or (A or B)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-299, u:((Am (or A (or A B))) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or A (or A B))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-79011
in-theory        79011
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A or (A or B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-890 tm-303 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       149
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-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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-79011.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-303, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79012
in-theory        79012
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-890 tm-304 ((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       137
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-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-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-79012.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-890, m:tm-304, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-79013
in-theory        79013
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> ((A or (A or B)) -> C))))
theorem-size     31
proof            (modus-ponens tm-890 tm-305 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (-> (or A (or A B)) C))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-79013.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> ((A or (A or B)) -> C)))), M:tm-890, m:tm-305, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (-> (or A (or A B)) C)))))
================================================================
tm-name          tm-79014
in-theory        79014
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> D)) or ((A or (A or B)) -> (C -> D))) -> (((A or (A or B)) -> (C -> D)) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-890 tm-306 ((Am (or A (or A B))) (C (-> Bm Cm)) (D (and (-> (or A (or A B)) (-> Bm Cm)) (-> (-> (or A (or A B)) Bm) (-> (or A (or A B)) Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       173
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-79014.        ((((A or B) -> (C -> D)) or ((A or (A or B)) -> (C -> D))) -> (((A or (A or B)) -> (C -> D)) and (((A or (A or B)) -> C) -> ((A or (A or B)) -> D)))), M:tm-890, m:tm-306, u:((Am (or A (or A B))) (C (-> Bm Cm)) (D (and (-> (or A (or A B)) (-> Bm Cm)) (-> (-> (or A (or A B)) Bm) (-> (or A (or A B)) Cm)))))
================================================================
tm-name          tm-79015
in-theory        79015
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (((A or (A or B)) -> C) and D))))
theorem-size     33
proof            (modus-ponens tm-890 tm-309 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (and (-> (or A (or A B)) C) Bm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-79015.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (((A or (A or B)) -> C) and D)))), M:tm-890, m:tm-309, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (and (-> (or A (or A B)) C) Bm)))))
================================================================
tm-name          tm-79016
in-theory        79016
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((A or (A or B)) -> C) or D)))
theorem-size     31
proof            (modus-ponens tm-890 tm-310 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (or (-> (or A (or A B)) C) Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-79016.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((A or (A or B)) -> C) or D))), M:tm-890, m:tm-310, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (or (-> (or A (or A B)) C) Bm))))
================================================================
tm-name          tm-79017
in-theory        79017
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D or ((A or (A or B)) -> C))))
theorem-size     31
proof            (modus-ponens tm-890 tm-311 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (or Bm (-> (or A (or A B)) C))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-7)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-79017.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D or ((A or (A or B)) -> C)))), M:tm-890, m:tm-311, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (or Bm (-> (or A (or A B)) C)))))
================================================================
tm-name          tm-79018
in-theory        79018
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((C -> D) -> (((A or (A or B)) or C) -> D))))
theorem-size     35
proof            (modus-ponens tm-890 tm-312 ((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (-> Bm Cm) (-> (or (or A (or A B)) Bm) 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-79018.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((C -> D) -> (((A or (A or B)) or C) -> D)))), M:tm-890, m:tm-312, u:((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (-> Bm Cm) (-> (or (or A (or A B)) Bm) Cm)))))
================================================================
tm-name          tm-79019
in-theory        79019
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((A or (A or B)) -> (not C)) -> (not (A or (A or B))))))
theorem-size     37
proof            (modus-ponens tm-890 tm-313 ((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (-> (or A (or A B)) (not Bm)) (not (or A (or A B))))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-9)
proof-size       161
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-79019.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((A or (A or B)) -> (not C)) -> (not (A or (A or B)))))), M:tm-890, m:tm-313, u:((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (-> (or A (or A B)) (not Bm)) (not (or A (or A B)))))))
================================================================
tm-name          tm-79020
in-theory        79020
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (E -> D))))
theorem-size     27
proof            (modus-ponens tm-890 tm-315 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-79020.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (E -> D)))), M:tm-890, m:tm-315, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-79021
in-theory        79021
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((A or (A or B)) -> (A or (A or B)))))
theorem-size     33
proof            (modus-ponens tm-890 tm-316 ((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (or A (or A B)) (or A (or A B)))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-79021.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((A or (A or B)) -> (A or (A or B))))), M:tm-890, m:tm-316, u:((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (or A (or A B)) (or A (or A B))))))
================================================================
tm-name          tm-79022
in-theory        79022
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-890 tm-318 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-79022.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-890, m:tm-318, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-79023
in-theory        79023
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-890 tm-320 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-79023.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D and E) -> D))), M:tm-890, m:tm-320, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-79024
in-theory        79024
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D and E) -> E)))
theorem-size     27
proof            (modus-ponens tm-890 tm-322 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-79024.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D and E) -> E))), M:tm-890, m:tm-322, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-79025
in-theory        79025
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (E -> D)) and ((A or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-890 tm-323 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> Bm (-> Cm Bm)) (-> (or A (or A B)) C))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-79025.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (E -> D)) and ((A or (A or B)) -> C)))), M:tm-890, m:tm-323, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> Bm (-> Cm Bm)) (-> (or A (or A B)) C)))))
================================================================
tm-name          tm-79026
in-theory        79026
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> C))))
theorem-size     43
proof            (modus-ponens tm-890 tm-324 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (or A B)) C))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-79026.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (A or B)) -> C)))), M:tm-890, m:tm-324, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (or A B)) C)))))
================================================================
tm-name          tm-79027
in-theory        79027
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((D and E) -> D) and ((A or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-890 tm-325 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> (and Bm Cm) Bm) (-> (or A (or A B)) C))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-79027.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((D and E) -> D) and ((A or (A or B)) -> C)))), M:tm-890, m:tm-325, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> (and Bm Cm) Bm) (-> (or A (or A B)) C)))))
================================================================
tm-name          tm-79028
in-theory        79028
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((D and E) -> E) and ((A or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-890 tm-326 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> (and Bm Cm) Cm) (-> (or A (or A B)) C))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-79028.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((D and E) -> E) and ((A or (A or B)) -> C)))), M:tm-890, m:tm-326, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> (and Bm Cm) Cm) (-> (or A (or A B)) C)))))
================================================================
tm-name          tm-79029
in-theory        79029
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> C))))
theorem-size     37
proof            (modus-ponens tm-890 tm-327 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (or A B)) C))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-79029.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (E -> (D and E))) and ((A or (A or B)) -> C)))), M:tm-890, m:tm-327, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (or A B)) C)))))
================================================================
tm-name          tm-79030
in-theory        79030
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((A or (A or B)) -> ((A or (A or B)) and C))))
theorem-size     35
proof            (modus-ponens tm-890 tm-328 ((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (or A (or A B)) (and (or A (or A B)) Bm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-79030.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((A or (A or B)) -> ((A or (A or B)) and C)))), M:tm-890, m:tm-328, u:((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (or A (or A B)) (and (or A (or A B)) Bm)))))
================================================================
tm-name          tm-79031
in-theory        79031
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-338 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       149
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-79031.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-338, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79032
in-theory        79032
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-890 tm-340 ((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2 tm-5)
proof-size       137
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-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-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-79032.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> (D -> (D and E)))), M:tm-890, m:tm-340, u:((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-79033
in-theory        79033
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-890 tm-341 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-79033.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (E -> (D and E))))), M:tm-890, m:tm-341, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-79034
in-theory        79034
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> ((C -> ((A or (A or B)) and C)) -> D)) or ((A or (A or B)) -> ((C -> ((A or (A or B)) and C)) -> D))) -> ((A or (A or B)) -> D))
theorem-size     41
proof            (modus-ponens tm-890 tm-349 ((Am (or A (or A B))) (C (-> (-> Bm (and (or A (or A B)) Bm)) Cm)) (D (-> (or A (or A B)) Cm))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79034.        ((((A or B) -> ((C -> ((A or (A or B)) and C)) -> D)) or ((A or (A or B)) -> ((C -> ((A or (A or B)) and C)) -> D))) -> ((A or (A or B)) -> D)), M:tm-890, m:tm-349, u:((Am (or A (or A B))) (C (-> (-> Bm (and (or A (or A B)) Bm)) Cm)) (D (-> (or A (or A B)) Cm)))
================================================================
tm-name          tm-79035
in-theory        79035
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (D -> (C and D))))) or ((A or (A or B)) -> (not (C -> (D -> (C and D)))))) -> (not (A or (A or B))))
theorem-size     34
proof            (modus-ponens tm-890 tm-350 ((Am (or A (or A B))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-1 tm-5)
proof-size       148
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-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-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-79035.        ((((A or B) -> (not (C -> (D -> (C and D))))) or ((A or (A or B)) -> (not (C -> (D -> (C and D)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-350, u:((Am (or A (or A B))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-79036
in-theory        79036
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-354 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-79036.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-354, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79037
in-theory        79037
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (D -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-890 tm-355 ((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-5)
proof-size       139
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-79037.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (D -> (C and D)))), M:tm-890, m:tm-355, u:((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-79038
in-theory        79038
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-890 tm-356 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
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-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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-79038.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (F -> (E and F))))), M:tm-890, m:tm-356, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-79039
in-theory        79039
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> D)) or F) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-364 ((Am (-> (or A (or A B)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 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-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-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-79039.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> D)) or F) and ((A or (A or B)) -> C))), M:tm-890, m:tm-364, u:((Am (-> (or A (or A B)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79040
in-theory        79040
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-890 tm-365 ((Am (-> (or A (or A B)) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       121
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-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-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-79040.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> D)) or F)), M:tm-890, m:tm-365, u:((Am (-> (or A (or A B)) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-79041
in-theory        79041
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-890 tm-373 ((Am (-> (or A (or A B)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
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-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-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-79041.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A or (A or B)) -> C))), M:tm-890, m:tm-373, u:((Am (-> (or A (or A B)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79042
in-theory        79042
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-890 tm-374 ((Am (-> (or A (or A B)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-6 tm-1 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-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-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-79042.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-890, m:tm-374, u:((Am (-> (or A (or A B)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-79043
in-theory        79043
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D and E) -> D) or F) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-382 ((Am (-> (or A (or A B)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
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-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-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-79043.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D and E) -> D) or F) and ((A or (A or B)) -> C))), M:tm-890, m:tm-382, u:((Am (-> (or A (or A B)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79044
in-theory        79044
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-890 tm-383 ((Am (-> (or A (or A B)) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
proof-size       121
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-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-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-79044.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and E) -> D) or F)), M:tm-890, m:tm-383, u:((Am (-> (or A (or A B)) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-79045
in-theory        79045
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D and E) -> E) or F) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-391 ((Am (-> (or A (or A B)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
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-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-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-79045.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D and E) -> E) or F) and ((A or (A or B)) -> C))), M:tm-890, m:tm-391, u:((Am (-> (or A (or A B)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79046
in-theory        79046
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-890 tm-392 ((Am (-> (or A (or A B)) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
proof-size       121
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-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-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-79046.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D and E) -> E) or F)), M:tm-890, m:tm-392, u:((Am (-> (or A (or A B)) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-79047
in-theory        79047
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> (D and E))) or F) and ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-400 ((Am (-> (or A (or A B)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-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-79047.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E -> (D and E))) or F) and ((A or (A or B)) -> C))), M:tm-890, m:tm-400, u:((Am (-> (or A (or A B)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79048
in-theory        79048
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-890 tm-401 ((Am (-> (or A (or A B)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
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-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-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-79048.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (D and E))) or F)), M:tm-890, m:tm-401, u:((Am (-> (or A (or A B)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-79049
in-theory        79049
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (D or E)) or F) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-409 ((Am (-> (or A (or A B)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-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-79049.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (D or E)) or F) and ((A or (A or B)) -> C))), M:tm-890, m:tm-409, u:((Am (-> (or A (or A B)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79050
in-theory        79050
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-890 tm-410 ((Am (-> (or A (or A B)) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       121
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-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-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-79050.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (D or E)) or F)), M:tm-890, m:tm-410, u:((Am (-> (or A (or A B)) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-79051
in-theory        79051
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (D or E)) and ((A or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-890 tm-443 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> Bm (or Bm Cm)) (-> (or A (or A B)) C))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-79051.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (D or E)) and ((A or (A or B)) -> C)))), M:tm-890, m:tm-443, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> Bm (or Bm Cm)) (-> (or A (or A B)) C)))))
================================================================
tm-name          tm-79052
in-theory        79052
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (C or D)) and (A or (A or B))))) or ((A or (A or B)) -> (not ((C -> (C or D)) and (A or (A or B)))))) -> (not (A or (A or B))))
theorem-size     42
proof            (modus-ponens tm-890 tm-449 ((Am (or A (or A B))) (C (not (and (-> Bm (or Bm Cm)) (or A (or A B))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-5)
proof-size       156
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-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-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-79052.        ((((A or B) -> (not ((C -> (C or D)) and (A or (A or B))))) or ((A or (A or B)) -> (not ((C -> (C or D)) and (A or (A or B)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-449, u:((Am (or A (or A B))) (C (not (and (-> Bm (or Bm Cm)) (or A (or A B))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-79053
in-theory        79053
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-453 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-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-79053.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-453, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79054
in-theory        79054
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-890 tm-454 ((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
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-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-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-79054.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (E or F)) and D))), M:tm-890, m:tm-454, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-79055
in-theory        79055
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (D or E))))
theorem-size     27
proof            (modus-ponens tm-890 tm-456 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-79055.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (D or E)))), M:tm-890, m:tm-456, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-79056
in-theory        79056
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (((A or (A or B)) or C) -> D)) or ((A or (A or B)) -> (((A or (A or B)) or C) -> D))) -> ((A or (A or B)) -> D))
theorem-size     37
proof            (modus-ponens tm-890 tm-464 ((Am (or A (or A B))) (C (-> (or (or A (or A B)) Bm) Cm)) (D (-> (or A (or A B)) Cm))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79056.        ((((A or B) -> (((A or (A or B)) or C) -> D)) or ((A or (A or B)) -> (((A or (A or B)) or C) -> D))) -> ((A or (A or B)) -> D)), M:tm-890, m:tm-464, u:((Am (or A (or A B))) (C (-> (or (or A (or A B)) Bm) Cm)) (D (-> (or A (or A B)) Cm)))
================================================================
tm-name          tm-79057
in-theory        79057
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (C or D)))) or ((A or (A or B)) -> (not (C -> (C or D))))) -> (not (A or (A or B))))
theorem-size     30
proof            (modus-ponens tm-890 tm-465 ((Am (or A (or A B))) (C (not (-> Bm (or Bm Cm)))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-1)
proof-size       138
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-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-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-79057.        ((((A or B) -> (not (C -> (C or D)))) or ((A or (A or B)) -> (not (C -> (C or D))))) -> (not (A or (A or B)))), M:tm-890, m:tm-465, u:((Am (or A (or A B))) (C (not (-> Bm (or Bm Cm)))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-79058
in-theory        79058
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (E or F))) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-469 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 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-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-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-79058.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (E or F))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-469, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79059
in-theory        79059
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (C or D)))
theorem-size     23
proof            (modus-ponens tm-890 tm-470 ((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (or Bm Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
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-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-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-79059.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (C or D))), M:tm-890, m:tm-470, u:((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (or Bm Cm))))
================================================================
tm-name          tm-79060
in-theory        79060
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-890 tm-471 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       121
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-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-1.            (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-79060.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (E or F)))), M:tm-890, m:tm-471, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-79061
in-theory        79061
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (E -> (F -> E))) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-480 ((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7 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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-79061.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (E -> (F -> E))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-480, u:((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79062
in-theory        79062
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-890 tm-481 ((Am (-> (or A (or A B)) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       121
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-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-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-79062.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or (E -> (F -> E)))), M:tm-890, m:tm-481, u:((Am (-> (or A (or A B)) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-79063
in-theory        79063
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-890 tm-490 ((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7 tm-2)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-79063.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-490, u:((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79064
in-theory        79064
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-890 tm-491 ((Am (-> (or A (or A B)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7 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-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-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-79064.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-890, m:tm-491, u:((Am (-> (or A (or A B)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-79065
in-theory        79065
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or ((E and F) -> E)) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-500 ((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7 tm-3)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-79065.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or ((E and F) -> E)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-500, u:((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79066
in-theory        79066
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-890 tm-501 ((Am (-> (or A (or A B)) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7 tm-3)
proof-size       121
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-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-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-79066.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((E and F) -> E))), M:tm-890, m:tm-501, u:((Am (-> (or A (or A B)) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-79067
in-theory        79067
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or ((E and F) -> F)) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-510 ((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7 tm-4)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-79067.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or ((E and F) -> F)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-510, u:((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79068
in-theory        79068
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-890 tm-511 ((Am (-> (or A (or A B)) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7 tm-4)
proof-size       121
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-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-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-79068.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((E and F) -> F))), M:tm-890, m:tm-511, u:((Am (-> (or A (or A B)) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-79069
in-theory        79069
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-520 ((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-79069.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-520, u:((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79070
in-theory        79070
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-890 tm-521 ((Am (-> (or A (or A B)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7 tm-5)
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-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-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-79070.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or (E -> (F -> (E and F))))), M:tm-890, m:tm-521, u:((Am (-> (or A (or A B)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-79071
in-theory        79071
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (E -> (E or F))) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-530 ((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-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-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-79071.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (E -> (E or F))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-530, u:((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79072
in-theory        79072
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-890 tm-531 ((Am (-> (or A (or A B)) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       121
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-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-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-79072.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or (E -> (E or F)))), M:tm-890, m:tm-531, u:((Am (-> (or A (or A B)) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-79073
in-theory        79073
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (E -> (F or E))) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-540 ((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-79073.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (E -> (F or E))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-540, u:((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79074
in-theory        79074
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-890 tm-541 ((Am (-> (or A (or A B)) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       121
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-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-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-79074.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or (E -> (F or E)))), M:tm-890, m:tm-541, u:((Am (-> (or A (or A B)) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-79075
in-theory        79075
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E or D)) or F) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-550 ((Am (-> (or A (or A B)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-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-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-79075.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E or D)) or F) and ((A or (A or B)) -> C))), M:tm-890, m:tm-550, u:((Am (-> (or A (or A B)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79076
in-theory        79076
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-890 tm-551 ((Am (-> (or A (or A B)) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       121
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-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-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-79076.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E or D)) or F)), M:tm-890, m:tm-551, u:((Am (-> (or A (or A B)) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-79077
in-theory        79077
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (E or D)) and ((A or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-890 tm-595 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> Bm (or Cm Bm)) (-> (or A (or A B)) C))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-79077.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((D -> (E or D)) and ((A or (A or B)) -> C)))), M:tm-890, m:tm-595, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (and (-> Bm (or Cm Bm)) (-> (or A (or A B)) C)))))
================================================================
tm-name          tm-79078
in-theory        79078
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (D or C)) and (A or (A or B))))) or ((A or (A or B)) -> (not ((C -> (D or C)) and (A or (A or B)))))) -> (not (A or (A or B))))
theorem-size     42
proof            (modus-ponens tm-890 tm-601 ((Am (or A (or A B))) (C (not (and (-> Bm (or Cm Bm)) (or A (or A B))))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-5 tm-7)
proof-size       156
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-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-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-79078.        ((((A or B) -> (not ((C -> (D or C)) and (A or (A or B))))) or ((A or (A or B)) -> (not ((C -> (D or C)) and (A or (A or B)))))) -> (not (A or (A or B)))), M:tm-890, m:tm-601, u:((Am (or A (or A B))) (C (not (and (-> Bm (or Cm Bm)) (or A (or A B))))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-79079
in-theory        79079
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-605 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-79079.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-605, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79080
in-theory        79080
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-890 tm-606 ((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-7)
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-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-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-79080.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> ((E -> (F or E)) and D))), M:tm-890, m:tm-606, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-79081
in-theory        79081
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (E or D))))
theorem-size     27
proof            (modus-ponens tm-890 tm-609 ((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-79081.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (D -> (E or D)))), M:tm-890, m:tm-609, u:((Am (-> (or A (or A B)) C)) (D (and (-> (or A (or A B)) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-79082
in-theory        79082
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> ((C or (A or (A or B))) -> D)) or ((A or (A or B)) -> ((C or (A or (A or B))) -> D))) -> ((A or (A or B)) -> D))
theorem-size     37
proof            (modus-ponens tm-890 tm-617 ((Am (or A (or A B))) (C (-> (or Bm (or A (or A B))) Cm)) (D (-> (or A (or A B)) Cm))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79082.        ((((A or B) -> ((C or (A or (A or B))) -> D)) or ((A or (A or B)) -> ((C or (A or (A or B))) -> D))) -> ((A or (A or B)) -> D)), M:tm-890, m:tm-617, u:((Am (or A (or A B))) (C (-> (or Bm (or A (or A B))) Cm)) (D (-> (or A (or A B)) Cm)))
================================================================
tm-name          tm-79083
in-theory        79083
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (D or C)))) or ((A or (A or B)) -> (not (C -> (D or C))))) -> (not (A or (A or B))))
theorem-size     30
proof            (modus-ponens tm-890 tm-618 ((Am (or A (or A B))) (C (not (-> Bm (or Cm Bm)))) (D (not (or A (or A B))))))
axioms-used      (tm-8 tm-6 tm-9 tm-1 tm-7)
proof-size       138
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-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-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-79083.        ((((A or B) -> (not (C -> (D or C)))) or ((A or (A or B)) -> (not (C -> (D or C))))) -> (not (A or (A or B)))), M:tm-890, m:tm-618, u:((Am (or A (or A B))) (C (not (-> Bm (or Cm Bm)))) (D (not (or A (or A B)))))
================================================================
tm-name          tm-79084
in-theory        79084
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (F or E))) and ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-890 tm-622 ((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-79084.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> (E -> (F or E))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-622, u:((Am (-> (or A (or A B)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79085
in-theory        79085
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (D or C)))
theorem-size     23
proof            (modus-ponens tm-890 tm-623 ((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (or Cm Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-7)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-79085.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> (D or C))), M:tm-890, m:tm-623, u:((Am (or A (or A B))) (C Bm) (D (-> (or A (or A B)) (or Cm Bm))))
================================================================
tm-name          tm-79086
in-theory        79086
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-890 tm-624 ((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       121
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-79086.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D -> (E -> (F or E)))), M:tm-890, m:tm-624, u:((Am (-> (or A (or A B)) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-79087
in-theory        79087
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-890 tm-665 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       159
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-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-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-79087.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-665, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79088
in-theory        79088
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-890 tm-667 ((Am (-> (or A (or A B)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-6 tm-1)
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-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-1.            (A -> (B -> A)), 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-79088.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-890, m:tm-667, u:((Am (-> (or A (or A B)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-79089
in-theory        79089
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A or (A or B)) -> C)))
theorem-size     47
proof            (modus-ponens tm-890 tm-708 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       203
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-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-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-79089.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-708, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79090
in-theory        79090
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (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-890 tm-710 ((Am (-> (or 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-6 tm-1 tm-2)
proof-size       191
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-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-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-79090.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-890, m:tm-710, u:((Am (-> (or A (or A B)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-79091
in-theory        79091
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((((A or (A or B)) and D) or (A or (A or B))) -> C)))
theorem-size     37
proof            (modus-ponens tm-890 tm-747 ((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (or (and (or A (or A B)) Cm) (or A (or A B))) Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-79091.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((((A or (A or B)) and D) or (A or (A or B))) -> C))), M:tm-890, m:tm-747, u:((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (or (and (or A (or A B)) Cm) (or A (or A B))) Bm))))
================================================================
tm-name          tm-79092
in-theory        79092
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A or (A or B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-890 tm-757 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 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-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-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-79092.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-757, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79093
in-theory        79093
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-890 tm-759 ((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
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-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-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-79093.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-890, m:tm-759, u:((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-79094
in-theory        79094
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((D and (A or (A or B))) or (A or (A or B))) -> C)))
theorem-size     37
proof            (modus-ponens tm-890 tm-798 ((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (or (and Cm (or A (or A B))) (or A (or A B))) Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-79094.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((D and (A or (A or B))) or (A or (A or B))) -> C))), M:tm-890, m:tm-798, u:((Am (or A (or A B))) (C Bm) (D (and (-> (or A (or A B)) Bm) (-> (or (and Cm (or A (or A B))) (or A (or A B))) Bm))))
================================================================
tm-name          tm-79095
in-theory        79095
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A or (A or B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-890 tm-808 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-79095.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-808, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79096
in-theory        79096
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-890 tm-810 ((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-79096.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-890, m:tm-810, u:((Am (-> (or A (or A B)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-79097
in-theory        79097
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A or (A or B)) -> C)))
theorem-size     39
proof            (modus-ponens tm-890 tm-855 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       173
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-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-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-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-79097.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-855, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-79098
in-theory        79098
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-890 tm-857 ((Am (-> (or A (or A B)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       161
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-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-1.            (A -> (B -> A)), 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-79098.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-890, m:tm-857, u:((Am (-> (or A (or A B)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-79099
in-theory        79099
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((A or (A or (A or B))) -> C)))
theorem-size     31
proof            (modus-ponens tm-890 tm-882 ((A Am) (Bm (or Am B)) (C Cm) (D (and (-> (or Am (or Am B)) Cm) (-> (or Am (or Am (or Am B))) Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and 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-79099.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and ((A or (A or (A or B))) -> C))), M:tm-890, m:tm-882, u:((A Am) (Bm (or Am B)) (C Cm) (D (and (-> (or Am (or Am B)) Cm) (-> (or Am (or Am (or Am B))) Cm))))
================================================================
tm-name          tm-79100
in-theory        79100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-855 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79100.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-855, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79101
in-theory        79101
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> (D and ((A or (A or B)) -> C))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D and ((A or (A or B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-850 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (Dm (and B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (and B (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79101.        ((((A or (A or B)) -> C) -> (D and ((A or (A or B)) -> C))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D and ((A or (A or B)) -> C)))), M:tm-850, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (Dm (and B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (and B (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79102
in-theory        79102
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> (D and ((A or (A or B)) -> C))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D and ((A or (A or B)) -> C)))) and ((D or (((A or (A or B)) -> C) -> (D and ((A or (A or B)) -> C)))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D and ((A or (A or B)) -> C)))))
theorem-size     85
proof            (modus-ponens tm-844 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (Dm (and B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (and B (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79102.        (((((A or (A or B)) -> C) -> (D and ((A or (A or B)) -> C))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D and ((A or (A or B)) -> C)))) and ((D or (((A or (A or B)) -> C) -> (D and ((A or (A or B)) -> C)))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D and ((A or (A or B)) -> C))))), M:tm-844, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (Dm (and B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (and B (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79103
in-theory        79103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-808 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79103.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-808, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79104
in-theory        79104
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((E and (((A or (A or B)) -> C) -> D)) or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))
theorem-size     63
proof            (modus-ponens tm-798 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79104.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((E and (((A or (A or B)) -> C) -> D)) or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))), M:tm-798, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79105
in-theory        79105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-757 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-79105.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-757, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79106
in-theory        79106
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((((((A or (A or B)) -> C) -> D) and E) or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))
theorem-size     63
proof            (modus-ponens tm-747 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-79106.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((((((A or (A or B)) -> C) -> D) and E) or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))), M:tm-747, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79107
in-theory        79107
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-708 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79107.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H))), M:tm-708, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79108
in-theory        79108
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> ((A or (A or B)) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> D)))
theorem-size     37
proof            (modus-ponens tm-703 tm-890 ((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or Am (or Am Bm)) C)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or Am (or Am Bm)) C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79108.        ((((A or (A or B)) -> C) -> ((A or (A or B)) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> D))), M:tm-703, m:tm-890, u:((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or Am (or Am Bm)) C)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or Am (or Am Bm)) C))))
================================================================
tm-name          tm-79109
in-theory        79109
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> ((A or (A or B)) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> D))) and ((((A or (A or B)) -> (C -> D)) or (((A or (A or B)) -> C) -> ((A or (A or B)) -> D))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> D))))
theorem-size     85
proof            (modus-ponens tm-697 tm-890 ((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or Am (or Am Bm)) C)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or Am (or Am Bm)) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79109.        (((((A or (A or B)) -> C) -> ((A or (A or B)) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> D))) and ((((A or (A or B)) -> (C -> D)) or (((A or (A or B)) -> C) -> ((A or (A or B)) -> D))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> D)))), M:tm-697, m:tm-890, u:((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or Am (or Am Bm)) C)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or Am (or Am Bm)) C))))
================================================================
tm-name          tm-79110
in-theory        79110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-665 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-79110.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-665, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79111
in-theory        79111
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((D or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))
theorem-size     53
proof            (modus-ponens tm-654 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (B Dm) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-79111.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((D or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))), M:tm-654, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (B Dm) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79112
in-theory        79112
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> (E or ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-623 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79112.        ((((A or (A or B)) -> C) -> D) -> (E or ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))), M:tm-623, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79113
in-theory        79113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-622 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79113.        ((A -> (B -> (C or B))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-622, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79114
in-theory        79114
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (B or C)) -> D) -> (E or ((B or (B or C)) -> D)))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (E or ((B or (B or C)) -> D))))
theorem-size     43
proof            (modus-ponens tm-619 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (Dm (or B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (or B (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 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-7.            (A -> (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-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-79114.        ((A or (((B or (B or C)) -> D) -> (E or ((B or (B or C)) -> D)))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (E or ((B or (B or C)) -> D)))), M:tm-619, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (Dm (or B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (or B (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79115
in-theory        79115
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-79115.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79116
in-theory        79116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-605 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79116.        ((A -> ((B -> (C or B)) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-605, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79117
in-theory        79117
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (F or E)) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-595 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-79117.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (F or E)) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-595, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79118
in-theory        79118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-550 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-49.           (((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-79118.        (((A -> (B or A)) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-550, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79119
in-theory        79119
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-540 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79119.        ((A or (B -> (C or B))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-540, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79120
in-theory        79120
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-530 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-49.           (((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-79120.        ((A or (B -> (B or C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-530, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79121
in-theory        79121
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-520 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79121.        ((A or (B -> (C -> (B and C)))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-520, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79122
in-theory        79122
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-510 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79122.        ((A or ((B and C) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-510, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79123
in-theory        79123
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-500 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79123.        ((A or ((B and C) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-500, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79124
in-theory        79124
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-490 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79124.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H))), M:tm-490, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79125
in-theory        79125
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-480 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79125.        ((A or (B -> (C -> B))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-480, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79126
in-theory        79126
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> (((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) 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-49.           (((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-79126.        ((((A or (A or B)) -> C) -> D) -> (((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) or E)), M:tm-470, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79127
in-theory        79127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-469 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) 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-49.           (((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-79127.        ((A -> (B -> (B or C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-469, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79128
in-theory        79128
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (B or C)) -> D) -> (((B or (B or C)) -> D) or E))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (((B or (B or C)) -> D) or E)))
theorem-size     43
proof            (modus-ponens tm-466 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (Dm (or (-> (or Am (or Am Bm)) Cm) B)) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (or (-> (or Am (or Am Bm)) 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-49.           (((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-79128.        ((A or (((B or (B or C)) -> D) -> (((B or (B or C)) -> D) or E))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (((B or (B or C)) -> D) or E))), M:tm-466, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (Dm (or (-> (or Am (or Am Bm)) Cm) B)) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (or (-> (or Am (or Am Bm)) Cm) B))))
================================================================
tm-name          tm-79129
in-theory        79129
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) 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-49.           (((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-79129.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79130
in-theory        79130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-453 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-79130.        ((A -> ((B -> (B or C)) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-453, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79131
in-theory        79131
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (E or F)) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-443 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-79131.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (E or F)) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-443, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79132
in-theory        79132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-409 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-79132.        (((A -> (A or B)) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-409, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79133
in-theory        79133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-400 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-79133.        (((A -> (B -> (A and B))) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-400, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79134
in-theory        79134
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-391 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-49.           (((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-79134.        ((((A and B) -> B) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-391, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79135
in-theory        79135
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-382 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-49.           (((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-79135.        ((((A and B) -> A) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-382, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79136
in-theory        79136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-373 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-79136.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H))), M:tm-373, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79137
in-theory        79137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-364 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) 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-49.           (((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-79137.        (((A -> (B -> A)) or C) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-364, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79138
in-theory        79138
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> (E -> (((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) and E)))
theorem-size     29
proof            (modus-ponens tm-355 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-79138.        ((((A or (A or B)) -> C) -> D) -> (E -> (((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) and E))), M:tm-355, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79139
in-theory        79139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-354 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79139.        ((A -> (B -> (C -> (B and C)))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-354, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79140
in-theory        79140
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (B or C)) -> D) -> (E -> (((B or (B or C)) -> D) and E)))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (E -> (((B or (B or C)) -> D) and E))))
theorem-size     47
proof            (modus-ponens tm-351 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (Dm (-> B (and (-> (or Am (or Am Bm)) Cm) B))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> B (and (-> (or Am (or Am Bm)) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79140.        ((A or (((B or (B or C)) -> D) -> (E -> (((B or (B or C)) -> D) and E)))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (E -> (((B or (B or C)) -> D) and E)))), M:tm-351, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (Dm (-> B (and (-> (or Am (or Am Bm)) Cm) B))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> B (and (-> (or Am (or Am Bm)) Cm) B)))))
================================================================
tm-name          tm-79141
in-theory        79141
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-79141.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79142
in-theory        79142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-338 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-79142.        (((A -> B) -> (A -> (A and B))) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F))), M:tm-338, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79143
in-theory        79143
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) or (((A or (A or B)) -> C) -> (((A or (A or B)) -> C) and D))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and D)))
theorem-size     51
proof            (modus-ponens tm-335 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (Dm (and (-> (or Am (or Am Bm)) Cm) B)) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (and (-> (or Am (or Am Bm)) Cm) B)))))
axioms-used      (tm-8 tm-2 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-5.            (A -> (B -> (A and B))), axiom
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-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-79143.        (((((A or (A or B)) -> C) -> D) or (((A or (A or B)) -> C) -> (((A or (A or B)) -> C) and D))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and D))), M:tm-335, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (Dm (and (-> (or Am (or Am Bm)) Cm) B)) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (and (-> (or Am (or Am Bm)) Cm) B))))
================================================================
tm-name          tm-79144
in-theory        79144
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((((A or (A or B)) -> C) -> D) -> ((((A or (A or B)) -> C) -> D) and ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-328 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) 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-328.          ((A -> 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-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-79144.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((((A or (A or B)) -> C) -> D) -> ((((A or (A or B)) -> C) -> D) and ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-328, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79145
in-theory        79145
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     59
proof            (modus-ponens tm-327 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-79145.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-327, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79146
in-theory        79146
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((E and F) -> F) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-326 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-79146.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((E and F) -> F) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-326, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79147
in-theory        79147
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((E and F) -> E) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-325 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-79147.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((E and F) -> E) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-325, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79148
in-theory        79148
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     65
proof            (modus-ponens tm-324 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79148.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-324, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79149
in-theory        79149
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (F -> E)) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-323 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-79149.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (F -> E)) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-323, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79150
in-theory        79150
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-79150.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79151
in-theory        79151
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-79151.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79152
in-theory        79152
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-79152.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79153
in-theory        79153
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((((A or (A or B)) -> C) -> D) -> (((A or (A or B)) -> C) -> D)))
theorem-size     45
proof            (modus-ponens tm-316 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-79153.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((((A or (A or B)) -> C) -> D) -> (((A or (A or B)) -> C) -> D))), M:tm-316, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79154
in-theory        79154
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-79154.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79155
in-theory        79155
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((((A or (A or B)) -> C) -> D) -> (not ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))) -> (not (((A or (A or B)) -> C) -> D))))
theorem-size     63
proof            (modus-ponens tm-313 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79155.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((((A or (A or B)) -> C) -> D) -> (not ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))) -> (not (((A or (A or B)) -> C) -> D)))), M:tm-313, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79156
in-theory        79156
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) -> E) -> (((((A or (A or B)) -> C) -> D) or ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) -> E)))
theorem-size     71
proof            (modus-ponens tm-312 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79156.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and ((((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) -> E) -> (((((A or (A or B)) -> C) -> D) or ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) -> E))), M:tm-312, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79157
in-theory        79157
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E or ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-311 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-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-79157.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E or ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-311, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79158
in-theory        79158
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (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-6.            (A -> (A or 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-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-79158.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) or E)), M:tm-310, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79159
in-theory        79159
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) 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-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-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-79159.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and E))), M:tm-309, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79160
in-theory        79160
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((((A or (A or B)) -> C) -> D) -> (((A or B) -> C) or ((A or (A or B)) -> C))) -> ((((A or (A or B)) -> C) -> D) -> D)))
theorem-size     61
proof            (modus-ponens tm-306 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79160.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (((((A or (A or B)) -> C) -> D) -> (((A or B) -> C) or ((A or (A or B)) -> C))) -> ((((A or (A or B)) -> C) -> D) -> D))), M:tm-306, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (C Dm))
================================================================
tm-name          tm-79161
in-theory        79161
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-305 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-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-79161.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) and (E -> ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))), M:tm-305, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79162
in-theory        79162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-303 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79162.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-303, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79163
in-theory        79163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-270 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79163.        ((A -> (((B and C) -> C) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-270, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79164
in-theory        79164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-239 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79164.        ((A -> (((B and C) -> B) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-239, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79165
in-theory        79165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H)))
theorem-size     43
proof            (modus-ponens tm-210 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
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-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-79165.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H))), M:tm-210, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79166
in-theory        79166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-183 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79166.        ((A -> ((B -> (C -> B)) and A)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-183, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79167
in-theory        79167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-157 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79167.        ((A -> ((B and C) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-157, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79168
in-theory        79168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-147 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79168.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-147, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79169
in-theory        79169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-134 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79169.        ((A -> ((B and C) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-134, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79170
in-theory        79170
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-125 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79170.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-125, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79171
in-theory        79171
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> (D -> E)) -> (((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> E)))
theorem-size     43
proof            (modus-ponens tm-114 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) (-> C D))) (B (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79171.        ((((A or (A or B)) -> C) -> (D -> E)) -> (((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> E))), M:tm-114, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) (-> C D))) (B (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-79172
in-theory        79172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-113 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79172.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H))), M:tm-113, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79173
in-theory        79173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (B or C)) -> (D -> E)) -> (((B or (B or C)) -> D) -> ((B or (B or C)) -> E)))) -> ((((B or C) -> (D -> E)) or ((B or (B or C)) -> (D -> E))) -> (((B or (B or C)) -> D) -> ((B or (B or C)) -> E))))
theorem-size     61
proof            (modus-ponens tm-110 tm-890 ((A (or Am (or Am Bm))) (Cm (-> B C)) (Dm (-> (-> (or Am (or Am Bm)) B) (-> (or Am (or Am Bm)) C))) (D (-> (or (-> (or Am Bm) (-> B C)) (-> (or Am (or Am Bm)) (-> B C))) (-> (-> (or Am (or Am Bm)) B) (-> (or Am (or Am Bm)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79173.        ((A or (((B or (B or C)) -> (D -> E)) -> (((B or (B or C)) -> D) -> ((B or (B or C)) -> E)))) -> ((((B or C) -> (D -> E)) or ((B or (B or C)) -> (D -> E))) -> (((B or (B or C)) -> D) -> ((B or (B or C)) -> E)))), M:tm-110, m:tm-890, u:((A (or Am (or Am Bm))) (Cm (-> B C)) (Dm (-> (-> (or Am (or Am Bm)) B) (-> (or Am (or Am Bm)) C))) (D (-> (or (-> (or Am Bm) (-> B C)) (-> (or Am (or Am Bm)) (-> B C))) (-> (-> (or Am (or Am Bm)) B) (-> (or Am (or Am Bm)) C)))))
================================================================
tm-name          tm-79174
in-theory        79174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-105 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79174.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-105, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79175
in-theory        79175
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> (C -> D)) -> ((A or (A or B)) -> C)) or (((A or (A or B)) -> (C -> D)) -> ((A or (A or B)) -> D))) -> ((((A or B) -> (C -> D)) or ((A or (A or B)) -> (C -> D))) -> ((A or (A or B)) -> D)))
theorem-size     61
proof            (modus-ponens tm-102 tm-890 ((A (or Am (or Am Bm))) (Cm (-> B C)) (Dm (-> (or Am (or Am Bm)) C)) (D (-> (or (-> (or Am Bm) (-> B C)) (-> (or Am (or Am Bm)) (-> B C))) (-> (or Am (or Am Bm)) C)))))
axioms-used      (tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79175.        (((((A or (A or B)) -> (C -> D)) -> ((A or (A or B)) -> C)) or (((A or (A or B)) -> (C -> D)) -> ((A or (A or B)) -> D))) -> ((((A or B) -> (C -> D)) or ((A or (A or B)) -> (C -> D))) -> ((A or (A or B)) -> D))), M:tm-102, m:tm-890, u:((A (or Am (or Am Bm))) (Cm (-> B C)) (Dm (-> (or Am (or Am Bm)) C)) (D (-> (or (-> (or Am Bm) (-> B C)) (-> (or Am (or Am Bm)) (-> B C))) (-> (or Am (or Am Bm)) C))))
================================================================
tm-name          tm-79176
in-theory        79176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-95 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-79176.        (((A -> B) -> (A -> A)) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F))), M:tm-95, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79177
in-theory        79177
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) or (((A or (A or B)) -> C) -> ((A or (A or B)) -> C))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> C)))
theorem-size     47
proof            (modus-ponens tm-92 tm-890 ((Dm (-> (or Am (or Am Bm)) Cm)) (A (-> (or Am (or Am Bm)) Cm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79177.        (((((A or (A or B)) -> C) -> D) or (((A or (A or B)) -> C) -> ((A or (A or B)) -> C))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> C))), M:tm-92, m:tm-890, u:((Dm (-> (or Am (or Am Bm)) Cm)) (A (-> (or Am (or Am Bm)) Cm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-79178
in-theory        79178
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> (E -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-84 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79178.        ((((A or (A or B)) -> C) -> D) -> (E -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))), M:tm-84, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79179
in-theory        79179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-83 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79179.        ((A -> (B -> (C -> B))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-83, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79180
in-theory        79180
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (B or C)) -> D) -> (E -> ((B or (B or C)) -> D)))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (E -> ((B or (B or C)) -> D))))
theorem-size     43
proof            (modus-ponens tm-80 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (Dm (-> B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> B (-> (or Am (or Am Bm)) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-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-79180.        ((A or (((B or (B or C)) -> D) -> (E -> ((B or (B or C)) -> D)))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (E -> ((B or (B or C)) -> D)))), M:tm-80, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (Dm (-> B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> B (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79181
in-theory        79181
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or (B or C)) -> D) -> E) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-76 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79181.        (((not (not A)) -> A) and ((((B or (B or C)) -> D) -> E) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E))), M:tm-76, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79182
in-theory        79182
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A or (A or B)) -> C) -> D))) or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-73 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79182.        (((not (not (((A or (A or B)) -> C) -> D))) or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)), M:tm-73, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79183
in-theory        79183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-69 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79183.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F))), M:tm-69, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79184
in-theory        79184
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) or (((A or (A or B)) -> (not C)) -> (not (A or (A or B))))) -> ((((A or B) -> (not C)) or ((A or (A or B)) -> (not C))) -> (not (A or (A or B)))))
theorem-size     46
proof            (modus-ponens tm-66 tm-890 ((A (or Am (or Am Bm))) (Cm (not B)) (Dm (not (or Am (or Am Bm)))) (C (-> (or (-> (or Am Bm) (not B)) (-> (or Am (or Am Bm)) (not B))) (not (or Am (or Am Bm)))))))
axioms-used      (tm-8 tm-9 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79184.        ((((A or (A or B)) -> C) or (((A or (A or B)) -> (not C)) -> (not (A or (A or B))))) -> ((((A or B) -> (not C)) or ((A or (A or B)) -> (not C))) -> (not (A or (A or B))))), M:tm-66, m:tm-890, u:((A (or Am (or Am Bm))) (Cm (not B)) (Dm (not (or Am (or Am Bm)))) (C (-> (or (-> (or Am Bm) (not B)) (-> (or Am (or Am Bm)) (not B))) (not (or Am (or Am Bm))))))
================================================================
tm-name          tm-79185
in-theory        79185
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> (((A or B) -> C) or ((A or (A or B)) -> C))) -> ((((A or (A or B)) -> C) or (((A or B) -> C) or ((A or (A or B)) -> C))) -> (((A or B) -> C) or ((A or (A or B)) -> C))))
theorem-size     57
proof            (modus-ponens tm-55 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (Dm (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (B (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (C (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79185.        ((((A or (A or B)) -> C) -> (((A or B) -> C) or ((A or (A or B)) -> C))) -> ((((A or (A or B)) -> C) or (((A or B) -> C) or ((A or (A or B)) -> C))) -> (((A or B) -> C) or ((A or (A or B)) -> C)))), M:tm-55, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (Dm (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (B (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (C (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-79186
in-theory        79186
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-54 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79186.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-54, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79187
in-theory        79187
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or (B or C))) or (((B or (B or C)) -> D) -> ((A or (B or (B or C))) -> D))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> ((A or (B or (B or C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-51 tm-890 ((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or C (or Am (or Am Bm))) Cm)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or C (or Am (or Am Bm))) Cm)))))
axioms-used      (tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79187.        (((A -> (B or (B or C))) or (((B or (B or C)) -> D) -> ((A or (B or (B or C))) -> D))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> ((A or (B or (B or C))) -> D))), M:tm-51, m:tm-890, u:((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or C (or Am (or Am Bm))) Cm)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or C (or Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-79188
in-theory        79188
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or (B or C)) -> D) -> (A and ((B or (B or C)) -> D)))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (A and ((B or (B or C)) -> D))))
theorem-size     43
proof            (modus-ponens tm-48 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (Dm (and B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (and B (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79188.        ((A or (((B or (B or C)) -> D) -> (A and ((B or (B or C)) -> D)))) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> (A and ((B or (B or C)) -> D)))), M:tm-48, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (Dm (and B (-> (or Am (or Am Bm)) Cm))) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (and B (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79189
in-theory        79189
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B or (B or C)) -> D) -> E)) or (((B or (B or C)) -> D) -> E)) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-47 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79189.        (((A and (((B or (B or C)) -> D) -> E)) or (((B or (B or C)) -> D) -> E)) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E)), M:tm-47, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79190
in-theory        79190
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or (A or B)) -> C) -> D) and E) or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-46 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79190.        ((((((A or (A or B)) -> C) -> D) and E) or (((A or (A or B)) -> C) -> D)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)), M:tm-46, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79191
in-theory        79191
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> (C -> D)) or (((A or (A or B)) -> C) -> ((A or (A or B)) -> D))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> D)))
theorem-size     47
proof            (modus-ponens tm-45 tm-890 ((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or Am (or Am Bm)) C)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or Am (or Am Bm)) C)))))
axioms-used      (tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79191.        ((((A or (A or B)) -> (C -> D)) or (((A or (A or B)) -> C) -> ((A or (A or B)) -> D))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((A or (A or B)) -> D))), M:tm-45, m:tm-890, u:((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or Am (or Am Bm)) C)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or Am (or Am Bm)) C))))
================================================================
tm-name          tm-79192
in-theory        79192
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or (B or C)) -> D) -> A)) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> A))
theorem-size     27
proof            (modus-ponens tm-44 tm-890 ((A (-> (or Am (or Am Bm)) Cm)) (B Dm) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79192.        ((A or (((B or (B or C)) -> D) -> A)) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> A)), M:tm-44, m:tm-890, u:((A (-> (or Am (or Am Bm)) Cm)) (B Dm) (C (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79193
in-theory        79193
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-42 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79193.        ((A -> (B or A)) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F))), M:tm-42, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79194
in-theory        79194
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-32 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-49.           (((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-79194.        ((A -> (A or B)) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F))), M:tm-32, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79195
in-theory        79195
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> ((((A or (A or B)) -> C) -> D) and ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))
theorem-size     35
proof            (modus-ponens tm-24 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79195.        ((((A or (A or B)) -> C) -> D) -> ((((A or (A or B)) -> C) -> D) and ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))), M:tm-24, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79196
in-theory        79196
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-23 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-79196.        ((A -> (B -> (A and B))) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F))), M:tm-23, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79197
in-theory        79197
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-22 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79197.        (((A and B) -> B) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F))), M:tm-22, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79198
in-theory        79198
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-21 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79198.        (((A and B) -> A) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F))), M:tm-21, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79199
in-theory        79199
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-20 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79199.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-20, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79200
in-theory        79200
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-19 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79200.        ((A -> (B -> A)) and ((((C or (C or D)) -> E) -> F) -> ((((C or D) -> E) or ((C or (C or D)) -> E)) -> F))), M:tm-19, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79201
in-theory        79201
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> (((A or (A or B)) -> C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79201.        ((((A or (A or B)) -> C) -> D) -> (((A or (A or B)) -> C) -> D)), M:tm-12, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79202
in-theory        79202
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> (not ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))) -> (not (((A or (A or B)) -> C) -> D)))
theorem-size     37
proof            (modus-ponens tm-9 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79202.        (((((A or (A or B)) -> C) -> D) -> (not ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))) -> (not (((A or (A or B)) -> C) -> D))), M:tm-9, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79203
in-theory        79203
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) -> E) -> (((((A or (A or B)) -> C) -> D) or ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) -> E))
theorem-size     45
proof            (modus-ponens tm-8 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-6)
proof-size       127
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-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-79203.        ((((((A or B) -> C) or ((A or (A or B)) -> C)) -> D) -> E) -> (((((A or (A or B)) -> C) -> D) or ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) -> E)), M:tm-8, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79204
in-theory        79204
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B or (B or C)) -> D) -> E) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-7 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79204.        (A or ((((B or (B or C)) -> D) -> E) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E))), M:tm-7, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79205
in-theory        79205
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-6 tm-8)
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-49.           (((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-79205.        (((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)) or E), M:tm-6, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79206
in-theory        79206
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B or (B or C)) -> D) -> E) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79206.        (A -> (((((B or (B or C)) -> D) -> E) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E)) and A)), M:tm-5, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79207
in-theory        79207
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> D) -> (((A or B) -> C) or ((A or (A or B)) -> C))) -> ((((A or (A or B)) -> C) -> D) -> D))
theorem-size     35
proof            (modus-ponens tm-2 tm-890 ((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79207.        (((((A or (A or B)) -> C) -> D) -> (((A or B) -> C) or ((A or (A or B)) -> C))) -> ((((A or (A or B)) -> C) -> D) -> D)), M:tm-2, m:tm-890, u:((A (-> (-> (or Am (or Am Bm)) Cm) Dm)) (B (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (C Dm))
================================================================
tm-name          tm-79208
in-theory        79208
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B or (B or C)) -> D) -> E) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-1 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-6)
proof-size       101
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-49.           (((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-79208.        (A -> ((((B or (B or C)) -> D) -> E) -> ((((B or C) -> D) or ((B or (B or C)) -> D)) -> E))), M:tm-1, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79209
in-theory        79209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-855 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-79209.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-855, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79210
in-theory        79210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-808 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-6)
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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-79210.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-808, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79211
in-theory        79211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-757 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79211.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-757, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79212
in-theory        79212
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) -> ((F or (F or G)) -> H))))
theorem-size     41
proof            (modus-ponens tm-708 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-49.           (((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-79212.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-708, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79213
in-theory        79213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-665 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-79213.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-665, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79214
in-theory        79214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-622 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-79214.        ((A -> (B -> (C or B))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-622, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79215
in-theory        79215
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-79215.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79216
in-theory        79216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-605 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79216.        ((A -> ((B -> (C or B)) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-605, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79217
in-theory        79217
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F or E)) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-79217.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F or E)) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-595, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79218
in-theory        79218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-550 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-79218.        (((A -> (B or A)) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-550, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79219
in-theory        79219
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-540 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79219.        ((A or (B -> (C or B))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-540, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79220
in-theory        79220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-530 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-79220.        ((A or (B -> (B or C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-530, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79221
in-theory        79221
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-520 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79221.        ((A or (B -> (C -> (B and C)))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-520, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79222
in-theory        79222
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-510 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79222.        ((A or ((B and C) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-510, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79223
in-theory        79223
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-500 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79223.        ((A or ((B and C) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-500, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79224
in-theory        79224
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-490 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79224.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-490, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79225
in-theory        79225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-480 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79225.        ((A or (B -> (C -> B))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-480, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79226
in-theory        79226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-469 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-79226.        ((A -> (B -> (B or C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-469, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79227
in-theory        79227
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-79227.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79228
in-theory        79228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-453 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), 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-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-79228.        ((A -> ((B -> (B or C)) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-453, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79229
in-theory        79229
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (E or F)) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-79229.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (E or F)) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-443, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79230
in-theory        79230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-409 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-49.           (((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-79230.        (((A -> (A or B)) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-409, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79231
in-theory        79231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-400 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), 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-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-79231.        (((A -> (B -> (A and B))) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-400, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79232
in-theory        79232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-391 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-79232.        ((((A and B) -> B) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-391, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79233
in-theory        79233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-382 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-49.           (((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-79233.        ((((A and B) -> A) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-382, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79234
in-theory        79234
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-373 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 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-7.            (A -> (B or A)), 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-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-79234.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-373, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79235
in-theory        79235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-364 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-79235.        (((A -> (B -> A)) or C) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-364, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79236
in-theory        79236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-354 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79236.        ((A -> (B -> (C -> (B and C)))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-354, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79237
in-theory        79237
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79237.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79238
in-theory        79238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-338 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79238.        (((A -> B) -> (A -> (A and B))) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-338, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79239
in-theory        79239
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> (E and F))) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79239.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> (E and F))) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-327, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79240
in-theory        79240
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and F) -> F) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79240.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and F) -> F) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-326, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79241
in-theory        79241
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and F) -> E) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79241.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and F) -> E) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-325, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79242
in-theory        79242
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-79242.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-324, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79243
in-theory        79243
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> E)) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-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-79243.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> E)) and (A or (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-323, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79244
in-theory        79244
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79244.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79245
in-theory        79245
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79245.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79246
in-theory        79246
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79246.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79247
in-theory        79247
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79247.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79248
in-theory        79248
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E or (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
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-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-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-79248.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E or (A or (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-311, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79249
in-theory        79249
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-49.           (((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-79249.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) or E)), M:tm-310, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79250
in-theory        79250
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79250.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and E))), M:tm-309, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79251
in-theory        79251
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79251.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (A or (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-305, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79252
in-theory        79252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-303 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79252.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-303, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79253
in-theory        79253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-270 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79253.        ((A -> (((B and C) -> C) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-270, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79254
in-theory        79254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-239 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79254.        ((A -> (((B and C) -> B) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-239, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79255
in-theory        79255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-210 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79255.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-210, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79256
in-theory        79256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-183 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79256.        ((A -> ((B -> (C -> B)) and A)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-183, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79257
in-theory        79257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-157 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79257.        ((A -> ((B and C) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-157, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79258
in-theory        79258
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-147 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79258.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-147, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79259
in-theory        79259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-134 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79259.        ((A -> ((B and C) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-134, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79260
in-theory        79260
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-125 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79260.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-125, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79261
in-theory        79261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-113 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79261.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-113, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79262
in-theory        79262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-105 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79262.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-105, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79263
in-theory        79263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-95 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79263.        (((A -> B) -> (A -> A)) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-95, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79264
in-theory        79264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-83 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79264.        ((A -> (B -> (C -> B))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-83, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79265
in-theory        79265
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     21
proof            (modus-ponens tm-76 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79265.        (((not (not A)) -> A) and (B or (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-76, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79266
in-theory        79266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-69 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8 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-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-79266.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-69, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79267
in-theory        79267
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-54 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-79267.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-54, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79268
in-theory        79268
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-42 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79268.        ((A -> (B or A)) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-42, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79269
in-theory        79269
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-32 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-49.           (((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-79269.        ((A -> (A or B)) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-32, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79270
in-theory        79270
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-23 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79270.        ((A -> (B -> (A and B))) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-23, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79271
in-theory        79271
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-22 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79271.        (((A and B) -> B) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-22, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79272
in-theory        79272
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-21 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79272.        (((A and B) -> A) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-21, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79273
in-theory        79273
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-20 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 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-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-79273.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-20, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79274
in-theory        79274
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-19 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79274.        ((A -> (B -> A)) and (C or (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-19, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79275
in-theory        79275
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-7 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79275.        (A or (B or (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-7, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79276
in-theory        79276
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-6 tm-7 tm-8)
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-49.           (((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-79276.        ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) or E), M:tm-6, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79277
in-theory        79277
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C or D) -> E) -> ((C or (C or D)) -> E))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79277.        (A -> ((B or (((C or D) -> E) -> ((C or (C or D)) -> E))) and A)), M:tm-5, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79278
in-theory        79278
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-1 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79278.        (A -> (B or (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-1, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-79279
in-theory        79279
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-879 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (or B C) (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79279.        ((A or (A or B)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-879, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (or B C) (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79280
in-theory        79280
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-876 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (or B C) (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (or B C))))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-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-79280.        ((A or (A or B)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B))), M:tm-876, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (or B C) (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (or B C)))))
================================================================
tm-name          tm-79281
in-theory        79281
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-874 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79281.        ((A -> (B or A)) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F)), M:tm-874, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79282
in-theory        79282
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-872 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79282.        ((A -> (A or B)) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F)), M:tm-872, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79283
in-theory        79283
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-870 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79283.        ((A -> (B -> (A and B))) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F)), M:tm-870, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79284
in-theory        79284
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-869 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79284.        (((A and B) -> B) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F)), M:tm-869, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79285
in-theory        79285
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-868 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79285.        (((A and B) -> A) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F)), M:tm-868, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79286
in-theory        79286
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-867 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79286.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-867, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79287
in-theory        79287
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-866 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79287.        ((A -> (B -> A)) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F)), M:tm-866, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79288
in-theory        79288
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B or C) -> D) -> ((B or (B or C)) -> D)) or E))
theorem-size     17
proof            (modus-ponens tm-861 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 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-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-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-79288.        (A or ((((B or C) -> D) -> ((B or (B or C)) -> D)) or E)), M:tm-861, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79289
in-theory        79289
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) or E)
theorem-size     17
proof            (modus-ponens tm-860 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6)
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-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-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-79289.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) or E), M:tm-860, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79290
in-theory        79290
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) -> ((B or (B or C)) -> D)) or E) and A))
theorem-size     19
proof            (modus-ponens tm-859 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       121
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-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-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-79290.        (A -> (((((B or C) -> D) -> ((B or (B or C)) -> D)) or E) and A)), M:tm-859, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79291
in-theory        79291
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) or E))
theorem-size     17
proof            (modus-ponens tm-858 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-1)
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-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-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-79291.        (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) or E)), M:tm-858, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-79292
in-theory        79292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-855 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79292.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-855, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79293
in-theory        79293
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-841 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> B (and C B)) (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79293.        ((A or (B -> (A and B))) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-841, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> B (and C B)) (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79294
in-theory        79294
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (B -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-837 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> B (and C B)) (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> B (and C B)))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79294.        ((A or (B -> (A and B))) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (B -> (A and B)))), M:tm-837, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> B (and C B)) (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> B (and C B))))))
================================================================
tm-name          tm-79295
in-theory        79295
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B))
theorem-size     21
proof            (modus-ponens tm-836 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79295.        (((A and B) or B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B)), M:tm-836, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79296
in-theory        79296
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and A))
theorem-size     21
proof            (modus-ponens tm-835 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79296.        (((A and B) or A) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and A)), M:tm-835, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79297
in-theory        79297
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-834 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79297.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> (A -> C)))), M:tm-834, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-79298
in-theory        79298
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-833 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> B C) (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> B C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79298.        ((A or (B -> A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (B -> A))), M:tm-833, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> B C) (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> B C)))))
================================================================
tm-name          tm-79299
in-theory        79299
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-831 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79299.        ((A -> (B or A)) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C))), M:tm-831, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79300
in-theory        79300
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-829 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-49.           (((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-79300.        ((A -> (A or B)) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C))), M:tm-829, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79301
in-theory        79301
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))
theorem-size     19
proof            (modus-ponens tm-827 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79301.        (A -> (A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))), M:tm-827, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79302
in-theory        79302
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-826 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79302.        ((A -> (B -> (A and B))) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C))), M:tm-826, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79303
in-theory        79303
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-825 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79303.        (((A and B) -> B) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C))), M:tm-825, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79304
in-theory        79304
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-824 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79304.        (((A and B) -> A) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C))), M:tm-824, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79305
in-theory        79305
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-823 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79305.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-823, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79306
in-theory        79306
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-822 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79306.        ((A -> (B -> A)) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C))), M:tm-822, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79307
in-theory        79307
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-816 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-9 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79307.        ((A -> (not ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))) -> (not A)), M:tm-816, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79308
in-theory        79308
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> ((A or (A or B)) -> C)) and D) -> E) -> ((D or ((((A or B) -> C) -> ((A or (A or B)) -> C)) and D)) -> E))
theorem-size     37
proof            (modus-ponens tm-815 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79308.        ((((((A or B) -> C) -> ((A or (A or B)) -> C)) and D) -> E) -> ((D or ((((A or B) -> C) -> ((A or (A or B)) -> C)) and D)) -> E)), M:tm-815, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79309
in-theory        79309
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B)))
theorem-size     19
proof            (modus-ponens tm-814 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79309.        (A or (B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B))), M:tm-814, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79310
in-theory        79310
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) or E)
theorem-size     19
proof            (modus-ponens tm-813 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
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-48.           (((A -> (B and 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-49.           (((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-79310.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) or E), M:tm-813, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79311
in-theory        79311
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B)) and A))
theorem-size     21
proof            (modus-ponens tm-812 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79311.        (A -> ((B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B)) and A)), M:tm-812, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79312
in-theory        79312
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B)))
theorem-size     19
proof            (modus-ponens tm-811 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B)))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79312.        (A -> (B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B))), M:tm-811, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-79313
in-theory        79313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-808 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79313.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-808, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79314
in-theory        79314
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-795 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-6)
proof-size       143
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79314.        (((A and B) or B) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-795, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79315
in-theory        79315
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B or C) -> D) -> (B or (B or C)))) or (((B or C) -> D) -> (B or (B or C)))) -> (((B or C) -> D) -> D))
theorem-size     33
proof            (modus-ponens tm-794 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-6)
proof-size       191
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79315.        (((A and (((B or C) -> D) -> (B or (B or C)))) or (((B or C) -> D) -> (B or (B or C)))) -> (((B or C) -> D) -> D)), M:tm-794, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79316
in-theory        79316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-757 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
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-49.           (((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-79316.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-757, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79317
in-theory        79317
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-744 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-6)
proof-size       143
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-49.           (((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-79317.        (((A and B) or A) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-744, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79318
in-theory        79318
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> (A or (A or B))) and D) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-743 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-6)
proof-size       191
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-49.           (((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-79318.        ((((((A or B) -> C) -> (A or (A or B))) and D) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C)), M:tm-743, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79319
in-theory        79319
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)) or H))
theorem-size     41
proof            (modus-ponens tm-708 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-79319.        (((((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)) or H)), M:tm-708, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79320
in-theory        79320
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-694 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       187
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-49.           (((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-79320.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-694, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79321
in-theory        79321
times-derived    2
----------------------------------------------------------------
theorem          (((A or (A or B)) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C))
theorem-size     25
proof            (modus-ponens tm-692 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-49.           (((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-79321.        (((A or (A or B)) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C)), M:tm-692, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79322
in-theory        79322
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-690 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6)
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-7.            (A -> (B or 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-49.           (((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-79322.        ((A -> (B or A)) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E))), M:tm-690, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79323
in-theory        79323
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-688 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
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-6.            (A -> (A or 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-49.           (((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-79323.        ((A -> (A or B)) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E))), M:tm-688, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79324
in-theory        79324
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (A or (A or B))) -> ((((A or B) -> C) -> (A or (A or B))) and (((A or B) -> C) -> C)))
theorem-size     31
proof            (modus-ponens tm-686 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       187
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-49.           (((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-79324.        ((((A or B) -> C) -> (A or (A or B))) -> ((((A or B) -> C) -> (A or (A or B))) and (((A or B) -> C) -> C))), M:tm-686, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79325
in-theory        79325
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-685 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
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-5.            (A -> (B -> (A and B))), axiom
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-49.           (((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-79325.        ((A -> (B -> (A and B))) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E))), M:tm-685, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79326
in-theory        79326
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-684 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-6)
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-4.            ((A and B) -> 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-49.           (((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-79326.        (((A and B) -> B) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E))), M:tm-684, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79327
in-theory        79327
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-683 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-6)
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-3.            ((A and B) -> 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-49.           (((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-79327.        (((A and B) -> A) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E))), M:tm-683, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79328
in-theory        79328
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-682 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
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-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-49.           (((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-79328.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-682, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79329
in-theory        79329
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-681 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
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-1.            (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-49.           (((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-79329.        ((A -> (B -> A)) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E))), M:tm-681, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79330
in-theory        79330
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> (A or (A or B))))
theorem-size     23
proof            (modus-ponens tm-676 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-49.           (((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-79330.        ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> (A or (A or B)))), M:tm-676, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79331
in-theory        79331
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (not (((A or B) -> C) -> C))) -> (not (((A or B) -> C) -> (A or (A or B)))))
theorem-size     33
proof            (modus-ponens tm-674 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-9 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-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-49.           (((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-79331.        (((((A or B) -> C) -> (A or (A or B))) -> (not (((A or B) -> C) -> C))) -> (not (((A or B) -> C) -> (A or (A or B))))), M:tm-674, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79332
in-theory        79332
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> C) -> D) -> (((((A or B) -> C) -> (A or (A or B))) or (((A or B) -> C) -> C)) -> D))
theorem-size     31
proof            (modus-ponens tm-673 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-6)
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-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-49.           (((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-79332.        (((((A or B) -> C) -> C) -> D) -> (((((A or B) -> C) -> (A or (A or B))) or (((A or B) -> C) -> C)) -> D)), M:tm-673, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79333
in-theory        79333
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B or C) -> D) -> (B or (B or C))) -> (((B or C) -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-672 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-7 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-49.           (((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-79333.        (A or ((((B or C) -> D) -> (B or (B or C))) -> (((B or C) -> D) -> D))), M:tm-672, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79334
in-theory        79334
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) or D)
theorem-size     21
proof            (modus-ponens tm-671 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-49.           (((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-79334.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) or D), M:tm-671, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79335
in-theory        79335
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) -> (B or (B or C))) -> (((B or C) -> D) -> D)) and A))
theorem-size     23
proof            (modus-ponens tm-670 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-49.           (((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-79335.        (A -> (((((B or C) -> D) -> (B or (B or C))) -> (((B or C) -> D) -> D)) and A)), M:tm-670, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79336
in-theory        79336
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> ((A or B) -> C)) -> ((((A or B) -> C) -> (A or (A or B))) -> C))
theorem-size     31
proof            (modus-ponens tm-669 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-49.           (((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-79336.        (((((A or B) -> C) -> (A or (A or B))) -> ((A or B) -> C)) -> ((((A or B) -> C) -> (A or (A or B))) -> C)), M:tm-669, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79337
in-theory        79337
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> (B or (B or C))) -> (((B or C) -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-668 tm-892 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-49.           (((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-79337.        (A -> ((((B or C) -> D) -> (B or (B or C))) -> (((B or C) -> D) -> D))), M:tm-668, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-79338
in-theory        79338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-665 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79338.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-665, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79339
in-theory        79339
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-651 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> B C) (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79339.        ((A or (B -> A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-651, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (-> B C) (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79340
in-theory        79340
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-649 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79340.        ((A -> (B or A)) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-649, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79341
in-theory        79341
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-647 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79341.        ((A -> (A or B)) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-647, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79342
in-theory        79342
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B or C) -> D) -> ((B or (B or C)) -> D))))
theorem-size     17
proof            (modus-ponens tm-645 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79342.        (A -> (A and (((B or C) -> D) -> ((B or (B or C)) -> D)))), M:tm-645, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79343
in-theory        79343
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-644 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79343.        ((A -> (B -> (A and B))) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-644, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79344
in-theory        79344
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-643 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79344.        (((A and B) -> B) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-643, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79345
in-theory        79345
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-642 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79345.        (((A and B) -> A) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-642, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79346
in-theory        79346
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-641 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79346.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-641, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79347
in-theory        79347
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-640 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79347.        ((A -> (B -> A)) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-640, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79348
in-theory        79348
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E)) -> E)
theorem-size     19
proof            (modus-ponens tm-638 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (and B (-> (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) C)) (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79348.        ((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E)) -> E), M:tm-638, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (and B (-> (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) C)) (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79349
in-theory        79349
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) and E) -> D)
theorem-size     19
proof            (modus-ponens tm-636 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (and (-> (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B) C) (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79349.        ((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) and E) -> D), M:tm-636, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> (and (-> (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) B) C) (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79350
in-theory        79350
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> D))
theorem-size     23
proof            (modus-ponens tm-634 tm-892 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)) (Dm (-> (-> (-> (or Am Bm) Cm) (-> (-> (or Am (or Am Bm)) Cm) C)) (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79350.        ((((A or B) -> C) -> (((A or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> D)), M:tm-634, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)) (Dm (-> (-> (-> (or Am Bm) Cm) (-> (-> (or Am (or Am Bm)) Cm) C)) (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79351
in-theory        79351
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B or C) -> D) -> ((B or (B or C)) -> D)))) -> (not A))
theorem-size     19
proof            (modus-ponens tm-631 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79351.        ((A -> (not (((B or C) -> D) -> ((B or (B or C)) -> D)))) -> (not A)), M:tm-631, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79352
in-theory        79352
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) -> ((E or (((A or B) -> C) -> ((A or (A or B)) -> C))) -> D))
theorem-size     33
proof            (modus-ponens tm-630 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79352.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) -> ((E or (((A or B) -> C) -> ((A or (A or B)) -> C))) -> D)), M:tm-630, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79353
in-theory        79353
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-629 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79353.        (A or (B -> (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-629, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79354
in-theory        79354
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) or E)
theorem-size     17
proof            (modus-ponens tm-628 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79354.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) or E), M:tm-628, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79355
in-theory        79355
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and A))
theorem-size     19
proof            (modus-ponens tm-627 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79355.        (A -> ((B -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and A)), M:tm-627, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79356
in-theory        79356
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or C) -> D)) -> (A -> ((B or (B or C)) -> D)))
theorem-size     17
proof            (modus-ponens tm-626 tm-892 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)) (Dm (-> C (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79356.        ((A -> ((B or C) -> D)) -> (A -> ((B or (B or C)) -> D))), M:tm-626, m:tm-892, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)) (Dm (-> C (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79357
in-theory        79357
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-625 tm-892 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79357.        (A -> (B -> (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-625, m:tm-892, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-79358
in-theory        79358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-622 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79358.        ((A -> (B -> (C or B))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-622, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79359
in-theory        79359
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79359.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (F or E))), M:tm-609, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79360
in-theory        79360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-605 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 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-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-79360.        ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-605, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79361
in-theory        79361
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (F or E)) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-595 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-49.           (((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-79361.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (F or E)) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))), M:tm-595, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79362
in-theory        79362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-550 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-79362.        (((A -> (B or A)) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-550, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79363
in-theory        79363
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-540 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-49.           (((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-79363.        ((A or (B -> (C or B))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-540, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79364
in-theory        79364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-530 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-79364.        ((A or (B -> (B or C))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-530, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79365
in-theory        79365
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-520 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 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-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-79365.        ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-520, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79366
in-theory        79366
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-510 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-49.           (((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-79366.        ((A or ((B and C) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-510, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79367
in-theory        79367
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-500 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-49.           (((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-79367.        ((A or ((B and C) -> B)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-500, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79368
in-theory        79368
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-490 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 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-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-79368.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H)), M:tm-490, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79369
in-theory        79369
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-480 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79369.        ((A or (B -> (C -> B))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-480, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79370
in-theory        79370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-469 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79370.        ((A -> (B -> (B or C))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-469, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79371
in-theory        79371
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79371.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (E or F))), M:tm-456, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79372
in-theory        79372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-453 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 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-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-79372.        ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-453, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79373
in-theory        79373
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (E or F)) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-443 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-79373.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (E or F)) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))), M:tm-443, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79374
in-theory        79374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-409 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 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-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-79374.        (((A -> (A or B)) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-409, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79375
in-theory        79375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-400 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 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-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-79375.        (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-400, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79376
in-theory        79376
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-391 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 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-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-79376.        ((((A and B) -> B) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-391, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79377
in-theory        79377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-382 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
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-49.           (((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-79377.        ((((A and B) -> A) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-382, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79378
in-theory        79378
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-373 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 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-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-79378.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H)), M:tm-373, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79379
in-theory        79379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-364 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79379.        (((A -> (B -> A)) or C) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-364, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79380
in-theory        79380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-354 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79380.        ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-354, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79381
in-theory        79381
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79381.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79382
in-theory        79382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-338 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 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-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-79382.        (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F)), M:tm-338, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79383
in-theory        79383
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)))
theorem-size     39
proof            (modus-ponens tm-327 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 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-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-79383.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))), M:tm-327, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79384
in-theory        79384
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (((E and F) -> F) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-326 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-49.           (((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-79384.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (((E and F) -> F) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))), M:tm-326, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79385
in-theory        79385
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (((E and F) -> E) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-325 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-49.           (((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-79385.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (((E and F) -> E) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))), M:tm-325, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79386
in-theory        79386
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)))
theorem-size     45
proof            (modus-ponens tm-324 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-49.           (((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-79386.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))), M:tm-324, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79387
in-theory        79387
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (F -> E)) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-323 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79387.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (F -> E)) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))), M:tm-323, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79388
in-theory        79388
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79388.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E and F) -> F)), M:tm-322, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79389
in-theory        79389
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79389.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E and F) -> E)), M:tm-320, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79390
in-theory        79390
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79390.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79391
in-theory        79391
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79391.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (F -> E))), M:tm-315, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79392
in-theory        79392
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E or ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)))
theorem-size     33
proof            (modus-ponens tm-311 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-49.           (((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-79392.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E or ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))), M:tm-311, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79393
in-theory        79393
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
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-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-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-79393.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) or E)), M:tm-310, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79394
in-theory        79394
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (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-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-49.           (((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-79394.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and E))), M:tm-309, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79395
in-theory        79395
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)))
theorem-size     33
proof            (modus-ponens tm-305 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79395.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) or D) and (E -> ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))), M:tm-305, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79396
in-theory        79396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-303 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 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-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-79396.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-303, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79397
in-theory        79397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-270 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 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-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-79397.        ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-270, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79398
in-theory        79398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-239 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 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-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-79398.        ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-239, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79399
in-theory        79399
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)) or H))
theorem-size     33
proof            (modus-ponens tm-210 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 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-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-79399.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H)), M:tm-210, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79400
in-theory        79400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-183 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79400.        ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-183, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79401
in-theory        79401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-157 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79401.        ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-157, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79402
in-theory        79402
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)) or G))
theorem-size     31
proof            (modus-ponens tm-147 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 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-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-79402.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-147, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79403
in-theory        79403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-134 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79403.        ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-134, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79404
in-theory        79404
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)) or G))
theorem-size     31
proof            (modus-ponens tm-125 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-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-79404.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-125, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79405
in-theory        79405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-113 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79405.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H)), M:tm-113, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79406
in-theory        79406
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)) or G))
theorem-size     35
proof            (modus-ponens tm-105 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-49.           (((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-79406.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-105, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79407
in-theory        79407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-95 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79407.        (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F)), M:tm-95, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79408
in-theory        79408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-83 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or 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-49.           (((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-79408.        ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-83, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79409
in-theory        79409
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or C) -> D) -> ((B or (B or C)) -> D)) or E))
theorem-size     21
proof            (modus-ponens tm-76 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 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-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-79409.        (((not (not A)) -> A) and ((((B or C) -> D) -> ((B or (B or C)) -> D)) or E)), M:tm-76, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79410
in-theory        79410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F))
theorem-size     27
proof            (modus-ponens tm-69 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 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-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-79410.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> ((C or (C or D)) -> E)) or F)), M:tm-69, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79411
in-theory        79411
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-54 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-79411.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-54, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-79412
in-theory        79412
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79412.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-893, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-79413
in-theory        79413
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-79413.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-893, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-79414
in-theory        79414
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-893 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-10.           ((not (not A)) -> A), axiom
tm-79414.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((not (not D)) -> D)), M:tm-893, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-79415
in-theory        79415
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-893 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79415.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> E)))), M:tm-893, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-79416
in-theory        79416
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-893 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-79416.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> D))), M:tm-893, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-79417
in-theory        79417
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-893 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-79417.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-893, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-79418
in-theory        79418
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-79418.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-893, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-79419
in-theory        79419
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-893 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-79419.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-893, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-79420
in-theory        79420
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-893 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-79420.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E and F) -> E))), M:tm-893, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-79421
in-theory        79421
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-893 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-79421.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-893, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-79422
in-theory        79422
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-893 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-79422.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E and F) -> F))), M:tm-893, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-79423
in-theory        79423
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79423.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> E)) and D))), M:tm-893, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-79424
in-theory        79424
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-893 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-79424.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-893, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-79425
in-theory        79425
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-79425.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and F) -> E) and D))), M:tm-893, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-79426
in-theory        79426
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-79426.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and F) -> F) and D))), M:tm-893, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-79427
in-theory        79427
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-79427.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-893, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-79428
in-theory        79428
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-893 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-79428.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (D and E)))), M:tm-893, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-79429
in-theory        79429
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-79429.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (E and F))))), M:tm-893, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-79430
in-theory        79430
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-893 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79430.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) or F)), M:tm-893, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-79431
in-theory        79431
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-893 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-79431.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-893, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-79432
in-theory        79432
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-893 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-79432.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) or F)), M:tm-893, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-79433
in-theory        79433
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-893 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-79433.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) or F)), M:tm-893, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-79434
in-theory        79434
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-893 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-79434.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) or F)), M:tm-893, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-79435
in-theory        79435
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-893 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-79435.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) or F)), M:tm-893, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-79436
in-theory        79436
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-79436.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (E or F)) and D))), M:tm-893, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-79437
in-theory        79437
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-893 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-79437.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (E or F)))), M:tm-893, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-79438
in-theory        79438
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-893 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79438.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> E)))), M:tm-893, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-79439
in-theory        79439
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-79439.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-893, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-79440
in-theory        79440
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-893 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-79440.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E and F) -> E))), M:tm-893, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-79441
in-theory        79441
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-893 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-79441.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E and F) -> F))), M:tm-893, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-79442
in-theory        79442
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-79442.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (E and F))))), M:tm-893, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-79443
in-theory        79443
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-893 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79443.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (E or F)))), M:tm-893, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-79444
in-theory        79444
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-893 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-79444.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F or E)))), M:tm-893, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-79445
in-theory        79445
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-893 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-79445.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) or F)), M:tm-893, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-79446
in-theory        79446
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-79446.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F or E)) and D))), M:tm-893, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-79447
in-theory        79447
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-893 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-79447.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F or E)))), M:tm-893, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-79448
in-theory        79448
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-893 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-79448.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-893, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-79449
in-theory        79449
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-79449.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-893, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-79450
in-theory        79450
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-893 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-79450.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-893, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-79451
in-theory        79451
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-893 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-79451.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-893, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-79452
in-theory        79452
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-893 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-79452.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-893, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-79453
in-theory        79453
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-893 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-79453.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-893, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-79454
in-theory        79454
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-893 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-79454.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-893, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-79455
in-theory        79455
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-79455.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-893, 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-79456
in-theory        79456
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79456.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-893, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-79457
in-theory        79457
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-893 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79457.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-893, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-79458
in-theory        79458
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-893 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-79458.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-893, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-79459
in-theory        79459
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-893 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79459.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-893, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-79460
in-theory        79460
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79460.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-893, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-79461
in-theory        79461
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79461.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> D))) -> (not D))), M:tm-893, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-79462
in-theory        79462
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79462.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-893, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-79463
in-theory        79463
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79463.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-893, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-79464
in-theory        79464
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79464.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-893, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-79465
in-theory        79465
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79465.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-893, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-79466
in-theory        79466
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79466.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (D or E))) -> (not D))), M:tm-893, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-79467
in-theory        79467
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79467.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E or D))) -> (not D))), M:tm-893, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-79468
in-theory        79468
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-893 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79468.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-893, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-79469
in-theory        79469
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-893 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79469.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-893, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-79470
in-theory        79470
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79470.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-893, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-79471
in-theory        79471
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79471.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-893, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-79472
in-theory        79472
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     27
proof            (modus-ponens tm-893 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79472.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-893, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-79473
in-theory        79473
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-79473.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-893, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-79474
in-theory        79474
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79474.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-893, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-79475
in-theory        79475
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79475.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-893, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-79476
in-theory        79476
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     25
proof            (modus-ponens tm-893 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79476.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-893, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-79477
in-theory        79477
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-893 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-79477.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-893, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-79478
in-theory        79478
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-893 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79478.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((not (not E)) -> E))), M:tm-893, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-79479
in-theory        79479
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((not (not D)) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-893 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79479.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((not (not D)) -> D) or E)), M:tm-893, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-79480
in-theory        79480
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-79480.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((not (not E)) -> E) and D))), M:tm-893, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-79481
in-theory        79481
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     29
proof            (modus-ponens tm-893 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79481.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-893, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-79482
in-theory        79482
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-893 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79482.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((not (not E)) -> E))), M:tm-893, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-79483
in-theory        79483
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79483.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-893, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-79484
in-theory        79484
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-893 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79484.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-893, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-79485
in-theory        79485
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79485.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (G -> F))))), M:tm-893, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-79486
in-theory        79486
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79486.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (F -> E))) or G)), M:tm-893, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-79487
in-theory        79487
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-79487.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-893, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-79488
in-theory        79488
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-893 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-79488.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (F -> E)))), M:tm-893, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-79489
in-theory        79489
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79489.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (G -> F))))), M:tm-893, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-79490
in-theory        79490
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> D))
theorem-size     17
proof            (modus-ponens tm-893 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79490.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> D)), M:tm-893, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-79491
in-theory        79491
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79491.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-893, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-79492
in-theory        79492
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> (D and E)))
theorem-size     21
proof            (modus-ponens tm-893 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79492.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> (D and E))), M:tm-893, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-79493
in-theory        79493
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-893 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79493.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> E))), M:tm-893, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-79494
in-theory        79494
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((not (not D)) -> (not (not D))))
theorem-size     21
proof            (modus-ponens tm-893 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79494.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((not (not D)) -> (not (not D)))), M:tm-893, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-79495
in-theory        79495
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-893 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79495.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-893, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-79496
in-theory        79496
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-893 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79496.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-893, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-79497
in-theory        79497
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-893 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79497.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> (E -> E)))), M:tm-893, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-79498
in-theory        79498
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (D -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-893 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79498.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (D -> D)) or F)), M:tm-893, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-79499
in-theory        79499
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-79499.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-893, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-79500
in-theory        79500
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79500.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-893, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-79501
in-theory        79501
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-893 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79501.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> (E -> E)))), M:tm-893, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-79502
in-theory        79502
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79502.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-893, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-79503
in-theory        79503
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-893 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79503.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D -> E)) -> (D -> E))), M:tm-893, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-79504
in-theory        79504
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     33
proof            (modus-ponens tm-893 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79504.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-893, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-79505
in-theory        79505
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79505.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-893, 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-79506
in-theory        79506
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-79506.        ((((A or B) -> C) -> ((A or (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-893, 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-79507
in-theory        79507
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79507.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-893, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-79508
in-theory        79508
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     35
proof            (modus-ponens tm-893 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       161
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-79508.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-893, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-79509
in-theory        79509
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-79509.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-893, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-79510
in-theory        79510
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-79510.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-893, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-79511
in-theory        79511
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79511.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-893, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-79512
in-theory        79512
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-893 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79512.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-893, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-79513
in-theory        79513
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-893 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79513.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-893, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-79514
in-theory        79514
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-79514.        ((((A or B) -> C) -> ((A or (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-893, 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-79515
in-theory        79515
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-893 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79515.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-893, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-79516
in-theory        79516
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-893 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       141
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-79516.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-893, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-79517
in-theory        79517
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-893 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-79517.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-893, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-79518
in-theory        79518
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-893 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79518.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-893, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-79519
in-theory        79519
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-893 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-79519.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-893, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-79520
in-theory        79520
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) and D) -> E))
theorem-size     21
proof            (modus-ponens tm-893 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-79520.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) and D) -> E)), M:tm-893, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-79521
in-theory        79521
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-893 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-79521.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-893, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-79522
in-theory        79522
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     33
proof            (modus-ponens tm-893 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-3 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-79522.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-893, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-79523
in-theory        79523
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-79523.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-893, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-79524
in-theory        79524
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79524.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-893, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-79525
in-theory        79525
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79525.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-893, 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-79526
in-theory        79526
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-79526.        ((((A or B) -> C) -> ((A or (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-893, 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-79527
in-theory        79527
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-893 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79527.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-893, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-79528
in-theory        79528
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     31
proof            (modus-ponens tm-893 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       141
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-79528.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-893, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-79529
in-theory        79529
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-79529.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-893, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-79530
in-theory        79530
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-79530.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-893, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-79531
in-theory        79531
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-893 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79531.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-893, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-79532
in-theory        79532
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-893 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-79532.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-893, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-79533
in-theory        79533
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-893 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79533.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-893, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-79534
in-theory        79534
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79534.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-893, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-79535
in-theory        79535
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     31
proof            (modus-ponens tm-893 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-79535.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-893, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-79536
in-theory        79536
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-893 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79536.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F and G) -> F)))), M:tm-893, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-79537
in-theory        79537
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-79537.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E and F) -> E)) or G)), M:tm-893, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-79538
in-theory        79538
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-79538.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-893, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-79539
in-theory        79539
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-893 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79539.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E and F)) -> (D -> E))), M:tm-893, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-79540
in-theory        79540
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-893 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-79540.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F and G) -> F)))), M:tm-893, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-79541
in-theory        79541
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and (D -> E)) -> E))
theorem-size     21
proof            (modus-ponens tm-893 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-79541.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and (D -> E)) -> E)), M:tm-893, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-79542
in-theory        79542
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-893 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-79542.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-893, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-79543
in-theory        79543
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     33
proof            (modus-ponens tm-893 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-79543.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-893, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-79544
in-theory        79544
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-893 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-79544.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-893, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-79545
in-theory        79545
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-79545.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-893, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-79546
in-theory        79546
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     29
proof            (modus-ponens tm-893 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-79546.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-893, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-79547
in-theory        79547
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79547.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-893, 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-79548
in-theory        79548
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-79548.        ((((A or B) -> C) -> ((A or (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-893, 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-79549
in-theory        79549
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-893 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79549.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-893, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-79550
in-theory        79550
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     31
proof            (modus-ponens tm-893 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       141
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-79550.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-893, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-79551
in-theory        79551
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-79551.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-893, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-79552
in-theory        79552
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-79552.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-893, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-79553
in-theory        79553
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-893 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79553.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-893, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-79554
in-theory        79554
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-893 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-79554.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-893, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-79555
in-theory        79555
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-893 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-79555.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-893, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-79556
in-theory        79556
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-893 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79556.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-893, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-79557
in-theory        79557
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79557.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-893, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-79558
in-theory        79558
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-893 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-79558.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-893, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-79559
in-theory        79559
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-893 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79559.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F and G) -> G)))), M:tm-893, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-79560
in-theory        79560
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-79560.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E and F) -> F)) or G)), M:tm-893, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-79561
in-theory        79561
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-79561.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-893, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-79562
in-theory        79562
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-893 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79562.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E and F)) -> (D -> F))), M:tm-893, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-79563
in-theory        79563
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-893 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-79563.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F and G) -> G)))), M:tm-893, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-79564
in-theory        79564
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79564.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-893, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-79565
in-theory        79565
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-79565.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-79566
in-theory        79566
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79566.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-893, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-79567
in-theory        79567
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79567.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-893, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-79568
in-theory        79568
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79568.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-893, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-79569
in-theory        79569
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79569.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-893, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-79570
in-theory        79570
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-79570.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-893, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-79571
in-theory        79571
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79571.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-893, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-79572
in-theory        79572
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-893 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79572.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-893, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-79573
in-theory        79573
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79573.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-893, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-79574
in-theory        79574
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79574.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-893, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79575
in-theory        79575
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-79575.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-893, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-79576
in-theory        79576
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-79576.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-893, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-79577
in-theory        79577
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-893 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-79577.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79578
in-theory        79578
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-79578.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-893, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-79579
in-theory        79579
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79579.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-893, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79580
in-theory        79580
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-79580.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-893, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-79581
in-theory        79581
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79581.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-893, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79582
in-theory        79582
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79582.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-893, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-79583
in-theory        79583
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79583.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-893, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-79584
in-theory        79584
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79584.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-893, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-79585
in-theory        79585
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79585.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-893, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-79586
in-theory        79586
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-893 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79586.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-893, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-79587
in-theory        79587
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-79587.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-893, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-79588
in-theory        79588
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79588.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-893, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-79589
in-theory        79589
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79589.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-893, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-79590
in-theory        79590
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79590.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-893, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-79591
in-theory        79591
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-893 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79591.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-893, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-79592
in-theory        79592
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-893 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79592.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-893, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-79593
in-theory        79593
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79593.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-893, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-79594
in-theory        79594
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79594.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-893, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-79595
in-theory        79595
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79595.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-893, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-79596
in-theory        79596
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79596.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-893, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-79597
in-theory        79597
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79597.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-893, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-79598
in-theory        79598
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-893 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79598.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-893, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-79599
in-theory        79599
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79599.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-893, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-79600
in-theory        79600
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-893 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79600.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-893, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-79601
in-theory        79601
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79601.        ((((A or B) -> C) -> ((A or (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-893, 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-79602
in-theory        79602
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79602.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-893, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-79603
in-theory        79603
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79603.        ((((A or B) -> C) -> ((A or (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-893, 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-79604
in-theory        79604
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79604.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-893, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-79605
in-theory        79605
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79605.        ((((A or B) -> C) -> ((A or (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-893, 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-79606
in-theory        79606
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79606.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-893, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-79607
in-theory        79607
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79607.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-893, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-79608
in-theory        79608
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79608.        ((((A or B) -> C) -> ((A or (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-893, 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-79609
in-theory        79609
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-79609.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-893, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-79610
in-theory        79610
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79610.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-893, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-79611
in-theory        79611
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79611.        ((((A or B) -> C) -> ((A or (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-893, 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-79612
in-theory        79612
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-893 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79612.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-893, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-79613
in-theory        79613
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     33
proof            (modus-ponens tm-893 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       149
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79613.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-893, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-79614
in-theory        79614
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-79614.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-893, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-79615
in-theory        79615
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-893 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79615.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-893, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-79616
in-theory        79616
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-79616.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-893, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-79617
in-theory        79617
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-79617.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-79618
in-theory        79618
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79618.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-893, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-79619
in-theory        79619
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79619.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-893, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-79620
in-theory        79620
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79620.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-893, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-79621
in-theory        79621
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79621.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-893, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-79622
in-theory        79622
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-79622.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-893, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-79623
in-theory        79623
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79623.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-893, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-79624
in-theory        79624
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-893 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79624.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-893, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-79625
in-theory        79625
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79625.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-893, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-79626
in-theory        79626
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-79626.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-893, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79627
in-theory        79627
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-79627.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-893, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-79628
in-theory        79628
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-79628.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-893, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-79629
in-theory        79629
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-79629.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79630
in-theory        79630
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-79630.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-893, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-79631
in-theory        79631
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-79631.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-893, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79632
in-theory        79632
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-79632.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-893, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-79633
in-theory        79633
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-79633.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-893, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79634
in-theory        79634
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-79634.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-893, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-79635
in-theory        79635
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-79635.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-893, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-79636
in-theory        79636
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79636.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-893, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-79637
in-theory        79637
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79637.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-893, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-79638
in-theory        79638
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79638.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-893, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-79639
in-theory        79639
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79639.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-893, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-79640
in-theory        79640
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79640.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-893, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-79641
in-theory        79641
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79641.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-893, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-79642
in-theory        79642
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-893 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79642.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-893, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-79643
in-theory        79643
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-79643.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-893, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-79644
in-theory        79644
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79644.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-893, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-79645
in-theory        79645
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-79645.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-893, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-79646
in-theory        79646
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-79646.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-79647
in-theory        79647
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79647.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-893, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-79648
in-theory        79648
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79648.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-893, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-79649
in-theory        79649
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79649.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-893, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-79650
in-theory        79650
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79650.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-893, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-79651
in-theory        79651
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-79651.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-893, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-79652
in-theory        79652
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79652.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-893, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-79653
in-theory        79653
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-893 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79653.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-893, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-79654
in-theory        79654
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79654.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-893, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-79655
in-theory        79655
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-79655.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-893, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79656
in-theory        79656
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-79656.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-893, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-79657
in-theory        79657
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-79657.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-893, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-79658
in-theory        79658
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-79658.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79659
in-theory        79659
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-79659.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-893, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-79660
in-theory        79660
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-79660.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-893, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79661
in-theory        79661
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-79661.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-893, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-79662
in-theory        79662
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-79662.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-893, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79663
in-theory        79663
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-79663.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-893, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-79664
in-theory        79664
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-79664.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-893, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-79665
in-theory        79665
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79665.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-893, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-79666
in-theory        79666
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79666.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-893, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-79667
in-theory        79667
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79667.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-893, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-79668
in-theory        79668
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79668.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-893, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-79669
in-theory        79669
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79669.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-893, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-79670
in-theory        79670
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79670.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-893, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-79671
in-theory        79671
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79671.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-893, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-79672
in-theory        79672
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79672.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-893, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-79673
in-theory        79673
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-893 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79673.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-893, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-79674
in-theory        79674
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-79674.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-893, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-79675
in-theory        79675
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79675.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-893, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-79676
in-theory        79676
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-79676.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-893, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-79677
in-theory        79677
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-79677.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-79678
in-theory        79678
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-893 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79678.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-893, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-79679
in-theory        79679
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-893 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79679.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-893, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-79680
in-theory        79680
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79680.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-893, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-79681
in-theory        79681
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79681.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-893, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-79682
in-theory        79682
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and 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-79682.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-893, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-79683
in-theory        79683
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79683.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-893, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-79684
in-theory        79684
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79684.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-893, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-79685
in-theory        79685
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-893 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79685.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-893, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-79686
in-theory        79686
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-79686.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-893, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79687
in-theory        79687
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-79687.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-893, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-79688
in-theory        79688
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-79688.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-893, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-79689
in-theory        79689
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-79689.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79690
in-theory        79690
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-79690.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-893, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-79691
in-theory        79691
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-893 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-79691.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-893, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79692
in-theory        79692
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-79692.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-893, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-79693
in-theory        79693
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-893 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-79693.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-893, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79694
in-theory        79694
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-893 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-79694.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-893, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-79695
in-theory        79695
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-79695.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-893, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-79696
in-theory        79696
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79696.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-893, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-79697
in-theory        79697
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79697.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-893, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-79698
in-theory        79698
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79698.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-893, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-79699
in-theory        79699
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79699.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-893, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-79700
in-theory        79700
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79700.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-893, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-79701
in-theory        79701
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79701.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-893, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-79702
in-theory        79702
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-893 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79702.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-893, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-79703
in-theory        79703
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79703.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-893, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-79704
in-theory        79704
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79704.        ((((A or B) -> C) -> ((A or (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-893, 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-79705
in-theory        79705
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-893 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79705.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-893, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-79706
in-theory        79706
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-893 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79706.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-893, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-79707
in-theory        79707
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-79707.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-893, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-79708
in-theory        79708
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-893 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79708.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-893, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-79709
in-theory        79709
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> D))))
theorem-size     21
proof            (modus-ponens tm-893 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-79709.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> D)))), M:tm-893, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-79710
in-theory        79710
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-79710.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-893, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-79711
in-theory        79711
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> ((D and E) and D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-79711.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> ((D and E) and D))), M:tm-893, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-79712
in-theory        79712
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> ((D and E) and E)))
theorem-size     23
proof            (modus-ponens tm-893 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-79712.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> ((D and E) and E))), M:tm-893, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-79713
in-theory        79713
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-79713.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (D and E))))), M:tm-893, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-79714
in-theory        79714
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (D or E))))
theorem-size     21
proof            (modus-ponens tm-893 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-79714.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (D or E)))), M:tm-893, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-79715
in-theory        79715
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E or D))))
theorem-size     21
proof            (modus-ponens tm-893 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-79715.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E or D)))), M:tm-893, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-79716
in-theory        79716
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     31
proof            (modus-ponens tm-893 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-79716.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-79717
in-theory        79717
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-79717.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-893, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-79718
in-theory        79718
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-79718.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-893, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-79719
in-theory        79719
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (F -> E)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-79719.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (F -> E))))), M:tm-893, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-79720
in-theory        79720
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-79720.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-893, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-79721
in-theory        79721
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-79721.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-893, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-79722
in-theory        79722
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     31
proof            (modus-ponens tm-893 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-79722.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-893, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-79723
in-theory        79723
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-79723.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-893, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-79724
in-theory        79724
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-893 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-79724.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E and F) -> E)))), M:tm-893, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-79725
in-theory        79725
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-79725.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-893, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-79726
in-theory        79726
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E and F) -> F))))
theorem-size     23
proof            (modus-ponens tm-893 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-79726.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E and F) -> F)))), M:tm-893, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-79727
in-theory        79727
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-79727.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-893, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-79728
in-theory        79728
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     33
proof            (modus-ponens tm-893 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-79728.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-893, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-79729
in-theory        79729
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-79729.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-893, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-79730
in-theory        79730
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-79730.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-893, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-79731
in-theory        79731
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     27
proof            (modus-ponens tm-893 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-79731.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-893, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-79732
in-theory        79732
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-79732.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-893, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-79733
in-theory        79733
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-893 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-79733.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-893, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-79734
in-theory        79734
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-79734.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-893, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-79735
in-theory        79735
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-79735.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-893, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-79736
in-theory        79736
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79736.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-893, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-79737
in-theory        79737
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-79737.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-893, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-79738
in-theory        79738
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-893 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79738.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-893, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-79739
in-theory        79739
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-79739.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-893, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-79740
in-theory        79740
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-893 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79740.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-893, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-79741
in-theory        79741
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     25
proof            (modus-ponens tm-893 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-79741.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-893, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-79742
in-theory        79742
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-79742.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-893, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-79743
in-theory        79743
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-893 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-79743.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-893, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-79744
in-theory        79744
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-893 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79744.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-893, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-79745
in-theory        79745
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     25
proof            (modus-ponens tm-893 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-79745.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-893, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-79746
in-theory        79746
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-893 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-79746.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-893, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79747
in-theory        79747
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-79747.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-893, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79748
in-theory        79748
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-79748.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-893, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79749
in-theory        79749
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79749.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-893, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-79750
in-theory        79750
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79750.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-893, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79751
in-theory        79751
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-893 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-79751.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-893, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-79752
in-theory        79752
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-893 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-79752.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-893, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-79753
in-theory        79753
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-893 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79753.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-893, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-79754
in-theory        79754
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79754.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-893, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-79755
in-theory        79755
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> 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-79755.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-893, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-79756
in-theory        79756
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-893 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79756.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-893, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-79757
in-theory        79757
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-893 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> 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-79757.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-893, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-79758
in-theory        79758
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-79758.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-893, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-79759
in-theory        79759
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-893 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79759.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-893, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-79760
in-theory        79760
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-893 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> 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-79760.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-893, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-79761
in-theory        79761
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-79761.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-893, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-79762
in-theory        79762
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-79762.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-893, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-79763
in-theory        79763
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-79763.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-893, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-79764
in-theory        79764
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79764.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-893, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-79765
in-theory        79765
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79765.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-893, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-79766
in-theory        79766
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79766.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (F -> E)) or G))), M:tm-893, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-79767
in-theory        79767
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79767.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> D)) or F) or G)), M:tm-893, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-79768
in-theory        79768
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-79768.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-893, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-79769
in-theory        79769
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79769.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> E)) or G))), M:tm-893, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-79770
in-theory        79770
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       173
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-79770.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-893, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-79771
in-theory        79771
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-79771.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-893, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-79772
in-theory        79772
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-79772.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-893, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-79773
in-theory        79773
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79773.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-893, 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-79774
in-theory        79774
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-79774.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-893, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-79775
in-theory        79775
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-893 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79775.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-893, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-79776
in-theory        79776
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-893 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       141
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-79776.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-893, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-79777
in-theory        79777
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-893 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       147
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-79777.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-893, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-79778
in-theory        79778
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-893 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79778.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-893, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-79779
in-theory        79779
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-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-79779.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-893, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-79780
in-theory        79780
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79780.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-893, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-79781
in-theory        79781
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79781.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-893, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-79782
in-theory        79782
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79782.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-893, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-79783
in-theory        79783
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79783.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-893, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-79784
in-theory        79784
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79784.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E and F) -> E) or G))), M:tm-893, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-79785
in-theory        79785
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) -> D) or F) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and 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-79785.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) -> D) or F) or G)), M:tm-893, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-79786
in-theory        79786
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-79786.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-893, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-79787
in-theory        79787
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79787.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and F) -> E) or G))), M:tm-893, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-79788
in-theory        79788
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-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-79788.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-893, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-79789
in-theory        79789
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79789.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-893, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-79790
in-theory        79790
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79790.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-893, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-79791
in-theory        79791
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79791.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-893, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-79792
in-theory        79792
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79792.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-893, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-79793
in-theory        79793
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79793.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E and F) -> F) or G))), M:tm-893, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-79794
in-theory        79794
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) -> E) or F) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and 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-79794.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) -> E) or F) or G)), M:tm-893, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-79795
in-theory        79795
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-79795.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-893, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-79796
in-theory        79796
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79796.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E and F) -> F) or G))), M:tm-893, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-79797
in-theory        79797
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       149
proof-steps      13
----------------------------------------------------------------
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-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-79797.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-893, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-79798
in-theory        79798
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-893 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79798.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-893, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-79799
in-theory        79799
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-893 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79799.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-893, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-79800
in-theory        79800
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79800.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-893, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-79801
in-theory        79801
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-893 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79801.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-893, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-79802
in-theory        79802
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79802.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-893, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-79803
in-theory        79803
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     25
proof            (modus-ponens tm-893 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79803.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-893, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-79804
in-theory        79804
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-79804.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-893, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-79805
in-theory        79805
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79805.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-893, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-79806
in-theory        79806
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-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-79806.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-893, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-79807
in-theory        79807
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79807.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-893, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-79808
in-theory        79808
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79808.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-893, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-79809
in-theory        79809
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79809.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-893, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-79810
in-theory        79810
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79810.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-893, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-79811
in-theory        79811
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79811.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (E or F)) or G))), M:tm-893, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-79812
in-theory        79812
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (D or E)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79812.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (D or E)) or F) or G)), M:tm-893, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-79813
in-theory        79813
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-79813.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-893, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-79814
in-theory        79814
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79814.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (E or F)) or G))), M:tm-893, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-79815
in-theory        79815
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (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-79815.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-893, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-79816
in-theory        79816
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 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       141
proof-steps      11
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-79816.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-79817
in-theory        79817
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B 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-79817.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-893, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-79818
in-theory        79818
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B 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-79818.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-893, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-79819
in-theory        79819
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79819.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-893, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-79820
in-theory        79820
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79820.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-893, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-79821
in-theory        79821
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B 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-79821.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-893, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-79822
in-theory        79822
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       141
proof-steps      11
----------------------------------------------------------------
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-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-79822.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-893, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-79823
in-theory        79823
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-893 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       135
proof-steps      11
----------------------------------------------------------------
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-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-79823.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-893, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-79824
in-theory        79824
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79824.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-893, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-79825
in-theory        79825
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (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-79825.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-893, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79826
in-theory        79826
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-79826.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-893, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-79827
in-theory        79827
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       185
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-79827.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-893, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-79828
in-theory        79828
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       165
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-79828.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79829
in-theory        79829
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       165
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-79829.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-893, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-79830
in-theory        79830
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-79830.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-893, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79831
in-theory        79831
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       165
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-79831.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-893, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-79832
in-theory        79832
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-79832.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-893, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79833
in-theory        79833
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-79833.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-893, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-79834
in-theory        79834
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       173
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-79834.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-893, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-79835
in-theory        79835
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79835.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-893, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-79836
in-theory        79836
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79836.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-893, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-79837
in-theory        79837
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       149
proof-steps      13
----------------------------------------------------------------
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-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-79837.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-893, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-79838
in-theory        79838
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-893 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       149
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-79838.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-893, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-79839
in-theory        79839
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-79839.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-893, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79840
in-theory        79840
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-79840.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-893, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-79841
in-theory        79841
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       165
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-79841.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-893, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-79842
in-theory        79842
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79842.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-893, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-79843
in-theory        79843
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79843.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-893, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-79844
in-theory        79844
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-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-79844.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-893, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-79845
in-theory        79845
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79845.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-893, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-79846
in-theory        79846
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-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-79846.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-893, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-79847
in-theory        79847
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-79847.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-893, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-79848
in-theory        79848
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       149
proof-steps      13
----------------------------------------------------------------
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-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-79848.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-893, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-79849
in-theory        79849
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-79849.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-893, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-79850
in-theory        79850
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-79850.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-893, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-79851
in-theory        79851
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-79851.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-893, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-79852
in-theory        79852
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79852.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-893, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-79853
in-theory        79853
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79853.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-893, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-79854
in-theory        79854
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       145
proof-steps      11
----------------------------------------------------------------
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-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-79854.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-893, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-79855
in-theory        79855
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79855.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-893, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-79856
in-theory        79856
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-893 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79856.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-893, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-79857
in-theory        79857
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-79857.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-893, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-79858
in-theory        79858
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79858.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-893, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-79859
in-theory        79859
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-79859.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-893, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79860
in-theory        79860
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (E or F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-79860.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (E or F))))), M:tm-893, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-79861
in-theory        79861
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-79861.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-893, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79862
in-theory        79862
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-79862.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-893, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79863
in-theory        79863
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-79863.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-893, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79864
in-theory        79864
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-79864.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-893, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-79865
in-theory        79865
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79865.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-893, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79866
in-theory        79866
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-893 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-79866.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-893, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-79867
in-theory        79867
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-893 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-79867.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-893, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-79868
in-theory        79868
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-79868.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-893, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-79869
in-theory        79869
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79869.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-893, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-79870
in-theory        79870
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-893 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79870.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-893, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-79871
in-theory        79871
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79871.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (F or G))))), M:tm-893, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-79872
in-theory        79872
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79872.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (E or F))) or G)), M:tm-893, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-79873
in-theory        79873
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79873.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-893, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-79874
in-theory        79874
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-893 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79874.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (E or F)))), M:tm-893, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-79875
in-theory        79875
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-79875.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (F or G))))), M:tm-893, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-79876
in-theory        79876
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79876.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-893, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79877
in-theory        79877
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and 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-79877.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-893, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79878
in-theory        79878
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-79878.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-893, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79879
in-theory        79879
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-79879.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-893, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79880
in-theory        79880
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79880.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-893, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-79881
in-theory        79881
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-79881.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-893, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79882
in-theory        79882
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-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-79882.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or (F -> (G -> F))))), M:tm-893, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-79883
in-theory        79883
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-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-79883.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (F -> E))) or G)), M:tm-893, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-79884
in-theory        79884
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-79884.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-893, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-79885
in-theory        79885
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79885.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or (F -> (G -> F))))), M:tm-893, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-79886
in-theory        79886
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       165
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79886.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79887
in-theory        79887
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and 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-79887.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79888
in-theory        79888
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-79888.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79889
in-theory        79889
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-79889.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79890
in-theory        79890
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79890.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-893, 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-79891
in-theory        79891
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-79891.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79892
in-theory        79892
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-893 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-79892.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-893, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-79893
in-theory        79893
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-893 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       141
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-79893.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-893, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-79894
in-theory        79894
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-893 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-79894.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-893, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-79895
in-theory        79895
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-893 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79895.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-893, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-79896
in-theory        79896
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79896.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-893, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79897
in-theory        79897
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-893 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and 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-79897.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-893, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79898
in-theory        79898
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-79898.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-893, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79899
in-theory        79899
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-79899.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-893, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79900
in-theory        79900
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79900.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-893, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-79901
in-theory        79901
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-79901.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-893, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79902
in-theory        79902
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-893 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-79902.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or ((F and G) -> F)))), M:tm-893, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-79903
in-theory        79903
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-893 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       109
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-79903.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E and F) -> E)) or G)), M:tm-893, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-79904
in-theory        79904
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-79904.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-893, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-79905
in-theory        79905
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-893 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79905.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or ((F and G) -> F)))), M:tm-893, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-79906
in-theory        79906
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79906.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-893, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79907
in-theory        79907
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-893 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and 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-79907.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-893, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79908
in-theory        79908
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-79908.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-893, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79909
in-theory        79909
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-79909.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-893, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79910
in-theory        79910
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79910.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-893, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-79911
in-theory        79911
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-79911.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-893, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79912
in-theory        79912
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-893 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-79912.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or ((F and G) -> G)))), M:tm-893, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-79913
in-theory        79913
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-893 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       109
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-79913.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E and F) -> F)) or G)), M:tm-893, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-79914
in-theory        79914
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-79914.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-893, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-79915
in-theory        79915
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-893 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79915.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or ((F and G) -> G)))), M:tm-893, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-79916
in-theory        79916
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79916.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-893, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79917
in-theory        79917
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and 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-79917.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-893, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79918
in-theory        79918
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-79918.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-893, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79919
in-theory        79919
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-79919.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-893, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79920
in-theory        79920
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79920.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-893, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-79921
in-theory        79921
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-79921.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-893, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79922
in-theory        79922
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-893 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), 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-79922.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-893, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-79923
in-theory        79923
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-893 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), 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-79923.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-893, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-79924
in-theory        79924
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-79924.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-893, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-79925
in-theory        79925
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-893 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79925.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-893, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-79926
in-theory        79926
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79926.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-893, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79927
in-theory        79927
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and 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-79927.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-893, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79928
in-theory        79928
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-79928.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-893, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79929
in-theory        79929
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-79929.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-893, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79930
in-theory        79930
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79930.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-893, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-79931
in-theory        79931
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-79931.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-893, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79932
in-theory        79932
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79932.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or (F -> (F or G))))), M:tm-893, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-79933
in-theory        79933
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79933.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (E or F))) or G)), M:tm-893, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-79934
in-theory        79934
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79934.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-893, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-79935
in-theory        79935
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79935.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or (F -> (F or G))))), M:tm-893, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-79936
in-theory        79936
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79936.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-893, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-79937
in-theory        79937
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and 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-79937.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-893, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-79938
in-theory        79938
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-79938.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-893, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-79939
in-theory        79939
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-79939.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-893, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-79940
in-theory        79940
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79940.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-893, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-79941
in-theory        79941
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-79941.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-893, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-79942
in-theory        79942
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B 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-79942.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or (F -> (G or F))))), M:tm-893, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-79943
in-theory        79943
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B 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-79943.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (F or E))) or G)), M:tm-893, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-79944
in-theory        79944
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-79944.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-893, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-79945
in-theory        79945
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79945.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or (F -> (G or F))))), M:tm-893, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-79946
in-theory        79946
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79946.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-893, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-79947
in-theory        79947
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-79947.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-893, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-79948
in-theory        79948
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-79948.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-893, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-79949
in-theory        79949
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-79949.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-893, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-79950
in-theory        79950
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-79950.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-893, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-79951
in-theory        79951
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-79951.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-893, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-79952
in-theory        79952
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B 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-79952.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> (F or E)) or G))), M:tm-893, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-79953
in-theory        79953
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E or D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B 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-79953.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E or D)) or F) or G)), M:tm-893, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-79954
in-theory        79954
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-79954.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-893, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-79955
in-theory        79955
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-893 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-79955.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F or E)) or G))), M:tm-893, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-79956
in-theory        79956
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79956.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-893, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-79957
in-theory        79957
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-79957.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-79958
in-theory        79958
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79958.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-893, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-79959
in-theory        79959
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79959.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-893, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-79960
in-theory        79960
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79960.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-893, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-79961
in-theory        79961
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79961.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-893, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-79962
in-theory        79962
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79962.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-893, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-79963
in-theory        79963
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79963.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-893, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-79964
in-theory        79964
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-893 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79964.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-893, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-79965
in-theory        79965
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79965.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-893, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-79966
in-theory        79966
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79966.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-893, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79967
in-theory        79967
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-79967.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-893, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-79968
in-theory        79968
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-79968.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-893, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-79969
in-theory        79969
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79969.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79970
in-theory        79970
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-79970.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-893, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-79971
in-theory        79971
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79971.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-893, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79972
in-theory        79972
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-79972.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-893, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-79973
in-theory        79973
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79973.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-893, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79974
in-theory        79974
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79974.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-893, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-79975
in-theory        79975
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-79975.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-893, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-79976
in-theory        79976
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79976.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-893, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-79977
in-theory        79977
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79977.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-893, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-79978
in-theory        79978
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79978.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-893, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-79979
in-theory        79979
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-79979.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-893, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-79980
in-theory        79980
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79980.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-893, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79981
in-theory        79981
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79981.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-893, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-79982
in-theory        79982
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-79982.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-893, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-79983
in-theory        79983
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79983.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-893, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-79984
in-theory        79984
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79984.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-893, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-79985
in-theory        79985
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-893 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79985.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-893, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-79986
in-theory        79986
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79986.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-893, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-79987
in-theory        79987
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79987.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-893, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-79988
in-theory        79988
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79988.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-893, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79989
in-theory        79989
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-79989.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-893, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-79990
in-theory        79990
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-79990.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-893, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-79991
in-theory        79991
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79991.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-893, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-79992
in-theory        79992
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-893 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79992.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-893, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-79993
in-theory        79993
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-893 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79993.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-893, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-79994
in-theory        79994
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79994.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-893, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-79995
in-theory        79995
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79995.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-893, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-79996
in-theory        79996
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-893 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79996.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-893, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-79997
in-theory        79997
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-79997.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-893, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-79998
in-theory        79998
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 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       141
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-79998.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-893, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-79999
in-theory        79999
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-79999.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-893, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-80000
in-theory        80000
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and 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-80000.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-893, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-80001
in-theory        80001
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-80001.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-893, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-80002
in-theory        80002
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-80002.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-893, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-80003
in-theory        80003
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-80003.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-893, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-80004
in-theory        80004
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-80004.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-893, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-80005
in-theory        80005
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80005.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-893, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-80006
in-theory        80006
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-80006.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-893, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-80007
in-theory        80007
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-80007.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-893, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-80008
in-theory        80008
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-893 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-80008.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-893, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-80009
in-theory        80009
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-80009.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-893, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-80010
in-theory        80010
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80010.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-893, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-80011
in-theory        80011
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-80011.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-893, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-80012
in-theory        80012
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 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       133
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-80012.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-893, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-80013
in-theory        80013
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (F or E)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-80013.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D and (E -> (F or E))))), M:tm-893, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-80014
in-theory        80014
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-80014.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-893, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-80015
in-theory        80015
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-80015.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-893, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-80016
in-theory        80016
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-80016.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-893, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-80017
in-theory        80017
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-80017.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-893, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-80018
in-theory        80018
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-80018.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-893, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-80019
in-theory        80019
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-893 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-80019.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-893, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-80020
in-theory        80020
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-893 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-80020.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-893, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-80021
in-theory        80021
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-80021.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-893, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-80022
in-theory        80022
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80022.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-893, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-80023
in-theory        80023
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-893 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-80023.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-893, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-80024
in-theory        80024
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80024.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E -> (F -> (G or F))))), M:tm-893, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-80025
in-theory        80025
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-893 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-80025.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (F or E))) or G)), M:tm-893, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-80026
in-theory        80026
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-893 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-80026.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-893, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-80027
in-theory        80027
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-893 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-80027.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> (D -> (F or E)))), M:tm-893, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-80028
in-theory        80028
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-893 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-80028.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (F -> (G or F))))), M:tm-893, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-80029
in-theory        80029
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80029.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-893, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-80030
in-theory        80030
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     31
proof            (modus-ponens tm-893 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-80030.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-893, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-80031
in-theory        80031
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80031.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-893, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-80032
in-theory        80032
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80032.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-893, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-80033
in-theory        80033
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80033.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-893, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-80034
in-theory        80034
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80034.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-893, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-80035
in-theory        80035
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-893 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80035.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-893, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-80036
in-theory        80036
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80036.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-893, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80037
in-theory        80037
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-893 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-80037.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (E -> E))), M:tm-893, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-80038
in-theory        80038
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-80038.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-893, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-80039
in-theory        80039
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-80039.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-80040
in-theory        80040
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-893 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-80040.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-893, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-80041
in-theory        80041
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80041.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-893, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-80042
in-theory        80042
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-893 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-80042.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-893, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-80043
in-theory        80043
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80043.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-893, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-80044
in-theory        80044
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80044.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-893, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-80045
in-theory        80045
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-80045.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-893, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-80046
in-theory        80046
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80046.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-893, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-80047
in-theory        80047
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80047.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-893, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-80048
in-theory        80048
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-893 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80048.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-893, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-80049
in-theory        80049
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-80049.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-893, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-80050
in-theory        80050
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80050.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-893, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-80051
in-theory        80051
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80051.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-893, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-80052
in-theory        80052
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80052.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-893, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-80053
in-theory        80053
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80053.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-893, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-80054
in-theory        80054
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80054.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-893, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-80055
in-theory        80055
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80055.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-893, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-80056
in-theory        80056
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-80056.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-893, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-80057
in-theory        80057
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       159
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-80057.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-893, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-80058
in-theory        80058
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-893 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-80058.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-893, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-80059
in-theory        80059
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B 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-80059.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-893, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-80060
in-theory        80060
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-80060.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-893, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-80061
in-theory        80061
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-80061.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-893, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-80062
in-theory        80062
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-80062.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-893, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-80063
in-theory        80063
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-80063.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-893, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-80064
in-theory        80064
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-80064.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-893, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-80065
in-theory        80065
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80065.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-893, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-80066
in-theory        80066
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-80066.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-893, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-80067
in-theory        80067
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-893 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80067.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-893, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-80068
in-theory        80068
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-893 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       135
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-80068.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-893, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-80069
in-theory        80069
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-893 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-80069.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-893, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80070
in-theory        80070
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-893 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80070.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-893, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80071
in-theory        80071
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-893 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80071.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-893, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-80072
in-theory        80072
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80072.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-893, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-80073
in-theory        80073
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80073.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-893, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-80074
in-theory        80074
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80074.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-893, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-80075
in-theory        80075
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80075.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-893, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-80076
in-theory        80076
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80076.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-893, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-80077
in-theory        80077
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80077.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-893, 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-80078
in-theory        80078
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80078.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-893, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-80079
in-theory        80079
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80079.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-893, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-80080
in-theory        80080
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     35
proof            (modus-ponens tm-893 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80080.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-893, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-80081
in-theory        80081
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80081.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-893, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-80082
in-theory        80082
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 tm-2 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80082.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-893, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-80083
in-theory        80083
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-893 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80083.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-893, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-80084
in-theory        80084
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-893 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80084.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-893, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-80085
in-theory        80085
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80085.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-893, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-80086
in-theory        80086
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80086.        ((((A or B) -> C) -> ((A or (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-893, 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-80087
in-theory        80087
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80087.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-893, 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-80088
in-theory        80088
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80088.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-893, 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-80089
in-theory        80089
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80089.        ((((A or B) -> C) -> ((A or (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-893, 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-80090
in-theory        80090
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80090.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-893, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-80091
in-theory        80091
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80091.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-893, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-80092
in-theory        80092
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80092.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-893, 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-80093
in-theory        80093
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80093.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-893, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-80094
in-theory        80094
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80094.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-893, 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-80095
in-theory        80095
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80095.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-893, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-80096
in-theory        80096
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-80096.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-893, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-80097
in-theory        80097
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80097.        ((((A or B) -> C) -> ((A or (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-893, 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-80098
in-theory        80098
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-80098.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-893, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-80099
in-theory        80099
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-80099.        ((((A or B) -> C) -> ((A or (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-893, 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-80100
in-theory        80100
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       203
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-80100.        ((((A or B) -> C) -> ((A or (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-893, 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-80101
in-theory        80101
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-80101.        ((((A or B) -> C) -> ((A or (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-893, 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-80102
in-theory        80102
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-80102.        ((((A or B) -> C) -> ((A or (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-893, 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-80103
in-theory        80103
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-80103.        ((((A or B) -> C) -> ((A or (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-893, 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-80104
in-theory        80104
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-80104.        ((((A or B) -> C) -> ((A or (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-893, 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-80105
in-theory        80105
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-80105.        ((((A or B) -> C) -> ((A or (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-893, 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-80106
in-theory        80106
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-80106.        ((((A or B) -> C) -> ((A or (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-893, 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-80107
in-theory        80107
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-893 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-80107.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-893, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-80108
in-theory        80108
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80108.        ((((A or B) -> C) -> ((A or (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-893, 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-80109
in-theory        80109
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-80109.        ((((A or B) -> C) -> ((A or (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-893, 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-80110
in-theory        80110
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80110.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-893, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-80111
in-theory        80111
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       179
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80111.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-893, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-80112
in-theory        80112
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-80112.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-893, 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-80113
in-theory        80113
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80113.        ((((A or B) -> C) -> ((A or (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-893, 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-80114
in-theory        80114
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80114.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-893, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-80115
in-theory        80115
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80115.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> D))), M:tm-893, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-80116
in-theory        80116
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-80116.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-893, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-80117
in-theory        80117
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     25
proof            (modus-ponens tm-893 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80117.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-893, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-80118
in-theory        80118
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     25
proof            (modus-ponens tm-893 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80118.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-893, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-80119
in-theory        80119
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80119.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-893, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-80120
in-theory        80120
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (D or F)))
theorem-size     23
proof            (modus-ponens tm-893 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80120.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (D or F))), M:tm-893, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-80121
in-theory        80121
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F or D)))
theorem-size     23
proof            (modus-ponens tm-893 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80121.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F or D))), M:tm-893, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-80122
in-theory        80122
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80122.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-893, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-80123
in-theory        80123
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     31
proof            (modus-ponens tm-893 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80123.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-893, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-80124
in-theory        80124
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     25
proof            (modus-ponens tm-893 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80124.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-893, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-80125
in-theory        80125
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80125.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-893, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80126
in-theory        80126
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-80126.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-893, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-80127
in-theory        80127
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-80127.        ((((A or B) -> C) -> ((A or (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-893, 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-80128
in-theory        80128
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80128.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-80129
in-theory        80129
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-80129.        ((((A or B) -> C) -> ((A or (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-893, 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-80130
in-theory        80130
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80130.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-893, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-80131
in-theory        80131
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-80131.        ((((A or B) -> C) -> ((A or (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-893, 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-80132
in-theory        80132
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80132.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-893, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-80133
in-theory        80133
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80133.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-893, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-80134
in-theory        80134
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-80134.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-893, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-80135
in-theory        80135
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80135.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-893, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-80136
in-theory        80136
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80136.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-893, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-80137
in-theory        80137
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80137.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-893, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-80138
in-theory        80138
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-893 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-80138.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-893, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-80139
in-theory        80139
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80139.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-893, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-80140
in-theory        80140
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80140.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-893, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-80141
in-theory        80141
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80141.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-893, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-80142
in-theory        80142
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80142.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-893, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-80143
in-theory        80143
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80143.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-893, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-80144
in-theory        80144
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-80144.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-893, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-80145
in-theory        80145
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-80145.        ((((A or B) -> C) -> ((A or (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-893, 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-80146
in-theory        80146
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80146.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-893, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-80147
in-theory        80147
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80147.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-893, 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-80148
in-theory        80148
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80148.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-893, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-80149
in-theory        80149
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-80149.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-893, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-80150
in-theory        80150
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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       153
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-80150.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-893, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-80151
in-theory        80151
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-893 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-80151.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-893, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-80152
in-theory        80152
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80152.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-893, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-80153
in-theory        80153
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-80153.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-893, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-80154
in-theory        80154
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-80154.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-893, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-80155
in-theory        80155
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-80155.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-893, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-80156
in-theory        80156
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-893 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-80156.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-893, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-80157
in-theory        80157
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-893 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80157.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-893, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-80158
in-theory        80158
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-80158.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-893, 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-80159
in-theory        80159
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80159.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-893, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-80160
in-theory        80160
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-893 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       129
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-80160.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-893, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-80161
in-theory        80161
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-80161.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-893, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-80162
in-theory        80162
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-893 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80162.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-893, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-80163
in-theory        80163
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80163.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-893, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-80164
in-theory        80164
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-893 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-80164.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> E))), M:tm-893, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-80165
in-theory        80165
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-80165.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-893, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-80166
in-theory        80166
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     25
proof            (modus-ponens tm-893 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80166.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-893, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-80167
in-theory        80167
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     25
proof            (modus-ponens tm-893 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80167.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-893, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-80168
in-theory        80168
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80168.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-893, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-80169
in-theory        80169
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-893 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80169.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (E or F))), M:tm-893, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-80170
in-theory        80170
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-893 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80170.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F or E))), M:tm-893, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-80171
in-theory        80171
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80171.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-893, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-80172
in-theory        80172
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-893 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80172.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-893, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-80173
in-theory        80173
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     25
proof            (modus-ponens tm-893 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80173.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-893, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-80174
in-theory        80174
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-80174.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-893, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80175
in-theory        80175
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     27
proof            (modus-ponens tm-893 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-80175.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-893, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-80176
in-theory        80176
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-80176.        ((((A or B) -> C) -> ((A or (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-893, 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-80177
in-theory        80177
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-80177.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-80178
in-theory        80178
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-80178.        ((((A or B) -> C) -> ((A or (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-893, 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-80179
in-theory        80179
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-80179.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-893, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-80180
in-theory        80180
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 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-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-80180.        ((((A or B) -> C) -> ((A or (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-893, 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-80181
in-theory        80181
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-80181.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-893, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-80182
in-theory        80182
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-893 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-80182.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-893, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-80183
in-theory        80183
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (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-893 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-80183.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-893, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-80184
in-theory        80184
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     27
proof            (modus-ponens tm-893 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80184.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-893, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-80185
in-theory        80185
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     27
proof            (modus-ponens tm-893 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80185.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-893, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-80186
in-theory        80186
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-893 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80186.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-893, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-80187
in-theory        80187
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-893 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-80187.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-893, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-80188
in-theory        80188
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), 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-80188.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-893, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-80189
in-theory        80189
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     27
proof            (modus-ponens tm-893 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-80189.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-893, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-80190
in-theory        80190
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-80190.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-893, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-80191
in-theory        80191
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     27
proof            (modus-ponens tm-893 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-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-80191.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-893, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-80192
in-theory        80192
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-80192.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-893, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-80193
in-theory        80193
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-893 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-80193.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-893, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-80194
in-theory        80194
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     51
proof            (modus-ponens tm-893 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-80194.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-893, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-80195
in-theory        80195
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-893 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80195.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-893, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-80196
in-theory        80196
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-893 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80196.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-893, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-80197
in-theory        80197
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-893 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-80197.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-893, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-80198
in-theory        80198
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-893 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-80198.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-893, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-80199
in-theory        80199
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-893 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-4)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80199.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-893, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-80200
in-theory        80200
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-893 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-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-80200.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-893, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-80201
in-theory        80201
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-893 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (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-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-80201.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-893, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-80202
in-theory        80202
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-893 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-80202.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-893, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-80203
in-theory        80203
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-80203.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-893, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-80204
in-theory        80204
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-893 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-80204.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-893, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-80205
in-theory        80205
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-893 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-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-80205.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-893, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-80206
in-theory        80206
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-893 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-80206.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-893, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-80207
in-theory        80207
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-893 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-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-80207.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-893, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-80208
in-theory        80208
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-893 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
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-80208.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-893, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-80209
in-theory        80209
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-893 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80209.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-893, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-80210
in-theory        80210
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 tm-4)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
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-80210.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-893, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-80211
in-theory        80211
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-893 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80211.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-893, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-80212
in-theory        80212
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-80212.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-893, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-80213
in-theory        80213
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-893 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-80213.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-893, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-80214
in-theory        80214
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-4)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-80214.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-893, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-80215
in-theory        80215
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80215.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-893, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-80216
in-theory        80216
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     31
proof            (modus-ponens tm-893 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80216.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-893, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-80217
in-theory        80217
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     29
proof            (modus-ponens tm-893 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-80217.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-893, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-80218
in-theory        80218
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80218.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-893, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-80219
in-theory        80219
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-893 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80219.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-893, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-80220
in-theory        80220
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-893 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-9)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80220.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-893, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-80221
in-theory        80221
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80221.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-893, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80222
in-theory        80222
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-893 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80222.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-893, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-80223
in-theory        80223
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80223.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-80224
in-theory        80224
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-893 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80224.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-893, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-80225
in-theory        80225
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-893 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80225.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-893, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-80226
in-theory        80226
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80226.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-893, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-80227
in-theory        80227
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-893 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80227.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-893, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-80228
in-theory        80228
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80228.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-893, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-80229
in-theory        80229
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80229.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-893, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-80230
in-theory        80230
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80230.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-893, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-80231
in-theory        80231
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80231.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-893, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-80232
in-theory        80232
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-893 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80232.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-893, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-80233
in-theory        80233
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-80233.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-893, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-80234
in-theory        80234
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-893 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-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-80234.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-893, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-80235
in-theory        80235
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80235.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-893, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-80236
in-theory        80236
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80236.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-893, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-80237
in-theory        80237
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-893 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80237.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-893, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-80238
in-theory        80238
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     57
proof            (modus-ponens tm-893 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80238.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-893, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-80239
in-theory        80239
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-893 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80239.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-893, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-80240
in-theory        80240
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-893 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80240.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-893, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-80241
in-theory        80241
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     45
proof            (modus-ponens tm-893 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80241.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-893, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-80242
in-theory        80242
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-893 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-80242.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-893, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-80243
in-theory        80243
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     41
proof            (modus-ponens tm-893 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-80243.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-893, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-80244
in-theory        80244
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-893 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-80244.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-893, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-80245
in-theory        80245
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     33
proof            (modus-ponens tm-893 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-80245.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-893, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-80246
in-theory        80246
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-893 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48.           (((A -> (B and 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-80246.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-893, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-80247
in-theory        80247
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-893 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-80247.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-893, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-80248
in-theory        80248
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     39
proof            (modus-ponens tm-893 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-80248.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-893, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-80249
in-theory        80249
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-893 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (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-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-80249.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-893, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-80250
in-theory        80250
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-893 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-80250.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-893, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-80251
in-theory        80251
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-893 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48.           (((A -> (B and 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-80251.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-893, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-80252
in-theory        80252
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-893 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-80252.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-893, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-80253
in-theory        80253
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-893 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48.           (((A -> (B and 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-80253.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-893, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-80254
in-theory        80254
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-893 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-80254.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-893, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-80255
in-theory        80255
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     41
proof            (modus-ponens tm-893 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-9)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-80255.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-893, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-80256
in-theory        80256
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-893 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80256.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-893, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-80257
in-theory        80257
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), 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-80257.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-893, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-80258
in-theory        80258
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-893 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80258.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-893, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-80259
in-theory        80259
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-893 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-80259.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-893, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-80260
in-theory        80260
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     39
proof            (modus-ponens tm-893 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-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-80260.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-893, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-80261
in-theory        80261
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80261.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-893, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-80262
in-theory        80262
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80262.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-893, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-80263
in-theory        80263
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80263.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-893, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-80264
in-theory        80264
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80264.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-893, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-80265
in-theory        80265
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     25
proof            (modus-ponens tm-893 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80265.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-893, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-80266
in-theory        80266
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80266.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-893, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80267
in-theory        80267
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-80267.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-80268
in-theory        80268
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-80268.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-893, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-80269
in-theory        80269
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-80269.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-893, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-80270
in-theory        80270
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-893 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-80270.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-893, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-80271
in-theory        80271
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-893 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-80271.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-893, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-80272
in-theory        80272
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-893 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> 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-80272.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-893, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-80273
in-theory        80273
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-893 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> 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-80273.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-893, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-80274
in-theory        80274
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-893 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80274.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-893, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-80275
in-theory        80275
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-80275.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-893, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-80276
in-theory        80276
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-893 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80276.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-893, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-80277
in-theory        80277
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (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-80277.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-893, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-80278
in-theory        80278
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-893 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or 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-80278.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-893, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-80279
in-theory        80279
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-80279.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-893, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-80280
in-theory        80280
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-893 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and 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-80280.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-893, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-80281
in-theory        80281
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-893 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-80281.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-893, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80282
in-theory        80282
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-893 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
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-80282.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-893, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-80283
in-theory        80283
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
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-80283.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-893, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-80284
in-theory        80284
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-80284.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-893, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-80285
in-theory        80285
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (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-80285.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-893, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-80286
in-theory        80286
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-893 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and 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-80286.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-893, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-80287
in-theory        80287
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-893 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-80287.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-893, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-80288
in-theory        80288
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-80288.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-893, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-80289
in-theory        80289
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-80289.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-893, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-80290
in-theory        80290
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-893 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
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-80290.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-893, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-80291
in-theory        80291
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-80291.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-893, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-80292
in-theory        80292
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
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-80292.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-893, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-80293
in-theory        80293
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-893 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
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-80293.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-893, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-80294
in-theory        80294
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-893 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80294.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-893, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-80295
in-theory        80295
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-893 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
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-80295.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-893, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80296
in-theory        80296
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-893 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80296.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-893, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-80297
in-theory        80297
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-893 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80297.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-893, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80298
in-theory        80298
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-890 tm-893 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       159
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-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-5.            (A -> (B -> (A and B))), axiom
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-80298.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-893, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-80299
in-theory        80299
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-888 tm-893 ((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
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-80299.        ((A or B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B))), M:tm-888, m:tm-893, u:((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-80300
in-theory        80300
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-882 tm-893 ((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (or A B)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80300.        (((A or B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B)))), M:tm-882, m:tm-893, u:((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-80301
in-theory        80301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-855 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80301.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-855, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80302
in-theory        80302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B or (A -> (B and A))) -> C)))
theorem-size     41
proof            (modus-ponens tm-852 tm-893 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80302.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-893, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-80303
in-theory        80303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-850 tm-893 ((Am (-> A (and B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80303.        ((A -> (B and A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> (B and A)))), M:tm-850, m:tm-893, u:((Am (-> A (and B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-80304
in-theory        80304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> (B and A)))))
theorem-size     53
proof            (modus-ponens tm-844 tm-893 ((Am (-> A (and B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80304.        (((A -> (B and A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> (B and A))))), M:tm-844, m:tm-893, u:((Am (-> A (and B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-80305
in-theory        80305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-808 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80305.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-808, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80306
in-theory        80306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((C and A) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-805 tm-893 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80306.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((C and A) or A) -> B))), M:tm-805, m:tm-893, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-80307
in-theory        80307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((E and A) or A) -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))
theorem-size     39
proof            (modus-ponens tm-798 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80307.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((E and A) or A) -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))), M:tm-798, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80308
in-theory        80308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-757 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-49.           (((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-80308.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-757, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80309
in-theory        80309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((A and C) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-754 tm-893 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80309.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((A and C) or A) -> B))), M:tm-754, m:tm-893, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-80310
in-theory        80310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((A and E) or A) -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))
theorem-size     39
proof            (modus-ponens tm-747 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-80310.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((A and E) or A) -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))), M:tm-747, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80311
in-theory        80311
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E)))
theorem-size     43
proof            (modus-ponens tm-708 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-49.           (((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-80311.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E))), M:tm-708, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80312
in-theory        80312
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     55
proof            (modus-ponens tm-705 tm-893 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80312.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-893, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-80313
in-theory        80313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-703 tm-893 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80313.        (((A -> B) -> (A -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-893, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-80314
in-theory        80314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-697 tm-893 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80314.        ((((A -> B) -> (A -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-893, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-80315
in-theory        80315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-665 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-49.           (((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-80315.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-665, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80316
in-theory        80316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B or (A -> B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-662 tm-893 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((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-49.           (((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-80316.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-893, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-80317
in-theory        80317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> B)))
theorem-size     21
proof            (modus-ponens tm-660 tm-893 ((Am (-> A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80317.        ((A -> B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> B))), M:tm-660, m:tm-893, u:((Am (-> A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A B))))
================================================================
tm-name          tm-80318
in-theory        80318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> B))))
theorem-size     45
proof            (modus-ponens tm-654 tm-893 ((Am (-> A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A B)))))
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-49.           (((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-80318.        (((A -> B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> B)))), M:tm-654, m:tm-893, u:((Am (-> A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A B))))
================================================================
tm-name          tm-80319
in-theory        80319
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C or D) -> E) -> ((C or (C or D)) -> E)) and A)))
theorem-size     19
proof            (modus-ponens tm-623 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80319.        (A -> (B or ((((C or D) -> E) -> ((C or (C or D)) -> E)) and A))), M:tm-623, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80320
in-theory        80320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-622 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-80320.        ((A -> (B -> (C or B))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-622, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80321
in-theory        80321
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (B -> (C or B))))
theorem-size     27
proof            (modus-ponens tm-619 tm-893 ((Am (-> A (or B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 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-7.            (A -> (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-49.           (((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-80321.        ((A or (B -> (C or B))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (B -> (C or B)))), M:tm-619, m:tm-893, u:((Am (-> A (or B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (or B A)))))
================================================================
tm-name          tm-80322
in-theory        80322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-80322.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (F or E))), M:tm-609, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80323
in-theory        80323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-605 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-605.          (A -> ((B -> ((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-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-80323.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-605, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80324
in-theory        80324
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> (C or B)) and A)))
theorem-size     31
proof            (modus-ponens tm-602 tm-893 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80324.        ((A or ((B -> (C or B)) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-893, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-80325
in-theory        80325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-595 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-80325.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-595, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80326
in-theory        80326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-550 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-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-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-80326.        (((A -> (B or A)) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-550, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80327
in-theory        80327
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-540 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80327.        ((A or (B -> (C or B))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-540, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80328
in-theory        80328
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-530 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-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-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-80328.        ((A or (B -> (B or C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-530, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80329
in-theory        80329
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-520 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80329.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-520, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80330
in-theory        80330
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-510 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80330.        ((A or ((B and C) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-510, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80331
in-theory        80331
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-500 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80331.        ((A or ((B and C) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-500, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80332
in-theory        80332
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-490 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80332.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E))), M:tm-490, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80333
in-theory        80333
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-480 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80333.        ((A or (B -> (C -> B))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-480, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80334
in-theory        80334
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) -> ((B or (B or C)) -> D)) and A) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80334.        (A -> (((((B or C) -> D) -> ((B or (B or C)) -> D)) and A) or E)), M:tm-470, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80335
in-theory        80335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-469 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80335.        ((A -> (B -> (B or C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-469, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80336
in-theory        80336
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (B -> (B or C))))
theorem-size     27
proof            (modus-ponens tm-466 tm-893 ((Am (-> A (or A B))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80336.        ((A or (B -> (B or C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (B -> (B or C)))), M:tm-466, m:tm-893, u:((Am (-> A (or A B))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (or A B)))))
================================================================
tm-name          tm-80337
in-theory        80337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80337.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (E or F))), M:tm-456, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80338
in-theory        80338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-453 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-49.           (((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-80338.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-453, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80339
in-theory        80339
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> (B or C)) and A)))
theorem-size     31
proof            (modus-ponens tm-450 tm-893 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-49.           (((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-80339.        ((A or ((B -> (B or C)) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-893, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-80340
in-theory        80340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-443 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-80340.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-443, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80341
in-theory        80341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-409 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-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-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-80341.        (((A -> (A or B)) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-409, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80342
in-theory        80342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-400 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-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-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-80342.        (((A -> (B -> (A and B))) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-400, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80343
in-theory        80343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-391 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-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-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-80343.        ((((A and B) -> B) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-391, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80344
in-theory        80344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-382 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-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-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-80344.        ((((A and B) -> A) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-382, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80345
in-theory        80345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-373 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-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-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-80345.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E))), M:tm-373, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80346
in-theory        80346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-364 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80346.        (((A -> (B -> A)) or C) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-364, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80347
in-theory        80347
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C or D) -> E) -> ((C or (C or D)) -> E)) and A) and B)))
theorem-size     21
proof            (modus-ponens tm-355 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-80347.        (A -> (B -> (((((C or D) -> E) -> ((C or (C or D)) -> E)) and A) and B))), M:tm-355, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80348
in-theory        80348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-354 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80348.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-354, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80349
in-theory        80349
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (B -> (C -> (B and C)))))
theorem-size     31
proof            (modus-ponens tm-351 tm-893 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (-> B (and A B)))))))
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-5.            (A -> (B -> (A and 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-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-80349.        ((A or (B -> (C -> (B and C)))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-893, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-80350
in-theory        80350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-80350.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80351
in-theory        80351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-338 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80351.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C))), M:tm-338, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80352
in-theory        80352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-335 tm-893 ((Am (-> A (and A B))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80352.        (((A -> B) or (A -> (A and B))) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> (A and B)))), M:tm-335, m:tm-893, u:((Am (-> A (and A B))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (and A B)))))
================================================================
tm-name          tm-80353
in-theory        80353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (A -> (A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-328 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-80353.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (A -> (A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-328, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80354
in-theory        80354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     43
proof            (modus-ponens tm-327 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-80354.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-327, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80355
in-theory        80355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-326 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-80355.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-326, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80356
in-theory        80356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-325 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-80356.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-325, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80357
in-theory        80357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     49
proof            (modus-ponens tm-324 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80357.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-324, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80358
in-theory        80358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-323 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-80358.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-323, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80359
in-theory        80359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-80359.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80360
in-theory        80360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-80360.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80361
in-theory        80361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-80361.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80362
in-theory        80362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-80362.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (A -> A)), M:tm-316, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80363
in-theory        80363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-80363.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80364
in-theory        80364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((A -> (not ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80364.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((A -> (not ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))) -> (not A))), M:tm-313, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80365
in-theory        80365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((((((B or C) -> D) -> ((B or (B or C)) -> D)) and A) -> E) -> ((A or ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
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-312.          ((A -> B) -> ((A -> B) and ((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-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-80365.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((((((B or C) -> D) -> ((B or (B or C)) -> D)) and A) -> E) -> ((A or ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) -> E))), M:tm-312, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80366
in-theory        80366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E or (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-311 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-80366.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E or (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-311, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80367
in-theory        80367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-80367.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) or E)), M:tm-310, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80368
in-theory        80368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80368.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and E))), M:tm-309, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80369
in-theory        80369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-305 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-80369.        ((A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)) and (E -> (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)))), M:tm-305, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80370
in-theory        80370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-303 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80370.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-303, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80371
in-theory        80371
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> (C -> (B and C))) and A)))
theorem-size     35
proof            (modus-ponens tm-300 tm-893 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80371.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-893, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-80372
in-theory        80372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-270 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 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-270.          (A -> ((B -> (((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-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-80372.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-270, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80373
in-theory        80373
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((B and C) -> C) and A)))
theorem-size     31
proof            (modus-ponens tm-267 tm-893 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80373.        ((A or (((B and C) -> C) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((B and C) -> C) and A))), M:tm-267, m:tm-893, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-80374
in-theory        80374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-239 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 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-239.          (A -> ((B -> (((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-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-80374.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-239, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80375
in-theory        80375
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((B and C) -> B) and A)))
theorem-size     31
proof            (modus-ponens tm-236 tm-893 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80375.        ((A or (((B and C) -> B) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((B and C) -> B) and A))), M:tm-236, m:tm-893, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-80376
in-theory        80376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E)))
theorem-size     35
proof            (modus-ponens tm-210 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80376.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E))), M:tm-210, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80377
in-theory        80377
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     47
proof            (modus-ponens tm-207 tm-893 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80377.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-893, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-80378
in-theory        80378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-183 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 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-183.          (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-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-80378.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-183, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80379
in-theory        80379
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> (C -> B)) and A)))
theorem-size     31
proof            (modus-ponens tm-180 tm-893 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80379.        ((A or ((B -> (C -> B)) and A)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-893, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-80380
in-theory        80380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-157 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-80380.        ((A -> ((B and C) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-157, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80381
in-theory        80381
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B and C) -> C)))
theorem-size     27
proof            (modus-ponens tm-154 tm-893 ((Am (-> (and A B) B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 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-4.            ((A 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-49.           (((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-80381.        ((A or ((B and C) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B and C) -> C))), M:tm-154, m:tm-893, u:((Am (-> (and A B) B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (and A B) B))))
================================================================
tm-name          tm-80382
in-theory        80382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-147 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80382.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-147, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80383
in-theory        80383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A and (B -> C)) -> C)))
theorem-size     37
proof            (modus-ponens tm-144 tm-893 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80383.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-893, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-80384
in-theory        80384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-134 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-80384.        ((A -> ((B and C) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-134, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80385
in-theory        80385
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B and C) -> B)))
theorem-size     27
proof            (modus-ponens tm-131 tm-893 ((Am (-> (and A B) A)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 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-3.            ((A 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-49.           (((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-80385.        ((A or ((B and C) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B and C) -> B))), M:tm-131, m:tm-893, u:((Am (-> (and A B) A)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (and A B) A))))
================================================================
tm-name          tm-80386
in-theory        80386
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-125 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80386.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-125, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80387
in-theory        80387
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((A -> B) and C) -> B)))
theorem-size     37
proof            (modus-ponens tm-122 tm-893 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (or Bm Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80387.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-893, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-80388
in-theory        80388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-113 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80388.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E))), M:tm-113, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80389
in-theory        80389
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     43
proof            (modus-ponens tm-110 tm-893 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (or Bm Cm) Dm) (-> (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       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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80389.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-893, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-80390
in-theory        80390
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     37
proof            (modus-ponens tm-105 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80390.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-105, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80391
in-theory        80391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-102 tm-893 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80391.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-893, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-80392
in-theory        80392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-95 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80392.        (((A -> B) -> (A -> A)) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C))), M:tm-95, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80393
in-theory        80393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> A)))
theorem-size     25
proof            (modus-ponens tm-92 tm-893 ((Am (-> A A)) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80393.        (((A -> B) or (A -> A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A -> A))), M:tm-92, m:tm-893, u:((Am (-> A A)) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A A))))
================================================================
tm-name          tm-80394
in-theory        80394
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and A)))
theorem-size     19
proof            (modus-ponens tm-84 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80394.        (A -> (B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and A))), M:tm-84, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80395
in-theory        80395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-83 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-80395.        ((A -> (B -> (C -> B))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-83, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80396
in-theory        80396
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (B -> (C -> B))))
theorem-size     27
proof            (modus-ponens tm-80 tm-893 ((Am (-> A (-> B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (-> B A))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-49.           (((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-80396.        ((A or (B -> (C -> B))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and (B -> (C -> B)))), M:tm-80, m:tm-893, u:((Am (-> A (-> B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> A (-> B A)))))
================================================================
tm-name          tm-80397
in-theory        80397
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B)))
theorem-size     23
proof            (modus-ponens tm-76 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80397.        (((not (not A)) -> A) and (B -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and B))), M:tm-76, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80398
in-theory        80398
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-893 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80398.        (((not (not A)) or A) -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)), M:tm-73, m:tm-893, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-80399
in-theory        80399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C)))
theorem-size     29
proof            (modus-ponens tm-69 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80399.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and C))), M:tm-69, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80400
in-theory        80400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and ((A -> (not B)) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-66 tm-893 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80400.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-893, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-80401
in-theory        80401
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-54 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
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-49.           (((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-80401.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-54, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-80402
in-theory        80402
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-51 tm-893 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80402.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-893, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-80403
in-theory        80403
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-50 tm-893 ((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80403.        ((A or (B or A)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (B or A))), M:tm-50, m:tm-893, u:((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-80404
in-theory        80404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-894 tm-365 ((Am (-> (or (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))) (Dm (or (-> Bm (-> Cm Bm)) B))))
axioms-used      (tm-2 tm-8 tm-6 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80404.        ((((A -> (B -> A)) or C) -> D) -> D), M:tm-894, m:tm-365, u:((Am (-> (or (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))) (Dm (or (-> Bm (-> Cm Bm)) B)))
================================================================
tm-name          tm-80405
in-theory        80405
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) -> E)
theorem-size     19
proof            (modus-ponens tm-894 tm-374 ((Am (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B))))
axioms-used      (tm-2 tm-8 tm-6 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80405.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) -> E), M:tm-894, m:tm-374, u:((Am (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)))
================================================================
tm-name          tm-80406
in-theory        80406
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-894 tm-383 ((Am (-> (or (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)) (Dm (or (-> (and Bm Cm) Bm) B))))
axioms-used      (tm-2 tm-8 tm-6 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80406.        (((((A and B) -> A) or C) -> D) -> D), M:tm-894, m:tm-383, u:((Am (-> (or (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)) (Dm (or (-> (and Bm Cm) Bm) B)))
================================================================
tm-name          tm-80407
in-theory        80407
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-894 tm-392 ((Am (-> (or (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)) (Dm (or (-> (and Bm Cm) Cm) B))))
axioms-used      (tm-2 tm-8 tm-6 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80407.        (((((A and B) -> B) or C) -> D) -> D), M:tm-894, m:tm-392, u:((Am (-> (or (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)) (Dm (or (-> (and Bm Cm) Cm) B)))
================================================================
tm-name          tm-80408
in-theory        80408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) -> D) -> D)
theorem-size     13
proof            (modus-ponens tm-894 tm-401 ((Am (-> (or (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))) (Dm (or (-> Bm (-> Cm (and Bm Cm))) B))))
axioms-used      (tm-2 tm-8 tm-6 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80408.        ((((A -> (B -> (A and B))) or C) -> D) -> D), M:tm-894, m:tm-401, u:((Am (-> (or (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))) (Dm (or (-> Bm (-> Cm (and Bm Cm))) B)))
================================================================
tm-name          tm-80409
in-theory        80409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-894 tm-410 ((Am (-> (or (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))) (Dm (or (-> Bm (or Bm Cm)) B))))
axioms-used      (tm-2 tm-8 tm-6 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80409.        ((((A -> (A or B)) or C) -> D) -> D), M:tm-894, m:tm-410, u:((Am (-> (or (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))) (Dm (or (-> Bm (or Bm Cm)) B)))
================================================================
tm-name          tm-80410
in-theory        80410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-894 tm-551 ((Am (-> (or (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))) (Dm (or (-> Bm (or Cm Bm)) B))))
axioms-used      (tm-2 tm-8 tm-6 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80410.        ((((A -> (B or A)) or C) -> D) -> D), M:tm-894, m:tm-551, u:((Am (-> (or (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))) (Dm (or (-> Bm (or Cm Bm)) B)))
================================================================
tm-name          tm-80411
in-theory        80411
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-893 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-80411.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-893, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80412
in-theory        80412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     37
proof            (modus-ponens tm-855 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80412.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-855, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80413
in-theory        80413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-808 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80413.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-808, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80414
in-theory        80414
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((D and (((A or B) -> C) -> (A or (A or B)))) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C)))
theorem-size     53
proof            (modus-ponens tm-798 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80414.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((D and (((A or B) -> C) -> (A or (A or B)))) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C))), M:tm-798, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80415
in-theory        80415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-757 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80415.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-757, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80416
in-theory        80416
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((((((A or B) -> C) -> (A or (A or B))) and D) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C)))
theorem-size     53
proof            (modus-ponens tm-747 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-80416.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((((((A or B) -> C) -> (A or (A or B))) and D) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C))), M:tm-747, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80417
in-theory        80417
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))) -> (((E or F) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-708 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80417.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G))), M:tm-708, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80418
in-theory        80418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-665 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80418.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-665, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80419
in-theory        80419
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((A or (A or B)) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C)))
theorem-size     45
proof            (modus-ponens tm-654 tm-894 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C (-> (-> (or Am Bm) Cm) Cm))))
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-49.           (((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-80419.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((A or (A or B)) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C))), M:tm-654, m:tm-894, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80420
in-theory        80420
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (A or (A or B))) -> (D or (((A or B) -> C) -> C)))
theorem-size     21
proof            (modus-ponens tm-623 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80420.        ((((A or B) -> C) -> (A or (A or B))) -> (D or (((A or B) -> C) -> C))), M:tm-623, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80421
in-theory        80421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-622 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80421.        ((A -> (B -> (C or B))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-622, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80422
in-theory        80422
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-80422.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E or D))), M:tm-609, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80423
in-theory        80423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-605 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-605.          (A -> ((B -> ((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80423.        ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-605, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80424
in-theory        80424
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E or D)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-595 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-80424.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E or D)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-595, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80425
in-theory        80425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-550 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-49.           (((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-80425.        (((A -> (B or A)) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-550, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80426
in-theory        80426
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-540 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80426.        ((A or (B -> (C or B))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-540, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80427
in-theory        80427
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-530 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-49.           (((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-80427.        ((A or (B -> (B or C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-530, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80428
in-theory        80428
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-520 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80428.        ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-520, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80429
in-theory        80429
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-510 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80429.        ((A or ((B and C) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-510, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80430
in-theory        80430
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-500 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80430.        ((A or ((B and C) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-500, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80431
in-theory        80431
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-490 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80431.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G))), M:tm-490, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80432
in-theory        80432
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-480 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80432.        ((A or (B -> (C -> B))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-480, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80433
in-theory        80433
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (A or (A or B))) -> ((((A or B) -> C) -> C) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or 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-49.           (((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-80433.        ((((A or B) -> C) -> (A or (A or B))) -> ((((A or B) -> C) -> C) or D)), M:tm-470, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80434
in-theory        80434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-469 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or 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-49.           (((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-80434.        ((A -> (B -> (B or C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-469, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80435
in-theory        80435
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or 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-49.           (((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-80435.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (D or E))), M:tm-456, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80436
in-theory        80436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-453 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-80436.        ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-453, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80437
in-theory        80437
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (D or E)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-443 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
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-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-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-80437.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (D or E)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-443, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80438
in-theory        80438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-409 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-49.           (((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-80438.        (((A -> (A or B)) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-409, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80439
in-theory        80439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-400 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-80439.        (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-400, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80440
in-theory        80440
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-391 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-49.           (((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-80440.        ((((A and B) -> B) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-391, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80441
in-theory        80441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-382 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-49.           (((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-80441.        ((((A and B) -> A) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-382, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80442
in-theory        80442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-373 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-49.           (((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-80442.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G))), M:tm-373, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80443
in-theory        80443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-364 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or 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-49.           (((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-80443.        (((A -> (B -> A)) or C) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-364, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80444
in-theory        80444
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (A or (A or B))) -> (D -> ((((A or B) -> C) -> C) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80444.        ((((A or B) -> C) -> (A or (A or B))) -> (D -> ((((A or B) -> C) -> C) and D))), M:tm-355, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80445
in-theory        80445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-354 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80445.        ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-354, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80446
in-theory        80446
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-80446.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80447
in-theory        80447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-338 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-80447.        (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E))), M:tm-338, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80448
in-theory        80448
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((((A or B) -> C) -> (A or (A or B))) -> ((((A or B) -> C) -> (A or (A or B))) and (((A or B) -> C) -> C))))
theorem-size     51
proof            (modus-ponens tm-328 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-80448.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((((A or B) -> C) -> (A or (A or B))) -> ((((A or B) -> C) -> (A or (A or B))) and (((A or B) -> C) -> C)))), M:tm-328, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80449
in-theory        80449
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> (D and E))) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     47
proof            (modus-ponens tm-327 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-80449.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> (D and E))) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-327, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80450
in-theory        80450
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((D and E) -> E) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-326 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-80450.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((D and E) -> E) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-326, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80451
in-theory        80451
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((D and E) -> D) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-325 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-80451.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((D and E) -> D) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-325, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80452
in-theory        80452
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     53
proof            (modus-ponens tm-324 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-80452.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-324, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80453
in-theory        80453
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> D)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-323 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-80453.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> D)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-323, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80454
in-theory        80454
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-80454.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80455
in-theory        80455
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-80455.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80456
in-theory        80456
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-80456.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80457
in-theory        80457
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> (A or (A or B)))))
theorem-size     43
proof            (modus-ponens tm-316 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-80457.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> (A or (A or B))))), M:tm-316, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80458
in-theory        80458
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-80458.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80459
in-theory        80459
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (A or (A or B))) -> (not (((A or B) -> C) -> C))) -> (not (((A or B) -> C) -> (A or (A or B))))))
theorem-size     53
proof            (modus-ponens tm-313 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80459.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (A or (A or B))) -> (not (((A or B) -> C) -> C))) -> (not (((A or B) -> C) -> (A or (A or B)))))), M:tm-313, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80460
in-theory        80460
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> C) -> D) -> (((((A or B) -> C) -> (A or (A or B))) or (((A or B) -> C) -> C)) -> D)))
theorem-size     51
proof            (modus-ponens tm-312 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
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-49.           (((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-80460.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> C) -> D) -> (((((A or B) -> C) -> (A or (A or B))) or (((A or B) -> C) -> C)) -> D))), M:tm-312, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80461
in-theory        80461
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D or ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     41
proof            (modus-ponens tm-311 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-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-80461.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D or ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-311, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80462
in-theory        80462
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-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-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-80462.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) or D)), M:tm-310, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80463
in-theory        80463
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-80463.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and D))), M:tm-309, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80464
in-theory        80464
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (A or (A or B))) -> ((A or B) -> C)) -> ((((A or B) -> C) -> (A or (A or B))) -> C)))
theorem-size     51
proof            (modus-ponens tm-306 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (or Am Bm) Cm)) (C Cm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-80464.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (A or (A or B))) -> ((A or B) -> C)) -> ((((A or B) -> C) -> (A or (A or B))) -> C))), M:tm-306, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (or Am Bm) Cm)) (C Cm))
================================================================
tm-name          tm-80465
in-theory        80465
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     41
proof            (modus-ponens tm-305 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-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-80465.        (((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)) and (D -> ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-305, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80466
in-theory        80466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-303 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80466.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-303, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80467
in-theory        80467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-270 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 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-270.          (A -> ((B -> (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80467.        ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-270, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80468
in-theory        80468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-239 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 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-239.          (A -> ((B -> (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80468.        ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-239, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80469
in-theory        80469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     37
proof            (modus-ponens tm-210 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80469.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G))), M:tm-210, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80470
in-theory        80470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-183 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80470.        ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-183, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80471
in-theory        80471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-157 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80471.        ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-157, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80472
in-theory        80472
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-147 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-80472.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-147, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80473
in-theory        80473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-134 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80473.        ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-134, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80474
in-theory        80474
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-125 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-80474.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-125, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80475
in-theory        80475
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> D)) -> (A or (A or B))) -> ((((A or B) -> (C -> D)) -> C) -> (((A or B) -> (C -> D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-114 tm-894 ((A (-> (-> (or Am Bm) (-> C D)) (or Am (or Am Bm)))) (B (-> (or Am Bm) (-> C D))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80475.        ((((A or B) -> (C -> D)) -> (A or (A or B))) -> ((((A or B) -> (C -> D)) -> C) -> (((A or B) -> (C -> D)) -> D))), M:tm-114, m:tm-894, u:((A (-> (-> (or Am Bm) (-> C D)) (or Am (or Am Bm)))) (B (-> (or Am Bm) (-> C D))) (Cm (-> C D)))
================================================================
tm-name          tm-80476
in-theory        80476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-113 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80476.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G))), M:tm-113, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80477
in-theory        80477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     39
proof            (modus-ponens tm-105 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-80477.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-105, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80478
in-theory        80478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-95 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-80478.        (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E))), M:tm-95, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80479
in-theory        80479
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (A or (A or B))) -> (D -> (((A or B) -> C) -> C)))
theorem-size     21
proof            (modus-ponens tm-84 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80479.        ((((A or B) -> C) -> (A or (A or B))) -> (D -> (((A or B) -> C) -> C))), M:tm-84, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80480
in-theory        80480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-83 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80480.        ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-83, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80481
in-theory        80481
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or C) -> D) -> (B or (B or C))) -> (((B or C) -> D) -> D)))
theorem-size     25
proof            (modus-ponens tm-76 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80481.        (((not (not A)) -> A) and ((((B or C) -> D) -> (B or (B or C))) -> (((B or C) -> D) -> D))), M:tm-76, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80482
in-theory        80482
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A or B) -> C) -> (A or (A or B))))) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-73 tm-894 ((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80482.        (((not (not (((A or B) -> C) -> (A or (A or B))))) or (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C)), M:tm-73, m:tm-894, u:((A (-> (-> (or Am Bm) Cm) (or Am (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-80483
in-theory        80483
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (A or (A or B)))) -> (A or (A or B))) -> (not ((A or B) -> (not (A or (A or B))))))
theorem-size     28
proof            (modus-ponens tm-70 tm-894 ((B (or Am (or Am Bm))) (A (-> (or Am Bm) (not (or Am (or Am Bm))))) (Cm (not (or Am (or Am Bm))))))
axioms-used      (tm-2 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80483.        ((((A or B) -> (not (A or (A or B)))) -> (A or (A or B))) -> (not ((A or B) -> (not (A or (A or B)))))), M:tm-70, m:tm-894, u:((B (or Am (or Am Bm))) (A (-> (or Am Bm) (not (or Am (or Am Bm))))) (Cm (not (or Am (or Am Bm)))))
================================================================
tm-name          tm-80484
in-theory        80484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-69 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80484.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> (C or (C or D))) -> (((C or D) -> E) -> E))), M:tm-69, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80485
in-theory        80485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-54 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80485.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-54, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-80486
in-theory        80486
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-893 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
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-80486.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-893, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80487
in-theory        80487
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-890 tm-895 ((Am (-> (or A (or A B)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-6 tm-1)
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-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-1.            (A -> (B -> A)), axiom
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-80487.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-890, m:tm-895, u:((Am (-> (or A (or A B)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80488
in-theory        80488
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     17
proof            (modus-ponens tm-888 tm-895 ((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-80488.        ((A or B) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-888, m:tm-895, u:((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80489
in-theory        80489
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((A or (A or B)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     37
proof            (modus-ponens tm-882 tm-895 ((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
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-80489.        (((A or B) -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((A or (A or B)) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-882, m:tm-895, u:((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80490
in-theory        80490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-855 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80490.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-855, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80491
in-theory        80491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-852 tm-895 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80491.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-852, m:tm-895, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80492
in-theory        80492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-850 tm-895 ((Am (-> A (and B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80492.        ((A -> (B and A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-850, m:tm-895, u:((Am (-> A (and B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80493
in-theory        80493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((B or (A -> (B and A))) -> (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     41
proof            (modus-ponens tm-844 tm-895 ((Am (-> A (and B A))) (C (-> (-> (or Bm Cm) Dm) (-> (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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80493.        (((A -> (B and A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((B or (A -> (B and A))) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-844, m:tm-895, u:((Am (-> A (and B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80494
in-theory        80494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-808 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-6)
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80494.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-808, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80495
in-theory        80495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-805 tm-895 ((Am (-> (or (and A B) B) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
proof-size       141
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80495.        (((A -> B) or (((C and A) or A) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-805, m:tm-895, u:((Am (-> (or (and A B) B) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80496
in-theory        80496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and A) or A) -> (((B or C) -> D) -> ((B or (B or C)) -> D))))
theorem-size     35
proof            (modus-ponens tm-798 tm-895 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-80496.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and A) or A) -> (((B or C) -> D) -> ((B or (B or C)) -> D)))), M:tm-798, m:tm-895, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80497
in-theory        80497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-757 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80497.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-757, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80498
in-theory        80498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-754 tm-895 ((Am (-> (or (and A B) A) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80498.        (((A -> B) or (((A and C) or A) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-754, m:tm-895, u:((Am (-> (or (and A B) A) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80499
in-theory        80499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((A and E) or A) -> (((B or C) -> D) -> ((B or (B or C)) -> D))))
theorem-size     35
proof            (modus-ponens tm-747 tm-895 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-49.           (((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-80499.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((A and E) or A) -> (((B or C) -> D) -> ((B or (B or C)) -> D)))), M:tm-747, m:tm-895, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80500
in-theory        80500
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     41
proof            (modus-ponens tm-708 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-49.           (((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-80500.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-708, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80501
in-theory        80501
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-705 tm-895 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) 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-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), 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-49.           (((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-80501.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-705, m:tm-895, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80502
in-theory        80502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-703 tm-895 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-49.           (((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-80502.        (((A -> B) -> (A -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-703, m:tm-895, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80503
in-theory        80503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     49
proof            (modus-ponens tm-697 tm-895 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-49.           (((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-80503.        ((((A -> B) -> (A -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-697, m:tm-895, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80504
in-theory        80504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-665 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80504.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-665, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80505
in-theory        80505
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-662 tm-895 ((Am (-> (or A (-> B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80505.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-662, m:tm-895, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80506
in-theory        80506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     17
proof            (modus-ponens tm-660 tm-895 ((Am (-> A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80506.        ((A -> B) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-660, m:tm-895, u:((Am (-> A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80507
in-theory        80507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((B or (A -> B)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     37
proof            (modus-ponens tm-654 tm-895 ((Am (-> A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-80507.        (((A -> B) -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((B or (A -> B)) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-654, m:tm-895, u:((Am (-> A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80508
in-theory        80508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-622 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-80508.        ((A -> (B -> (C or B))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-622, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80509
in-theory        80509
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-619 tm-895 ((Am (-> A (or B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 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-7.            (A -> (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-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-80509.        ((A or (B -> (C or B))) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-619, m:tm-895, u:((Am (-> A (or B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80510
in-theory        80510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-80510.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80511
in-theory        80511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-605 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80511.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-605, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80512
in-theory        80512
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-602 tm-895 ((Am (and (-> A (or B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80512.        ((A or ((B -> (C or B)) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-602, m:tm-895, u:((Am (and (-> A (or B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80513
in-theory        80513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F or E)) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80513.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F or E)) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-595, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80514
in-theory        80514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-550 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80514.        (((A -> (B or A)) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-550, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80515
in-theory        80515
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-540 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80515.        ((A or (B -> (C or B))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-540, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80516
in-theory        80516
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-530 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80516.        ((A or (B -> (B or C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-530, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80517
in-theory        80517
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-520 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80517.        ((A or (B -> (C -> (B and C)))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-520, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80518
in-theory        80518
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-510 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80518.        ((A or ((B and C) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-510, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80519
in-theory        80519
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-500 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80519.        ((A or ((B and C) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-500, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80520
in-theory        80520
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-490 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80520.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-490, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80521
in-theory        80521
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-480 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80521.        ((A or (B -> (C -> B))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-480, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80522
in-theory        80522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-469 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80522.        ((A -> (B -> (B or C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-469, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80523
in-theory        80523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-466 tm-895 ((Am (-> A (or A B))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80523.        ((A or (B -> (B or C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-466, m:tm-895, u:((Am (-> A (or A B))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80524
in-theory        80524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80524.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80525
in-theory        80525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-453 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80525.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-453, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80526
in-theory        80526
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-450 tm-895 ((Am (and (-> A (or A B)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80526.        ((A or ((B -> (B or C)) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-450, m:tm-895, u:((Am (and (-> A (or A B)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80527
in-theory        80527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (E or F)) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80527.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (E or F)) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-443, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80528
in-theory        80528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-409 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80528.        (((A -> (A or B)) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-409, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80529
in-theory        80529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-400 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80529.        (((A -> (B -> (A and B))) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-400, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80530
in-theory        80530
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-391 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80530.        ((((A and B) -> B) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-391, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80531
in-theory        80531
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-382 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80531.        ((((A and B) -> A) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-382, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80532
in-theory        80532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-373 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80532.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-373, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80533
in-theory        80533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-364 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80533.        (((A -> (B -> A)) or C) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-364, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80534
in-theory        80534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-354 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80534.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-354, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80535
in-theory        80535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-351 tm-895 ((Am (-> A (-> B (and A B)))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
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-5.            (A -> (B -> (A and 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-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-80535.        ((A or (B -> (C -> (B and C)))) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-351, m:tm-895, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80536
in-theory        80536
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (A and (B or C))))
theorem-size     13
proof            (modus-ponens tm-349 tm-895 ((A Am) (B (or Bm Cm)) (Dm (and Am (or Bm Cm))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80536.        (A -> ((B or (B or C)) -> (A and (B or C)))), M:tm-349, m:tm-895, u:((A Am) (B (or Bm Cm)) (Dm (and Am (or Bm Cm))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-80537
in-theory        80537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-80537.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80538
in-theory        80538
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) -> ((((A or B) -> C) -> ((A or (A or B)) -> C)) and D))
theorem-size     31
proof            (modus-ponens tm-339 tm-895 ((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B)) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80538.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) -> ((((A or B) -> C) -> ((A or (A or B)) -> C)) and D)), M:tm-339, m:tm-895, u:((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B)) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80539
in-theory        80539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-338 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80539.        (((A -> B) -> (A -> (A and B))) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-338, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80540
in-theory        80540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-335 tm-895 ((Am (-> A (and A B))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
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-49.           (((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-80540.        (((A -> B) or (A -> (A and B))) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-335, m:tm-895, u:((Am (-> A (and A B))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80541
in-theory        80541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (A -> (A and (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-328 tm-895 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-328.          ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80541.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (A -> (A and (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-328, m:tm-895, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80542
in-theory        80542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80542.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-327, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80543
in-theory        80543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and F) -> F) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80543.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and F) -> F) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-326, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80544
in-theory        80544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and F) -> E) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80544.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E and F) -> E) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-325, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80545
in-theory        80545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-80545.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-324, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80546
in-theory        80546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> E)) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
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-49.           (((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-80546.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> E)) and (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-323, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80547
in-theory        80547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-80547.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80548
in-theory        80548
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E)) -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E)) -> E))
theorem-size     51
proof            (modus-ponens tm-321 tm-895 ((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) C))) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 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-17.           (((A and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80548.        (((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E)) -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E)) -> E)), M:tm-321, m:tm-895, u:((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) C))) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80549
in-theory        80549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-80549.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80550
in-theory        80550
times-derived    1
----------------------------------------------------------------
theorem          (((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) and E) -> (((A or B) -> C) -> ((A or (A or B)) -> C))) and ((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) and E) -> D))
theorem-size     51
proof            (modus-ponens tm-319 tm-895 ((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B) C)) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80550.        (((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) and E) -> (((A or B) -> C) -> ((A or (A or B)) -> C))) and ((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) and E) -> D)), M:tm-319, m:tm-895, u:((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B) C)) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80551
in-theory        80551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-80551.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80552
in-theory        80552
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (((A or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> ((A or (A or B)) -> C))) and ((((A or B) -> C) -> (((A or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> D)))
theorem-size     53
proof            (modus-ponens tm-317 tm-895 ((Am (-> (-> (or Bm Cm) Dm) (-> (-> (or Bm (or Bm Cm)) Dm) C))) (A (-> (or Bm Cm) Dm)) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-13.           (((A -> (B -> C)) -> (A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80552.        (((((A or B) -> C) -> (((A or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> ((A or (A or B)) -> C))) and ((((A or B) -> C) -> (((A or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> D))), M:tm-317, m:tm-895, u:((Am (-> (-> (or Bm Cm) Dm) (-> (-> (or Bm (or Bm Cm)) Dm) C))) (A (-> (or Bm Cm) Dm)) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-80553
in-theory        80553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (A -> A))
theorem-size     19
proof            (modus-ponens tm-316 tm-895 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80553.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (A -> A)), M:tm-316, m:tm-895, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80554
in-theory        80554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-80554.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80555
in-theory        80555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A -> (not (((B or C) -> D) -> ((B or (B or C)) -> D)))) -> (not A)))
theorem-size     35
proof            (modus-ponens tm-313 tm-895 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80555.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A -> (not (((B or C) -> D) -> ((B or (B or C)) -> D)))) -> (not A))), M:tm-313, m:tm-895, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80556
in-theory        80556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E) -> ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-895 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80556.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E) -> ((A or (((B or C) -> D) -> ((B or (B or C)) -> D))) -> E))), M:tm-312, m:tm-895, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80557
in-theory        80557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E or (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80557.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E or (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-311, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80558
in-theory        80558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-49.           (((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-80558.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) or E)), M:tm-310, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80559
in-theory        80559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80559.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and E))), M:tm-309, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80560
in-theory        80560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A -> ((B or C) -> D)) -> (A -> ((B or (B or C)) -> D))))
theorem-size     33
proof            (modus-ponens tm-306 tm-895 ((A Am) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80560.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and ((A -> ((B or C) -> D)) -> (A -> ((B or (B or C)) -> D)))), M:tm-306, m:tm-895, u:((A Am) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-80561
in-theory        80561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
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-49.           (((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-80561.        ((A -> (((B or C) -> D) -> ((B or (B or C)) -> D))) and (E -> (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))))), M:tm-305, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80562
in-theory        80562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-303 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80562.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-303, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80563
in-theory        80563
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-300 tm-895 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80563.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-300, m:tm-895, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80564
in-theory        80564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-270 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80564.        ((A -> (((B and C) -> C) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-270, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80565
in-theory        80565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-267 tm-895 ((Am (and (-> (and A B) B) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80565.        ((A or (((B and C) -> C) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-267, m:tm-895, u:((Am (and (-> (and A B) B) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80566
in-theory        80566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-239 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80566.        ((A -> (((B and C) -> B) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-239, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80567
in-theory        80567
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-236 tm-895 ((Am (and (-> (and A B) A) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80567.        ((A or (((B and C) -> B) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-236, m:tm-895, u:((Am (and (-> (and A B) A) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80568
in-theory        80568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-210 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80568.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-210, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80569
in-theory        80569
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-207 tm-895 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80569.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-207, m:tm-895, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80570
in-theory        80570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-183 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80570.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-183, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80571
in-theory        80571
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-180 tm-895 ((Am (and (-> A (-> B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80571.        ((A or ((B -> (C -> B)) and A)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-180, m:tm-895, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80572
in-theory        80572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-157 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-80572.        ((A -> ((B and C) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-157, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80573
in-theory        80573
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-154 tm-895 ((Am (-> (and A B) B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-4 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-4.            ((A 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-49.           (((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-80573.        ((A or ((B and C) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-154, m:tm-895, u:((Am (-> (and A B) B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80574
in-theory        80574
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or C) -> D)) -> ((B or (B or C)) -> D))
theorem-size     15
proof            (modus-ponens tm-152 tm-895 ((Am (and A (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80574.        ((A and ((B or C) -> D)) -> ((B or (B or C)) -> D)), M:tm-152, m:tm-895, u:((Am (and A (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-80575
in-theory        80575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-147 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80575.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-147, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80576
in-theory        80576
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-144 tm-895 ((Am (-> (and A (-> B C)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80576.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-144, m:tm-895, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80577
in-theory        80577
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E)) -> (((B or C) -> D) -> ((B or (B or C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-142 tm-895 ((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) C))) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80577.        ((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> E)) -> (((B or C) -> D) -> ((B or (B or C)) -> D))), M:tm-142, m:tm-895, u:((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) C))) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80578
in-theory        80578
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> ((B or C) -> D))) -> ((B or (B or C)) -> D))
theorem-size     29
proof            (modus-ponens tm-141 tm-895 ((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or Bm Cm) Dm)))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-4 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80578.        ((A and ((((B or C) -> D) -> ((B or (B or C)) -> D)) -> ((B or C) -> D))) -> ((B or (B or C)) -> D)), M:tm-141, m:tm-895, u:((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or Bm Cm) Dm)))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-80579
in-theory        80579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-134 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-80579.        ((A -> ((B and C) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-134, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80580
in-theory        80580
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-131 tm-895 ((Am (-> (and A B) A)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-3 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-3.            ((A 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-49.           (((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-80580.        ((A or ((B and C) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-131, m:tm-895, u:((Am (-> (and A B) A)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80581
in-theory        80581
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) and D) -> ((A or (A or B)) -> C))
theorem-size     15
proof            (modus-ponens tm-129 tm-895 ((Am (and (-> (or Bm Cm) Dm) B)) (A (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80581.        ((((A or B) -> C) and D) -> ((A or (A or B)) -> C)), M:tm-129, m:tm-895, u:((Am (and (-> (or Bm Cm) Dm) B)) (A (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-80582
in-theory        80582
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-125 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80582.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-125, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80583
in-theory        80583
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-122 tm-895 ((Am (-> (and (-> A B) C) B)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80583.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-122, m:tm-895, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80584
in-theory        80584
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) and E) -> (((A or B) -> C) -> ((A or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-120 tm-895 ((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B) C)) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80584.        ((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) and E) -> (((A or B) -> C) -> ((A or (A or B)) -> C))), M:tm-120, m:tm-895, u:((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B) C)) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80585
in-theory        80585
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> ((A or B) -> C)) and D) -> ((A or (A or B)) -> C))
theorem-size     29
proof            (modus-ponens tm-119 tm-895 ((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or Bm Cm) Dm)) C)) (A (-> (or Bm Cm) Dm)) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80585.        ((((((A or B) -> C) -> ((A or (A or B)) -> C)) -> ((A or B) -> C)) and D) -> ((A or (A or B)) -> C)), M:tm-119, m:tm-895, u:((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or Bm Cm) Dm)) C)) (A (-> (or Bm Cm) Dm)) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-80586
in-theory        80586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-113 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80586.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-113, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80587
in-theory        80587
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-110 tm-895 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80587.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-110, m:tm-895, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80588
in-theory        80588
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-106 tm-895 ((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> (or Bm Cm) Dm) (or Bm (or Bm Cm))))) (A (-> (or Bm Cm) Dm)) (B (or Bm (or Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80588.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> (((A or B) -> C) -> (A or (A or B)))) -> (((A or B) -> C) -> C)), M:tm-106, m:tm-895, u:((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> (or Bm Cm) Dm) (or Bm (or Bm Cm))))) (A (-> (or Bm Cm) Dm)) (B (or Bm (or Bm Cm))) (C Dm))
================================================================
tm-name          tm-80589
in-theory        80589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-105 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80589.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-105, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80590
in-theory        80590
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-102 tm-895 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80590.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-102, m:tm-895, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80591
in-theory        80591
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-100 tm-895 ((Am (-> (-> (or Bm Cm) Dm) (-> (-> (or Bm (or Bm Cm)) Dm) C))) (A (-> (or Bm Cm) Dm)) (B (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80591.        ((((A or B) -> C) -> (((A or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> ((A or (A or B)) -> C))), M:tm-100, m:tm-895, u:((Am (-> (-> (or Bm Cm) Dm) (-> (-> (or Bm (or Bm Cm)) Dm) C))) (A (-> (or Bm Cm) Dm)) (B (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-80592
in-theory        80592
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> A))
theorem-size     9
proof            (modus-ponens tm-98 tm-895 ((Dm Am) (B (or Bm Cm)) (A Am) (C (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80592.        (A -> ((B or (B or C)) -> A)), M:tm-98, m:tm-895, u:((Dm Am) (B (or Bm Cm)) (A Am) (C (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-80593
in-theory        80593
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) -> (((A or B) -> C) -> ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-96 tm-895 ((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B)) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80593.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) -> (((A or B) -> C) -> ((A or (A or B)) -> C))), M:tm-96, m:tm-895, u:((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B)) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80594
in-theory        80594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-95 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-80594.        (((A -> B) -> (A -> A)) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-95, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80595
in-theory        80595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-92 tm-895 ((Am (-> A A)) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 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-1.            (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-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-80595.        (((A -> B) or (A -> A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-92, m:tm-895, u:((Am (-> A A)) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80596
in-theory        80596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-83 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-80596.        ((A -> (B -> (C -> B))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-83, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80597
in-theory        80597
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-80 tm-895 ((Am (-> A (-> B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-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-80597.        ((A or (B -> (C -> B))) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-80, m:tm-895, u:((Am (-> A (-> B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80598
in-theory        80598
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D))) -> D)
theorem-size     19
proof            (modus-ponens tm-77 tm-895 ((Am (not (not (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B)))) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80598.        ((not (not ((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D))) -> D), M:tm-77, m:tm-895, u:((Am (not (not (-> (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) B)))) (A (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80599
in-theory        80599
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     21
proof            (modus-ponens tm-76 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80599.        (((not (not A)) -> A) and (B -> (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-76, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80600
in-theory        80600
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B or C) -> D) -> ((B or (B or C)) -> D)))
theorem-size     19
proof            (modus-ponens tm-73 tm-895 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80600.        (((not (not A)) or A) -> (((B or C) -> D) -> ((B or (B or C)) -> D))), M:tm-73, m:tm-895, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80601
in-theory        80601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-69 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8 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-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-80601.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-69, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80602
in-theory        80602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-66 tm-895 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80602.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-66, m:tm-895, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80603
in-theory        80603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or C) -> D)) -> ((A or ((B or C) -> D)) -> ((B or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-55 tm-895 ((Am (-> A (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80603.        ((A -> ((B or C) -> D)) -> ((A or ((B or C) -> D)) -> ((B or (B or C)) -> D))), M:tm-55, m:tm-895, u:((Am (-> A (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-80604
in-theory        80604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-54 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or 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-54.           (A -> (((B -> C) -> ((C -> 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-49.           (((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-80604.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-54, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-80605
in-theory        80605
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-51 tm-895 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80605.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-51, m:tm-895, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80606
in-theory        80606
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-50 tm-895 ((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-80606.        ((A or (B or A)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-50, m:tm-895, u:((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-80607
in-theory        80607
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80607.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-893, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80608
in-theory        80608
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((A or (A or (B or A))) -> (C -> (B or A))))
theorem-size     25
proof            (modus-ponens tm-882 tm-896 ((A Am) (B (or Bm Am)) (C (-> Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80608.        (((A or (B or A)) -> (C -> (B or A))) and ((A or (A or (B or A))) -> (C -> (B or A)))), M:tm-882, m:tm-896, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80609
in-theory        80609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80609.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-855, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80610
in-theory        80610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80610.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-808, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80611
in-theory        80611
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (((D and (A or (B or A))) or (A or (B or A))) -> (C -> (B or A))))
theorem-size     31
proof            (modus-ponens tm-798 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80611.        (((A or (B or A)) -> (C -> (B or A))) and (((D and (A or (B or A))) or (A or (B or A))) -> (C -> (B or A)))), M:tm-798, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80612
in-theory        80612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80612.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-757, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80613
in-theory        80613
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((((A or (B or A)) and D) or (A or (B or A))) -> (C -> (B or A))))
theorem-size     31
proof            (modus-ponens tm-747 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80613.        (((A or (B or A)) -> (C -> (B or A))) and ((((A or (B or A)) and D) or (A or (B or A))) -> (C -> (B or A)))), M:tm-747, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80614
in-theory        80614
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (F or E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80614.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (F or E)))), M:tm-708, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80615
in-theory        80615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80615.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-665, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80616
in-theory        80616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D -> (B or A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80616.        ((A or (B or A)) -> (C or (D -> (B or A)))), M:tm-623, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80617
in-theory        80617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80617.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-622, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80618
in-theory        80618
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80618.        (((A or (B or A)) -> (C -> (B or A))) and (D -> (E or D))), M:tm-609, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80619
in-theory        80619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80619.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-605, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80620
in-theory        80620
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((D -> (E or D)) and ((A or (B or A)) -> (C -> (B or A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80620.        (((A or (B or A)) -> (C -> (B or A))) and ((D -> (E or D)) and ((A or (B or A)) -> (C -> (B or A))))), M:tm-595, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80621
in-theory        80621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80621.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-550, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80622
in-theory        80622
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80622.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-540, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80623
in-theory        80623
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80623.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-530, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80624
in-theory        80624
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80624.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-520, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80625
in-theory        80625
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80625.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-510, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80626
in-theory        80626
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80626.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-500, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80627
in-theory        80627
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80627.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (F or E)))), M:tm-490, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80628
in-theory        80628
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80628.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-480, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80629
in-theory        80629
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (B or A)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80629.        ((A or (B or A)) -> ((C -> (B or A)) or D)), M:tm-470, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80630
in-theory        80630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80630.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-469, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80631
in-theory        80631
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80631.        (((A or (B or A)) -> (C -> (B or A))) and (D -> (D or E))), M:tm-456, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80632
in-theory        80632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80632.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-453, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80633
in-theory        80633
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((D -> (D or E)) and ((A or (B or A)) -> (C -> (B or A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-80633.        (((A or (B or A)) -> (C -> (B or A))) and ((D -> (D or E)) and ((A or (B or A)) -> (C -> (B or A))))), M:tm-443, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80634
in-theory        80634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80634.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-409, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80635
in-theory        80635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80635.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-400, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80636
in-theory        80636
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80636.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-391, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80637
in-theory        80637
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80637.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-382, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80638
in-theory        80638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80638.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (F or E)))), M:tm-373, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80639
in-theory        80639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80639.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-364, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80640
in-theory        80640
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (B or A)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80640.        ((A or (B or A)) -> (C -> ((D -> (B or A)) and C))), M:tm-355, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80641
in-theory        80641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80641.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-354, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80642
in-theory        80642
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80642.        (((A or (B or A)) -> (C -> (B or A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80643
in-theory        80643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (D or C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80643.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (D or C)))), M:tm-338, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80644
in-theory        80644
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (B or A)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-80644.        (((A or (B or A)) -> (C -> (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (B or A))))), M:tm-328, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80645
in-theory        80645
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((D -> (E -> (D and E))) and ((A or (B or A)) -> (C -> (B or A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-80645.        (((A or (B or A)) -> (C -> (B or A))) and ((D -> (E -> (D and E))) and ((A or (B or A)) -> (C -> (B or A))))), M:tm-327, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80646
in-theory        80646
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (((D and E) -> E) and ((A or (B or A)) -> (C -> (B or A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-80646.        (((A or (B or A)) -> (C -> (B or A))) and (((D and E) -> E) and ((A or (B or A)) -> (C -> (B or A))))), M:tm-326, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80647
in-theory        80647
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (((D and E) -> D) and ((A or (B or A)) -> (C -> (B or A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-80647.        (((A or (B or A)) -> (C -> (B or A))) and (((D and E) -> D) and ((A or (B or A)) -> (C -> (B or A))))), M:tm-325, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80648
in-theory        80648
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B or A)) -> (C -> (B or A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-80648.        (((A or (B or A)) -> (C -> (B or A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B or A)) -> (C -> (B or A))))), M:tm-324, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80649
in-theory        80649
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((D -> (E -> D)) and ((A or (B or A)) -> (C -> (B or A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80649.        (((A or (B or A)) -> (C -> (B or A))) and ((D -> (E -> D)) and ((A or (B or A)) -> (C -> (B or A))))), M:tm-323, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80650
in-theory        80650
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80650.        (((A or (B or A)) -> (C -> (B or A))) and ((D and E) -> E)), M:tm-322, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80651
in-theory        80651
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80651.        (((A or (B or A)) -> (C -> (B or A))) and ((D and E) -> D)), M:tm-320, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80652
in-theory        80652
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80652.        (((A or (B or A)) -> (C -> (B or A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80653
in-theory        80653
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80653.        (((A or (B or A)) -> (C -> (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80654
in-theory        80654
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80654.        (((A or (B or A)) -> (C -> (B or A))) and (D -> (E -> D))), M:tm-315, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80655
in-theory        80655
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (((A or (B or A)) -> (not (C -> (B or A)))) -> (not (A or (B or A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-80655.        (((A or (B or A)) -> (C -> (B or A))) and (((A or (B or A)) -> (not (C -> (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80656
in-theory        80656
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (((C -> (B or A)) -> D) -> (((A or (B or A)) or (C -> (B or A))) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-80656.        (((A or (B or A)) -> (C -> (B or A))) and (((C -> (B or A)) -> D) -> (((A or (B or A)) or (C -> (B or A))) -> D))), M:tm-312, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80657
in-theory        80657
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (D or ((A or (B or A)) -> (C -> (B or A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80657.        (((A or (B or A)) -> (C -> (B or A))) and (D or ((A or (B or A)) -> (C -> (B or A))))), M:tm-311, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80658
in-theory        80658
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (((A or (B or A)) -> (C -> (B or A))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-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-80658.        (((A or (B or A)) -> (C -> (B or A))) and (((A or (B or A)) -> (C -> (B or A))) or D)), M:tm-310, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80659
in-theory        80659
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (D -> (((A or (B or A)) -> (C -> (B or A))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80659.        (((A or (B or A)) -> (C -> (B or A))) and (D -> (((A or (B or A)) -> (C -> (B or A))) and D))), M:tm-309, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80660
in-theory        80660
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (B or A))))
theorem-size     29
proof            (modus-ponens tm-306 tm-896 ((A (or Am (or Bm Am))) (B Cm) (C (or Bm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80660.        (((A or (B or A)) -> (C -> (B or A))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (B or A)))), M:tm-306, m:tm-896, u:((A (or Am (or Bm Am))) (B Cm) (C (or Bm Am)))
================================================================
tm-name          tm-80661
in-theory        80661
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (D -> ((A or (B or A)) -> (C -> (B or A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80661.        (((A or (B or A)) -> (C -> (B or A))) and (D -> ((A or (B or A)) -> (C -> (B or A))))), M:tm-305, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80662
in-theory        80662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80662.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-303, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80663
in-theory        80663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80663.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-270, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80664
in-theory        80664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80664.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-239, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80665
in-theory        80665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (F or E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-80665.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (F or E)))), M:tm-210, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80666
in-theory        80666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80666.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-183, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80667
in-theory        80667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80667.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-157, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80668
in-theory        80668
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80668.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-147, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80669
in-theory        80669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80669.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-134, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80670
in-theory        80670
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80670.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-125, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80671
in-theory        80671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80671.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (F or E)))), M:tm-113, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80672
in-theory        80672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80672.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-105, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80673
in-theory        80673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (D or C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80673.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (D or C)))), M:tm-95, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80674
in-theory        80674
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> (B or A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80674.        ((A or (B or A)) -> (C -> (D -> (B or A)))), M:tm-84, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80675
in-theory        80675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80675.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-83, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80676
in-theory        80676
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (C or B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80676.        (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (C or B)))), M:tm-76, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80677
in-theory        80677
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-73 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80677.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (B or A))), M:tm-73, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80678
in-theory        80678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (D or C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80678.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (D or C)))), M:tm-69, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80679
in-theory        80679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80679.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-54, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80680
in-theory        80680
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (C -> (A or B)))
theorem-size     15
proof            (modus-ponens tm-50 tm-896 ((A Am) (B (or Bm Am)) (C (-> Cm (or 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-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-80680.        (((A or B) or (B or (A or B))) -> (C -> (A or B))), M:tm-50, m:tm-896, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80681
in-theory        80681
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (C -> (B or A)))
theorem-size     13
proof            (modus-ponens tm-49 tm-896 ((A Am) (B (or Bm Am)) (C (-> Cm (or Bm Am)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80681.        ((A or (A or (B or A))) -> (C -> (B or A))), M:tm-49, m:tm-896, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80682
in-theory        80682
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (C or B)))
theorem-size     19
proof            (modus-ponens tm-47 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80682.        (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (C or B))), M:tm-47, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80683
in-theory        80683
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-46 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80683.        ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (B or A))), M:tm-46, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80684
in-theory        80684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (E -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80684.        ((A -> (B or A)) and ((C or (D or C)) -> (E -> (D or C)))), M:tm-42, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80685
in-theory        80685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (E -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80685.        ((A -> (A or B)) and ((C or (D or C)) -> (E -> (D or C)))), M:tm-32, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80686
in-theory        80686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (C -> (B or A))))
theorem-size     17
proof            (modus-ponens tm-24 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80686.        ((A or (B or A)) -> ((A or (B or A)) and (C -> (B or A)))), M:tm-24, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80687
in-theory        80687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (D or C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-80687.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (D or C)))), M:tm-23, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80688
in-theory        80688
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (E -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80688.        (((A and B) -> B) and ((C or (D or C)) -> (E -> (D or C)))), M:tm-22, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80689
in-theory        80689
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (E -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80689.        (((A and B) -> A) and ((C or (D or C)) -> (E -> (D or C)))), M:tm-21, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80690
in-theory        80690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80690.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-20, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80691
in-theory        80691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80691.        ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (D or C)))), M:tm-19, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80692
in-theory        80692
times-derived    19
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (A or (B or A)))
theorem-size     11
proof            (modus-ponens tm-12 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80692.        ((A or (B or A)) -> (A or (B or A))), M:tm-12, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80693
in-theory        80693
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (C -> (B or A)))) -> (not (A or (B or A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80693.        (((A or (B or A)) -> (not (C -> (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80694
in-theory        80694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or C)) -> D) -> (((C or (B or C)) or (A -> (B or C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-896 ((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       81
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-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-80694.        (((A -> (B or C)) -> D) -> (((C or (B or C)) or (A -> (B or C))) -> D)), M:tm-8, m:tm-896, u:((A (or Am (or Bm Am))) (B (-> Cm (or Bm Am))))
================================================================
tm-name          tm-80695
in-theory        80695
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (D -> (C or B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-50.           (((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-80695.        (A or ((B or (C or B)) -> (D -> (C or B)))), M:tm-7, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80696
in-theory        80696
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80696.        (((A or (B or A)) -> (C -> (B or A))) or D), M:tm-6, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80697
in-theory        80697
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (D -> (C or B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80697.        (A -> (((B or (C or B)) -> (D -> (C or B))) and A)), M:tm-5, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80698
in-theory        80698
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> C) -> ((A or (B or A)) -> (B or A)))
theorem-size     17
proof            (modus-ponens tm-2 tm-896 ((A (or Am (or Bm Am))) (B Cm) (C (or Bm Am))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80698.        (((A or (B or A)) -> C) -> ((A or (B or A)) -> (B or A))), M:tm-2, m:tm-896, u:((A (or Am (or Bm Am))) (B Cm) (C (or Bm Am)))
================================================================
tm-name          tm-80699
in-theory        80699
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (D -> (C or B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80699.        (A -> ((B or (C or B)) -> (D -> (C or B)))), M:tm-1, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-80700
in-theory        80700
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     27
proof            (modus-ponens tm-893 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80700.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-893, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80701
in-theory        80701
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((A or (A or (B or A))) -> (C -> ((B or A) and C))))
theorem-size     29
proof            (modus-ponens tm-882 tm-897 ((A Am) (B (or Bm Am)) (C (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80701.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((A or (A or (B or A))) -> (C -> ((B or A) and C)))), M:tm-882, m:tm-897, u:((A Am) (B (or Bm Am)) (C (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80702
in-theory        80702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     31
proof            (modus-ponens tm-855 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80702.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-855, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80703
in-theory        80703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     25
proof            (modus-ponens tm-808 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80703.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-808, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80704
in-theory        80704
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (((D and (A or (B or A))) or (A or (B or A))) -> (C -> ((B or A) and C))))
theorem-size     35
proof            (modus-ponens tm-798 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80704.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (((D and (A or (B or A))) or (A or (B or A))) -> (C -> ((B or A) and C)))), M:tm-798, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80705
in-theory        80705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-80705.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-757, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80706
in-theory        80706
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((((A or (B or A)) and D) or (A or (B or A))) -> (C -> ((B or A) and C))))
theorem-size     35
proof            (modus-ponens tm-747 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-80706.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((((A or (B or A)) and D) or (A or (B or A))) -> (C -> ((B or A) and C)))), M:tm-747, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80707
in-theory        80707
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> ((F or E) and G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-80707.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> ((F or E) and G)))), M:tm-708, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80708
in-theory        80708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80708.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-665, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80709
in-theory        80709
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D -> ((B or A) and D))))
theorem-size     15
proof            (modus-ponens tm-623 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or 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-50.           (((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-80709.        ((A or (B or A)) -> (C or (D -> ((B or A) and D)))), M:tm-623, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80710
in-theory        80710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80710.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-622, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80711
in-theory        80711
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C or (A or (B or A)))))
theorem-size     17
proof            (modus-ponens tm-617 tm-897 ((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (and (or Bm Am) (or B (or Am (or 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-50.           (((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-80711.        ((A or (B or A)) -> ((B or A) and (C or (A or (B or A))))), M:tm-617, m:tm-897, u:((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (and (or Bm Am) (or B (or Am (or Bm Am))))))
================================================================
tm-name          tm-80712
in-theory        80712
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80712.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (E or D))), M:tm-609, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80713
in-theory        80713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-80713.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-605, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80714
in-theory        80714
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (E or D)) and ((A or (B or A)) -> (C -> ((B or A) and C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-80714.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (E or D)) and ((A or (B or A)) -> (C -> ((B or A) and C))))), M:tm-595, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80715
in-theory        80715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80715.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-550, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80716
in-theory        80716
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80716.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-540, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80717
in-theory        80717
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80717.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-530, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80718
in-theory        80718
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-80718.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-520, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80719
in-theory        80719
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80719.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-510, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80720
in-theory        80720
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80720.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-500, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80721
in-theory        80721
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> ((F or E) and G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80721.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> ((F or E) and G)))), M:tm-490, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80722
in-theory        80722
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80722.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-480, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80723
in-theory        80723
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> ((B or A) and C)) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80723.        ((A or (B or A)) -> ((C -> ((B or A) and C)) or D)), M:tm-470, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80724
in-theory        80724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80724.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-469, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80725
in-theory        80725
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and ((A or (B or A)) or C)))
theorem-size     17
proof            (modus-ponens tm-464 tm-897 ((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (and (or Bm Am) (or (or Am (or Bm Am)) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80725.        ((A or (B or A)) -> ((B or A) and ((A or (B or A)) or C))), M:tm-464, m:tm-897, u:((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (and (or Bm Am) (or (or Am (or Bm Am)) B))))
================================================================
tm-name          tm-80726
in-theory        80726
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80726.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (D or E))), M:tm-456, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80727
in-theory        80727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80727.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-453, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80728
in-theory        80728
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (D or E)) and ((A or (B or A)) -> (C -> ((B or A) and C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-80728.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (D or E)) and ((A or (B or A)) -> (C -> ((B or A) and C))))), M:tm-443, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80729
in-theory        80729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-80729.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-409, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80730
in-theory        80730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80730.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-400, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80731
in-theory        80731
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-80731.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-391, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80732
in-theory        80732
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-80732.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-382, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80733
in-theory        80733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> ((F or E) and G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80733.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> ((F or E) and G)))), M:tm-373, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80734
in-theory        80734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80734.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-364, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80735
in-theory        80735
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> ((B or A) and D)) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80735.        ((A or (B or A)) -> (C -> ((D -> ((B or A) and D)) and C))), M:tm-355, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80736
in-theory        80736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80736.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-354, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80737
in-theory        80737
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C -> ((A or (B or A)) and C))))
theorem-size     19
proof            (modus-ponens tm-349 tm-897 ((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (and (or Bm Am) (-> B (and (or Am (or Bm Am)) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80737.        ((A or (B or A)) -> ((B or A) and (C -> ((A or (B or A)) and C)))), M:tm-349, m:tm-897, u:((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (and (or Bm Am) (-> B (and (or Am (or Bm Am)) B)))))
================================================================
tm-name          tm-80738
in-theory        80738
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80738.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80739
in-theory        80739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> ((D or C) and E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80739.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> ((D or C) and E)))), M:tm-338, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80740
in-theory        80740
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> ((B or A) and C)))))
theorem-size     33
proof            (modus-ponens tm-328 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-80740.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> ((B or A) and C))))), M:tm-328, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80741
in-theory        80741
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (E -> (D and E))) and ((A or (B or A)) -> (C -> ((B or A) and C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-80741.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (E -> (D and E))) and ((A or (B or A)) -> (C -> ((B or A) and C))))), M:tm-327, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80742
in-theory        80742
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (((D and E) -> E) and ((A or (B or A)) -> (C -> ((B or A) and C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-80742.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (((D and E) -> E) and ((A or (B or A)) -> (C -> ((B or A) and C))))), M:tm-326, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80743
in-theory        80743
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (((D and E) -> D) and ((A or (B or A)) -> (C -> ((B or A) and C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-80743.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (((D and E) -> D) and ((A or (B or A)) -> (C -> ((B or A) and C))))), M:tm-325, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80744
in-theory        80744
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B or A)) -> (C -> ((B or A) and C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-80744.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B or A)) -> (C -> ((B or A) and C))))), M:tm-324, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80745
in-theory        80745
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (E -> D)) and ((A or (B or A)) -> (C -> ((B or A) and C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-80745.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (E -> D)) and ((A or (B or A)) -> (C -> ((B or A) and C))))), M:tm-323, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80746
in-theory        80746
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80746.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D and E) -> E)), M:tm-322, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80747
in-theory        80747
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80747.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D and E) -> D)), M:tm-320, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80748
in-theory        80748
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80748.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80749
in-theory        80749
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     25
proof            (modus-ponens tm-316 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-80749.        (((A or (B or A)) -> (C -> ((B or A) and C))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80750
in-theory        80750
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80750.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (E -> D))), M:tm-315, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80751
in-theory        80751
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (((A or (B or A)) -> (not (C -> ((B or A) and C)))) -> (not (A or (B or A)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-80751.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (((A or (B or A)) -> (not (C -> ((B or A) and C)))) -> (not (A or (B or A))))), M:tm-313, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80752
in-theory        80752
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (((C -> ((B or A) and C)) -> D) -> (((A or (B or A)) or (C -> ((B or A) and C))) -> D)))
theorem-size     39
proof            (modus-ponens tm-312 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-312.          ((A -> B) -> ((A -> B) and ((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-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-80752.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (((C -> ((B or A) and C)) -> D) -> (((A or (B or A)) or (C -> ((B or A) and C))) -> D))), M:tm-312, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80753
in-theory        80753
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (D or ((A or (B or A)) -> (C -> ((B or A) and C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-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-80753.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (D or ((A or (B or A)) -> (C -> ((B or A) and C))))), M:tm-311, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80754
in-theory        80754
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (((A or (B or A)) -> (C -> ((B or A) and C))) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-80754.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (((A or (B or A)) -> (C -> ((B or A) and C))) or D)), M:tm-310, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80755
in-theory        80755
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (((A or (B or A)) -> (C -> ((B or A) and C))) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-80755.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> (((A or (B or A)) -> (C -> ((B or A) and C))) and D))), M:tm-309, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80756
in-theory        80756
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> ((B or A) and C))))
theorem-size     33
proof            (modus-ponens tm-306 tm-897 ((A (or Am (or Bm Am))) (B Cm) (C (and (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-80756.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> ((B or A) and C)))), M:tm-306, m:tm-897, u:((A (or Am (or Bm Am))) (B Cm) (C (and (or Bm Am) Cm)))
================================================================
tm-name          tm-80757
in-theory        80757
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> ((A or (B or A)) -> (C -> ((B or A) and C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) 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-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-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-80757.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (D -> ((A or (B or A)) -> (C -> ((B or A) and C))))), M:tm-305, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80758
in-theory        80758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80758.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-303, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80759
in-theory        80759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80759.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-270, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80760
in-theory        80760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80760.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-239, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80761
in-theory        80761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> ((F or E) and G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80761.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> ((F or E) and G)))), M:tm-210, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80762
in-theory        80762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80762.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-183, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80763
in-theory        80763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80763.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-157, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80764
in-theory        80764
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80764.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-147, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80765
in-theory        80765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80765.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-134, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80766
in-theory        80766
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80766.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-125, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80767
in-theory        80767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> ((F or E) and G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80767.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> ((F or E) and G)))), M:tm-113, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80768
in-theory        80768
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-80768.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-105, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80769
in-theory        80769
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (A or (B or A))))
theorem-size     15
proof            (modus-ponens tm-99 tm-897 ((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (and (or Bm Am) (or Am (or Bm Am))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80769.        ((A or (B or A)) -> ((B or A) and (A or (B or A)))), M:tm-99, m:tm-897, u:((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (and (or Bm Am) (or Am (or Bm Am)))))
================================================================
tm-name          tm-80770
in-theory        80770
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C -> (A or (B or A)))))
theorem-size     17
proof            (modus-ponens tm-98 tm-897 ((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (and (or Bm Am) (-> B (or Am (or Bm Am)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80770.        ((A or (B or A)) -> ((B or A) and (C -> (A or (B or A))))), M:tm-98, m:tm-897, u:((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (and (or Bm Am) (-> B (or Am (or Bm Am))))))
================================================================
tm-name          tm-80771
in-theory        80771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> ((D or C) and E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80771.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> ((D or C) and E)))), M:tm-95, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80772
in-theory        80772
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> ((B or A) and D))))
theorem-size     15
proof            (modus-ponens tm-84 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80772.        ((A or (B or A)) -> (C -> (D -> ((B or A) and D)))), M:tm-84, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80773
in-theory        80773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80773.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-83, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80774
in-theory        80774
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (D -> ((C or B) and D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-10 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80774.        (((not (not A)) -> A) and ((B or (C or B)) -> (D -> ((C or B) and D)))), M:tm-76, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80775
in-theory        80775
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> ((B or A) and C)))
theorem-size     21
proof            (modus-ponens tm-73 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80775.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> ((B or A) and C))), M:tm-73, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80776
in-theory        80776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> ((D or C) and E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80776.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> ((D or C) and E)))), M:tm-69, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80777
in-theory        80777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80777.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-54, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80778
in-theory        80778
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (C -> ((A or B) and C)))
theorem-size     17
proof            (modus-ponens tm-50 tm-897 ((A Am) (B (or Bm Am)) (C (-> Cm (and (or Bm Am) Cm)))))
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-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-80778.        (((A or B) or (B or (A or B))) -> (C -> ((A or B) and C))), M:tm-50, m:tm-897, u:((A Am) (B (or Bm Am)) (C (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80779
in-theory        80779
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (C -> ((B or A) and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-897 ((A Am) (B (or Bm Am)) (C (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80779.        ((A or (A or (B or A))) -> (C -> ((B or A) and C))), M:tm-49, m:tm-897, u:((A Am) (B (or Bm Am)) (C (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80780
in-theory        80780
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (D -> ((C or B) and D)))
theorem-size     21
proof            (modus-ponens tm-47 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80780.        (((A and (B or (C or B))) or (B or (C or B))) -> (D -> ((C or B) and D))), M:tm-47, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80781
in-theory        80781
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> ((B or A) and D)))
theorem-size     21
proof            (modus-ponens tm-46 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80781.        ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> ((B or A) and D))), M:tm-46, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80782
in-theory        80782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (E -> ((D or C) and E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-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-80782.        ((A -> (B or A)) and ((C or (D or C)) -> (E -> ((D or C) and E)))), M:tm-42, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80783
in-theory        80783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (E -> ((D or C) and E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80783.        ((A -> (A or B)) and ((C or (D or C)) -> (E -> ((D or C) and E)))), M:tm-32, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80784
in-theory        80784
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (C -> ((B or A) and C))))
theorem-size     19
proof            (modus-ponens tm-24 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80784.        ((A or (B or A)) -> ((A or (B or A)) and (C -> ((B or A) and C)))), M:tm-24, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80785
in-theory        80785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> ((D or C) and E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80785.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> ((D or C) and E)))), M:tm-23, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80786
in-theory        80786
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (E -> ((D or C) and E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80786.        (((A and B) -> B) and ((C or (D or C)) -> (E -> ((D or C) and E)))), M:tm-22, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80787
in-theory        80787
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (E -> ((D or C) and E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80787.        (((A and B) -> A) and ((C or (D or C)) -> (E -> ((D or C) and E)))), M:tm-21, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80788
in-theory        80788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80788.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-20, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80789
in-theory        80789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (E -> ((D or C) and E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80789.        ((A -> (B -> A)) and ((C or (D or C)) -> (E -> ((D or C) and E)))), M:tm-19, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80790
in-theory        80790
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (C -> ((B or A) and C)))) -> (not (A or (B or A))))
theorem-size     21
proof            (modus-ponens tm-9 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80790.        (((A or (B or A)) -> (not (C -> ((B or A) and C)))) -> (not (A or (B or A)))), M:tm-9, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80791
in-theory        80791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or C) and A)) -> D) -> (((C or (B or C)) or (A -> ((B or C) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-897 ((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       89
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-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-80791.        (((A -> ((B or C) and A)) -> D) -> (((C or (B or C)) or (A -> ((B or C) and A))) -> D)), M:tm-8, m:tm-897, u:((A (or Am (or Bm Am))) (B (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-80792
in-theory        80792
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (D -> ((C or B) and D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-7 tm-8 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-50.           (((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-80792.        (A or ((B or (C or B)) -> (D -> ((C or B) and D)))), M:tm-7, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80793
in-theory        80793
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80793.        (((A or (B or A)) -> (C -> ((B or A) and C))) or D), M:tm-6, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80794
in-theory        80794
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (D -> ((C or B) and D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80794.        (A -> (((B or (C or B)) -> (D -> ((C or B) and D))) and A)), M:tm-5, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80795
in-theory        80795
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> C) -> ((A or (B or A)) -> ((B or A) and C)))
theorem-size     19
proof            (modus-ponens tm-2 tm-897 ((A (or Am (or Bm Am))) (B Cm) (C (and (or Bm Am) Cm))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80795.        (((A or (B or A)) -> C) -> ((A or (B or A)) -> ((B or A) and C))), M:tm-2, m:tm-897, u:((A (or Am (or Bm Am))) (B Cm) (C (and (or Bm Am) Cm)))
================================================================
tm-name          tm-80796
in-theory        80796
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (D -> ((C or B) and D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80796.        (A -> ((B or (C or B)) -> (D -> ((C or B) and D)))), M:tm-1, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-80797
in-theory        80797
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80797.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-893, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80798
in-theory        80798
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((A or (A or (B or A))) -> ((B or A) or C)))
theorem-size     25
proof            (modus-ponens tm-882 tm-898 ((A Am) (B (or Bm Am)) (C (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80798.        (((A or (B or A)) -> ((B or A) or C)) and ((A or (A or (B or A))) -> ((B or A) or C))), M:tm-882, m:tm-898, u:((A Am) (B (or Bm Am)) (C (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80799
in-theory        80799
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80799.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-855, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80800
in-theory        80800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80800.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-808, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80801
in-theory        80801
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (((D and (A or (B or A))) or (A or (B or A))) -> ((B or A) or C)))
theorem-size     31
proof            (modus-ponens tm-798 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80801.        (((A or (B or A)) -> ((B or A) or C)) and (((D and (A or (B or A))) or (A or (B or A))) -> ((B or A) or C))), M:tm-798, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80802
in-theory        80802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80802.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-757, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80803
in-theory        80803
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((((A or (B or A)) and D) or (A or (B or A))) -> ((B or A) or C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80803.        (((A or (B or A)) -> ((B or A) or C)) and ((((A or (B or A)) and D) or (A or (B or A))) -> ((B or A) or C))), M:tm-747, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80804
in-theory        80804
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((F or E) or G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80804.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((F or E) or G))), M:tm-708, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80805
in-theory        80805
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80805.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-665, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80806
in-theory        80806
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((B or A) or D)))
theorem-size     13
proof            (modus-ponens tm-623 tm-898 ((A (or Am (or Bm Am))) (B (or (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-50.           (((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-80806.        ((A or (B or A)) -> (C or ((B or A) or D))), M:tm-623, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80807
in-theory        80807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-898 ((A (-> (or Am (or Bm Am)) (or (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-50.           (((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-80807.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-622, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80808
in-theory        80808
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-898 ((A (-> (or Am (or Bm Am)) (or (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-50.           (((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-80808.        (((A or (B or A)) -> ((B or A) or C)) and (D -> (E or D))), M:tm-609, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80809
in-theory        80809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-80809.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-605, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80810
in-theory        80810
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((D -> (E or D)) and ((A or (B or A)) -> ((B or A) or C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-80810.        (((A or (B or A)) -> ((B or A) or C)) and ((D -> (E or D)) and ((A or (B or A)) -> ((B or A) or C)))), M:tm-595, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80811
in-theory        80811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80811.        (((A -> (B or A)) or C) and ((D or (E or D)) -> ((E or D) or F))), M:tm-550, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80812
in-theory        80812
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-80812.        ((A or (B -> (C or B))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-540, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80813
in-theory        80813
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80813.        ((A or (B -> (B or C))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-530, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80814
in-theory        80814
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-80814.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-520, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80815
in-theory        80815
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-80815.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-510, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80816
in-theory        80816
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-80816.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-500, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80817
in-theory        80817
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((F or E) or G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-50.           (((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-80817.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((F or E) or G))), M:tm-490, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80818
in-theory        80818
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-898 ((A (-> (or Am (or Bm Am)) (or (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-50.           (((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-80818.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-480, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80819
in-theory        80819
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((B or A) or C) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80819.        ((A or (B or A)) -> (((B or A) or C) or D)), M:tm-470, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80820
in-theory        80820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80820.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-469, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80821
in-theory        80821
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80821.        (((A or (B or A)) -> ((B or A) or C)) and (D -> (D or E))), M:tm-456, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80822
in-theory        80822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80822.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-453, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80823
in-theory        80823
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((D -> (D or E)) and ((A or (B or A)) -> ((B or A) or C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-80823.        (((A or (B or A)) -> ((B or A) or C)) and ((D -> (D or E)) and ((A or (B or A)) -> ((B or A) or C)))), M:tm-443, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80824
in-theory        80824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-80824.        (((A -> (A or B)) or C) and ((D or (E or D)) -> ((E or D) or F))), M:tm-409, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80825
in-theory        80825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80825.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((E or D) or F))), M:tm-400, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80826
in-theory        80826
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-80826.        ((((A and B) -> B) or C) and ((D or (E or D)) -> ((E or D) or F))), M:tm-391, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80827
in-theory        80827
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-80827.        ((((A and B) -> A) or C) and ((D or (E or D)) -> ((E or D) or F))), M:tm-382, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80828
in-theory        80828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((F or E) or G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80828.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((F or E) or G))), M:tm-373, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80829
in-theory        80829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80829.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((E or D) or F))), M:tm-364, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80830
in-theory        80830
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((B or A) or D) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80830.        ((A or (B or A)) -> (C -> (((B or A) or D) and C))), M:tm-355, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80831
in-theory        80831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80831.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-354, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80832
in-theory        80832
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-80832.        (((A or (B or A)) -> ((B or A) or C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80833
in-theory        80833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((D or C) or E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80833.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((D or C) or E))), M:tm-338, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80834
in-theory        80834
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((A or (B or A)) -> ((A or (B or A)) and ((B or A) or C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-80834.        (((A or (B or A)) -> ((B or A) or C)) and ((A or (B or A)) -> ((A or (B or A)) and ((B or A) or C)))), M:tm-328, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80835
in-theory        80835
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((D -> (E -> (D and E))) and ((A or (B or A)) -> ((B or A) or C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-80835.        (((A or (B or A)) -> ((B or A) or C)) and ((D -> (E -> (D and E))) and ((A or (B or A)) -> ((B or A) or C)))), M:tm-327, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80836
in-theory        80836
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (((D and E) -> E) and ((A or (B or A)) -> ((B or A) or C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-80836.        (((A or (B or A)) -> ((B or A) or C)) and (((D and E) -> E) and ((A or (B or A)) -> ((B or A) or C)))), M:tm-326, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80837
in-theory        80837
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (((D and E) -> D) and ((A or (B or A)) -> ((B or A) or C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-80837.        (((A or (B or A)) -> ((B or A) or C)) and (((D and E) -> D) and ((A or (B or A)) -> ((B or A) or C)))), M:tm-325, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80838
in-theory        80838
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B or A)) -> ((B or A) or C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80838.        (((A or (B or A)) -> ((B or A) or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B or A)) -> ((B or A) or C)))), M:tm-324, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80839
in-theory        80839
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((D -> (E -> D)) and ((A or (B or A)) -> ((B or A) or C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-80839.        (((A or (B or A)) -> ((B or A) or C)) and ((D -> (E -> D)) and ((A or (B or A)) -> ((B or A) or C)))), M:tm-323, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80840
in-theory        80840
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80840.        (((A or (B or A)) -> ((B or A) or C)) and ((D and E) -> E)), M:tm-322, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80841
in-theory        80841
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80841.        (((A or (B or A)) -> ((B or A) or C)) and ((D and E) -> D)), M:tm-320, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80842
in-theory        80842
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80842.        (((A or (B or A)) -> ((B or A) or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80843
in-theory        80843
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-80843.        (((A or (B or A)) -> ((B or A) or C)) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80844
in-theory        80844
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80844.        (((A or (B or A)) -> ((B or A) or C)) and (D -> (E -> D))), M:tm-315, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80845
in-theory        80845
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (((A or (B or A)) -> (not ((B or A) or C))) -> (not (A or (B or A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-80845.        (((A or (B or A)) -> ((B or A) or C)) and (((A or (B or A)) -> (not ((B or A) or C))) -> (not (A or (B or A))))), M:tm-313, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80846
in-theory        80846
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and ((((B or A) or C) -> D) -> (((A or (B or A)) or ((B or A) or C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-80846.        (((A or (B or A)) -> ((B or A) or C)) and ((((B or A) or C) -> D) -> (((A or (B or A)) or ((B or A) or C)) -> D))), M:tm-312, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80847
in-theory        80847
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (D or ((A or (B or A)) -> ((B or A) or C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-80847.        (((A or (B or A)) -> ((B or A) or C)) and (D or ((A or (B or A)) -> ((B or A) or C)))), M:tm-311, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80848
in-theory        80848
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (((A or (B or A)) -> ((B or A) or C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-80848.        (((A or (B or A)) -> ((B or A) or C)) and (((A or (B or A)) -> ((B or A) or C)) or D)), M:tm-310, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80849
in-theory        80849
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (D -> (((A or (B or A)) -> ((B or A) or C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80849.        (((A or (B or A)) -> ((B or A) or C)) and (D -> (((A or (B or A)) -> ((B or A) or C)) and D))), M:tm-309, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80850
in-theory        80850
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (D -> ((A or (B or A)) -> ((B or A) or C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-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-80850.        (((A or (B or A)) -> ((B or A) or C)) and (D -> ((A or (B or A)) -> ((B or A) or C)))), M:tm-305, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80851
in-theory        80851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80851.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-303, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80852
in-theory        80852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80852.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-270, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80853
in-theory        80853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80853.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-239, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80854
in-theory        80854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((F or E) or G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-80854.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((F or E) or G))), M:tm-210, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80855
in-theory        80855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80855.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-183, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80856
in-theory        80856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80856.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-157, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80857
in-theory        80857
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80857.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-147, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80858
in-theory        80858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80858.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-134, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80859
in-theory        80859
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80859.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-125, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80860
in-theory        80860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((F or E) or G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80860.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((F or E) or G))), M:tm-113, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80861
in-theory        80861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80861.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-105, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80862
in-theory        80862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((D or C) or E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80862.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((D or C) or E))), M:tm-95, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80863
in-theory        80863
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((B or A) or D)))
theorem-size     13
proof            (modus-ponens tm-84 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80863.        ((A or (B or A)) -> (C -> ((B or A) or D))), M:tm-84, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80864
in-theory        80864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80864.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-83, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80865
in-theory        80865
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> ((C or B) or D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80865.        (((not (not A)) -> A) and ((B or (C or B)) -> ((C or B) or D))), M:tm-76, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80866
in-theory        80866
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> ((B or A) or C))
theorem-size     19
proof            (modus-ponens tm-73 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80866.        (((not (not (A or (B or A)))) or (A or (B or A))) -> ((B or A) or C)), M:tm-73, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80867
in-theory        80867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((D or C) or E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80867.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((D or C) or E))), M:tm-69, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80868
in-theory        80868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80868.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-54, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80869
in-theory        80869
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> ((A or B) or C))
theorem-size     15
proof            (modus-ponens tm-50 tm-898 ((A Am) (B (or Bm Am)) (C (or (or Bm Am) Cm))))
axioms-used      (tm-8 tm-7 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-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-80869.        (((A or B) or (B or (A or B))) -> ((A or B) or C)), M:tm-50, m:tm-898, u:((A Am) (B (or Bm Am)) (C (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80870
in-theory        80870
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> ((B or A) or C))
theorem-size     13
proof            (modus-ponens tm-49 tm-898 ((A Am) (B (or Bm Am)) (C (or (or Bm Am) Cm))))
axioms-used      (tm-8 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80870.        ((A or (A or (B or A))) -> ((B or A) or C)), M:tm-49, m:tm-898, u:((A Am) (B (or Bm Am)) (C (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80871
in-theory        80871
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> ((C or B) or D))
theorem-size     19
proof            (modus-ponens tm-47 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80871.        (((A and (B or (C or B))) or (B or (C or B))) -> ((C or B) or D)), M:tm-47, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80872
in-theory        80872
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> ((B or A) or D))
theorem-size     19
proof            (modus-ponens tm-46 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80872.        ((((A or (B or A)) and C) or (A or (B or A))) -> ((B or A) or D)), M:tm-46, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80873
in-theory        80873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> ((D or C) or E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-80873.        ((A -> (B or A)) and ((C or (D or C)) -> ((D or C) or E))), M:tm-42, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80874
in-theory        80874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> ((D or C) or E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80874.        ((A -> (A or B)) and ((C or (D or C)) -> ((D or C) or E))), M:tm-32, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80875
in-theory        80875
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and ((B or A) or C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80875.        ((A or (B or A)) -> ((A or (B or A)) and ((B or A) or C))), M:tm-24, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80876
in-theory        80876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((D or C) or E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-80876.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((D or C) or E))), M:tm-23, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80877
in-theory        80877
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> ((D or C) or E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80877.        (((A and B) -> B) and ((C or (D or C)) -> ((D or C) or E))), M:tm-22, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80878
in-theory        80878
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> ((D or C) or E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80878.        (((A and B) -> A) and ((C or (D or C)) -> ((D or C) or E))), M:tm-21, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80879
in-theory        80879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80879.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((E or D) or F))), M:tm-20, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80880
in-theory        80880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> ((D or C) or E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80880.        ((A -> (B -> A)) and ((C or (D or C)) -> ((D or C) or E))), M:tm-19, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80881
in-theory        80881
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not ((B or A) or C))) -> (not (A or (B or A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80881.        (((A or (B or A)) -> (not ((B or A) or C))) -> (not (A or (B or A)))), M:tm-9, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80882
in-theory        80882
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) or C) -> D) -> (((B or (A or B)) or ((A or B) or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-898 ((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm))))
axioms-used      (tm-8 tm-7 tm-6)
proof-size       81
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-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-80882.        ((((A or B) or C) -> D) -> (((B or (A or B)) or ((A or B) or C)) -> D)), M:tm-8, m:tm-898, u:((A (or Am (or Bm Am))) (B (or (or Bm Am) Cm)))
================================================================
tm-name          tm-80883
in-theory        80883
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> ((C or B) or D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-7 tm-8 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-50.           (((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-80883.        (A or ((B or (C or B)) -> ((C or B) or D))), M:tm-7, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80884
in-theory        80884
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80884.        (((A or (B or A)) -> ((B or A) or C)) or D), M:tm-6, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80885
in-theory        80885
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> ((C or B) or D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80885.        (A -> (((B or (C or B)) -> ((C or B) or D)) and A)), M:tm-5, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80886
in-theory        80886
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> ((C or B) or D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80886.        (A -> ((B or (C or B)) -> ((C or B) or D))), M:tm-1, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-80887
in-theory        80887
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     25
proof            (modus-ponens tm-893 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80887.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-893, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80888
in-theory        80888
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((A or (A or (B or A))) -> (C or (B or A))))
theorem-size     25
proof            (modus-ponens tm-882 tm-899 ((A Am) (B (or Bm Am)) (C (or Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80888.        (((A or (B or A)) -> (C or (B or A))) and ((A or (A or (B or A))) -> (C or (B or A)))), M:tm-882, m:tm-899, u:((A Am) (B (or Bm Am)) (C (or Cm (or Bm Am))))
================================================================
tm-name          tm-80889
in-theory        80889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     29
proof            (modus-ponens tm-855 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80889.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-855, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80890
in-theory        80890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     23
proof            (modus-ponens tm-808 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80890.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-808, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80891
in-theory        80891
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (((D and (A or (B or A))) or (A or (B or A))) -> (C or (B or A))))
theorem-size     31
proof            (modus-ponens tm-798 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80891.        (((A or (B or A)) -> (C or (B or A))) and (((D and (A or (B or A))) or (A or (B or A))) -> (C or (B or A)))), M:tm-798, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80892
in-theory        80892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-80892.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-757, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80893
in-theory        80893
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((((A or (B or A)) and D) or (A or (B or A))) -> (C or (B or A))))
theorem-size     31
proof            (modus-ponens tm-747 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80893.        (((A or (B or A)) -> (C or (B or A))) and ((((A or (B or A)) and D) or (A or (B or A))) -> (C or (B or A)))), M:tm-747, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80894
in-theory        80894
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G or (F or E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-80894.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G or (F or E)))), M:tm-708, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80895
in-theory        80895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-50.           (((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-80895.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-665, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80896
in-theory        80896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D or (B or A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or 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-50.           (((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-80896.        ((A or (B or A)) -> (C or (D or (B or A)))), M:tm-623, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80897
in-theory        80897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-50.           (((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-80897.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-622, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80898
in-theory        80898
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-50.           (((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-80898.        (((A or (B or A)) -> (C or (B or A))) and (D -> (E or D))), M:tm-609, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80899
in-theory        80899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-80899.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-605, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80900
in-theory        80900
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((D -> (E or D)) and ((A or (B or A)) -> (C or (B or A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-80900.        (((A or (B or A)) -> (C or (B or A))) and ((D -> (E or D)) and ((A or (B or A)) -> (C or (B or A))))), M:tm-595, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80901
in-theory        80901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-50.           (((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-80901.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (F or (E or D)))), M:tm-550, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80902
in-theory        80902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-80902.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-540, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80903
in-theory        80903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-50.           (((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-80903.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-530, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80904
in-theory        80904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-80904.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-520, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80905
in-theory        80905
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
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-50.           (((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-80905.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-510, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80906
in-theory        80906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
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-50.           (((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-80906.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-500, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80907
in-theory        80907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G or (F or E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-80907.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G or (F or E)))), M:tm-490, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80908
in-theory        80908
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-50.           (((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-80908.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-480, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80909
in-theory        80909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or (B or A)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80909.        ((A or (B or A)) -> ((C or (B or A)) or D)), M:tm-470, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80910
in-theory        80910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80910.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-469, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80911
in-theory        80911
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80911.        (((A or (B or A)) -> (C or (B or A))) and (D -> (D or E))), M:tm-456, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80912
in-theory        80912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80912.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-453, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80913
in-theory        80913
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((D -> (D or E)) and ((A or (B or A)) -> (C or (B or A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-80913.        (((A or (B or A)) -> (C or (B or A))) and ((D -> (D or E)) and ((A or (B or A)) -> (C or (B or A))))), M:tm-443, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80914
in-theory        80914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-80914.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (F or (E or D)))), M:tm-409, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80915
in-theory        80915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80915.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F or (E or D)))), M:tm-400, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80916
in-theory        80916
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-80916.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (F or (E or D)))), M:tm-391, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80917
in-theory        80917
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-80917.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (F or (E or D)))), M:tm-382, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80918
in-theory        80918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G or (F or E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80918.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G or (F or E)))), M:tm-373, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80919
in-theory        80919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80919.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F or (E or D)))), M:tm-364, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80920
in-theory        80920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D or (B or A)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80920.        ((A or (B or A)) -> (C -> ((D or (B or A)) and C))), M:tm-355, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80921
in-theory        80921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80921.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-354, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80922
in-theory        80922
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80922.        (((A or (B or A)) -> (C or (B or A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80923
in-theory        80923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E or (D or C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80923.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E or (D or C)))), M:tm-338, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80924
in-theory        80924
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (C or (B or A)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80924.        (((A or (B or A)) -> (C or (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (C or (B or A))))), M:tm-328, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80925
in-theory        80925
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((D -> (E -> (D and E))) and ((A or (B or A)) -> (C or (B or A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-80925.        (((A or (B or A)) -> (C or (B or A))) and ((D -> (E -> (D and E))) and ((A or (B or A)) -> (C or (B or A))))), M:tm-327, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80926
in-theory        80926
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (((D and E) -> E) and ((A or (B or A)) -> (C or (B or A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-80926.        (((A or (B or A)) -> (C or (B or A))) and (((D and E) -> E) and ((A or (B or A)) -> (C or (B or A))))), M:tm-326, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80927
in-theory        80927
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (((D and E) -> D) and ((A or (B or A)) -> (C or (B or A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-80927.        (((A or (B or A)) -> (C or (B or A))) and (((D and E) -> D) and ((A or (B or A)) -> (C or (B or A))))), M:tm-325, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80928
in-theory        80928
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B or A)) -> (C or (B or A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-80928.        (((A or (B or A)) -> (C or (B or A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B or A)) -> (C or (B or A))))), M:tm-324, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80929
in-theory        80929
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((D -> (E -> D)) and ((A or (B or A)) -> (C or (B or A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80929.        (((A or (B or A)) -> (C or (B or A))) and ((D -> (E -> D)) and ((A or (B or A)) -> (C or (B or A))))), M:tm-323, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80930
in-theory        80930
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80930.        (((A or (B or A)) -> (C or (B or A))) and ((D and E) -> E)), M:tm-322, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80931
in-theory        80931
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80931.        (((A or (B or A)) -> (C or (B or A))) and ((D and E) -> D)), M:tm-320, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80932
in-theory        80932
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80932.        (((A or (B or A)) -> (C or (B or A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80933
in-theory        80933
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80933.        (((A or (B or A)) -> (C or (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80934
in-theory        80934
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80934.        (((A or (B or A)) -> (C or (B or A))) and (D -> (E -> D))), M:tm-315, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80935
in-theory        80935
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (((A or (B or A)) -> (not (C or (B or A)))) -> (not (A or (B or A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-80935.        (((A or (B or A)) -> (C or (B or A))) and (((A or (B or A)) -> (not (C or (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80936
in-theory        80936
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (((C or (B or A)) -> D) -> (((A or (B or A)) or (C or (B or A))) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80936.        (((A or (B or A)) -> (C or (B or A))) and (((C or (B or A)) -> D) -> (((A or (B or A)) or (C or (B or A))) -> D))), M:tm-312, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80937
in-theory        80937
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (D or ((A or (B or A)) -> (C or (B or A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-80937.        (((A or (B or A)) -> (C or (B or A))) and (D or ((A or (B or A)) -> (C or (B or A))))), M:tm-311, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80938
in-theory        80938
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (((A or (B or A)) -> (C or (B or A))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-80938.        (((A or (B or A)) -> (C or (B or A))) and (((A or (B or A)) -> (C or (B or A))) or D)), M:tm-310, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80939
in-theory        80939
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (D -> (((A or (B or A)) -> (C or (B or A))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80939.        (((A or (B or A)) -> (C or (B or A))) and (D -> (((A or (B or A)) -> (C or (B or A))) and D))), M:tm-309, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80940
in-theory        80940
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (D -> ((A or (B or A)) -> (C or (B or A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80940.        (((A or (B or A)) -> (C or (B or A))) and (D -> ((A or (B or A)) -> (C or (B or A))))), M:tm-305, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80941
in-theory        80941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80941.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-303, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80942
in-theory        80942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80942.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-270, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80943
in-theory        80943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80943.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-239, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80944
in-theory        80944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G or (F or E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80944.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G or (F or E)))), M:tm-210, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80945
in-theory        80945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80945.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-183, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80946
in-theory        80946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80946.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-157, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80947
in-theory        80947
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80947.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-147, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80948
in-theory        80948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80948.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-134, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80949
in-theory        80949
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80949.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-125, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80950
in-theory        80950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G or (F or E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80950.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G or (F or E)))), M:tm-113, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80951
in-theory        80951
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-80951.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-105, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80952
in-theory        80952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E or (D or C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80952.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E or (D or C)))), M:tm-95, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80953
in-theory        80953
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D or (B or A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80953.        ((A or (B or A)) -> (C -> (D or (B or A)))), M:tm-84, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80954
in-theory        80954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80954.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-83, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80955
in-theory        80955
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (D or (C or B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80955.        (((not (not A)) -> A) and ((B or (C or B)) -> (D or (C or B)))), M:tm-76, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80956
in-theory        80956
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (C or (B or A)))
theorem-size     19
proof            (modus-ponens tm-73 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-8 tm-10 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80956.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (C or (B or A))), M:tm-73, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80957
in-theory        80957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E or (D or C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80957.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E or (D or C)))), M:tm-69, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80958
in-theory        80958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80958.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-54, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80959
in-theory        80959
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (C or (A or B)))
theorem-size     15
proof            (modus-ponens tm-50 tm-899 ((A Am) (B (or Bm Am)) (C (or Cm (or Bm Am)))))
axioms-used      (tm-8 tm-7)
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-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-80959.        (((A or B) or (B or (A or B))) -> (C or (A or B))), M:tm-50, m:tm-899, u:((A Am) (B (or Bm Am)) (C (or Cm (or Bm Am))))
================================================================
tm-name          tm-80960
in-theory        80960
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (C or (B or A)))
theorem-size     13
proof            (modus-ponens tm-49 tm-899 ((A Am) (B (or Bm Am)) (C (or Cm (or Bm Am)))))
axioms-used      (tm-8 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80960.        ((A or (A or (B or A))) -> (C or (B or A))), M:tm-49, m:tm-899, u:((A Am) (B (or Bm Am)) (C (or Cm (or Bm Am))))
================================================================
tm-name          tm-80961
in-theory        80961
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (D or (C or B)))
theorem-size     19
proof            (modus-ponens tm-47 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-8 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80961.        (((A and (B or (C or B))) or (B or (C or B))) -> (D or (C or B))), M:tm-47, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80962
in-theory        80962
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (D or (B or A)))
theorem-size     19
proof            (modus-ponens tm-46 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-8 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80962.        ((((A or (B or A)) and C) or (A or (B or A))) -> (D or (B or A))), M:tm-46, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80963
in-theory        80963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (E or (D or C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-80963.        ((A -> (B or A)) and ((C or (D or C)) -> (E or (D or C)))), M:tm-42, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80964
in-theory        80964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (E or (D or C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80964.        ((A -> (A or B)) and ((C or (D or C)) -> (E or (D or C)))), M:tm-32, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80965
in-theory        80965
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (C or (B or A))))
theorem-size     17
proof            (modus-ponens tm-24 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80965.        ((A or (B or A)) -> ((A or (B or A)) and (C or (B or A)))), M:tm-24, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80966
in-theory        80966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E or (D or C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80966.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E or (D or C)))), M:tm-23, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80967
in-theory        80967
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (E or (D or C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80967.        (((A and B) -> B) and ((C or (D or C)) -> (E or (D or C)))), M:tm-22, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80968
in-theory        80968
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (E or (D or C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80968.        (((A and B) -> A) and ((C or (D or C)) -> (E or (D or C)))), M:tm-21, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80969
in-theory        80969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80969.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F or (E or D)))), M:tm-20, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80970
in-theory        80970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (E or (D or C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80970.        ((A -> (B -> A)) and ((C or (D or C)) -> (E or (D or C)))), M:tm-19, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80971
in-theory        80971
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (C or (B or A)))) -> (not (A or (B or A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-9 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80971.        (((A or (B or A)) -> (not (C or (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80972
in-theory        80972
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or C)) -> D) -> (((C or (B or C)) or (A or (B or C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-899 ((A (or Am (or Bm Am))) (B (or Cm (or Bm Am)))))
axioms-used      (tm-8 tm-7)
proof-size       81
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-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-80972.        (((A or (B or C)) -> D) -> (((C or (B or C)) or (A or (B or C))) -> D)), M:tm-8, m:tm-899, u:((A (or Am (or Bm Am))) (B (or Cm (or Bm Am))))
================================================================
tm-name          tm-80973
in-theory        80973
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (D or (C or B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-7 tm-8)
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-50.           (((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-80973.        (A or ((B or (C or B)) -> (D or (C or B)))), M:tm-7, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80974
in-theory        80974
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80974.        (((A or (B or A)) -> (C or (B or A))) or D), M:tm-6, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80975
in-theory        80975
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (D or (C or B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80975.        (A -> (((B or (C or B)) -> (D or (C or B))) and A)), M:tm-5, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80976
in-theory        80976
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (D or (C or B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80976.        (A -> ((B or (C or B)) -> (D or (C or B)))), M:tm-1, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-80977
in-theory        80977
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80977.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-893, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80978
in-theory        80978
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((A or (A or (B or A))) -> (C -> (D -> C))))
theorem-size     25
proof            (modus-ponens tm-882 tm-900 ((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80978.        (((A or (B or A)) -> (C -> (D -> C))) and ((A or (A or (B or A))) -> (C -> (D -> C)))), M:tm-882, m:tm-900, u:((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-80979
in-theory        80979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80979.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-855, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80980
in-theory        80980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80980.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-808, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80981
in-theory        80981
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (((E and (A or (B or A))) or (A or (B or A))) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80981.        (((A or (B or A)) -> (C -> (D -> C))) and (((E and (A or (B or A))) or (A or (B or A))) -> (C -> (D -> C)))), M:tm-798, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-80982
in-theory        80982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80982.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-757, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80983
in-theory        80983
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-80983.        (((A or (B or A)) -> (C -> (D -> C))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (C -> (D -> C)))), M:tm-747, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-80984
in-theory        80984
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-80984.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (H -> G)))), M:tm-708, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80985
in-theory        80985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80985.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-665, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80986
in-theory        80986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-900 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80986.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-622, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80987
in-theory        80987
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D or (A or (B or A)))))
theorem-size     15
proof            (modus-ponens tm-617 tm-900 ((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (-> Dm (or B (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80987.        ((A or (B or A)) -> (C -> (D or (A or (B or A))))), M:tm-617, m:tm-900, u:((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (-> Dm (or B (or Am (or Bm Am))))))
================================================================
tm-name          tm-80988
in-theory        80988
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-900 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80988.        (((A or (B or A)) -> (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80989
in-theory        80989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-900 ((A (-> (or Am (or 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-50.           (((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-80989.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-605, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80990
in-theory        80990
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (F or E)) and ((A or (B or A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-900 ((A (-> (or Am (or 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-50.           (((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-80990.        (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (F or E)) and ((A or (B or A)) -> (C -> (D -> C))))), M:tm-595, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80991
in-theory        80991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-900 ((A (-> (or Am (or 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-50.           (((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-80991.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-550, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80992
in-theory        80992
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-900 ((A (-> (or Am (or 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-50.           (((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-80992.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-540, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80993
in-theory        80993
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-900 ((A (-> (or Am (or 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-50.           (((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-80993.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-530, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80994
in-theory        80994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-900 ((A (-> (or Am (or 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-50.           (((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-80994.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-520, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80995
in-theory        80995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-900 ((A (-> (or Am (or 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-50.           (((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-80995.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-510, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80996
in-theory        80996
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-900 ((A (-> (or Am (or 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-50.           (((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-80996.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-500, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80997
in-theory        80997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-900 ((A (-> (or Am (or 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-50.           (((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-80997.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H -> G)))), M:tm-490, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80998
in-theory        80998
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-900 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80998.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-480, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-80999
in-theory        80999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-80999.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-469, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81000
in-theory        81000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((A or (B or A)) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-900 ((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (-> Dm (or (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81000.        ((A or (B or A)) -> (C -> ((A or (B or A)) or D))), M:tm-464, m:tm-900, u:((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (-> Dm (or (or Am (or Bm Am)) B))))
================================================================
tm-name          tm-81001
in-theory        81001
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81001.        (((A or (B or A)) -> (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81002
in-theory        81002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81002.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-453, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81003
in-theory        81003
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (E or F)) and ((A or (B or A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81003.        (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (E or F)) and ((A or (B or A)) -> (C -> (D -> C))))), M:tm-443, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81004
in-theory        81004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81004.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-409, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81005
in-theory        81005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81005.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-400, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81006
in-theory        81006
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81006.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-391, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81007
in-theory        81007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81007.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-382, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81008
in-theory        81008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81008.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (H -> G)))), M:tm-373, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81009
in-theory        81009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81009.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-364, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81010
in-theory        81010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81010.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-354, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81011
in-theory        81011
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> ((A or (B or A)) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-900 ((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (-> Dm (-> B (and (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81011.        ((A or (B or A)) -> (C -> (D -> ((A or (B or A)) and D)))), M:tm-349, m:tm-900, u:((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (-> Dm (-> B (and (or Am (or Bm Am)) B)))))
================================================================
tm-name          tm-81012
in-theory        81012
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81012.        (((A or (B or A)) -> (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81013
in-theory        81013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81013.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (F -> E)))), M:tm-338, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81014
in-theory        81014
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81014.        (((A or (B or A)) -> (C -> (D -> C))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (D -> C))))), M:tm-328, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81015
in-theory        81015
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81015.        (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (C -> (D -> C))))), M:tm-327, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81016
in-theory        81016
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (((E and F) -> F) and ((A or (B or A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81016.        (((A or (B or A)) -> (C -> (D -> C))) and (((E and F) -> F) and ((A or (B or A)) -> (C -> (D -> C))))), M:tm-326, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81017
in-theory        81017
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (((E and F) -> E) and ((A or (B or A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81017.        (((A or (B or A)) -> (C -> (D -> C))) and (((E and F) -> E) and ((A or (B or A)) -> (C -> (D -> C))))), M:tm-325, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81018
in-theory        81018
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-81018.        (((A or (B or A)) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (C -> (D -> C))))), M:tm-324, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81019
in-theory        81019
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (F -> E)) and ((A or (B or A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81019.        (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (F -> E)) and ((A or (B or A)) -> (C -> (D -> C))))), M:tm-323, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81020
in-theory        81020
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81020.        (((A or (B or A)) -> (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81021
in-theory        81021
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81021.        (((A or (B or A)) -> (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81022
in-theory        81022
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81022.        (((A or (B or A)) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81023
in-theory        81023
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81023.        (((A or (B or A)) -> (C -> (D -> C))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81024
in-theory        81024
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81024.        (((A or (B or A)) -> (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81025
in-theory        81025
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (((A or (B or A)) -> (not (C -> (D -> C)))) -> (not (A or (B or A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-81025.        (((A or (B or A)) -> (C -> (D -> C))) and (((A or (B or A)) -> (not (C -> (D -> C)))) -> (not (A or (B or A))))), M:tm-313, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81026
in-theory        81026
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> (((A or (B or A)) or (C -> (D -> C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81026.        (((A or (B or A)) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> (((A or (B or A)) or (C -> (D -> C))) -> E))), M:tm-312, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81027
in-theory        81027
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (E or ((A or (B or A)) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-900 ((A (-> (or Am (or 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-50.           (((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-81027.        (((A or (B or A)) -> (C -> (D -> C))) and (E or ((A or (B or A)) -> (C -> (D -> C))))), M:tm-311, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81028
in-theory        81028
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (((A or (B or A)) -> (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-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-81028.        (((A or (B or A)) -> (C -> (D -> C))) and (((A or (B or A)) -> (C -> (D -> C))) or E)), M:tm-310, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81029
in-theory        81029
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (E -> (((A or (B or A)) -> (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-81029.        (((A or (B or A)) -> (C -> (D -> C))) and (E -> (((A or (B or A)) -> (C -> (D -> C))) and E))), M:tm-309, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81030
in-theory        81030
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D -> C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-900 ((A (or Am (or Bm Am))) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-81030.        (((A or (B or A)) -> (C -> (D -> C))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D -> C)))), M:tm-306, m:tm-900, u:((A (or Am (or Bm Am))) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-81031
in-theory        81031
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (E -> ((A or (B or A)) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81031.        (((A or (B or A)) -> (C -> (D -> C))) and (E -> ((A or (B or A)) -> (C -> (D -> C))))), M:tm-305, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81032
in-theory        81032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81032.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-303, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81033
in-theory        81033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81033.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-270, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81034
in-theory        81034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81034.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-239, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81035
in-theory        81035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81035.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (H -> G)))), M:tm-210, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81036
in-theory        81036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81036.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-183, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81037
in-theory        81037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81037.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-157, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81038
in-theory        81038
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81038.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-147, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81039
in-theory        81039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81039.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-134, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81040
in-theory        81040
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81040.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-125, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81041
in-theory        81041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81041.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H -> G)))), M:tm-113, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81042
in-theory        81042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81042.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-105, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81043
in-theory        81043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (A or (B or A))))
theorem-size     13
proof            (modus-ponens tm-99 tm-900 ((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (-> Dm (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81043.        ((A or (B or A)) -> (C -> (A or (B or A)))), M:tm-99, m:tm-900, u:((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (-> Dm (or Am (or Bm Am)))))
================================================================
tm-name          tm-81044
in-theory        81044
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> (A or (B or A)))))
theorem-size     15
proof            (modus-ponens tm-98 tm-900 ((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (-> Dm (-> B (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81044.        ((A or (B or A)) -> (C -> (D -> (A or (B or A))))), M:tm-98, m:tm-900, u:((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (-> Dm (-> B (or Am (or Bm Am))))))
================================================================
tm-name          tm-81045
in-theory        81045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81045.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (F -> E)))), M:tm-95, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81046
in-theory        81046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81046.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-83, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81047
in-theory        81047
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81047.        (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (E -> D)))), M:tm-76, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81048
in-theory        81048
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81048.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (D -> C))), M:tm-73, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81049
in-theory        81049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81049.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (F -> E)))), M:tm-69, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81050
in-theory        81050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81050.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-54, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81051
in-theory        81051
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-900 ((A Am) (B (or 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-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-81051.        (((A or B) or (B or (A or B))) -> (C -> (D -> C))), M:tm-50, m:tm-900, u:((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81052
in-theory        81052
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-49 tm-900 ((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81052.        ((A or (A or (B or A))) -> (C -> (D -> C))), M:tm-49, m:tm-900, u:((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81053
in-theory        81053
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81053.        (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (E -> D))), M:tm-47, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81054
in-theory        81054
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81054.        ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (E -> D))), M:tm-46, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81055
in-theory        81055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-900 ((A (-> (or Am (or 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-50.           (((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-81055.        ((A -> (B or A)) and ((C or (D or C)) -> (E -> (F -> E)))), M:tm-42, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81056
in-theory        81056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-81056.        ((A -> (A or B)) and ((C or (D or C)) -> (E -> (F -> E)))), M:tm-32, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81057
in-theory        81057
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (C -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81057.        ((A or (B or A)) -> ((A or (B or A)) and (C -> (D -> C)))), M:tm-24, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81058
in-theory        81058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81058.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (F -> E)))), M:tm-23, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81059
in-theory        81059
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-81059.        (((A and B) -> B) and ((C or (D or C)) -> (E -> (F -> E)))), M:tm-22, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81060
in-theory        81060
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-81060.        (((A and B) -> A) and ((C or (D or C)) -> (E -> (F -> E)))), M:tm-21, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81061
in-theory        81061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-81061.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-20, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81062
in-theory        81062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81062.        ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (F -> E)))), M:tm-19, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81063
in-theory        81063
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (C -> (D -> C)))) -> (not (A or (B or A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81063.        (((A or (B or A)) -> (not (C -> (D -> C)))) -> (not (A or (B or A)))), M:tm-9, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81064
in-theory        81064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (((D or (E or D)) or (A -> (B -> A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-900 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
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-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-81064.        (((A -> (B -> A)) -> C) -> (((D or (E or D)) or (A -> (B -> A))) -> C)), M:tm-8, m:tm-900, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-81065
in-theory        81065
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-900 ((A (-> (or Am (or 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-50.           (((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-81065.        (A or ((B or (C or B)) -> (D -> (E -> D)))), M:tm-7, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81066
in-theory        81066
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81066.        (((A or (B or A)) -> (C -> (D -> C))) or E), M:tm-6, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81067
in-theory        81067
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81067.        (A -> (((B or (C or B)) -> (D -> (E -> D))) and A)), M:tm-5, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81068
in-theory        81068
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-900 ((A (or Am (or Bm Am))) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81068.        (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D -> C))), M:tm-2, m:tm-900, u:((A (or Am (or Bm Am))) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-81069
in-theory        81069
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81069.        (A -> ((B or (C or B)) -> (D -> (E -> D)))), M:tm-1, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-81070
in-theory        81070
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-893 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81070.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-893, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81071
in-theory        81071
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-882 tm-901 ((A Am) (B (or Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81071.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-882, m:tm-901, u:((A Am) (B (or Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81072
in-theory        81072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-855 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81072.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-855, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81073
in-theory        81073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-808 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81073.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-808, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81074
in-theory        81074
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and (A or (B or A))) or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-798 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81074.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and (A or (B or A))) or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-798, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81075
in-theory        81075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81075.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81076
in-theory        81076
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A or (B or A)) and F) or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-747 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81076.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A or (B or A)) and F) or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-747, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81077
in-theory        81077
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81077.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81078
in-theory        81078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-901 ((A (-> (or 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       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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81078.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81079
in-theory        81079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-901 ((A (-> (or Am (or 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-50.           (((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-14.           (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-81079.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81080
in-theory        81080
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-901 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81080.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81081
in-theory        81081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-901 ((A (-> (or Am (or 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-50.           (((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-81081.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81082
in-theory        81082
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-901 ((A (-> (or Am (or 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-50.           (((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-14.           (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-81082.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81083
in-theory        81083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-901 ((A (-> (or Am (or 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-50.           (((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-81083.        (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81084
in-theory        81084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-901 ((A (-> (or Am (or 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-50.           (((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-81084.        ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81085
in-theory        81085
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-901 ((A (-> (or Am (or 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-50.           (((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-81085.        ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81086
in-theory        81086
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-901 ((A (-> (or Am (or 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-50.           (((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-81086.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81087
in-theory        81087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-901 ((A (-> (or Am (or 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-50.           (((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-81087.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81088
in-theory        81088
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-901 ((A (-> (or Am (or 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-50.           (((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-81088.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81089
in-theory        81089
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-901 ((A (-> (or Am (or 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-50.           (((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-14.           (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-81089.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81090
in-theory        81090
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-901 ((A (-> (or Am (or 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-50.           (((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-14.           (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-81090.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81091
in-theory        81091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81091.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81092
in-theory        81092
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-14.           (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-81092.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81093
in-theory        81093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81093.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81094
in-theory        81094
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81094.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81095
in-theory        81095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81095.        (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81096
in-theory        81096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81096.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81097
in-theory        81097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81097.        ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81098
in-theory        81098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81098.        ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81099
in-theory        81099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81099.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81100
in-theory        81100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81100.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81101
in-theory        81101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81101.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81102
in-theory        81102
times-derived    1
----------------------------------------------------------------
theorem          (((A or (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-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-14.           (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-81102.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81103
in-theory        81103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81103.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81104
in-theory        81104
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-328 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81104.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-328, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81105
in-theory        81105
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81105.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81106
in-theory        81106
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81106.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81107
in-theory        81107
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81107.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81108
in-theory        81108
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81108.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81109
in-theory        81109
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-14.           (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-81109.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81110
in-theory        81110
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-14.           (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-81110.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81111
in-theory        81111
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-14.           (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-81111.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81112
in-theory        81112
times-derived    1
----------------------------------------------------------------
theorem          (((A or (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-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-81112.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81113
in-theory        81113
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     31
proof            (modus-ponens tm-316 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-14.           (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-81113.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81114
in-theory        81114
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-14.           (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-81114.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81115
in-theory        81115
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B or A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B or A)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-81115.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B or A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B or A))))), M:tm-313, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81116
in-theory        81116
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> (((A or (B or A)) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     57
proof            (modus-ponens tm-312 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81116.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> (((A or (B or A)) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-312, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81117
in-theory        81117
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-901 ((A (-> (or Am (or 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-50.           (((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-14.           (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-81117.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81118
in-theory        81118
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-81118.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81119
in-theory        81119
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-14.           (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-81119.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81120
in-theory        81120
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B or A)) -> (C -> (D -> E))) -> ((A or (B or A)) -> ((C -> D) -> (C -> E)))))
theorem-size     45
proof            (modus-ponens tm-306 tm-901 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-81120.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B or A)) -> (C -> (D -> E))) -> ((A or (B or A)) -> ((C -> D) -> (C -> E))))), M:tm-306, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-81121
in-theory        81121
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-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-14.           (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-81121.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81122
in-theory        81122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81122.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81123
in-theory        81123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81123.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81124
in-theory        81124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81124.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81125
in-theory        81125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81125.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81126
in-theory        81126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81126.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81127
in-theory        81127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81127.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81128
in-theory        81128
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81128.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81129
in-theory        81129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81129.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81130
in-theory        81130
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81130.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81131
in-theory        81131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81131.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81132
in-theory        81132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81132.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81133
in-theory        81133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-14.           (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-81133.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81134
in-theory        81134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81134.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81135
in-theory        81135
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81135.        (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81136
in-theory        81136
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-73 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81136.        (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-73, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81137
in-theory        81137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81137.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81138
in-theory        81138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81138.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81139
in-theory        81139
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-50 tm-901 ((A Am) (B (or 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-81139.        (((A or B) or (B or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-50, m:tm-901, u:((A Am) (B (or Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81140
in-theory        81140
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-49 tm-901 ((A Am) (B (or Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81140.        ((A or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-49, m:tm-901, u:((A Am) (B (or Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81141
in-theory        81141
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-47 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81141.        (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-47, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81142
in-theory        81142
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-46 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81142.        ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-46, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81143
in-theory        81143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-901 ((A (-> (or Am (or 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-50.           (((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-81143.        ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81144
in-theory        81144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81144.        ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81145
in-theory        81145
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-24 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81145.        ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-24, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81146
in-theory        81146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81146.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81147
in-theory        81147
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81147.        (((A and B) -> B) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81148
in-theory        81148
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81148.        (((A and B) -> A) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81149
in-theory        81149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81149.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81150
in-theory        81150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81150.        ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81151
in-theory        81151
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B or A))))
theorem-size     27
proof            (modus-ponens tm-9 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81151.        (((A or (B or A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B or A)))), M:tm-9, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81152
in-theory        81152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or (F or E)) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-901 ((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       133
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-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-81152.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or (F or E)) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-81153
in-theory        81153
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-901 ((A (-> (or Am (or 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-50.           (((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-81153.        (A or ((B or (C or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81154
in-theory        81154
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81154.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81155
in-theory        81155
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81155.        (A -> (((B or (C or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81156
in-theory        81156
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> E))) -> ((A or (B or A)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-2 tm-901 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81156.        (((A or (B or A)) -> (C -> (D -> E))) -> ((A or (B or A)) -> ((C -> D) -> (C -> E)))), M:tm-2, m:tm-901, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-81157
in-theory        81157
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-14.           (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-81157.        (A -> ((B or (C or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-81158
in-theory        81158
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-893 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81158.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-893, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81159
in-theory        81159
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((A or (A or (B or A))) -> ((C and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-882 tm-902 ((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81159.        (((A or (B or A)) -> ((C and D) -> C)) and ((A or (A or (B or A))) -> ((C and D) -> C))), M:tm-882, m:tm-902, u:((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81160
in-theory        81160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-855 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81160.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-855, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81161
in-theory        81161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-808 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81161.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-808, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81162
in-theory        81162
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-798 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81162.        (((A or (B or A)) -> ((C and D) -> C)) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C and D) -> C))), M:tm-798, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81163
in-theory        81163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81163.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-757, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81164
in-theory        81164
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (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-81164.        (((A or (B or A)) -> ((C and D) -> C)) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C and D) -> C))), M:tm-747, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81165
in-theory        81165
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81165.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G and H) -> G))), M:tm-708, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81166
in-theory        81166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81166.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-665, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81167
in-theory        81167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-902 ((A (-> (or Am (or 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-50.           (((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-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-81167.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-622, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81168
in-theory        81168
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-902 ((A (-> (or Am (or 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-50.           (((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-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-81168.        (((A or (B or A)) -> ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81169
in-theory        81169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-902 ((A (-> (or Am (or 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-50.           (((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-81169.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-605, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81170
in-theory        81170
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (F or E)) and ((A or (B or A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-902 ((A (-> (or Am (or 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-50.           (((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-81170.        (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (F or E)) and ((A or (B or A)) -> ((C and D) -> C)))), M:tm-595, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81171
in-theory        81171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-902 ((A (-> (or Am (or 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-50.           (((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-81171.        (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-550, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81172
in-theory        81172
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-902 ((A (-> (or Am (or 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-50.           (((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-81172.        ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-540, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81173
in-theory        81173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-902 ((A (-> (or Am (or 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-50.           (((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-81173.        ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-530, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81174
in-theory        81174
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-902 ((A (-> (or Am (or 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-50.           (((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-81174.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-520, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81175
in-theory        81175
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-902 ((A (-> (or Am (or 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-50.           (((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-81175.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-510, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81176
in-theory        81176
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-902 ((A (-> (or Am (or 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-50.           (((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-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-81176.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-500, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81177
in-theory        81177
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-902 ((A (-> (or Am (or 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-50.           (((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-81177.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G and H) -> G))), M:tm-490, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81178
in-theory        81178
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-902 ((A (-> (or Am (or 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-50.           (((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-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-81178.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-480, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81179
in-theory        81179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81179.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-469, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81180
in-theory        81180
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81180.        (((A or (B or A)) -> ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81181
in-theory        81181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81181.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-453, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81182
in-theory        81182
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (E or F)) and ((A or (B or A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81182.        (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (E or F)) and ((A or (B or A)) -> ((C and D) -> C)))), M:tm-443, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81183
in-theory        81183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81183.        (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-409, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81184
in-theory        81184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81184.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-400, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81185
in-theory        81185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81185.        ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-391, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81186
in-theory        81186
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81186.        ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-382, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81187
in-theory        81187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81187.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G and H) -> G))), M:tm-373, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81188
in-theory        81188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81188.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-364, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81189
in-theory        81189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81189.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-354, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81190
in-theory        81190
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81190.        (((A or (B or A)) -> ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81191
in-theory        81191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81191.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E and F) -> E))), M:tm-338, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81192
in-theory        81192
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((A or (B or A)) -> ((A or (B or A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81192.        (((A or (B or A)) -> ((C and D) -> C)) and ((A or (B or A)) -> ((A or (B or A)) and ((C and D) -> C)))), M:tm-328, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81193
in-theory        81193
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81193.        (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C and D) -> C)))), M:tm-327, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81194
in-theory        81194
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (((E and F) -> F) and ((A or (B or A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81194.        (((A or (B or A)) -> ((C and D) -> C)) and (((E and F) -> F) and ((A or (B or A)) -> ((C and D) -> C)))), M:tm-326, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81195
in-theory        81195
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (((E and F) -> E) and ((A or (B or A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81195.        (((A or (B or A)) -> ((C and D) -> C)) and (((E and F) -> E) and ((A or (B or A)) -> ((C and D) -> C)))), M:tm-325, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81196
in-theory        81196
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81196.        (((A or (B or A)) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C and D) -> C)))), M:tm-324, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81197
in-theory        81197
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A 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-81197.        (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C and D) -> C)))), M:tm-323, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81198
in-theory        81198
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81198.        (((A or (B or A)) -> ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81199
in-theory        81199
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81199.        (((A or (B or A)) -> ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81200
in-theory        81200
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-3.            ((A 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-81200.        (((A or (B or A)) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81201
in-theory        81201
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81201.        (((A or (B or A)) -> ((C and D) -> C)) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81202
in-theory        81202
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81202.        (((A or (B or A)) -> ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81203
in-theory        81203
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (((A or (B or A)) -> (not ((C and D) -> C))) -> (not (A or (B or A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-81203.        (((A or (B or A)) -> ((C and D) -> C)) and (((A or (B or A)) -> (not ((C and D) -> C))) -> (not (A or (B or A))))), M:tm-313, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81204
in-theory        81204
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> (((A or (B or A)) or ((C and D) -> C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81204.        (((A or (B or A)) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> (((A or (B or A)) or ((C and D) -> C)) -> E))), M:tm-312, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81205
in-theory        81205
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (E or ((A or (B or A)) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-902 ((A (-> (or Am (or 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-50.           (((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-81205.        (((A or (B or A)) -> ((C and D) -> C)) and (E or ((A or (B or A)) -> ((C and D) -> C)))), M:tm-311, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81206
in-theory        81206
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (((A or (B or A)) -> ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-81206.        (((A or (B or A)) -> ((C and D) -> C)) and (((A or (B or A)) -> ((C and D) -> C)) or E)), M:tm-310, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81207
in-theory        81207
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (E -> (((A or (B or A)) -> ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-81207.        (((A or (B or A)) -> ((C and D) -> C)) and (E -> (((A or (B or A)) -> ((C and D) -> C)) and E))), M:tm-309, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81208
in-theory        81208
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (((A or (B or A)) -> (C and D)) -> ((A or (B or A)) -> C)))
theorem-size     29
proof            (modus-ponens tm-306 tm-902 ((A (or Am (or Bm Am))) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-81208.        (((A or (B or A)) -> ((C and D) -> C)) and (((A or (B or A)) -> (C and D)) -> ((A or (B or A)) -> C))), M:tm-306, m:tm-902, u:((A (or Am (or Bm Am))) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-81209
in-theory        81209
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (E -> ((A or (B or A)) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-3.            ((A 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-81209.        (((A or (B or A)) -> ((C and D) -> C)) and (E -> ((A or (B or A)) -> ((C and D) -> C)))), M:tm-305, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81210
in-theory        81210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81210.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-303, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81211
in-theory        81211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81211.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-270, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81212
in-theory        81212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81212.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-239, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81213
in-theory        81213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81213.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G and H) -> G))), M:tm-210, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81214
in-theory        81214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81214.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-183, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81215
in-theory        81215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81215.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-157, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81216
in-theory        81216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81216.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-147, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81217
in-theory        81217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81217.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-134, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81218
in-theory        81218
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81218.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-125, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81219
in-theory        81219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81219.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G and H) -> G))), M:tm-113, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81220
in-theory        81220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81220.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-105, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81221
in-theory        81221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81221.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E and F) -> E))), M:tm-95, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81222
in-theory        81222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81222.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-83, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81223
in-theory        81223
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81223.        (((not (not A)) -> A) and ((B or (C or B)) -> ((D and E) -> D))), M:tm-76, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81224
in-theory        81224
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-73 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81224.        (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C and D) -> C)), M:tm-73, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81225
in-theory        81225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81225.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E and F) -> E))), M:tm-69, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81226
in-theory        81226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81226.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-54, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81227
in-theory        81227
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-50 tm-902 ((A Am) (B (or 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-3.            ((A 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-81227.        (((A or B) or (B or (A or B))) -> ((C and D) -> C)), M:tm-50, m:tm-902, u:((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81228
in-theory        81228
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-49 tm-902 ((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81228.        ((A or (A or (B or A))) -> ((C and D) -> C)), M:tm-49, m:tm-902, u:((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81229
in-theory        81229
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-47 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81229.        (((A and (B or (C or B))) or (B or (C or B))) -> ((D and E) -> D)), M:tm-47, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81230
in-theory        81230
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-46 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81230.        ((((A or (B or A)) and C) or (A or (B or A))) -> ((D and E) -> D)), M:tm-46, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81231
in-theory        81231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-902 ((A (-> (or Am (or 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-50.           (((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-81231.        ((A -> (B or A)) and ((C or (D or C)) -> ((E and F) -> E))), M:tm-42, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81232
in-theory        81232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81232.        ((A -> (A or B)) and ((C or (D or C)) -> ((E and F) -> E))), M:tm-32, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81233
in-theory        81233
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81233.        ((A or (B or A)) -> ((A or (B or A)) and ((C and D) -> C))), M:tm-24, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81234
in-theory        81234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81234.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E and F) -> E))), M:tm-23, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81235
in-theory        81235
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81235.        (((A and B) -> B) and ((C or (D or C)) -> ((E and F) -> E))), M:tm-22, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81236
in-theory        81236
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81236.        (((A and B) -> A) and ((C or (D or C)) -> ((E and F) -> E))), M:tm-21, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81237
in-theory        81237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81237.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-20, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81238
in-theory        81238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81238.        ((A -> (B -> A)) and ((C or (D or C)) -> ((E and F) -> E))), M:tm-19, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81239
in-theory        81239
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not ((C and D) -> C))) -> (not (A or (B or A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81239.        (((A or (B or A)) -> (not ((C and D) -> C))) -> (not (A or (B or A)))), M:tm-9, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81240
in-theory        81240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (((D or (E or D)) or ((A and B) -> A)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-902 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
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-3.            ((A 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-81240.        ((((A and B) -> A) -> C) -> (((D or (E or D)) or ((A and B) -> A)) -> C)), M:tm-8, m:tm-902, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-81241
in-theory        81241
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-902 ((A (-> (or Am (or 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-50.           (((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-81241.        (A or ((B or (C or B)) -> ((D and E) -> D))), M:tm-7, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81242
in-theory        81242
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81242.        (((A or (B or A)) -> ((C and D) -> C)) or E), M:tm-6, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81243
in-theory        81243
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81243.        (A -> (((B or (C or B)) -> ((D and E) -> D)) and A)), M:tm-5, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81244
in-theory        81244
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C and D)) -> ((A or (B or A)) -> C))
theorem-size     17
proof            (modus-ponens tm-2 tm-902 ((A (or Am (or Bm Am))) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81244.        (((A or (B or A)) -> (C and D)) -> ((A or (B or A)) -> C)), M:tm-2, m:tm-902, u:((A (or Am (or Bm Am))) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-81245
in-theory        81245
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81245.        (A -> ((B or (C or B)) -> ((D and E) -> D))), M:tm-1, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-81246
in-theory        81246
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-893 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81246.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-893, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81247
in-theory        81247
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((A or (A or (B or A))) -> ((C and D) -> D)))
theorem-size     25
proof            (modus-ponens tm-882 tm-903 ((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81247.        (((A or (B or A)) -> ((C and D) -> D)) and ((A or (A or (B or A))) -> ((C and D) -> D))), M:tm-882, m:tm-903, u:((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81248
in-theory        81248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-855 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81248.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-855, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81249
in-theory        81249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-808 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81249.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-808, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81250
in-theory        81250
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-798 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81250.        (((A or (B or A)) -> ((C and D) -> D)) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C and D) -> D))), M:tm-798, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81251
in-theory        81251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81251.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-757, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81252
in-theory        81252
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-747 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81252.        (((A or (B or A)) -> ((C and D) -> D)) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C and D) -> D))), M:tm-747, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81253
in-theory        81253
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81253.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G and H) -> H))), M:tm-708, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81254
in-theory        81254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81254.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-665, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81255
in-theory        81255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-903 ((A (-> (or Am (or 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-50.           (((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-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-81255.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-622, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81256
in-theory        81256
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-903 ((A (-> (or Am (or 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-50.           (((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-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-81256.        (((A or (B or A)) -> ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81257
in-theory        81257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-903 ((A (-> (or Am (or 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-50.           (((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-81257.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-605, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81258
in-theory        81258
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (F or E)) and ((A or (B or A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-903 ((A (-> (or Am (or 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-50.           (((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-81258.        (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (F or E)) and ((A or (B or A)) -> ((C and D) -> D)))), M:tm-595, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81259
in-theory        81259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-903 ((A (-> (or Am (or 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-50.           (((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-81259.        (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-550, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81260
in-theory        81260
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-903 ((A (-> (or Am (or 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-50.           (((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-81260.        ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-540, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81261
in-theory        81261
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-903 ((A (-> (or Am (or 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-50.           (((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-81261.        ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-530, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81262
in-theory        81262
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-903 ((A (-> (or Am (or 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-50.           (((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-81262.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-520, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81263
in-theory        81263
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-903 ((A (-> (or Am (or 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-50.           (((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-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-81263.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-510, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81264
in-theory        81264
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-903 ((A (-> (or Am (or 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-50.           (((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-81264.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-500, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81265
in-theory        81265
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-903 ((A (-> (or Am (or 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-50.           (((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-81265.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G and H) -> H))), M:tm-490, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81266
in-theory        81266
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-903 ((A (-> (or Am (or 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-50.           (((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-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-81266.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-480, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81267
in-theory        81267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81267.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-469, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81268
in-theory        81268
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81268.        (((A or (B or A)) -> ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81269
in-theory        81269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81269.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-453, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81270
in-theory        81270
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (E or F)) and ((A or (B or A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81270.        (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (E or F)) and ((A or (B or A)) -> ((C and D) -> D)))), M:tm-443, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81271
in-theory        81271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81271.        (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-409, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81272
in-theory        81272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81272.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-400, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81273
in-theory        81273
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81273.        ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-391, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81274
in-theory        81274
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81274.        ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-382, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81275
in-theory        81275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81275.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G and H) -> H))), M:tm-373, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81276
in-theory        81276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81276.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-364, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81277
in-theory        81277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81277.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-354, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81278
in-theory        81278
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81278.        (((A or (B or A)) -> ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81279
in-theory        81279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81279.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E and F) -> F))), M:tm-338, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81280
in-theory        81280
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((A or (B or A)) -> ((A or (B or A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-328 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81280.        (((A or (B or A)) -> ((C and D) -> D)) and ((A or (B or A)) -> ((A or (B or A)) and ((C and D) -> D)))), M:tm-328, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81281
in-theory        81281
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81281.        (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C and D) -> D)))), M:tm-327, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81282
in-theory        81282
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (((E and F) -> F) and ((A or (B or A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81282.        (((A or (B or A)) -> ((C and D) -> D)) and (((E and F) -> F) and ((A or (B or A)) -> ((C and D) -> D)))), M:tm-326, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81283
in-theory        81283
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (((E and F) -> E) and ((A or (B or A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81283.        (((A or (B or A)) -> ((C and D) -> D)) and (((E and F) -> E) and ((A or (B or A)) -> ((C and D) -> D)))), M:tm-325, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81284
in-theory        81284
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81284.        (((A or (B or A)) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C and D) -> D)))), M:tm-324, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81285
in-theory        81285
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A 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-81285.        (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C and D) -> D)))), M:tm-323, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81286
in-theory        81286
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81286.        (((A or (B or A)) -> ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81287
in-theory        81287
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81287.        (((A or (B or A)) -> ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81288
in-theory        81288
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A 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-81288.        (((A or (B or A)) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81289
in-theory        81289
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81289.        (((A or (B or A)) -> ((C and D) -> D)) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81290
in-theory        81290
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81290.        (((A or (B or A)) -> ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81291
in-theory        81291
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (((A or (B or A)) -> (not ((C and D) -> D))) -> (not (A or (B or A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-81291.        (((A or (B or A)) -> ((C and D) -> D)) and (((A or (B or A)) -> (not ((C and D) -> D))) -> (not (A or (B or A))))), M:tm-313, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81292
in-theory        81292
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> (((A or (B or A)) or ((C and D) -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81292.        (((A or (B or A)) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> (((A or (B or A)) or ((C and D) -> D)) -> E))), M:tm-312, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81293
in-theory        81293
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (E or ((A or (B or A)) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-903 ((A (-> (or Am (or 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-50.           (((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-81293.        (((A or (B or A)) -> ((C and D) -> D)) and (E or ((A or (B or A)) -> ((C and D) -> D)))), M:tm-311, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81294
in-theory        81294
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (((A or (B or A)) -> ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-81294.        (((A or (B or A)) -> ((C and D) -> D)) and (((A or (B or A)) -> ((C and D) -> D)) or E)), M:tm-310, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81295
in-theory        81295
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (E -> (((A or (B or A)) -> ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-81295.        (((A or (B or A)) -> ((C and D) -> D)) and (E -> (((A or (B or A)) -> ((C and D) -> D)) and E))), M:tm-309, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81296
in-theory        81296
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (((A or (B or A)) -> (C and D)) -> ((A or (B or A)) -> D)))
theorem-size     29
proof            (modus-ponens tm-306 tm-903 ((A (or Am (or Bm Am))) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-81296.        (((A or (B or A)) -> ((C and D) -> D)) and (((A or (B or A)) -> (C and D)) -> ((A or (B or A)) -> D))), M:tm-306, m:tm-903, u:((A (or Am (or Bm Am))) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-81297
in-theory        81297
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (E -> ((A or (B or A)) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-4.            ((A 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-81297.        (((A or (B or A)) -> ((C and D) -> D)) and (E -> ((A or (B or A)) -> ((C and D) -> D)))), M:tm-305, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81298
in-theory        81298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81298.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-303, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81299
in-theory        81299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81299.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-270, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81300
in-theory        81300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81300.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-239, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81301
in-theory        81301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81301.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G and H) -> H))), M:tm-210, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81302
in-theory        81302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81302.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-183, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81303
in-theory        81303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81303.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-157, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81304
in-theory        81304
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81304.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-147, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81305
in-theory        81305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81305.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-134, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81306
in-theory        81306
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81306.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-125, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81307
in-theory        81307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81307.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G and H) -> H))), M:tm-113, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81308
in-theory        81308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81308.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-105, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81309
in-theory        81309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81309.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E and F) -> F))), M:tm-95, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81310
in-theory        81310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81310.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-83, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81311
in-theory        81311
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81311.        (((not (not A)) -> A) and ((B or (C or B)) -> ((D and E) -> E))), M:tm-76, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81312
in-theory        81312
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-73 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81312.        (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C and D) -> D)), M:tm-73, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81313
in-theory        81313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81313.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E and F) -> F))), M:tm-69, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81314
in-theory        81314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81314.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-54, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81315
in-theory        81315
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-50 tm-903 ((A Am) (B (or 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-4.            ((A 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-81315.        (((A or B) or (B or (A or B))) -> ((C and D) -> D)), M:tm-50, m:tm-903, u:((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81316
in-theory        81316
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-49 tm-903 ((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81316.        ((A or (A or (B or A))) -> ((C and D) -> D)), M:tm-49, m:tm-903, u:((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81317
in-theory        81317
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-47 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81317.        (((A and (B or (C or B))) or (B or (C or B))) -> ((D and E) -> E)), M:tm-47, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81318
in-theory        81318
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-46 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81318.        ((((A or (B or A)) and C) or (A or (B or A))) -> ((D and E) -> E)), M:tm-46, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81319
in-theory        81319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-903 ((A (-> (or Am (or 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-50.           (((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-81319.        ((A -> (B or A)) and ((C or (D or C)) -> ((E and F) -> F))), M:tm-42, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81320
in-theory        81320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81320.        ((A -> (A or B)) and ((C or (D or C)) -> ((E and F) -> F))), M:tm-32, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81321
in-theory        81321
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-24 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81321.        ((A or (B or A)) -> ((A or (B or A)) and ((C and D) -> D))), M:tm-24, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81322
in-theory        81322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81322.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E and F) -> F))), M:tm-23, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81323
in-theory        81323
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81323.        (((A and B) -> B) and ((C or (D or C)) -> ((E and F) -> F))), M:tm-22, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81324
in-theory        81324
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81324.        (((A and B) -> A) and ((C or (D or C)) -> ((E and F) -> F))), M:tm-21, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81325
in-theory        81325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81325.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-20, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81326
in-theory        81326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81326.        ((A -> (B -> A)) and ((C or (D or C)) -> ((E and F) -> F))), M:tm-19, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81327
in-theory        81327
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not ((C and D) -> D))) -> (not (A or (B or A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81327.        (((A or (B or A)) -> (not ((C and D) -> D))) -> (not (A or (B or A)))), M:tm-9, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81328
in-theory        81328
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (((D or (E or D)) or ((A and B) -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-903 ((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
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-4.            ((A 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-81328.        ((((A and B) -> B) -> C) -> (((D or (E or D)) or ((A and B) -> B)) -> C)), M:tm-8, m:tm-903, u:((A (or Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-81329
in-theory        81329
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-903 ((A (-> (or Am (or 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-50.           (((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-81329.        (A or ((B or (C or B)) -> ((D and E) -> E))), M:tm-7, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81330
in-theory        81330
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81330.        (((A or (B or A)) -> ((C and D) -> D)) or E), M:tm-6, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81331
in-theory        81331
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81331.        (A -> (((B or (C or B)) -> ((D and E) -> E)) and A)), M:tm-5, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81332
in-theory        81332
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C and D)) -> ((A or (B or A)) -> D))
theorem-size     17
proof            (modus-ponens tm-2 tm-903 ((A (or Am (or Bm Am))) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81332.        (((A or (B or A)) -> (C and D)) -> ((A or (B or A)) -> D)), M:tm-2, m:tm-903, u:((A (or Am (or Bm Am))) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-81333
in-theory        81333
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81333.        (A -> ((B or (C or B)) -> ((D and E) -> E))), M:tm-1, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-81334
in-theory        81334
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81334.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-893, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81335
in-theory        81335
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((A or (A or (B or A))) -> ((C -> (D -> C)) and (B or A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-904 ((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81335.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((A or (A or (B or A))) -> ((C -> (D -> C)) and (B or A)))), M:tm-882, m:tm-904, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81336
in-theory        81336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-855 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81336.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-855, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81337
in-theory        81337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81337.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-808, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81338
in-theory        81338
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C -> (D -> C)) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81338.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C -> (D -> C)) and (B or A)))), M:tm-798, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81339
in-theory        81339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81339.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-757, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81340
in-theory        81340
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C -> (D -> C)) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81340.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C -> (D -> C)) and (B or A)))), M:tm-747, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81341
in-theory        81341
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81341.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E)))), M:tm-708, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81342
in-theory        81342
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81342.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-665, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81343
in-theory        81343
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((D -> (E -> D)) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81343.        ((A or (B or A)) -> (C or ((D -> (E -> D)) and (B or A)))), M:tm-623, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81344
in-theory        81344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81344.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-622, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81345
in-theory        81345
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81345.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (F or E))), M:tm-609, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81346
in-theory        81346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81346.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-605, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81347
in-theory        81347
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81347.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))))), M:tm-595, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81348
in-theory        81348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81348.        (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-550, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81349
in-theory        81349
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81349.        ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-540, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81350
in-theory        81350
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81350.        ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-530, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81351
in-theory        81351
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81351.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-520, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81352
in-theory        81352
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81352.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-510, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81353
in-theory        81353
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81353.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-500, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81354
in-theory        81354
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81354.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E)))), M:tm-490, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81355
in-theory        81355
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81355.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-480, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81356
in-theory        81356
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D -> C)) and (B or A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81356.        ((A or (B or A)) -> (((C -> (D -> C)) and (B or A)) or E)), M:tm-470, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81357
in-theory        81357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81357.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-469, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81358
in-theory        81358
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81358.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (E or F))), M:tm-456, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81359
in-theory        81359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81359.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-453, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81360
in-theory        81360
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (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-81360.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))))), M:tm-443, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81361
in-theory        81361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81361.        (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-409, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81362
in-theory        81362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81362.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-400, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81363
in-theory        81363
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81363.        ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-391, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81364
in-theory        81364
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81364.        ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-382, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81365
in-theory        81365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81365.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E)))), M:tm-373, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81366
in-theory        81366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81366.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-364, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81367
in-theory        81367
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D -> (E -> D)) and (B or A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81367.        ((A or (B or A)) -> (C -> (((D -> (E -> D)) and (B or A)) and C))), M:tm-355, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81368
in-theory        81368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81368.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-354, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81369
in-theory        81369
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81369.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81370
in-theory        81370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81370.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C)))), M:tm-338, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81371
in-theory        81371
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81371.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> C)) and (B or A))))), M:tm-328, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81372
in-theory        81372
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (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-81372.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))))), M:tm-327, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81373
in-theory        81373
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (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-81373.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))))), M:tm-326, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81374
in-theory        81374
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (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-81374.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))))), M:tm-325, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81375
in-theory        81375
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81375.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))))), M:tm-324, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81376
in-theory        81376
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81376.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))))), M:tm-323, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81377
in-theory        81377
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81377.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E and F) -> F)), M:tm-322, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81378
in-theory        81378
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81378.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E and F) -> E)), M:tm-320, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81379
in-theory        81379
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81379.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81380
in-theory        81380
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81380.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81381
in-theory        81381
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81381.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (F -> E))), M:tm-315, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81382
in-theory        81382
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((A or (B or A)) -> (not ((C -> (D -> C)) and (B or A)))) -> (not (A or (B or A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (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-81382.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((A or (B or A)) -> (not ((C -> (D -> C)) and (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81383
in-theory        81383
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((((C -> (D -> C)) and (B or A)) -> E) -> (((A or (B or A)) or ((C -> (D -> C)) and (B or A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (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-81383.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and ((((C -> (D -> C)) and (B or A)) -> E) -> (((A or (B or A)) or ((C -> (D -> C)) and (B or A))) -> E))), M:tm-312, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81384
in-theory        81384
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E or ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81384.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E or ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))))), M:tm-311, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81385
in-theory        81385
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-1.            (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-81385.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) or E)), M:tm-310, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81386
in-theory        81386
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (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-81386.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and E))), M:tm-309, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81387
in-theory        81387
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81387.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (E -> ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))))), M:tm-305, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81388
in-theory        81388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81388.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-303, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81389
in-theory        81389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81389.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-270, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81390
in-theory        81390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81390.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-239, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81391
in-theory        81391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81391.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E)))), M:tm-210, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81392
in-theory        81392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81392.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-183, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81393
in-theory        81393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81393.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-157, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81394
in-theory        81394
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81394.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-147, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81395
in-theory        81395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81395.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-134, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81396
in-theory        81396
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81396.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-125, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81397
in-theory        81397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81397.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E)))), M:tm-113, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81398
in-theory        81398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81398.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-105, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81399
in-theory        81399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81399.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C)))), M:tm-95, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81400
in-theory        81400
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (E -> D)) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81400.        ((A or (B or A)) -> (C -> ((D -> (E -> D)) and (B or A)))), M:tm-84, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81401
in-theory        81401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81401.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-83, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81402
in-theory        81402
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (E -> D)) and (C or B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81402.        (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (E -> D)) and (C or B)))), M:tm-76, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81403
in-theory        81403
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (D -> C)) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-7 tm-5 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81403.        (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (D -> C)) and (B or A))), M:tm-73, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81404
in-theory        81404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81404.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C)))), M:tm-69, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81405
in-theory        81405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81405.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-54, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81406
in-theory        81406
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> ((C -> (D -> C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-904 ((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (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-81406.        (((A or B) or (B or (A or B))) -> ((C -> (D -> C)) and (A or B))), M:tm-50, m:tm-904, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81407
in-theory        81407
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> ((C -> (D -> C)) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-904 ((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-6 tm-7 tm-5 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81407.        ((A or (A or (B or A))) -> ((C -> (D -> C)) and (B or A))), M:tm-49, m:tm-904, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81408
in-theory        81408
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (E -> D)) and (C or B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-7 tm-5 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81408.        (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (E -> D)) and (C or B))), M:tm-47, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81409
in-theory        81409
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (E -> D)) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-7 tm-5 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81409.        ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (E -> D)) and (B or A))), M:tm-46, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81410
in-theory        81410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-50.           (((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-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-81410.        ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C)))), M:tm-42, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81411
in-theory        81411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81411.        ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C)))), M:tm-32, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81412
in-theory        81412
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> C)) and (B or A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81412.        ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> C)) and (B or A)))), M:tm-24, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81413
in-theory        81413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (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-81413.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C)))), M:tm-23, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81414
in-theory        81414
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81414.        (((A and B) -> B) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C)))), M:tm-22, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81415
in-theory        81415
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81415.        (((A and B) -> A) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C)))), M:tm-21, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81416
in-theory        81416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81416.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-20, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81417
in-theory        81417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81417.        ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (F -> E)) and (D or C)))), M:tm-19, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81418
in-theory        81418
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not ((C -> (D -> C)) and (B or A)))) -> (not (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-9 tm-8 tm-7 tm-5 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81418.        (((A or (B or A)) -> (not ((C -> (D -> C)) and (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81419
in-theory        81419
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and (C or D)) -> E) -> (((D or (C or D)) or ((A -> (B -> A)) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-904 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
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-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-81419.        ((((A -> (B -> A)) and (C or D)) -> E) -> (((D or (C or D)) or ((A -> (B -> A)) and (C or D))) -> E)), M:tm-8, m:tm-904, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-81420
in-theory        81420
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> ((D -> (E -> D)) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-7 tm-8 tm-5 tm-1)
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-50.           (((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-81420.        (A or ((B or (C or B)) -> ((D -> (E -> D)) and (C or B)))), M:tm-7, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81421
in-theory        81421
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-6 tm-8 tm-7 tm-5 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81421.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) or E), M:tm-6, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81422
in-theory        81422
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> ((D -> (E -> D)) and (C or B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81422.        (A -> (((B or (C or B)) -> ((D -> (E -> D)) and (C or B))) and A)), M:tm-5, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81423
in-theory        81423
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> ((D -> (E -> D)) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81423.        (A -> ((B or (C or B)) -> ((D -> (E -> D)) and (C or B)))), M:tm-1, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-81424
in-theory        81424
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-893 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81424.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-893, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81425
in-theory        81425
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((A or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))
theorem-size     49
proof            (modus-ponens tm-882 tm-905 ((A Am) (B (or Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81425.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((A or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))), M:tm-882, m:tm-905, u:((A Am) (B (or Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81426
in-theory        81426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     41
proof            (modus-ponens tm-855 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81426.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-855, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81427
in-theory        81427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-808 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81427.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-808, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81428
in-theory        81428
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((F and (A or (B or A))) or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))
theorem-size     55
proof            (modus-ponens tm-798 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81428.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((F and (A or (B or A))) or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))), M:tm-798, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81429
in-theory        81429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-757 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81429.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-757, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81430
in-theory        81430
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((((A or (B or A)) and F) or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))
theorem-size     55
proof            (modus-ponens tm-747 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-20.           (A -> (((B -> (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-81430.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((((A or (B or A)) and F) or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))), M:tm-747, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81431
in-theory        81431
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E))))
theorem-size     49
proof            (modus-ponens tm-708 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81431.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E)))), M:tm-708, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81432
in-theory        81432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-665 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81432.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-665, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81433
in-theory        81433
times-derived    1
----------------------------------------------------------------
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-623 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or 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-50.           (((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-20.           (A -> (((B -> (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-81433.        ((A or (B or A)) -> (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or A)))), M:tm-623, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81434
in-theory        81434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-622 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or 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-50.           (((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-20.           (A -> (((B -> (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-81434.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-622, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81435
in-theory        81435
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81435.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (G or F))), M:tm-609, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81436
in-theory        81436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-605 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81436.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-605, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81437
in-theory        81437
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (G or F)) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-20.           (A -> (((B -> (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-81437.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (G or F)) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-595, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81438
in-theory        81438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-550 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81438.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-550, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81439
in-theory        81439
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-540 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81439.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-540, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81440
in-theory        81440
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-530 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81440.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-530, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81441
in-theory        81441
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-520 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81441.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-520, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81442
in-theory        81442
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-510 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81442.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-510, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81443
in-theory        81443
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-500 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81443.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-500, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81444
in-theory        81444
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-490 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 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-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-20.           (A -> (((B -> (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-81444.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E)))), M:tm-490, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81445
in-theory        81445
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-480 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or 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-50.           (((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-20.           (A -> (((B -> (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-81445.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-480, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81446
in-theory        81446
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)) or F))
theorem-size     25
proof            (modus-ponens tm-470 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81446.        ((A or (B or A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)) or F)), M:tm-470, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81447
in-theory        81447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-469 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81447.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-469, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81448
in-theory        81448
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-20.           (A -> (((B -> (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-81448.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (F or G))), M:tm-456, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81449
in-theory        81449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-453 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81449.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-453, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81450
in-theory        81450
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (F or G)) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-20.           (A -> (((B -> (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-81450.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (F or G)) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-443, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81451
in-theory        81451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-409 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81451.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-409, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81452
in-theory        81452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-400 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81452.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-400, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81453
in-theory        81453
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-391 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81453.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-391, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81454
in-theory        81454
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-382 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81454.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-382, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81455
in-theory        81455
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-373 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81455.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E)))), M:tm-373, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81456
in-theory        81456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-364 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81456.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-364, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81457
in-theory        81457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or A)) and C)))
theorem-size     27
proof            (modus-ponens tm-355 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-20.           (A -> (((B -> (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-81457.        ((A or (B or A)) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or A)) and C))), M:tm-355, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81458
in-theory        81458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-354 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81458.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-354, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81459
in-theory        81459
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-20.           (A -> (((B -> (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-81459.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81460
in-theory        81460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C))))
theorem-size     33
proof            (modus-ponens tm-338 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81460.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C)))), M:tm-338, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81461
in-theory        81461
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-20.           (A -> (((B -> (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-81461.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-328, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81462
in-theory        81462
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (G -> (F and G))) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81462.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (G -> (F and G))) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-327, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81463
in-theory        81463
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((F and G) -> G) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-20.           (A -> (((B -> (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-81463.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((F and G) -> G) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-326, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81464
in-theory        81464
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((F and G) -> F) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-20.           (A -> (((B -> (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-81464.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((F and G) -> F) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-325, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81465
in-theory        81465
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81465.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-324, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81466
in-theory        81466
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (G -> F)) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-20.           (A -> (((B -> (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-81466.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (G -> F)) and ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-323, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81467
in-theory        81467
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-20.           (A -> (((B -> (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-81467.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F and G) -> G)), M:tm-322, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81468
in-theory        81468
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-20.           (A -> (((B -> (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-81468.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F and G) -> F)), M:tm-320, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81469
in-theory        81469
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-20.           (A -> (((B -> (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-81469.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81470
in-theory        81470
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     35
proof            (modus-ponens tm-316 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-20.           (A -> (((B -> (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-81470.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81471
in-theory        81471
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-20.           (A -> (((B -> (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-81471.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (G -> F))), M:tm-315, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81472
in-theory        81472
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((A or (B or A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))) -> (not (A or (B or A)))))
theorem-size     55
proof            (modus-ponens tm-313 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-20.           (A -> (((B -> (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-81472.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((A or (B or A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81473
in-theory        81473
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)) -> F) -> (((A or (B or A)) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) -> F)))
theorem-size     69
proof            (modus-ponens tm-312 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81473.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)) -> F) -> (((A or (B or A)) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) -> F))), M:tm-312, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81474
in-theory        81474
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F or ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
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-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-20.           (A -> (((B -> (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-81474.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F or ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-311, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81475
in-theory        81475
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-20.           (A -> (((B -> (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-81475.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) or F)), M:tm-310, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81476
in-theory        81476
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-20.           (A -> (((B -> (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-81476.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and F))), M:tm-309, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81477
in-theory        81477
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-20.           (A -> (((B -> (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-81477.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (F -> ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))), M:tm-305, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81478
in-theory        81478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-303 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81478.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-303, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81479
in-theory        81479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-270 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81479.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-270, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81480
in-theory        81480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-239 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81480.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-239, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81481
in-theory        81481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E))))
theorem-size     41
proof            (modus-ponens tm-210 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81481.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E)))), M:tm-210, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81482
in-theory        81482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-183 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81482.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-183, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81483
in-theory        81483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-157 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81483.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-157, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81484
in-theory        81484
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     39
proof            (modus-ponens tm-147 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-20.           (A -> (((B -> (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-81484.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-147, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81485
in-theory        81485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-134 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81485.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-134, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81486
in-theory        81486
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     39
proof            (modus-ponens tm-125 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-20.           (A -> (((B -> (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-81486.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-125, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81487
in-theory        81487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-113 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81487.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E)))), M:tm-113, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81488
in-theory        81488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     43
proof            (modus-ponens tm-105 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-20.           (A -> (((B -> (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-81488.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-105, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81489
in-theory        81489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C))))
theorem-size     31
proof            (modus-ponens tm-95 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-20.           (A -> (((B -> (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-81489.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C)))), M:tm-95, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81490
in-theory        81490
times-derived    1
----------------------------------------------------------------
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-84 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81490.        ((A or (B or A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or A)))), M:tm-84, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81491
in-theory        81491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-83 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81491.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-83, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81492
in-theory        81492
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B))))
theorem-size     29
proof            (modus-ponens tm-76 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81492.        (((not (not A)) -> A) and ((B or (C or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B)))), M:tm-76, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81493
in-theory        81493
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))
theorem-size     31
proof            (modus-ponens tm-73 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81493.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))), M:tm-73, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81494
in-theory        81494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C))))
theorem-size     35
proof            (modus-ponens tm-69 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81494.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C)))), M:tm-69, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81495
in-theory        81495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-54 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81495.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-54, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81496
in-theory        81496
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))
theorem-size     27
proof            (modus-ponens tm-50 tm-905 ((A Am) (B (or Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-7 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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81496.        (((A or B) or (B or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))), M:tm-50, m:tm-905, u:((A Am) (B (or Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81497
in-theory        81497
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-49 tm-905 ((A Am) (B (or Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81497.        ((A or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))), M:tm-49, m:tm-905, u:((A Am) (B (or Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81498
in-theory        81498
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B)))
theorem-size     31
proof            (modus-ponens tm-47 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81498.        (((A and (B or (C or B))) or (B or (C or B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B))), M:tm-47, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81499
in-theory        81499
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or A)))
theorem-size     31
proof            (modus-ponens tm-46 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81499.        ((((A or (B or A)) and C) or (A or (B or A))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B or A))), M:tm-46, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81500
in-theory        81500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-42 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-20.           (A -> (((B -> (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-81500.        ((A -> (B or A)) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C)))), M:tm-42, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81501
in-theory        81501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-32 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-32.           (A -> ((B -> (B or C)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81501.        ((A -> (A or B)) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C)))), M:tm-32, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81502
in-theory        81502
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))
theorem-size     29
proof            (modus-ponens tm-24 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81502.        ((A or (B or A)) -> ((A or (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))), M:tm-24, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81503
in-theory        81503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C))))
theorem-size     31
proof            (modus-ponens tm-23 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81503.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C)))), M:tm-23, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81504
in-theory        81504
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-22 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81504.        (((A and B) -> B) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C)))), M:tm-22, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81505
in-theory        81505
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-21 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81505.        (((A and B) -> A) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C)))), M:tm-21, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81506
in-theory        81506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-20 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81506.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-20, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81507
in-theory        81507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-19 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-81507.        ((A -> (B -> A)) and ((C or (D or C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D or C)))), M:tm-19, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81508
in-theory        81508
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))) -> (not (A or (B or A))))
theorem-size     31
proof            (modus-ponens tm-9 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81508.        (((A or (B or A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81509
in-theory        81509
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or E)) -> F) -> (((E or (D or E)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or E))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-905 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       149
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-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-81509.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or E)) -> F) -> (((E or (D or E)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or E))) -> F)), M:tm-8, m:tm-905, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-81510
in-theory        81510
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B))))
theorem-size     25
proof            (modus-ponens tm-7 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-7 tm-8 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-50.           (((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-81510.        (A or ((B or (C or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B)))), M:tm-7, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81511
in-theory        81511
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81511.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) or F), M:tm-6, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81512
in-theory        81512
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-81512.        (A -> (((B or (C or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B))) and A)), M:tm-5, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81513
in-theory        81513
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B))))
theorem-size     25
proof            (modus-ponens tm-1 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81513.        (A -> ((B or (C or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C or B)))), M:tm-1, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-81514
in-theory        81514
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81514.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-893, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81515
in-theory        81515
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((A or (A or (B or A))) -> (((C and D) -> C) and (B or A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-906 ((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81515.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((A or (A or (B or A))) -> (((C and D) -> C) and (B or A)))), M:tm-882, m:tm-906, u:((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81516
in-theory        81516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-855 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81516.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-855, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81517
in-theory        81517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81517.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-808, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81518
in-theory        81518
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> (((C and D) -> C) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81518.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> (((C and D) -> C) and (B or A)))), M:tm-798, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81519
in-theory        81519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-81519.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-757, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81520
in-theory        81520
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (((C and D) -> C) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81520.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (((C and D) -> C) and (B or A)))), M:tm-747, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81521
in-theory        81521
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (((G and H) -> G) and (F or E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81521.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (((G and H) -> G) and (F or E)))), M:tm-708, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81522
in-theory        81522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81522.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-665, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81523
in-theory        81523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (((D and E) -> D) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or 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-50.           (((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-81523.        ((A or (B or A)) -> (C or (((D and E) -> D) and (B or A)))), M:tm-623, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81524
in-theory        81524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or 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-50.           (((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-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-81524.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-622, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81525
in-theory        81525
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or 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-50.           (((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-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-81525.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (F or E))), M:tm-609, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81526
in-theory        81526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-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-81526.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-605, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81527
in-theory        81527
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> (((C and D) -> C) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-3.            ((A and B) -> 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-81527.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> (((C and D) -> C) and (B or A))))), M:tm-595, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81528
in-theory        81528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-3.            ((A and B) -> 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-81528.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-550, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81529
in-theory        81529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-3.            ((A and B) -> 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-81529.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-540, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81530
in-theory        81530
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-3.            ((A and B) -> 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-81530.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-530, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81531
in-theory        81531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-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-81531.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-520, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81532
in-theory        81532
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-3.            ((A and B) -> 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-81532.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-510, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81533
in-theory        81533
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81533.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-500, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81534
in-theory        81534
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G and H) -> G) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-50.           (((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-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-81534.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G and H) -> G) and (F or E)))), M:tm-490, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81535
in-theory        81535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or 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-50.           (((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-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-81535.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-480, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81536
in-theory        81536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C and D) -> C) and (B or A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81536.        ((A or (B or A)) -> ((((C and D) -> C) and (B or A)) or E)), M:tm-470, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81537
in-theory        81537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81537.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-469, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81538
in-theory        81538
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81538.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (E or F))), M:tm-456, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81539
in-theory        81539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81539.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-453, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81540
in-theory        81540
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> (((C and D) -> C) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-3.            ((A and B) -> 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-81540.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> (((C and D) -> C) and (B or A))))), M:tm-443, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81541
in-theory        81541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81541.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-409, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81542
in-theory        81542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81542.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-400, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81543
in-theory        81543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81543.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-391, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81544
in-theory        81544
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-81544.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-382, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81545
in-theory        81545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (((G and H) -> G) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81545.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (((G and H) -> G) and (F or E)))), M:tm-373, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81546
in-theory        81546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81546.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-364, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81547
in-theory        81547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((((D and E) -> D) and (B or A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81547.        ((A or (B or A)) -> (C -> ((((D and E) -> D) and (B or A)) and C))), M:tm-355, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81548
in-theory        81548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81548.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-354, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81549
in-theory        81549
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A and B) -> 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-81549.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81550
in-theory        81550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (((E and F) -> E) and (D or C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81550.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (((E and F) -> E) and (D or C)))), M:tm-338, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81551
in-theory        81551
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (((C and D) -> C) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81551.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (((C and D) -> C) and (B or A))))), M:tm-328, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81552
in-theory        81552
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (((C and D) -> C) and (B or A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81552.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (((C and D) -> C) and (B or A))))), M:tm-327, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81553
in-theory        81553
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> (((C and D) -> C) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-3.            ((A and B) -> 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-81553.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> (((C and D) -> C) and (B or A))))), M:tm-326, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81554
in-theory        81554
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> (((C and D) -> C) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-81554.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> (((C and D) -> C) and (B or A))))), M:tm-325, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81555
in-theory        81555
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (((C and D) -> C) and (B or A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81555.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (((C and D) -> C) and (B or A))))), M:tm-324, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81556
in-theory        81556
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> (((C and D) -> C) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A and B) -> 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-81556.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> (((C and D) -> C) and (B or A))))), M:tm-323, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81557
in-theory        81557
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81557.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E and F) -> F)), M:tm-322, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81558
in-theory        81558
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81558.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E and F) -> E)), M:tm-320, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81559
in-theory        81559
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81559.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81560
in-theory        81560
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81560.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81561
in-theory        81561
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81561.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (F -> E))), M:tm-315, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81562
in-theory        81562
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((A or (B or A)) -> (not (((C and D) -> C) and (B or A)))) -> (not (A or (B or A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-3.            ((A and B) -> 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-81562.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((A or (B or A)) -> (not (((C and D) -> C) and (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81563
in-theory        81563
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((((C and D) -> C) and (B or A)) -> E) -> (((A or (B or A)) or (((C and D) -> C) and (B or A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-3.            ((A and B) -> 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-81563.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((((C and D) -> C) and (B or A)) -> E) -> (((A or (B or A)) or (((C and D) -> C) and (B or A))) -> E))), M:tm-312, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81564
in-theory        81564
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E or ((A or (B or A)) -> (((C and D) -> C) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
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-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-3.            ((A and B) -> 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-81564.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E or ((A or (B or A)) -> (((C and D) -> C) and (B or A))))), M:tm-311, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81565
in-theory        81565
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((A or (B or A)) -> (((C and D) -> C) and (B or A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-3.            ((A and B) -> 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-81565.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((A or (B or A)) -> (((C and D) -> C) and (B or A))) or E)), M:tm-310, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81566
in-theory        81566
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-3.            ((A and B) -> 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-81566.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and E))), M:tm-309, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81567
in-theory        81567
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> ((A or (B or A)) -> (((C and D) -> C) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-3.            ((A and B) -> 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-81567.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (E -> ((A or (B or A)) -> (((C and D) -> C) and (B or A))))), M:tm-305, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81568
in-theory        81568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81568.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-303, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81569
in-theory        81569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81569.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-270, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81570
in-theory        81570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81570.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-239, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81571
in-theory        81571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (((G and H) -> G) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81571.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (((G and H) -> G) and (F or E)))), M:tm-210, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81572
in-theory        81572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81572.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-183, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81573
in-theory        81573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81573.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-157, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81574
in-theory        81574
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81574.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-147, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81575
in-theory        81575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81575.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-134, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81576
in-theory        81576
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-81576.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-125, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81577
in-theory        81577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G and H) -> G) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81577.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G and H) -> G) and (F or E)))), M:tm-113, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81578
in-theory        81578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81578.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-105, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81579
in-theory        81579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (((E and F) -> E) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81579.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (((E and F) -> E) and (D or C)))), M:tm-95, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81580
in-theory        81580
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D and E) -> D) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81580.        ((A or (B or A)) -> (C -> (((D and E) -> D) and (B or A)))), M:tm-84, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81581
in-theory        81581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81581.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-83, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81582
in-theory        81582
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (((D and E) -> D) and (C or B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81582.        (((not (not A)) -> A) and ((B or (C or B)) -> (((D and E) -> D) and (C or B)))), M:tm-76, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81583
in-theory        81583
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (((C and D) -> C) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81583.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (((C and D) -> C) and (B or A))), M:tm-73, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81584
in-theory        81584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (((E and F) -> E) and (D or C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81584.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (((E and F) -> E) and (D or C)))), M:tm-69, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81585
in-theory        81585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81585.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-54, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81586
in-theory        81586
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (((C and D) -> C) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-906 ((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-8 tm-7 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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-81586.        (((A or B) or (B or (A or B))) -> (((C and D) -> C) and (A or B))), M:tm-50, m:tm-906, u:((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81587
in-theory        81587
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (((C and D) -> C) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-906 ((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81587.        ((A or (A or (B or A))) -> (((C and D) -> C) and (B or A))), M:tm-49, m:tm-906, u:((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81588
in-theory        81588
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (((D and E) -> D) and (C or B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81588.        (((A and (B or (C or B))) or (B or (C or B))) -> (((D and E) -> D) and (C or B))), M:tm-47, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81589
in-theory        81589
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (((D and E) -> D) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81589.        ((((A or (B or A)) and C) or (A or (B or A))) -> (((D and E) -> D) and (B or A))), M:tm-46, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81590
in-theory        81590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (((E and F) -> E) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm 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-42.           (A -> ((B -> (C or B)) and A)), 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-3.            ((A and B) -> 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-81590.        ((A -> (B or A)) and ((C or (D or C)) -> (((E and F) -> E) and (D or C)))), M:tm-42, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81591
in-theory        81591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (((E and F) -> E) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81591.        ((A -> (A or B)) and ((C or (D or C)) -> (((E and F) -> E) and (D or C)))), M:tm-32, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81592
in-theory        81592
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (((C and D) -> C) and (B or A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81592.        ((A or (B or A)) -> ((A or (B or A)) and (((C and D) -> C) and (B or A)))), M:tm-24, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81593
in-theory        81593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (((E and F) -> E) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-3.            ((A and B) -> 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-81593.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (((E and F) -> E) and (D or C)))), M:tm-23, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81594
in-theory        81594
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (((E and F) -> E) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81594.        (((A and B) -> B) and ((C or (D or C)) -> (((E and F) -> E) and (D or C)))), M:tm-22, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81595
in-theory        81595
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (((E and F) -> E) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-81595.        (((A and B) -> A) and ((C or (D or C)) -> (((E and F) -> E) and (D or C)))), M:tm-21, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81596
in-theory        81596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81596.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-20, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81597
in-theory        81597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (((E and F) -> E) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81597.        ((A -> (B -> A)) and ((C or (D or C)) -> (((E and F) -> E) and (D or C)))), M:tm-19, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81598
in-theory        81598
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (((C and D) -> C) and (B or A)))) -> (not (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81598.        (((A or (B or A)) -> (not (((C and D) -> C) and (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81599
in-theory        81599
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and (C or D)) -> E) -> (((D or (C or D)) or (((A and B) -> A) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-906 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
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-3.            ((A and B) -> 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-81599.        (((((A and B) -> A) and (C or D)) -> E) -> (((D or (C or D)) or (((A and B) -> A) and (C or D))) -> E)), M:tm-8, m:tm-906, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-81600
in-theory        81600
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (((D and E) -> D) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-7 tm-8 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-50.           (((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-81600.        (A or ((B or (C or B)) -> (((D and E) -> D) and (C or B)))), M:tm-7, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81601
in-theory        81601
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81601.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) or E), M:tm-6, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81602
in-theory        81602
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (((D and E) -> D) and (C or B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81602.        (A -> (((B or (C or B)) -> (((D and E) -> D) and (C or B))) and A)), M:tm-5, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81603
in-theory        81603
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (((D and E) -> D) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81603.        (A -> ((B or (C or B)) -> (((D and E) -> D) and (C or B)))), M:tm-1, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-81604
in-theory        81604
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81604.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-893, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81605
in-theory        81605
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((A or (A or (B or A))) -> (((C and D) -> D) and (B or A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-907 ((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81605.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((A or (A or (B or A))) -> (((C and D) -> D) and (B or A)))), M:tm-882, m:tm-907, u:((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81606
in-theory        81606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-855 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81606.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-855, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81607
in-theory        81607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81607.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-808, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81608
in-theory        81608
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> (((C and D) -> D) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81608.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> (((C and D) -> D) and (B or A)))), M:tm-798, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81609
in-theory        81609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81609.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-757, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81610
in-theory        81610
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (((C and D) -> D) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81610.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (((C and D) -> D) and (B or A)))), M:tm-747, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81611
in-theory        81611
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (((G and H) -> H) and (F or E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81611.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (((G and H) -> H) and (F or E)))), M:tm-708, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81612
in-theory        81612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81612.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-665, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81613
in-theory        81613
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (((D and E) -> E) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or 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-50.           (((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-81613.        ((A or (B or A)) -> (C or (((D and E) -> E) and (B or A)))), M:tm-623, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81614
in-theory        81614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or 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-50.           (((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-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-81614.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-622, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81615
in-theory        81615
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or 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-50.           (((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-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-81615.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (F or E))), M:tm-609, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81616
in-theory        81616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-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-81616.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-605, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81617
in-theory        81617
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> (((C and D) -> D) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> 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-81617.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> (((C and D) -> D) and (B or A))))), M:tm-595, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81618
in-theory        81618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-4.            ((A and B) -> 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-81618.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-550, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81619
in-theory        81619
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> 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-81619.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-540, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81620
in-theory        81620
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-4.            ((A and B) -> 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-81620.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-530, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81621
in-theory        81621
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-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-81621.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-520, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81622
in-theory        81622
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81622.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-510, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81623
in-theory        81623
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-4.            ((A and B) -> 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-81623.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-500, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81624
in-theory        81624
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G and H) -> H) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-50.           (((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-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-81624.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G and H) -> H) and (F or E)))), M:tm-490, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81625
in-theory        81625
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or 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-50.           (((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-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-81625.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-480, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81626
in-theory        81626
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C and D) -> D) and (B or A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81626.        ((A or (B or A)) -> ((((C and D) -> D) and (B or A)) or E)), M:tm-470, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81627
in-theory        81627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81627.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-469, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81628
in-theory        81628
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81628.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (E or F))), M:tm-456, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81629
in-theory        81629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81629.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-453, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81630
in-theory        81630
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> (((C and D) -> D) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> 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-81630.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> (((C and D) -> D) and (B or A))))), M:tm-443, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81631
in-theory        81631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81631.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-409, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81632
in-theory        81632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81632.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-400, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81633
in-theory        81633
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-81633.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-391, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81634
in-theory        81634
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81634.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-382, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81635
in-theory        81635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (((G and H) -> H) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81635.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (((G and H) -> H) and (F or E)))), M:tm-373, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81636
in-theory        81636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81636.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-364, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81637
in-theory        81637
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((((D and E) -> E) and (B or A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81637.        ((A or (B or A)) -> (C -> ((((D and E) -> E) and (B or A)) and C))), M:tm-355, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81638
in-theory        81638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81638.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-354, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81639
in-theory        81639
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> 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-81639.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81640
in-theory        81640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (((E and F) -> F) and (D or C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81640.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (((E and F) -> F) and (D or C)))), M:tm-338, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81641
in-theory        81641
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (((C and D) -> D) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81641.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (((C and D) -> D) and (B or A))))), M:tm-328, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81642
in-theory        81642
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (((C and D) -> D) and (B or A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81642.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (((C and D) -> D) and (B or A))))), M:tm-327, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81643
in-theory        81643
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> (((C and D) -> D) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-81643.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> (((C and D) -> D) and (B or A))))), M:tm-326, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81644
in-theory        81644
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> (((C and D) -> D) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> 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-81644.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> (((C and D) -> D) and (B or A))))), M:tm-325, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81645
in-theory        81645
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (((C and D) -> D) and (B or A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81645.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (((C and D) -> D) and (B or A))))), M:tm-324, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81646
in-theory        81646
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> (((C and D) -> D) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> 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-81646.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> (((C and D) -> D) and (B or A))))), M:tm-323, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81647
in-theory        81647
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81647.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E and F) -> F)), M:tm-322, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81648
in-theory        81648
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81648.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E and F) -> E)), M:tm-320, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81649
in-theory        81649
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81649.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81650
in-theory        81650
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81650.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81651
in-theory        81651
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81651.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (F -> E))), M:tm-315, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81652
in-theory        81652
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((A or (B or A)) -> (not (((C and D) -> D) and (B or A)))) -> (not (A or (B or A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-4.            ((A and B) -> 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-81652.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((A or (B or A)) -> (not (((C and D) -> D) and (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81653
in-theory        81653
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((((C and D) -> D) and (B or A)) -> E) -> (((A or (B or A)) or (((C and D) -> D) and (B or A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-4.            ((A and B) -> 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-81653.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((((C and D) -> D) and (B or A)) -> E) -> (((A or (B or A)) or (((C and D) -> D) and (B or A))) -> E))), M:tm-312, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81654
in-theory        81654
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E or ((A or (B or A)) -> (((C and D) -> D) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-4.            ((A and B) -> 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-81654.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E or ((A or (B or A)) -> (((C and D) -> D) and (B or A))))), M:tm-311, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81655
in-theory        81655
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((A or (B or A)) -> (((C and D) -> D) and (B or A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-4.            ((A and B) -> 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-81655.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((A or (B or A)) -> (((C and D) -> D) and (B or A))) or E)), M:tm-310, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81656
in-theory        81656
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-4.            ((A and B) -> 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-81656.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and E))), M:tm-309, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81657
in-theory        81657
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> ((A or (B or A)) -> (((C and D) -> D) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-4.            ((A and B) -> 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-81657.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (E -> ((A or (B or A)) -> (((C and D) -> D) and (B or A))))), M:tm-305, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81658
in-theory        81658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81658.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-303, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81659
in-theory        81659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81659.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-270, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81660
in-theory        81660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81660.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-239, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81661
in-theory        81661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (((G and H) -> H) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81661.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (((G and H) -> H) and (F or E)))), M:tm-210, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81662
in-theory        81662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81662.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-183, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81663
in-theory        81663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81663.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-157, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81664
in-theory        81664
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-81664.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-147, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81665
in-theory        81665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81665.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-134, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81666
in-theory        81666
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81666.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-125, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81667
in-theory        81667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G and H) -> H) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81667.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G and H) -> H) and (F or E)))), M:tm-113, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81668
in-theory        81668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81668.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-105, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81669
in-theory        81669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (((E and F) -> F) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81669.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (((E and F) -> F) and (D or C)))), M:tm-95, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81670
in-theory        81670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D and E) -> E) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81670.        ((A or (B or A)) -> (C -> (((D and E) -> E) and (B or A)))), M:tm-84, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81671
in-theory        81671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81671.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-83, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81672
in-theory        81672
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (((D and E) -> E) and (C or B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81672.        (((not (not A)) -> A) and ((B or (C or B)) -> (((D and E) -> E) and (C or B)))), M:tm-76, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81673
in-theory        81673
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (((C and D) -> D) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81673.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (((C and D) -> D) and (B or A))), M:tm-73, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81674
in-theory        81674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (((E and F) -> F) and (D or C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81674.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (((E and F) -> F) and (D or C)))), M:tm-69, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81675
in-theory        81675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81675.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-54, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81676
in-theory        81676
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (((C and D) -> D) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-907 ((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-8 tm-7 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-81676.        (((A or B) or (B or (A or B))) -> (((C and D) -> D) and (A or B))), M:tm-50, m:tm-907, u:((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81677
in-theory        81677
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (((C and D) -> D) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-907 ((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81677.        ((A or (A or (B or A))) -> (((C and D) -> D) and (B or A))), M:tm-49, m:tm-907, u:((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81678
in-theory        81678
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (((D and E) -> E) and (C or B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81678.        (((A and (B or (C or B))) or (B or (C or B))) -> (((D and E) -> E) and (C or B))), M:tm-47, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81679
in-theory        81679
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (((D and E) -> E) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81679.        ((((A or (B or A)) and C) or (A or (B or A))) -> (((D and E) -> E) and (B or A))), M:tm-46, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81680
in-theory        81680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (((E and F) -> F) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
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-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-4.            ((A and B) -> 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-81680.        ((A -> (B or A)) and ((C or (D or C)) -> (((E and F) -> F) and (D or C)))), M:tm-42, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81681
in-theory        81681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (((E and F) -> F) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81681.        ((A -> (A or B)) and ((C or (D or C)) -> (((E and F) -> F) and (D or C)))), M:tm-32, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81682
in-theory        81682
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (((C and D) -> D) and (B or A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81682.        ((A or (B or A)) -> ((A or (B or A)) and (((C and D) -> D) and (B or A)))), M:tm-24, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81683
in-theory        81683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (((E and F) -> F) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-4.            ((A and B) -> 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-81683.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (((E and F) -> F) and (D or C)))), M:tm-23, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81684
in-theory        81684
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (((E and F) -> F) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81684.        (((A and B) -> B) and ((C or (D or C)) -> (((E and F) -> F) and (D or C)))), M:tm-22, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81685
in-theory        81685
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (((E and F) -> F) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81685.        (((A and B) -> A) and ((C or (D or C)) -> (((E and F) -> F) and (D or C)))), M:tm-21, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81686
in-theory        81686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81686.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-20, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81687
in-theory        81687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (((E and F) -> F) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81687.        ((A -> (B -> A)) and ((C or (D or C)) -> (((E and F) -> F) and (D or C)))), M:tm-19, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81688
in-theory        81688
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (((C and D) -> D) and (B or A)))) -> (not (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81688.        (((A or (B or A)) -> (not (((C and D) -> D) and (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81689
in-theory        81689
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and (C or D)) -> E) -> (((D or (C or D)) or (((A and B) -> B) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-907 ((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
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-4.            ((A and B) -> 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-81689.        (((((A and B) -> B) and (C or D)) -> E) -> (((D or (C or D)) or (((A and B) -> B) and (C or D))) -> E)), M:tm-8, m:tm-907, u:((A (or Am (or Bm Am))) (B (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-81690
in-theory        81690
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (((D and E) -> E) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-7 tm-8 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-50.           (((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-81690.        (A or ((B or (C or B)) -> (((D and E) -> E) and (C or B)))), M:tm-7, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81691
in-theory        81691
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81691.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) or E), M:tm-6, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81692
in-theory        81692
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (((D and E) -> E) and (C or B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81692.        (A -> (((B or (C or B)) -> (((D and E) -> E) and (C or B))) and A)), M:tm-5, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81693
in-theory        81693
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (((D and E) -> E) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81693.        (A -> ((B or (C or B)) -> (((D and E) -> E) and (C or B)))), M:tm-1, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-81694
in-theory        81694
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-893 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81694.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-893, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81695
in-theory        81695
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((A or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A))))
theorem-size     37
proof            (modus-ponens tm-882 tm-908 ((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81695.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((A or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A)))), M:tm-882, m:tm-908, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81696
in-theory        81696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-855 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81696.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-855, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81697
in-theory        81697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-808 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81697.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-808, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81698
in-theory        81698
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A))))
theorem-size     43
proof            (modus-ponens tm-798 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81698.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A)))), M:tm-798, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81699
in-theory        81699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-757 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-81699.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-757, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81700
in-theory        81700
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A))))
theorem-size     43
proof            (modus-ponens tm-747 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-81700.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A)))), M:tm-747, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81701
in-theory        81701
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E))))
theorem-size     43
proof            (modus-ponens tm-708 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81701.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E)))), M:tm-708, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81702
in-theory        81702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-665 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81702.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-665, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81703
in-theory        81703
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((D -> (E -> (D and E))) and (B or A))))
theorem-size     19
proof            (modus-ponens tm-623 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or 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-50.           (((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-81703.        ((A or (B or A)) -> (C or ((D -> (E -> (D and E))) and (B or A)))), M:tm-623, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81704
in-theory        81704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-622 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81704.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-622, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81705
in-theory        81705
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81705.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (F or E))), M:tm-609, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81706
in-theory        81706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-605 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-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-81706.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-605, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81707
in-theory        81707
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-81707.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))))), M:tm-595, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81708
in-theory        81708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-550 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-81708.        (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-550, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81709
in-theory        81709
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-540 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-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-81709.        ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-540, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81710
in-theory        81710
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-530 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-81710.        ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-530, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81711
in-theory        81711
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-520 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-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-81711.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-520, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81712
in-theory        81712
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-510 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-81712.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-510, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81713
in-theory        81713
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-500 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-81713.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-500, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81714
in-theory        81714
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-490 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-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-81714.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E)))), M:tm-490, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81715
in-theory        81715
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-480 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81715.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-480, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81716
in-theory        81716
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D -> (C and D))) and (B or A)) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81716.        ((A or (B or A)) -> (((C -> (D -> (C and D))) and (B or A)) or E)), M:tm-470, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81717
in-theory        81717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-469 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-81717.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-469, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81718
in-theory        81718
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-81718.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (E or F))), M:tm-456, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81719
in-theory        81719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-453 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81719.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-453, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81720
in-theory        81720
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-81720.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))))), M:tm-443, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81721
in-theory        81721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-409 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81721.        (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-409, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81722
in-theory        81722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-400 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81722.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-400, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81723
in-theory        81723
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-391 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81723.        ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-391, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81724
in-theory        81724
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-382 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81724.        ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-382, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81725
in-theory        81725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-373 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81725.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E)))), M:tm-373, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81726
in-theory        81726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-364 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81726.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-364, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81727
in-theory        81727
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D -> (E -> (D and E))) and (B or A)) and C)))
theorem-size     21
proof            (modus-ponens tm-355 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81727.        ((A or (B or A)) -> (C -> (((D -> (E -> (D and E))) and (B or A)) and C))), M:tm-355, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81728
in-theory        81728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-354 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81728.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-354, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81729
in-theory        81729
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-81729.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81730
in-theory        81730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C))))
theorem-size     27
proof            (modus-ponens tm-338 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81730.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C)))), M:tm-338, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81731
in-theory        81731
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     41
proof            (modus-ponens tm-328 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-81731.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> (C and D))) and (B or A))))), M:tm-328, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81732
in-theory        81732
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-81732.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))))), M:tm-327, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81733
in-theory        81733
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-81733.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))))), M:tm-326, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81734
in-theory        81734
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-81734.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))))), M:tm-325, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81735
in-theory        81735
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-81735.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))))), M:tm-324, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81736
in-theory        81736
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-81736.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))))), M:tm-323, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81737
in-theory        81737
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-81737.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E and F) -> F)), M:tm-322, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81738
in-theory        81738
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-81738.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E and F) -> E)), M:tm-320, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81739
in-theory        81739
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-81739.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81740
in-theory        81740
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     29
proof            (modus-ponens tm-316 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-81740.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81741
in-theory        81741
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-81741.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (F -> E))), M:tm-315, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81742
in-theory        81742
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((A or (B or A)) -> (not ((C -> (D -> (C and D))) and (B or A)))) -> (not (A or (B or A)))))
theorem-size     43
proof            (modus-ponens tm-313 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-81742.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((A or (B or A)) -> (not ((C -> (D -> (C and D))) and (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81743
in-theory        81743
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((((C -> (D -> (C and D))) and (B or A)) -> E) -> (((A or (B or A)) or ((C -> (D -> (C and D))) and (B or A))) -> E)))
theorem-size     51
proof            (modus-ponens tm-312 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-312.          ((A -> B) -> ((A -> B) and ((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-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-81743.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and ((((C -> (D -> (C and D))) and (B or A)) -> E) -> (((A or (B or A)) or ((C -> (D -> (C and D))) and (B or A))) -> E))), M:tm-312, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81744
in-theory        81744
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E or ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-81744.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E or ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))))), M:tm-311, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81745
in-theory        81745
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-81745.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) or E)), M:tm-310, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81746
in-theory        81746
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or 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-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-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-81746.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and E))), M:tm-309, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81747
in-theory        81747
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or 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-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-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-81747.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (E -> ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))))), M:tm-305, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81748
in-theory        81748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-303 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81748.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-303, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81749
in-theory        81749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-270 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81749.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-270, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81750
in-theory        81750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-239 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81750.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-239, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81751
in-theory        81751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E))))
theorem-size     35
proof            (modus-ponens tm-210 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81751.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E)))), M:tm-210, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81752
in-theory        81752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-183 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81752.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-183, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81753
in-theory        81753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-157 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-81753.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-157, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81754
in-theory        81754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-147 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-81754.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-147, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81755
in-theory        81755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-134 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-81755.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-134, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81756
in-theory        81756
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-125 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-81756.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-125, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81757
in-theory        81757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-113 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81757.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E)))), M:tm-113, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81758
in-theory        81758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-105 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-81758.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-105, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81759
in-theory        81759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C))))
theorem-size     25
proof            (modus-ponens tm-95 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-81759.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C)))), M:tm-95, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81760
in-theory        81760
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (E -> (D and E))) and (B or A))))
theorem-size     19
proof            (modus-ponens tm-84 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81760.        ((A or (B or A)) -> (C -> ((D -> (E -> (D and E))) and (B or A)))), M:tm-84, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81761
in-theory        81761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-83 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-81761.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-83, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81762
in-theory        81762
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (E -> (D and E))) and (C or B))))
theorem-size     23
proof            (modus-ponens tm-76 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81762.        (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (E -> (D and E))) and (C or B)))), M:tm-76, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81763
in-theory        81763
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-73 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81763.        (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A))), M:tm-73, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81764
in-theory        81764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-69 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81764.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C)))), M:tm-69, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81765
in-theory        81765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-54 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-81765.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-54, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81766
in-theory        81766
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> ((C -> (D -> (C and D))) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-50 tm-908 ((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-8 tm-7 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-5.            (A -> (B -> (A and B))), axiom
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-81766.        (((A or B) or (B or (A or B))) -> ((C -> (D -> (C and D))) and (A or B))), M:tm-50, m:tm-908, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81767
in-theory        81767
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-49 tm-908 ((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81767.        ((A or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A))), M:tm-49, m:tm-908, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81768
in-theory        81768
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (E -> (D and E))) and (C or B)))
theorem-size     25
proof            (modus-ponens tm-47 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81768.        (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (E -> (D and E))) and (C or B))), M:tm-47, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81769
in-theory        81769
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (E -> (D and E))) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-46 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81769.        ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (E -> (D and E))) and (B or A))), M:tm-46, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81770
in-theory        81770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-42 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-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-81770.        ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C)))), M:tm-42, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81771
in-theory        81771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-32 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81771.        ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C)))), M:tm-32, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81772
in-theory        81772
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> (C and D))) and (B or A))))
theorem-size     23
proof            (modus-ponens tm-24 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81772.        ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D -> (C and D))) and (B or A)))), M:tm-24, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81773
in-theory        81773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C))))
theorem-size     25
proof            (modus-ponens tm-23 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81773.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C)))), M:tm-23, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81774
in-theory        81774
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-22 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81774.        (((A and B) -> B) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C)))), M:tm-22, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81775
in-theory        81775
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-21 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81775.        (((A and B) -> A) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C)))), M:tm-21, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81776
in-theory        81776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-20 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81776.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-20, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81777
in-theory        81777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-19 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81777.        ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (F -> (E and F))) and (D or C)))), M:tm-19, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81778
in-theory        81778
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not ((C -> (D -> (C and D))) and (B or A)))) -> (not (A or (B or A))))
theorem-size     25
proof            (modus-ponens tm-9 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81778.        (((A or (B or A)) -> (not ((C -> (D -> (C and D))) and (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81779
in-theory        81779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and (C or D)) -> E) -> (((D or (C or D)) or ((A -> (B -> (A and B))) and (C or D))) -> E))
theorem-size     33
proof            (modus-ponens tm-8 tm-908 ((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       119
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-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-81779.        ((((A -> (B -> (A and B))) and (C or D)) -> E) -> (((D or (C or D)) or ((A -> (B -> (A and B))) and (C or D))) -> E)), M:tm-8, m:tm-908, u:((A (or Am (or Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-81780
in-theory        81780
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> ((D -> (E -> (D and E))) and (C or B))))
theorem-size     19
proof            (modus-ponens tm-7 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-7 tm-8 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-50.           (((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-81780.        (A or ((B or (C or B)) -> ((D -> (E -> (D and E))) and (C or B)))), M:tm-7, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81781
in-theory        81781
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81781.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) or E), M:tm-6, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81782
in-theory        81782
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> ((D -> (E -> (D and E))) and (C or B))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-81782.        (A -> (((B or (C or B)) -> ((D -> (E -> (D and E))) and (C or B))) and A)), M:tm-5, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81783
in-theory        81783
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> ((D -> (E -> (D and E))) and (C or B))))
theorem-size     19
proof            (modus-ponens tm-1 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81783.        (A -> ((B or (C or B)) -> ((D -> (E -> (D and E))) and (C or B)))), M:tm-1, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-81784
in-theory        81784
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-893 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81784.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-893, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81785
in-theory        81785
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((A or (A or (B or A))) -> (C -> (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-882 tm-909 ((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81785.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((A or (A or (B or A))) -> (C -> (D -> (C and D))))), M:tm-882, m:tm-909, u:((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81786
in-theory        81786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-855 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81786.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-855, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81787
in-theory        81787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-808 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81787.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-808, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81788
in-theory        81788
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((E and (A or (B or A))) or (A or (B or A))) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-798 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81788.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((E and (A or (B or A))) or (A or (B or A))) -> (C -> (D -> (C and D))))), M:tm-798, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81789
in-theory        81789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81789.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-757, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81790
in-theory        81790
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-747 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), 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-81790.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (C -> (D -> (C and D))))), M:tm-747, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81791
in-theory        81791
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81791.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (H -> (G and H))))), M:tm-708, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81792
in-theory        81792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-81792.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-665, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81793
in-theory        81793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-909 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81793.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-622, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81794
in-theory        81794
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D or (A or (B or A))) and C)))
theorem-size     17
proof            (modus-ponens tm-617 tm-909 ((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (-> Dm (and (or B (or Am (or 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-50.           (((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-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-81794.        ((A or (B or A)) -> (C -> ((D or (A or (B or A))) and C))), M:tm-617, m:tm-909, u:((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (-> Dm (and (or B (or Am (or Bm Am))) Dm))))
================================================================
tm-name          tm-81795
in-theory        81795
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-909 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81795.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81796
in-theory        81796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81796.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-605, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81797
in-theory        81797
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A or (B or A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81797.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A or (B or A)) -> (C -> (D -> (C and D)))))), M:tm-595, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81798
in-theory        81798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81798.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-550, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81799
in-theory        81799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81799.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-540, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81800
in-theory        81800
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81800.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-530, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81801
in-theory        81801
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81801.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-520, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81802
in-theory        81802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81802.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-510, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81803
in-theory        81803
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81803.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-500, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81804
in-theory        81804
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81804.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H -> (G and H))))), M:tm-490, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81805
in-theory        81805
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-909 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81805.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-480, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81806
in-theory        81806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-81806.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-469, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81807
in-theory        81807
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((A or (B or A)) or D) and C)))
theorem-size     17
proof            (modus-ponens tm-464 tm-909 ((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (-> Dm (and (or (or Am (or Bm Am)) B) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81807.        ((A or (B or A)) -> (C -> (((A or (B or A)) or D) and C))), M:tm-464, m:tm-909, u:((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (-> Dm (and (or (or Am (or Bm Am)) B) Dm))))
================================================================
tm-name          tm-81808
in-theory        81808
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-81808.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81809
in-theory        81809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81809.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-453, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81810
in-theory        81810
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A or (B or A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81810.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A or (B or A)) -> (C -> (D -> (C and D)))))), M:tm-443, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81811
in-theory        81811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81811.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-409, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81812
in-theory        81812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81812.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-400, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81813
in-theory        81813
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81813.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-391, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81814
in-theory        81814
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81814.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-382, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81815
in-theory        81815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81815.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (H -> (G and H))))), M:tm-373, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81816
in-theory        81816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81816.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-364, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81817
in-theory        81817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81817.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-354, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81818
in-theory        81818
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> ((A or (B or A)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-349 tm-909 ((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (-> Dm (and (-> B (and (or Am (or Bm Am)) B)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81818.        ((A or (B or A)) -> (C -> ((D -> ((A or (B or A)) and D)) and C))), M:tm-349, m:tm-909, u:((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (-> Dm (and (-> B (and (or Am (or Bm Am)) B)) Dm))))
================================================================
tm-name          tm-81819
in-theory        81819
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-81819.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81820
in-theory        81820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81820.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (F -> (E and F))))), M:tm-338, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81821
in-theory        81821
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-328 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81821.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (D -> (C and D)))))), M:tm-328, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81822
in-theory        81822
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81822.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (C -> (D -> (C and D)))))), M:tm-327, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81823
in-theory        81823
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A or (B or A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81823.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A or (B or A)) -> (C -> (D -> (C and D)))))), M:tm-326, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81824
in-theory        81824
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A or (B or A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81824.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A or (B or A)) -> (C -> (D -> (C and D)))))), M:tm-325, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81825
in-theory        81825
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81825.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (C -> (D -> (C and D)))))), M:tm-324, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81826
in-theory        81826
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A or (B or A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-81826.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A or (B or A)) -> (C -> (D -> (C and D)))))), M:tm-323, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81827
in-theory        81827
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-81827.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81828
in-theory        81828
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-81828.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81829
in-theory        81829
times-derived    1
----------------------------------------------------------------
theorem          (((A or (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-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-81829.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81830
in-theory        81830
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     25
proof            (modus-ponens tm-316 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-81830.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81831
in-theory        81831
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-81831.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81832
in-theory        81832
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((A or (B or A)) -> (not (C -> (D -> (C and D))))) -> (not (A or (B or A)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), 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-81832.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((A or (B or A)) -> (not (C -> (D -> (C and D))))) -> (not (A or (B or A))))), M:tm-313, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81833
in-theory        81833
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> (((A or (B or A)) or (C -> (D -> (C and D)))) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81833.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> (((A or (B or A)) or (C -> (D -> (C and D)))) -> E))), M:tm-312, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81834
in-theory        81834
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E or ((A or (B or A)) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81834.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E or ((A or (B or A)) -> (C -> (D -> (C and D)))))), M:tm-311, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81835
in-theory        81835
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((A or (B or A)) -> (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), 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-81835.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((A or (B or A)) -> (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81836
in-theory        81836
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (((A or (B or A)) -> (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), 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-81836.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> (((A or (B or A)) -> (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81837
in-theory        81837
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-306 tm-909 ((A (or Am (or Bm Am))) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), 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-81837.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D -> (C and D))))), M:tm-306, m:tm-909, u:((A (or Am (or Bm Am))) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-81838
in-theory        81838
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> ((A or (B or A)) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
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-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-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-81838.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (E -> ((A or (B or A)) -> (C -> (D -> (C and D)))))), M:tm-305, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81839
in-theory        81839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81839.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-303, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81840
in-theory        81840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81840.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-270, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81841
in-theory        81841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81841.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-239, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81842
in-theory        81842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81842.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (H -> (G and H))))), M:tm-210, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81843
in-theory        81843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81843.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-183, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81844
in-theory        81844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-81844.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-157, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81845
in-theory        81845
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81845.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-147, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81846
in-theory        81846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-81846.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-134, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81847
in-theory        81847
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81847.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-125, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81848
in-theory        81848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81848.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H -> (G and H))))), M:tm-113, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81849
in-theory        81849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81849.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-105, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81850
in-theory        81850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((A or (B or A)) and C)))
theorem-size     15
proof            (modus-ponens tm-99 tm-909 ((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (-> Dm (and (or Am (or Bm Am)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81850.        ((A or (B or A)) -> (C -> ((A or (B or A)) and C))), M:tm-99, m:tm-909, u:((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (-> Dm (and (or Am (or Bm Am)) Dm))))
================================================================
tm-name          tm-81851
in-theory        81851
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (A or (B or A))) and C)))
theorem-size     17
proof            (modus-ponens tm-98 tm-909 ((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (-> Dm (and (-> B (or Am (or Bm Am))) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81851.        ((A or (B or A)) -> (C -> ((D -> (A or (B or A))) and C))), M:tm-98, m:tm-909, u:((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (-> Dm (and (-> B (or Am (or Bm Am))) Dm))))
================================================================
tm-name          tm-81852
in-theory        81852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-81852.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (F -> (E and F))))), M:tm-95, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81853
in-theory        81853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-81853.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-83, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81854
in-theory        81854
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81854.        (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (E -> (D and E))))), M:tm-76, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81855
in-theory        81855
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-73 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81855.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (D -> (C and D)))), M:tm-73, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81856
in-theory        81856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81856.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (F -> (E and F))))), M:tm-69, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81857
in-theory        81857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-1.            (A -> (B -> A)), 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-81857.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-54, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81858
in-theory        81858
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-50 tm-909 ((A Am) (B (or 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-5.            (A -> (B -> (A and 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-81858.        (((A or B) or (B or (A or B))) -> (C -> (D -> (C and D)))), M:tm-50, m:tm-909, u:((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81859
in-theory        81859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-49 tm-909 ((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81859.        ((A or (A or (B or A))) -> (C -> (D -> (C and D)))), M:tm-49, m:tm-909, u:((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81860
in-theory        81860
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-47 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81860.        (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (E -> (D and E)))), M:tm-47, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81861
in-theory        81861
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-46 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81861.        ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (E -> (D and E)))), M:tm-46, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81862
in-theory        81862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-909 ((A (-> (or Am (or 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-50.           (((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-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-81862.        ((A -> (B or A)) and ((C or (D or C)) -> (E -> (F -> (E and F))))), M:tm-42, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81863
in-theory        81863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81863.        ((A -> (A or B)) and ((C or (D or C)) -> (E -> (F -> (E and F))))), M:tm-32, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81864
in-theory        81864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (C -> (D -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-24 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81864.        ((A or (B or A)) -> ((A or (B or A)) and (C -> (D -> (C and D))))), M:tm-24, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81865
in-theory        81865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81865.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (F -> (E and F))))), M:tm-23, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81866
in-theory        81866
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81866.        (((A and B) -> B) and ((C or (D or C)) -> (E -> (F -> (E and F))))), M:tm-22, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81867
in-theory        81867
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81867.        (((A and B) -> A) and ((C or (D or C)) -> (E -> (F -> (E and F))))), M:tm-21, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81868
in-theory        81868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81868.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-20, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81869
in-theory        81869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81869.        ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (F -> (E and F))))), M:tm-19, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81870
in-theory        81870
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (C -> (D -> (C and D))))) -> (not (A or (B or A))))
theorem-size     21
proof            (modus-ponens tm-9 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81870.        (((A or (B or A)) -> (not (C -> (D -> (C and D))))) -> (not (A or (B or A)))), M:tm-9, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81871
in-theory        81871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (((D or (E or D)) or (A -> (B -> (A and B)))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 tm-909 ((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
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-5.            (A -> (B -> (A and 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-81871.        (((A -> (B -> (A and B))) -> C) -> (((D or (E or D)) or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-909, u:((A (or Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-81872
in-theory        81872
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-909 ((A (-> (or Am (or 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-50.           (((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-81872.        (A or ((B or (C or B)) -> (D -> (E -> (D and E))))), M:tm-7, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81873
in-theory        81873
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81873.        (((A or (B or A)) -> (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81874
in-theory        81874
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81874.        (A -> (((B or (C or B)) -> (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81875
in-theory        81875
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-2 tm-909 ((A (or Am (or Bm Am))) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81875.        (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D -> (C and D)))), M:tm-2, m:tm-909, u:((A (or Am (or Bm Am))) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-81876
in-theory        81876
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81876.        (A -> ((B or (C or B)) -> (D -> (E -> (D and E))))), M:tm-1, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-81877
in-theory        81877
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81877.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-893, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81878
in-theory        81878
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((A or (A or (B or A))) -> ((C -> (C or D)) and (B or A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-910 ((A Am) (B (or Bm Am)) (C (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81878.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((A or (A or (B or A))) -> ((C -> (C or D)) and (B or A)))), M:tm-882, m:tm-910, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81879
in-theory        81879
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-855 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81879.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-855, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81880
in-theory        81880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81880.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-808, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81881
in-theory        81881
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C -> (C or D)) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81881.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C -> (C or D)) and (B or A)))), M:tm-798, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81882
in-theory        81882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81882.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-757, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81883
in-theory        81883
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C -> (C or D)) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81883.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C -> (C or D)) and (B or A)))), M:tm-747, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81884
in-theory        81884
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81884.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E)))), M:tm-708, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81885
in-theory        81885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81885.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-665, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81886
in-theory        81886
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((D -> (D or E)) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or 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-50.           (((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-81886.        ((A or (B or A)) -> (C or ((D -> (D or E)) and (B or A)))), M:tm-623, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81887
in-theory        81887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or 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-50.           (((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-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-81887.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-622, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81888
in-theory        81888
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or 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-50.           (((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-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-81888.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (F or E))), M:tm-609, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81889
in-theory        81889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-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-81889.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-605, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81890
in-theory        81890
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or 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-81890.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A))))), M:tm-595, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81891
in-theory        81891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81891.        (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-550, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81892
in-theory        81892
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-6.            (A -> (A or 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-81892.        ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-540, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81893
in-theory        81893
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81893.        ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-530, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81894
in-theory        81894
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-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-81894.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-520, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81895
in-theory        81895
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-6.            (A -> (A or 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-81895.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-510, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81896
in-theory        81896
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-6.            (A -> (A or 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-81896.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-500, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81897
in-theory        81897
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-50.           (((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-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-81897.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E)))), M:tm-490, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81898
in-theory        81898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or 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-50.           (((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-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-81898.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-480, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81899
in-theory        81899
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (C or D)) and (B or A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81899.        ((A or (B or A)) -> (((C -> (C or D)) and (B or A)) or E)), M:tm-470, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81900
in-theory        81900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81900.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-469, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81901
in-theory        81901
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81901.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (E or F))), M:tm-456, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81902
in-theory        81902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81902.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-453, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81903
in-theory        81903
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-81903.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A))))), M:tm-443, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81904
in-theory        81904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-81904.        (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-409, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81905
in-theory        81905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81905.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-400, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81906
in-theory        81906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-81906.        ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-391, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81907
in-theory        81907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-81907.        ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-382, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81908
in-theory        81908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81908.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E)))), M:tm-373, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81909
in-theory        81909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-81909.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-364, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81910
in-theory        81910
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D -> (D or E)) and (B or A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81910.        ((A or (B or A)) -> (C -> (((D -> (D or E)) and (B or A)) and C))), M:tm-355, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81911
in-theory        81911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81911.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-354, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81912
in-theory        81912
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or 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-81912.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81913
in-theory        81913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81913.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C)))), M:tm-338, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81914
in-theory        81914
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (C or D)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81914.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (C or D)) and (B or A))))), M:tm-328, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81915
in-theory        81915
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81915.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A))))), M:tm-327, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81916
in-theory        81916
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or 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-81916.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A))))), M:tm-326, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81917
in-theory        81917
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or 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-81917.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A))))), M:tm-325, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81918
in-theory        81918
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81918.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A))))), M:tm-324, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81919
in-theory        81919
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or 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-81919.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C -> (C or D)) and (B or A))))), M:tm-323, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81920
in-theory        81920
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81920.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E and F) -> F)), M:tm-322, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81921
in-theory        81921
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81921.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E and F) -> E)), M:tm-320, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81922
in-theory        81922
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81922.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81923
in-theory        81923
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81923.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81924
in-theory        81924
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81924.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (F -> E))), M:tm-315, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81925
in-theory        81925
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((A or (B or A)) -> (not ((C -> (C or D)) and (B or A)))) -> (not (A or (B or A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-6.            (A -> (A or 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-81925.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((A or (B or A)) -> (not ((C -> (C or D)) and (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81926
in-theory        81926
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((((C -> (C or D)) and (B or A)) -> E) -> (((A or (B or A)) or ((C -> (C or D)) and (B or A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-6.            (A -> (A or 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-81926.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and ((((C -> (C or D)) and (B or A)) -> E) -> (((A or (B or A)) or ((C -> (C or D)) and (B or A))) -> E))), M:tm-312, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81927
in-theory        81927
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E or ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-6.            (A -> (A or 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-81927.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E or ((A or (B or A)) -> ((C -> (C or D)) and (B or A))))), M:tm-311, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81928
in-theory        81928
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-81928.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) or E)), M:tm-310, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81929
in-theory        81929
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or 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-81929.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and E))), M:tm-309, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81930
in-theory        81930
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-6.            (A -> (A or 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-81930.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (E -> ((A or (B or A)) -> ((C -> (C or D)) and (B or A))))), M:tm-305, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81931
in-theory        81931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81931.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-303, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81932
in-theory        81932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81932.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-270, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81933
in-theory        81933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81933.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-239, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81934
in-theory        81934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81934.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E)))), M:tm-210, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81935
in-theory        81935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81935.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-183, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81936
in-theory        81936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81936.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-157, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81937
in-theory        81937
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81937.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-147, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81938
in-theory        81938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81938.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-134, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81939
in-theory        81939
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81939.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-125, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81940
in-theory        81940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81940.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E)))), M:tm-113, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81941
in-theory        81941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81941.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-105, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81942
in-theory        81942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81942.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C)))), M:tm-95, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81943
in-theory        81943
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (D or E)) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81943.        ((A or (B or A)) -> (C -> ((D -> (D or E)) and (B or A)))), M:tm-84, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81944
in-theory        81944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81944.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-83, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81945
in-theory        81945
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (D or E)) and (C or B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81945.        (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (D or E)) and (C or B)))), M:tm-76, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81946
in-theory        81946
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (C or D)) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81946.        (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (C or D)) and (B or A))), M:tm-73, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81947
in-theory        81947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81947.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C)))), M:tm-69, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81948
in-theory        81948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81948.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-54, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81949
in-theory        81949
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> ((C -> (C or D)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-910 ((A Am) (B (or Bm Am)) (C (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-8 tm-7 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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-81949.        (((A or B) or (B or (A or B))) -> ((C -> (C or D)) and (A or B))), M:tm-50, m:tm-910, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81950
in-theory        81950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> ((C -> (C or D)) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-910 ((A Am) (B (or Bm Am)) (C (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81950.        ((A or (A or (B or A))) -> ((C -> (C or D)) and (B or A))), M:tm-49, m:tm-910, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81951
in-theory        81951
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (D or E)) and (C or B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81951.        (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (D or E)) and (C or B))), M:tm-47, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81952
in-theory        81952
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (D or E)) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81952.        ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (D or E)) and (B or A))), M:tm-46, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81953
in-theory        81953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-50.           (((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-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-81953.        ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C)))), M:tm-42, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81954
in-theory        81954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81954.        ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C)))), M:tm-32, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81955
in-theory        81955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and ((C -> (C or D)) and (B or A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81955.        ((A or (B or A)) -> ((A or (B or A)) and ((C -> (C or D)) and (B or A)))), M:tm-24, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81956
in-theory        81956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-6.            (A -> (A or 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-81956.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C)))), M:tm-23, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81957
in-theory        81957
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81957.        (((A and B) -> B) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C)))), M:tm-22, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81958
in-theory        81958
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81958.        (((A and B) -> A) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C)))), M:tm-21, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81959
in-theory        81959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81959.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-20, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81960
in-theory        81960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81960.        ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (E or F)) and (D or C)))), M:tm-19, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81961
in-theory        81961
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not ((C -> (C or D)) and (B or A)))) -> (not (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81961.        (((A or (B or A)) -> (not ((C -> (C or D)) and (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81962
in-theory        81962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and (C or D)) -> E) -> (((D or (C or D)) or ((A -> (A or B)) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-910 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-6.            (A -> (A or 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-81962.        ((((A -> (A or B)) and (C or D)) -> E) -> (((D or (C or D)) or ((A -> (A or B)) and (C or D))) -> E)), M:tm-8, m:tm-910, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-81963
in-theory        81963
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> ((D -> (D or E)) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-7 tm-8 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-50.           (((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-81963.        (A or ((B or (C or B)) -> ((D -> (D or E)) and (C or B)))), M:tm-7, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81964
in-theory        81964
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81964.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) or E), M:tm-6, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81965
in-theory        81965
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> ((D -> (D or E)) and (C or B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81965.        (A -> (((B or (C or B)) -> ((D -> (D or E)) and (C or B))) and A)), M:tm-5, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81966
in-theory        81966
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> ((D -> (D or E)) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81966.        (A -> ((B or (C or B)) -> ((D -> (D or E)) and (C or B)))), M:tm-1, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-81967
in-theory        81967
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-893 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81967.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-893, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81968
in-theory        81968
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((A or (A or (B or A))) -> (C -> (C or D))))
theorem-size     25
proof            (modus-ponens tm-882 tm-911 ((A Am) (B (or Bm Am)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81968.        (((A or (B or A)) -> (C -> (C or D))) and ((A or (A or (B or A))) -> (C -> (C or D)))), M:tm-882, m:tm-911, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-81969
in-theory        81969
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-855 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81969.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-855, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81970
in-theory        81970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-808 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81970.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-808, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81971
in-theory        81971
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (((E and (A or (B or A))) or (A or (B or A))) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-798 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81971.        (((A or (B or A)) -> (C -> (C or D))) and (((E and (A or (B or A))) or (A or (B or A))) -> (C -> (C or D)))), M:tm-798, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-81972
in-theory        81972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81972.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-757, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81973
in-theory        81973
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-747 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-81973.        (((A or (B or A)) -> (C -> (C or D))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (C -> (C or D)))), M:tm-747, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-81974
in-theory        81974
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-81974.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (G or H)))), M:tm-708, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81975
in-theory        81975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81975.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-665, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81976
in-theory        81976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-911 ((A (-> (or Am (or 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-50.           (((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-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-81976.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-622, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81977
in-theory        81977
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or (A or (B or A))) or D))
theorem-size     15
proof            (modus-ponens tm-617 tm-911 ((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (or (or B (or Am (or 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-50.           (((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-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-81977.        ((A or (B or A)) -> ((C or (A or (B or A))) or D)), M:tm-617, m:tm-911, u:((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (or (or B (or Am (or Bm Am))) Dm)))
================================================================
tm-name          tm-81978
in-theory        81978
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-911 ((A (-> (or Am (or 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-50.           (((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-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-81978.        (((A or (B or A)) -> (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81979
in-theory        81979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-911 ((A (-> (or Am (or 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-50.           (((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-81979.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-605, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81980
in-theory        81980
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((E -> (F or E)) and ((A or (B or A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-911 ((A (-> (or Am (or 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-50.           (((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-81980.        (((A or (B or A)) -> (C -> (C or D))) and ((E -> (F or E)) and ((A or (B or A)) -> (C -> (C or D))))), M:tm-595, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81981
in-theory        81981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-911 ((A (-> (or Am (or 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-50.           (((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-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-81981.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-550, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81982
in-theory        81982
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-911 ((A (-> (or Am (or 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-50.           (((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-81982.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-540, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81983
in-theory        81983
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-911 ((A (-> (or Am (or 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-50.           (((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-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-81983.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-530, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81984
in-theory        81984
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-911 ((A (-> (or Am (or 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-50.           (((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-81984.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-520, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81985
in-theory        81985
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-911 ((A (-> (or Am (or 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-50.           (((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-81985.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-510, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81986
in-theory        81986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-911 ((A (-> (or Am (or 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-50.           (((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-81986.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-500, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81987
in-theory        81987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-911 ((A (-> (or Am (or 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-50.           (((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-81987.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (G or H)))), M:tm-490, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81988
in-theory        81988
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-911 ((A (-> (or Am (or 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-50.           (((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-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-81988.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-480, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81989
in-theory        81989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81989.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-469, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81990
in-theory        81990
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((A or (B or A)) or C) or D))
theorem-size     15
proof            (modus-ponens tm-464 tm-911 ((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (or (or (or Am (or Bm Am)) B) Dm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81990.        ((A or (B or A)) -> (((A or (B or A)) or C) or D)), M:tm-464, m:tm-911, u:((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (or (or (or Am (or Bm Am)) B) Dm)))
================================================================
tm-name          tm-81991
in-theory        81991
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81991.        (((A or (B or A)) -> (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81992
in-theory        81992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81992.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-453, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81993
in-theory        81993
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((E -> (E or F)) and ((A or (B or A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81993.        (((A or (B or A)) -> (C -> (C or D))) and ((E -> (E or F)) and ((A or (B or A)) -> (C -> (C or D))))), M:tm-443, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81994
in-theory        81994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81994.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-409, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81995
in-theory        81995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81995.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-400, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81996
in-theory        81996
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81996.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-391, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81997
in-theory        81997
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81997.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-382, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81998
in-theory        81998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-81998.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (G or H)))), M:tm-373, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-81999
in-theory        81999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-81999.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-364, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82000
in-theory        82000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82000.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-354, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82001
in-theory        82001
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> ((A or (B or A)) and C)) or D))
theorem-size     17
proof            (modus-ponens tm-349 tm-911 ((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (or (-> B (and (or Am (or Bm Am)) B)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82001.        ((A or (B or A)) -> ((C -> ((A or (B or A)) and C)) or D)), M:tm-349, m:tm-911, u:((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (or (-> B (and (or Am (or Bm Am)) B)) Dm)))
================================================================
tm-name          tm-82002
in-theory        82002
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82002.        (((A or (B or A)) -> (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82003
in-theory        82003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82003.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (E or F)))), M:tm-338, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82004
in-theory        82004
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82004.        (((A or (B or A)) -> (C -> (C or D))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (C or D))))), M:tm-328, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82005
in-theory        82005
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82005.        (((A or (B or A)) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (C -> (C or D))))), M:tm-327, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82006
in-theory        82006
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (((E and F) -> F) and ((A or (B or A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82006.        (((A or (B or A)) -> (C -> (C or D))) and (((E and F) -> F) and ((A or (B or A)) -> (C -> (C or D))))), M:tm-326, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82007
in-theory        82007
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (((E and F) -> E) and ((A or (B or A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82007.        (((A or (B or A)) -> (C -> (C or D))) and (((E and F) -> E) and ((A or (B or A)) -> (C -> (C or D))))), M:tm-325, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82008
in-theory        82008
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82008.        (((A or (B or A)) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (C -> (C or D))))), M:tm-324, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82009
in-theory        82009
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((E -> (F -> E)) and ((A or (B or A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82009.        (((A or (B or A)) -> (C -> (C or D))) and ((E -> (F -> E)) and ((A or (B or A)) -> (C -> (C or D))))), M:tm-323, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82010
in-theory        82010
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82010.        (((A or (B or A)) -> (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82011
in-theory        82011
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82011.        (((A or (B or A)) -> (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82012
in-theory        82012
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (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-82012.        (((A or (B or A)) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82013
in-theory        82013
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82013.        (((A or (B or A)) -> (C -> (C or D))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82014
in-theory        82014
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82014.        (((A or (B or A)) -> (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82015
in-theory        82015
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (((A or (B or A)) -> (not (C -> (C or D)))) -> (not (A or (B or A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82015.        (((A or (B or A)) -> (C -> (C or D))) and (((A or (B or A)) -> (not (C -> (C or D)))) -> (not (A or (B or A))))), M:tm-313, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82016
in-theory        82016
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> (((A or (B or A)) or (C -> (C or D))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82016.        (((A or (B or A)) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> (((A or (B or A)) or (C -> (C or D))) -> E))), M:tm-312, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82017
in-theory        82017
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (E or ((A or (B or A)) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-911 ((A (-> (or Am (or 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-50.           (((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-82017.        (((A or (B or A)) -> (C -> (C or D))) and (E or ((A or (B or A)) -> (C -> (C or D))))), M:tm-311, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82018
in-theory        82018
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (((A or (B or A)) -> (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), 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-82018.        (((A or (B or A)) -> (C -> (C or D))) and (((A or (B or A)) -> (C -> (C or D))) or E)), M:tm-310, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82019
in-theory        82019
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (E -> (((A or (B or A)) -> (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-82019.        (((A or (B or A)) -> (C -> (C or D))) and (E -> (((A or (B or A)) -> (C -> (C or D))) and E))), M:tm-309, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82020
in-theory        82020
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (C or D))))
theorem-size     29
proof            (modus-ponens tm-306 tm-911 ((A (or Am (or Bm Am))) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-82020.        (((A or (B or A)) -> (C -> (C or D))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (C or D)))), M:tm-306, m:tm-911, u:((A (or Am (or Bm Am))) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-82021
in-theory        82021
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (E -> ((A or (B or A)) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-6.            (A -> (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-82021.        (((A or (B or A)) -> (C -> (C or D))) and (E -> ((A or (B or A)) -> (C -> (C or D))))), M:tm-305, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82022
in-theory        82022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82022.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-303, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82023
in-theory        82023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82023.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-270, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82024
in-theory        82024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82024.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-239, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82025
in-theory        82025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82025.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (G or H)))), M:tm-210, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82026
in-theory        82026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82026.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-183, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82027
in-theory        82027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82027.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-157, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82028
in-theory        82028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82028.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-147, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82029
in-theory        82029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82029.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-134, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82030
in-theory        82030
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82030.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-125, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82031
in-theory        82031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82031.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (G or H)))), M:tm-113, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82032
in-theory        82032
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82032.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-105, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82033
in-theory        82033
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) or C))
theorem-size     13
proof            (modus-ponens tm-99 tm-911 ((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (or (or Am (or Bm Am)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82033.        ((A or (B or A)) -> ((A or (B or A)) or C)), M:tm-99, m:tm-911, u:((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (or (or Am (or Bm Am)) Dm)))
================================================================
tm-name          tm-82034
in-theory        82034
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (A or (B or A))) or D))
theorem-size     15
proof            (modus-ponens tm-98 tm-911 ((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (or (-> B (or Am (or Bm Am))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82034.        ((A or (B or A)) -> ((C -> (A or (B or A))) or D)), M:tm-98, m:tm-911, u:((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (or (-> B (or Am (or Bm Am))) Dm)))
================================================================
tm-name          tm-82035
in-theory        82035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82035.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (E or F)))), M:tm-95, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82036
in-theory        82036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82036.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-83, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82037
in-theory        82037
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82037.        (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (D or E)))), M:tm-76, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82038
in-theory        82038
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-73 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82038.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (C or D))), M:tm-73, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82039
in-theory        82039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82039.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (E or F)))), M:tm-69, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82040
in-theory        82040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82040.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-54, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82041
in-theory        82041
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-50 tm-911 ((A Am) (B (or 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-6.            (A -> (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-82041.        (((A or B) or (B or (A or B))) -> (C -> (C or D))), M:tm-50, m:tm-911, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82042
in-theory        82042
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-49 tm-911 ((A Am) (B (or Bm Am)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82042.        ((A or (A or (B or A))) -> (C -> (C or D))), M:tm-49, m:tm-911, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82043
in-theory        82043
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-47 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82043.        (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (D or E))), M:tm-47, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82044
in-theory        82044
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-46 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82044.        ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (D or E))), M:tm-46, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82045
in-theory        82045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-911 ((A (-> (or Am (or 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-50.           (((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-82045.        ((A -> (B or A)) and ((C or (D or C)) -> (E -> (E or F)))), M:tm-42, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82046
in-theory        82046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82046.        ((A -> (A or B)) and ((C or (D or C)) -> (E -> (E or F)))), M:tm-32, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82047
in-theory        82047
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (C -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-24 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82047.        ((A or (B or A)) -> ((A or (B or A)) and (C -> (C or D)))), M:tm-24, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82048
in-theory        82048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82048.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (E or F)))), M:tm-23, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82049
in-theory        82049
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82049.        (((A and B) -> B) and ((C or (D or C)) -> (E -> (E or F)))), M:tm-22, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82050
in-theory        82050
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82050.        (((A and B) -> A) and ((C or (D or C)) -> (E -> (E or F)))), M:tm-21, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82051
in-theory        82051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82051.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-20, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82052
in-theory        82052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82052.        ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (E or F)))), M:tm-19, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82053
in-theory        82053
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (C -> (C or D)))) -> (not (A or (B or A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82053.        (((A or (B or A)) -> (not (C -> (C or D)))) -> (not (A or (B or A)))), M:tm-9, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82054
in-theory        82054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (((D or (E or D)) or (A -> (A or B))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-911 ((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
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-6.            (A -> (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-82054.        (((A -> (A or B)) -> C) -> (((D or (E or D)) or (A -> (A or B))) -> C)), M:tm-8, m:tm-911, u:((A (or Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82055
in-theory        82055
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-911 ((A (-> (or Am (or 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-50.           (((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-82055.        (A or ((B or (C or B)) -> (D -> (D or E)))), M:tm-7, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82056
in-theory        82056
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82056.        (((A or (B or A)) -> (C -> (C or D))) or E), M:tm-6, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82057
in-theory        82057
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82057.        (A -> (((B or (C or B)) -> (D -> (D or E))) and A)), M:tm-5, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82058
in-theory        82058
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> C) -> ((A or (B or A)) -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-2 tm-911 ((A (or Am (or Bm Am))) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82058.        (((A or (B or A)) -> C) -> ((A or (B or A)) -> (C or D))), M:tm-2, m:tm-911, u:((A (or Am (or Bm Am))) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-82059
in-theory        82059
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82059.        (A -> ((B or (C or B)) -> (D -> (D or E)))), M:tm-1, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82060
in-theory        82060
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-893 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82060.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-893, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82061
in-theory        82061
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((A or (A or (B or A))) -> ((C -> (D or C)) and (B or A))))
theorem-size     33
proof            (modus-ponens tm-882 tm-912 ((A Am) (B (or Bm Am)) (C (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82061.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((A or (A or (B or A))) -> ((C -> (D or C)) and (B or A)))), M:tm-882, m:tm-912, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82062
in-theory        82062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-855 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82062.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-855, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82063
in-theory        82063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-808 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82063.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-808, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82064
in-theory        82064
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C -> (D or C)) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-798 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82064.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((E and (A or (B or A))) or (A or (B or A))) -> ((C -> (D or C)) and (B or A)))), M:tm-798, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82065
in-theory        82065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-82065.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-757, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82066
in-theory        82066
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C -> (D or C)) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82066.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((((A or (B or A)) and E) or (A or (B or A))) -> ((C -> (D or C)) and (B or A)))), M:tm-747, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82067
in-theory        82067
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-82067.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E)))), M:tm-708, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82068
in-theory        82068
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82068.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-665, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82069
in-theory        82069
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((D -> (E or D)) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or 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-50.           (((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-82069.        ((A or (B or A)) -> (C or ((D -> (E or D)) and (B or A)))), M:tm-623, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82070
in-theory        82070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82070.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-622, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82071
in-theory        82071
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82071.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (F or E))), M:tm-609, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82072
in-theory        82072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-82072.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-605, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82073
in-theory        82073
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-82073.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (F or E)) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A))))), M:tm-595, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82074
in-theory        82074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82074.        (((A -> (B or A)) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-550, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82075
in-theory        82075
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82075.        ((A or (B -> (C or B))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-540, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82076
in-theory        82076
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82076.        ((A or (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-530, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82077
in-theory        82077
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82077.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-520, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82078
in-theory        82078
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82078.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-510, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82079
in-theory        82079
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82079.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-500, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82080
in-theory        82080
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-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-82080.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E)))), M:tm-490, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82081
in-theory        82081
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82081.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-480, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82082
in-theory        82082
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D or C)) and (B or A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82082.        ((A or (B or A)) -> (((C -> (D or C)) and (B or A)) or E)), M:tm-470, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82083
in-theory        82083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82083.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-469, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82084
in-theory        82084
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82084.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (E or F))), M:tm-456, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82085
in-theory        82085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82085.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-453, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82086
in-theory        82086
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-82086.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (E or F)) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A))))), M:tm-443, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82087
in-theory        82087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-82087.        (((A -> (A or B)) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-409, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82088
in-theory        82088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82088.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-400, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82089
in-theory        82089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-82089.        ((((A and B) -> B) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-391, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82090
in-theory        82090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-82090.        ((((A and B) -> A) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-382, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82091
in-theory        82091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82091.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E)))), M:tm-373, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82092
in-theory        82092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82092.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-364, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82093
in-theory        82093
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D -> (E or D)) and (B or A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82093.        ((A or (B or A)) -> (C -> (((D -> (E or D)) and (B or A)) and C))), M:tm-355, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82094
in-theory        82094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82094.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-354, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82095
in-theory        82095
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82095.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82096
in-theory        82096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82096.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C)))), M:tm-338, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82097
in-theory        82097
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D or C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-82097.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D or C)) and (B or A))))), M:tm-328, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82098
in-theory        82098
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82098.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A))))), M:tm-327, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82099
in-theory        82099
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-82099.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((E and F) -> F) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A))))), M:tm-326, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82100
in-theory        82100
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-82100.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((E and F) -> E) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A))))), M:tm-325, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82101
in-theory        82101
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82101.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A))))), M:tm-324, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82102
in-theory        82102
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82102.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (F -> E)) and ((A or (B or A)) -> ((C -> (D or C)) and (B or A))))), M:tm-323, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82103
in-theory        82103
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82103.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E and F) -> F)), M:tm-322, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82104
in-theory        82104
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82104.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E and F) -> E)), M:tm-320, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82105
in-theory        82105
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82105.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82106
in-theory        82106
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82106.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82107
in-theory        82107
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82107.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (F -> E))), M:tm-315, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82108
in-theory        82108
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((A or (B or A)) -> (not ((C -> (D or C)) and (B or A)))) -> (not (A or (B or A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-82108.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((A or (B or A)) -> (not ((C -> (D or C)) and (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82109
in-theory        82109
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((((C -> (D or C)) and (B or A)) -> E) -> (((A or (B or A)) or ((C -> (D or C)) and (B or A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-82109.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and ((((C -> (D or C)) and (B or A)) -> E) -> (((A or (B or A)) or ((C -> (D or C)) and (B or A))) -> E))), M:tm-312, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82110
in-theory        82110
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E or ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-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-82110.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E or ((A or (B or A)) -> ((C -> (D or C)) and (B or A))))), M:tm-311, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82111
in-theory        82111
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-82111.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) or E)), M:tm-310, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82112
in-theory        82112
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82112.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and E))), M:tm-309, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82113
in-theory        82113
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82113.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (E -> ((A or (B or A)) -> ((C -> (D or C)) and (B or A))))), M:tm-305, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82114
in-theory        82114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82114.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-303, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82115
in-theory        82115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82115.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-270, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82116
in-theory        82116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82116.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-239, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82117
in-theory        82117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82117.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E)))), M:tm-210, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82118
in-theory        82118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82118.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-183, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82119
in-theory        82119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82119.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-157, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82120
in-theory        82120
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-82120.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-147, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82121
in-theory        82121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82121.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-134, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82122
in-theory        82122
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-82122.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-125, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82123
in-theory        82123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82123.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E)))), M:tm-113, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82124
in-theory        82124
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-82124.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-105, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82125
in-theory        82125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82125.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C)))), M:tm-95, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82126
in-theory        82126
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (E or D)) and (B or A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82126.        ((A or (B or A)) -> (C -> ((D -> (E or D)) and (B or A)))), M:tm-84, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82127
in-theory        82127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82127.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-83, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82128
in-theory        82128
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (E or D)) and (C or B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82128.        (((not (not A)) -> A) and ((B or (C or B)) -> ((D -> (E or D)) and (C or B)))), M:tm-76, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82129
in-theory        82129
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (D or C)) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82129.        (((not (not (A or (B or A)))) or (A or (B or A))) -> ((C -> (D or C)) and (B or A))), M:tm-73, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82130
in-theory        82130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82130.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C)))), M:tm-69, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82131
in-theory        82131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82131.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-54, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82132
in-theory        82132
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> ((C -> (D or C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-912 ((A Am) (B (or Bm Am)) (C (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-7 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-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-82132.        (((A or B) or (B or (A or B))) -> ((C -> (D or C)) and (A or B))), M:tm-50, m:tm-912, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82133
in-theory        82133
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> ((C -> (D or C)) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-912 ((A Am) (B (or Bm Am)) (C (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82133.        ((A or (A or (B or A))) -> ((C -> (D or C)) and (B or A))), M:tm-49, m:tm-912, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82134
in-theory        82134
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (E or D)) and (C or B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82134.        (((A and (B or (C or B))) or (B or (C or B))) -> ((D -> (E or D)) and (C or B))), M:tm-47, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82135
in-theory        82135
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (E or D)) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82135.        ((((A or (B or A)) and C) or (A or (B or A))) -> ((D -> (E or D)) and (B or A))), M:tm-46, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82136
in-theory        82136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-82136.        ((A -> (B or A)) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C)))), M:tm-42, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82137
in-theory        82137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82137.        ((A -> (A or B)) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C)))), M:tm-32, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82138
in-theory        82138
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D or C)) and (B or A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82138.        ((A or (B or A)) -> ((A or (B or A)) and ((C -> (D or C)) and (B or A)))), M:tm-24, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82139
in-theory        82139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82139.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C)))), M:tm-23, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82140
in-theory        82140
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82140.        (((A and B) -> B) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C)))), M:tm-22, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82141
in-theory        82141
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82141.        (((A and B) -> A) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C)))), M:tm-21, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82142
in-theory        82142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82142.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-20, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82143
in-theory        82143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82143.        ((A -> (B -> A)) and ((C or (D or C)) -> ((E -> (F or E)) and (D or C)))), M:tm-19, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82144
in-theory        82144
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not ((C -> (D or C)) and (B or A)))) -> (not (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82144.        (((A or (B or A)) -> (not ((C -> (D or C)) and (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82145
in-theory        82145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and (C or D)) -> E) -> (((D or (C or D)) or ((A -> (B or A)) and (C or D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-912 ((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-82145.        ((((A -> (B or A)) and (C or D)) -> E) -> (((D or (C or D)) or ((A -> (B or A)) and (C or D))) -> E)), M:tm-8, m:tm-912, u:((A (or Am (or Bm Am))) (B (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-82146
in-theory        82146
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> ((D -> (E or D)) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-7 tm-8 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-50.           (((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-82146.        (A or ((B or (C or B)) -> ((D -> (E or D)) and (C or B)))), M:tm-7, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82147
in-theory        82147
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82147.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) or E), M:tm-6, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82148
in-theory        82148
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> ((D -> (E or D)) and (C or B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-82148.        (A -> (((B or (C or B)) -> ((D -> (E or D)) and (C or B))) and A)), M:tm-5, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82149
in-theory        82149
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> ((D -> (E or D)) and (C or B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82149.        (A -> ((B or (C or B)) -> ((D -> (E or D)) and (C or B)))), M:tm-1, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-82150
in-theory        82150
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-893 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82150.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-893, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82151
in-theory        82151
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((A or (A or (B or A))) -> (C -> (D or C))))
theorem-size     25
proof            (modus-ponens tm-882 tm-913 ((A Am) (B (or Bm Am)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82151.        (((A or (B or A)) -> (C -> (D or C))) and ((A or (A or (B or A))) -> (C -> (D or C)))), M:tm-882, m:tm-913, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82152
in-theory        82152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-855 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82152.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-855, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82153
in-theory        82153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-808 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82153.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-808, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82154
in-theory        82154
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (((E and (A or (B or A))) or (A or (B or A))) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-798 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82154.        (((A or (B or A)) -> (C -> (D or C))) and (((E and (A or (B or A))) or (A or (B or A))) -> (C -> (D or C)))), M:tm-798, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82155
in-theory        82155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82155.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-757, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82156
in-theory        82156
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (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-82156.        (((A or (B or A)) -> (C -> (D or C))) and ((((A or (B or A)) and E) or (A or (B or A))) -> (C -> (D or C)))), M:tm-747, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82157
in-theory        82157
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82157.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (G -> (H or G)))), M:tm-708, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82158
in-theory        82158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-913 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82158.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-665, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82159
in-theory        82159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-913 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-82159.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-622, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82160
in-theory        82160
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D or (A or (B or A)))))
theorem-size     15
proof            (modus-ponens tm-617 tm-913 ((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (or Dm (or B (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-82160.        ((A or (B or A)) -> (C or (D or (A or (B or A))))), M:tm-617, m:tm-913, u:((A (or Am (or Bm Am))) (Cm (or B (or Am (or Bm Am)))) (C (or Dm (or B (or Am (or Bm Am))))))
================================================================
tm-name          tm-82161
in-theory        82161
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-913 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-82161.        (((A or (B or A)) -> (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82162
in-theory        82162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-913 ((A (-> (or Am (or 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-50.           (((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-82162.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-605, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82163
in-theory        82163
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((E -> (F or E)) and ((A or (B or A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-913 ((A (-> (or Am (or 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-50.           (((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-82163.        (((A or (B or A)) -> (C -> (D or C))) and ((E -> (F or E)) and ((A or (B or A)) -> (C -> (D or C))))), M:tm-595, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82164
in-theory        82164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-913 ((A (-> (or Am (or 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-50.           (((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-82164.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-550, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82165
in-theory        82165
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-913 ((A (-> (or Am (or 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-50.           (((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-82165.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-540, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82166
in-theory        82166
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-913 ((A (-> (or Am (or 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-50.           (((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-82166.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-530, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82167
in-theory        82167
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-913 ((A (-> (or Am (or 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-50.           (((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-82167.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-520, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82168
in-theory        82168
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-913 ((A (-> (or Am (or 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-50.           (((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-82168.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-510, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82169
in-theory        82169
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-913 ((A (-> (or Am (or 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-50.           (((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-82169.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-500, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82170
in-theory        82170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-913 ((A (-> (or Am (or 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-50.           (((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-82170.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H or G)))), M:tm-490, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82171
in-theory        82171
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-913 ((A (-> (or Am (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82171.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-480, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82172
in-theory        82172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82172.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-469, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82173
in-theory        82173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((A or (B or A)) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-913 ((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (or Dm (or (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82173.        ((A or (B or A)) -> (C or ((A or (B or A)) or D))), M:tm-464, m:tm-913, u:((A (or Am (or Bm Am))) (Cm (or (or Am (or Bm Am)) B)) (C (or Dm (or (or Am (or Bm Am)) B))))
================================================================
tm-name          tm-82174
in-theory        82174
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82174.        (((A or (B or A)) -> (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82175
in-theory        82175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82175.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-453, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82176
in-theory        82176
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((E -> (E or F)) and ((A or (B or A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82176.        (((A or (B or A)) -> (C -> (D or C))) and ((E -> (E or F)) and ((A or (B or A)) -> (C -> (D or C))))), M:tm-443, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82177
in-theory        82177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82177.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-409, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82178
in-theory        82178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82178.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-400, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82179
in-theory        82179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82179.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-391, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82180
in-theory        82180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82180.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-382, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82181
in-theory        82181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82181.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (G -> (H or G)))), M:tm-373, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82182
in-theory        82182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82182.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-364, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82183
in-theory        82183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82183.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-354, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82184
in-theory        82184
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D -> ((A or (B or A)) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-913 ((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (or Dm (-> B (and (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82184.        ((A or (B or A)) -> (C or (D -> ((A or (B or A)) and D)))), M:tm-349, m:tm-913, u:((A (or Am (or Bm Am))) (Cm (-> B (and (or Am (or Bm Am)) B))) (C (or Dm (-> B (and (or Am (or Bm Am)) B)))))
================================================================
tm-name          tm-82185
in-theory        82185
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82185.        (((A or (B or A)) -> (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82186
in-theory        82186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82186.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (E -> (F or E)))), M:tm-338, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82187
in-theory        82187
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82187.        (((A or (B or A)) -> (C -> (D or C))) and ((A or (B or A)) -> ((A or (B or A)) and (C -> (D or C))))), M:tm-328, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82188
in-theory        82188
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82188.        (((A or (B or A)) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A or (B or A)) -> (C -> (D or C))))), M:tm-327, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82189
in-theory        82189
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (((E and F) -> F) and ((A or (B or A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82189.        (((A or (B or A)) -> (C -> (D or C))) and (((E and F) -> F) and ((A or (B or A)) -> (C -> (D or C))))), M:tm-326, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82190
in-theory        82190
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (((E and F) -> E) and ((A or (B or A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82190.        (((A or (B or A)) -> (C -> (D or C))) and (((E and F) -> E) and ((A or (B or A)) -> (C -> (D or C))))), M:tm-325, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82191
in-theory        82191
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (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-82191.        (((A or (B or A)) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B or A)) -> (C -> (D or C))))), M:tm-324, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82192
in-theory        82192
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((E -> (F -> E)) and ((A or (B or A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82192.        (((A or (B or A)) -> (C -> (D or C))) and ((E -> (F -> E)) and ((A or (B or A)) -> (C -> (D or C))))), M:tm-323, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82193
in-theory        82193
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82193.        (((A or (B or A)) -> (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82194
in-theory        82194
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82194.        (((A or (B or A)) -> (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82195
in-theory        82195
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82195.        (((A or (B or A)) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82196
in-theory        82196
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-913 ((A (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82196.        (((A or (B or A)) -> (C -> (D or C))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82197
in-theory        82197
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82197.        (((A or (B or A)) -> (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82198
in-theory        82198
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (((A or (B or A)) -> (not (C -> (D or C)))) -> (not (A or (B or A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (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-82198.        (((A or (B or A)) -> (C -> (D or C))) and (((A or (B or A)) -> (not (C -> (D or C)))) -> (not (A or (B or A))))), M:tm-313, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82199
in-theory        82199
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> (((A or (B or A)) or (C -> (D or C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82199.        (((A or (B or A)) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> (((A or (B or A)) or (C -> (D or C))) -> E))), M:tm-312, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82200
in-theory        82200
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (E or ((A or (B or A)) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-913 ((A (-> (or Am (or 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-50.           (((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-82200.        (((A or (B or A)) -> (C -> (D or C))) and (E or ((A or (B or A)) -> (C -> (D or C))))), M:tm-311, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82201
in-theory        82201
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (((A or (B or A)) -> (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-1.            (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-82201.        (((A or (B or A)) -> (C -> (D or C))) and (((A or (B or A)) -> (C -> (D or C))) or E)), M:tm-310, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82202
in-theory        82202
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (E -> (((A or (B or A)) -> (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (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-82202.        (((A or (B or A)) -> (C -> (D or C))) and (E -> (((A or (B or A)) -> (C -> (D or C))) and E))), M:tm-309, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82203
in-theory        82203
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D or C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-913 ((A (or Am (or Bm Am))) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (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-82203.        (((A or (B or A)) -> (C -> (D or C))) and (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D or C)))), M:tm-306, m:tm-913, u:((A (or Am (or Bm Am))) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-82204
in-theory        82204
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (E -> ((A or (B or A)) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82204.        (((A or (B or A)) -> (C -> (D or C))) and (E -> ((A or (B or A)) -> (C -> (D or C))))), M:tm-305, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82205
in-theory        82205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82205.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-303, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82206
in-theory        82206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82206.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-270, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82207
in-theory        82207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82207.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-239, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82208
in-theory        82208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82208.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (G -> (H or G)))), M:tm-210, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82209
in-theory        82209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82209.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-183, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82210
in-theory        82210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82210.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-157, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82211
in-theory        82211
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82211.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-147, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82212
in-theory        82212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82212.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-134, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82213
in-theory        82213
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82213.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-125, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82214
in-theory        82214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82214.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (G -> (H or G)))), M:tm-113, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82215
in-theory        82215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82215.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-105, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82216
in-theory        82216
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (A or (B or A))))
theorem-size     13
proof            (modus-ponens tm-99 tm-913 ((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (or Dm (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82216.        ((A or (B or A)) -> (C or (A or (B or A)))), M:tm-99, m:tm-913, u:((Cm (or Am (or Bm Am))) (A (or Am (or Bm Am))) (B (or Dm (or Am (or Bm Am)))))
================================================================
tm-name          tm-82217
in-theory        82217
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D -> (A or (B or A)))))
theorem-size     15
proof            (modus-ponens tm-98 tm-913 ((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (or Dm (-> B (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82217.        ((A or (B or A)) -> (C or (D -> (A or (B or A))))), M:tm-98, m:tm-913, u:((A (or Am (or Bm Am))) (Cm (-> B (or Am (or Bm Am)))) (C (or Dm (-> B (or Am (or Bm Am))))))
================================================================
tm-name          tm-82218
in-theory        82218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82218.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (E -> (F or E)))), M:tm-95, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82219
in-theory        82219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82219.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-83, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82220
in-theory        82220
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82220.        (((not (not A)) -> A) and ((B or (C or B)) -> (D -> (E or D)))), M:tm-76, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82221
in-theory        82221
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82221.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (C -> (D or C))), M:tm-73, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82222
in-theory        82222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82222.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (E -> (F or E)))), M:tm-69, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82223
in-theory        82223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82223.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-54, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82224
in-theory        82224
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-913 ((A Am) (B (or 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-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-82224.        (((A or B) or (B or (A or B))) -> (C -> (D or C))), M:tm-50, m:tm-913, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82225
in-theory        82225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-49 tm-913 ((A Am) (B (or Bm Am)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82225.        ((A or (A or (B or A))) -> (C -> (D or C))), M:tm-49, m:tm-913, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82226
in-theory        82226
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82226.        (((A and (B or (C or B))) or (B or (C or B))) -> (D -> (E or D))), M:tm-47, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82227
in-theory        82227
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82227.        ((((A or (B or A)) and C) or (A or (B or A))) -> (D -> (E or D))), M:tm-46, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82228
in-theory        82228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-913 ((A (-> (or Am (or 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-50.           (((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-82228.        ((A -> (B or A)) and ((C or (D or C)) -> (E -> (F or E)))), M:tm-42, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82229
in-theory        82229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-82229.        ((A -> (A or B)) and ((C or (D or C)) -> (E -> (F or E)))), M:tm-32, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82230
in-theory        82230
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (C -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82230.        ((A or (B or A)) -> ((A or (B or A)) and (C -> (D or C)))), M:tm-24, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82231
in-theory        82231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82231.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (E -> (F or E)))), M:tm-23, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82232
in-theory        82232
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-82232.        (((A and B) -> B) and ((C or (D or C)) -> (E -> (F or E)))), M:tm-22, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82233
in-theory        82233
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-82233.        (((A and B) -> A) and ((C or (D or C)) -> (E -> (F or E)))), M:tm-21, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82234
in-theory        82234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (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-82234.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-20, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82235
in-theory        82235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82235.        ((A -> (B -> A)) and ((C or (D or C)) -> (E -> (F or E)))), M:tm-19, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82236
in-theory        82236
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (C -> (D or C)))) -> (not (A or (B or A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82236.        (((A or (B or A)) -> (not (C -> (D or C)))) -> (not (A or (B or A)))), M:tm-9, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82237
in-theory        82237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (((D or (E or D)) or (A -> (B or A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-913 ((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
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-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-82237.        (((A -> (B or A)) -> C) -> (((D or (E or D)) or (A -> (B or A))) -> C)), M:tm-8, m:tm-913, u:((A (or Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82238
in-theory        82238
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-913 ((A (-> (or Am (or 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-50.           (((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-82238.        (A or ((B or (C or B)) -> (D -> (E or D)))), M:tm-7, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82239
in-theory        82239
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82239.        (((A or (B or A)) -> (C -> (D or C))) or E), M:tm-6, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82240
in-theory        82240
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82240.        (A -> (((B or (C or B)) -> (D -> (E or D))) and A)), M:tm-5, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82241
in-theory        82241
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-913 ((A (or Am (or Bm Am))) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82241.        (((A or (B or A)) -> C) -> ((A or (B or A)) -> (D or C))), M:tm-2, m:tm-913, u:((A (or Am (or Bm Am))) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-82242
in-theory        82242
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-913 ((A (-> (or Am (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-82242.        (A -> ((B or (C or B)) -> (D -> (E or D)))), M:tm-1, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82243
in-theory        82243
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-893 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-82243.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-893, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82244
in-theory        82244
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((A or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C)))))
theorem-size     49
proof            (modus-ponens tm-882 tm-914 ((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-82244.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((A or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C))))), M:tm-882, m:tm-914, u:((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82245
in-theory        82245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     41
proof            (modus-ponens tm-855 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82245.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-855, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82246
in-theory        82246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     35
proof            (modus-ponens tm-808 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-82246.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-808, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82247
in-theory        82247
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((D and (A or ((B or C) -> (A and (B or C))))) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C)))))
theorem-size     61
proof            (modus-ponens tm-798 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-82247.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((D and (A or ((B or C) -> (A and (B or C))))) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C))))), M:tm-798, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82248
in-theory        82248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     35
proof            (modus-ponens tm-757 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82248.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-757, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82249
in-theory        82249
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((((A or ((B or C) -> (A and (B or C)))) and D) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C)))))
theorem-size     61
proof            (modus-ponens tm-747 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82249.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((((A or ((B or C) -> (A and (B or C)))) and D) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C))))), M:tm-747, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82250
in-theory        82250
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G)))))
theorem-size     49
proof            (modus-ponens tm-708 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-48.           (((A -> (B and 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-82250.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G))))), M:tm-708, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82251
in-theory        82251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-665 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82251.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-665, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82252
in-theory        82252
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (D or ((C or (B or C)) -> (A and (B or C)))))
theorem-size     25
proof            (modus-ponens tm-623 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
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-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-50.           (((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-82252.        ((A or ((B or C) -> (A and (B or C)))) -> (D or ((C or (B or C)) -> (A and (B or C))))), M:tm-623, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82253
in-theory        82253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-622 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 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-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-50.           (((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-82253.        ((A -> (B -> (C or B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-622, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82254
in-theory        82254
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am 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-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-82254.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (E or D))), M:tm-609, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82255
in-theory        82255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-605 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-82255.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-605, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82256
in-theory        82256
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (E or D)) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-82256.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (E or D)) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))))), M:tm-595, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82257
in-theory        82257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-550 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 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-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-50.           (((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-82257.        (((A -> (B or A)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-550, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82258
in-theory        82258
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-540 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-82258.        ((A or (B -> (C or B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-540, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82259
in-theory        82259
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-530 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 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-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-50.           (((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-82259.        ((A or (B -> (B or C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-530, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82260
in-theory        82260
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-520 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-82260.        ((A or (B -> (C -> (B and C)))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-520, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82261
in-theory        82261
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-510 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 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-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-50.           (((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-82261.        ((A or ((B and C) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-510, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82262
in-theory        82262
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-500 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 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-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-50.           (((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-82262.        ((A or ((B and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-500, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82263
in-theory        82263
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-490 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 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-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-50.           (((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-82263.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G))))), M:tm-490, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82264
in-theory        82264
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-480 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-50.           (((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-82264.        ((A or (B -> (C -> B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-480, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82265
in-theory        82265
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (((C or (B or C)) -> (A and (B or C))) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-7)
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-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-82265.        ((A or ((B or C) -> (A and (B or C)))) -> (((C or (B or C)) -> (A and (B or C))) or D)), M:tm-470, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82266
in-theory        82266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-469 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82266.        ((A -> (B -> (B or C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-469, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82267
in-theory        82267
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82267.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (D or E))), M:tm-456, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82268
in-theory        82268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-453 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-48.           (((A -> (B and 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-82268.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-453, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82269
in-theory        82269
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (D or E)) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82269.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (D or E)) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))))), M:tm-443, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82270
in-theory        82270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-409 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-48.           (((A -> (B and 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-82270.        (((A -> (A or B)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-409, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82271
in-theory        82271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-400 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-48.           (((A -> (B and 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-82271.        (((A -> (B -> (A and B))) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-400, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82272
in-theory        82272
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-391 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-48.           (((A -> (B and 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-82272.        ((((A and B) -> B) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-391, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82273
in-theory        82273
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-382 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-48.           (((A -> (B and 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-82273.        ((((A and B) -> A) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-382, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82274
in-theory        82274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-373 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-48.           (((A -> (B and 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-82274.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G))))), M:tm-373, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82275
in-theory        82275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-364 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-48.           (((A -> (B and 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-82275.        (((A -> (B -> A)) or C) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-364, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82276
in-theory        82276
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (D -> (((C or (B or C)) -> (A and (B or C))) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82276.        ((A or ((B or C) -> (A and (B or C)))) -> (D -> (((C or (B or C)) -> (A and (B or C))) and D))), M:tm-355, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82277
in-theory        82277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-354 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-48.           (((A -> (B and 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-82277.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-354, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82278
in-theory        82278
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82278.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82279
in-theory        82279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E)))))
theorem-size     33
proof            (modus-ponens tm-338 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-48.           (((A -> (B and 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-82279.        (((A -> B) -> (A -> (A and B))) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E))))), M:tm-338, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82280
in-theory        82280
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((A or ((B or C) -> (A and (B or C)))) -> ((A or ((B or C) -> (A and (B or C)))) and ((C or (B or C)) -> (A and (B or C))))))
theorem-size     59
proof            (modus-ponens tm-328 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82280.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((A or ((B or C) -> (A and (B or C)))) -> ((A or ((B or C) -> (A and (B or C)))) and ((C or (B or C)) -> (A and (B or C)))))), M:tm-328, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82281
in-theory        82281
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (E -> (D and E))) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-82281.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (E -> (D and E))) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))))), M:tm-327, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82282
in-theory        82282
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((D and E) -> E) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82282.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((D and E) -> E) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))))), M:tm-326, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82283
in-theory        82283
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((D and E) -> D) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82283.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((D and E) -> D) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))))), M:tm-325, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82284
in-theory        82284
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-82284.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))))), M:tm-324, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82285
in-theory        82285
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (E -> D)) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82285.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (E -> D)) and ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))))), M:tm-323, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82286
in-theory        82286
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82286.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D and E) -> E)), M:tm-322, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82287
in-theory        82287
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82287.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D and E) -> D)), M:tm-320, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82288
in-theory        82288
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82288.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82289
in-theory        82289
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((A or ((B or C) -> (A and (B or C)))) -> (A or ((B or C) -> (A and (B or C))))))
theorem-size     47
proof            (modus-ponens tm-316 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82289.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((A or ((B or C) -> (A and (B or C)))) -> (A or ((B or C) -> (A and (B or C)))))), M:tm-316, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82290
in-theory        82290
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82290.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (E -> D))), M:tm-315, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82291
in-theory        82291
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> (not ((C or (B or C)) -> (A and (B or C))))) -> (not (A or ((B or C) -> (A and (B or C)))))))
theorem-size     61
proof            (modus-ponens tm-313 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82291.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> (not ((C or (B or C)) -> (A and (B or C))))) -> (not (A or ((B or C) -> (A and (B or C))))))), M:tm-313, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82292
in-theory        82292
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((((C or (B or C)) -> (A and (B or C))) -> D) -> (((A or ((B or C) -> (A and (B or C)))) or ((C or (B or C)) -> (A and (B or C)))) -> D)))
theorem-size     63
proof            (modus-ponens tm-312 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
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-312.          ((A -> B) -> ((A -> B) and ((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82292.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((((C or (B or C)) -> (A and (B or C))) -> D) -> (((A or ((B or C) -> (A and (B or C)))) or ((C or (B or C)) -> (A and (B or C)))) -> D))), M:tm-312, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82293
in-theory        82293
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D or ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
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-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-50.           (((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-82293.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D or ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))))), M:tm-311, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82294
in-theory        82294
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82294.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) or D)), M:tm-310, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82295
in-theory        82295
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82295.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and D))), M:tm-309, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82296
in-theory        82296
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> (C or (B or C))) -> ((A or ((B or C) -> (A and (B or C)))) -> (A and (B or C)))))
theorem-size     59
proof            (modus-ponens tm-306 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (or Cm (or Bm Cm))) (C (and Am (or Bm 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-306.          ((A -> (B -> C)) -> ((A -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82296.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (((A or ((B or C) -> (A and (B or C)))) -> (C or (B or C))) -> ((A or ((B or C) -> (A and (B or C)))) -> (A and (B or C))))), M:tm-306, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (or Cm (or Bm Cm))) (C (and Am (or Bm Cm))))
================================================================
tm-name          tm-82297
in-theory        82297
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82297.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and (D -> ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))))), M:tm-305, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82298
in-theory        82298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     35
proof            (modus-ponens tm-303 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-82298.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-303, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82299
in-theory        82299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-270 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-48.           (((A -> (B and 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-82299.        ((A -> (((B and C) -> C) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-270, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82300
in-theory        82300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-239 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-48.           (((A -> (B and 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-82300.        ((A -> (((B and C) -> B) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-239, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82301
in-theory        82301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G)))))
theorem-size     41
proof            (modus-ponens tm-210 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-48.           (((A -> (B and 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-82301.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G))))), M:tm-210, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82302
in-theory        82302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     33
proof            (modus-ponens tm-183 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-48.           (((A -> (B and 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-82302.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-183, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82303
in-theory        82303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-157 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82303.        ((A -> ((B and C) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-157, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82304
in-theory        82304
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     39
proof            (modus-ponens tm-147 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82304.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-147, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82305
in-theory        82305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-134 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82305.        ((A -> ((B and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-134, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82306
in-theory        82306
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     39
proof            (modus-ponens tm-125 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82306.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-125, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82307
in-theory        82307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-113 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-48.           (((A -> (B and 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-82307.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G))))), M:tm-113, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82308
in-theory        82308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     43
proof            (modus-ponens tm-105 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82308.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-105, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82309
in-theory        82309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E)))))
theorem-size     31
proof            (modus-ponens tm-95 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82309.        (((A -> B) -> (A -> A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E))))), M:tm-95, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82310
in-theory        82310
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (D -> ((C or (B or C)) -> (A and (B or C)))))
theorem-size     25
proof            (modus-ponens tm-84 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-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-82310.        ((A or ((B or C) -> (A and (B or C)))) -> (D -> ((C or (B or C)) -> (A and (B or C))))), M:tm-84, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82311
in-theory        82311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     31
proof            (modus-ponens tm-83 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82311.        ((A -> (B -> (C -> B))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-83, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82312
in-theory        82312
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C or D) -> (B and (C or D)))) -> ((D or (C or D)) -> (B and (C or D)))))
theorem-size     29
proof            (modus-ponens tm-76 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-48.           (((A -> (B and 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-82312.        (((not (not A)) -> A) and ((B or ((C or D) -> (B and (C or D)))) -> ((D or (C or D)) -> (B and (C or D))))), M:tm-76, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82313
in-theory        82313
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or ((B or C) -> (A and (B or C)))))) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C))))
theorem-size     37
proof            (modus-ponens tm-73 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
proof-size       157
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-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-82313.        (((not (not (A or ((B or C) -> (A and (B or C)))))) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C)))), M:tm-73, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82314
in-theory        82314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E)))))
theorem-size     35
proof            (modus-ponens tm-69 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-48.           (((A -> (B and 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-82314.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E))))), M:tm-69, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82315
in-theory        82315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-54 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82315.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-54, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82316
in-theory        82316
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and (A or B))) or (C or ((A or B) -> (C and (A or B))))) -> ((B or (A or B)) -> (C and (A or B))))
theorem-size     33
proof            (modus-ponens tm-50 tm-914 ((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       155
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-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-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-82316.        ((((A or B) -> (C and (A or B))) or (C or ((A or B) -> (C and (A or B))))) -> ((B or (A or B)) -> (C and (A or B)))), M:tm-50, m:tm-914, u:((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82317
in-theory        82317
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C))))
theorem-size     25
proof            (modus-ponens tm-49 tm-914 ((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-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-82317.        ((A or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C)))), M:tm-49, m:tm-914, u:((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82318
in-theory        82318
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or ((C or D) -> (B and (C or D))))) or (B or ((C or D) -> (B and (C or D))))) -> ((D or (C or D)) -> (B and (C or D))))
theorem-size     37
proof            (modus-ponens tm-47 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
proof-size       157
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-48.           (((A -> (B and 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-82318.        (((A and (B or ((C or D) -> (B and (C or D))))) or (B or ((C or D) -> (B and (C or D))))) -> ((D or (C or D)) -> (B and (C or D)))), M:tm-47, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82319
in-theory        82319
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B or C) -> (A and (B or C)))) and D) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C))))
theorem-size     37
proof            (modus-ponens tm-46 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
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-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-82319.        ((((A or ((B or C) -> (A and (B or C)))) and D) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C)))), M:tm-46, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82320
in-theory        82320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-42 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-82320.        ((A -> (B or A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E))))), M:tm-42, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82321
in-theory        82321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-32 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-48.           (((A -> (B and 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-82321.        ((A -> (A or B)) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E))))), M:tm-32, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82322
in-theory        82322
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> ((A or ((B or C) -> (A and (B or C)))) and ((C or (B or C)) -> (A and (B or C)))))
theorem-size     35
proof            (modus-ponens tm-24 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-48.           (((A -> (B and 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-82322.        ((A or ((B or C) -> (A and (B or C)))) -> ((A or ((B or C) -> (A and (B or C)))) and ((C or (B or C)) -> (A and (B or C))))), M:tm-24, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82323
in-theory        82323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E)))))
theorem-size     31
proof            (modus-ponens tm-23 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-82323.        ((A -> (B -> (A and B))) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E))))), M:tm-23, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82324
in-theory        82324
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-22 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-48.           (((A -> (B and 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-82324.        (((A and B) -> B) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E))))), M:tm-22, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82325
in-theory        82325
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-21 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-48.           (((A -> (B and 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-82325.        (((A and B) -> A) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E))))), M:tm-21, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82326
in-theory        82326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-20 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-48.           (((A -> (B and 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-82326.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-20, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82327
in-theory        82327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E)))))
theorem-size     29
proof            (modus-ponens tm-19 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-48.           (((A -> (B and 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-82327.        ((A -> (B -> A)) and ((C or ((D or E) -> (C and (D or E)))) -> ((E or (D or E)) -> (C and (D or E))))), M:tm-19, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82328
in-theory        82328
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> (not ((C or (B or C)) -> (A and (B or C))))) -> (not (A or ((B or C) -> (A and (B or C))))))
theorem-size     37
proof            (modus-ponens tm-9 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-7)
proof-size       139
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-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-82328.        (((A or ((B or C) -> (A and (B or C)))) -> (not ((C or (B or C)) -> (A and (B or C))))) -> (not (A or ((B or C) -> (A and (B or C)))))), M:tm-9, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82329
in-theory        82329
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> (C and (B or A))) -> D) -> (((C or ((B or A) -> (C and (B or A)))) or ((A or (B or A)) -> (C and (B or A)))) -> D))
theorem-size     39
proof            (modus-ponens tm-8 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82329.        ((((A or (B or A)) -> (C and (B or A))) -> D) -> (((C or ((B or A) -> (C and (B or A)))) or ((A or (B or A)) -> (C and (B or A)))) -> D)), M:tm-8, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-82330
in-theory        82330
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or ((C or D) -> (B and (C or D)))) -> ((D or (C or D)) -> (B and (C or D)))))
theorem-size     25
proof            (modus-ponens tm-7 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-7 tm-8 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-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-50.           (((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-82330.        (A or ((B or ((C or D) -> (B and (C or D)))) -> ((D or (C or D)) -> (B and (C or D))))), M:tm-7, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82331
in-theory        82331
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-7)
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-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-82331.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) or D), M:tm-6, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82332
in-theory        82332
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C or D) -> (B and (C or D)))) -> ((D or (C or D)) -> (B and (C or D)))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-82332.        (A -> (((B or ((C or D) -> (B and (C or D)))) -> ((D or (C or D)) -> (B and (C or D)))) and A)), M:tm-5, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82333
in-theory        82333
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> (C or (B or C))) -> ((A or ((B or C) -> (A and (B or C)))) -> (A and (B or C))))
theorem-size     35
proof            (modus-ponens tm-2 tm-914 ((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (or Cm (or Bm Cm))) (C (and Am (or Bm Cm)))))
axioms-used      (tm-2 tm-8 tm-5 tm-7)
proof-size       139
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-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-82333.        (((A or ((B or C) -> (A and (B or C)))) -> (C or (B or C))) -> ((A or ((B or C) -> (A and (B or C)))) -> (A and (B or C)))), M:tm-2, m:tm-914, u:((A (or Am (-> (or Bm Cm) (and Am (or Bm Cm))))) (B (or Cm (or Bm Cm))) (C (and Am (or Bm Cm))))
================================================================
tm-name          tm-82334
in-theory        82334
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or ((C or D) -> (B and (C or D)))) -> ((D or (C or D)) -> (B and (C or D)))))
theorem-size     25
proof            (modus-ponens tm-1 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-7)
proof-size       121
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82334.        (A -> ((B or ((C or D) -> (B and (C or D)))) -> ((D or (C or D)) -> (B and (C or D))))), M:tm-1, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-82335
in-theory        82335
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-893 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 tm-7)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-82335.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-893, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82336
in-theory        82336
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D)))
theorem-size     51
proof            (modus-ponens tm-882 tm-915 ((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-82336.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D))), M:tm-882, m:tm-915, u:((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82337
in-theory        82337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-855 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-82337.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-855, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82338
in-theory        82338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-808 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82338.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-808, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82339
in-theory        82339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((E and ((A and ((B or C) -> D)) or ((B or C) -> D))) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D)))
theorem-size     59
proof            (modus-ponens tm-798 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82339.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((E and ((A and ((B or C) -> D)) or ((B or C) -> D))) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D))), M:tm-798, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82340
in-theory        82340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-757 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-50.           (((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-82340.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-757, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82341
in-theory        82341
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((((A and ((B or C) -> D)) or ((B or C) -> D)) and E) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D)))
theorem-size     59
proof            (modus-ponens tm-747 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82341.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((((A and ((B or C) -> D)) or ((B or C) -> D)) and E) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D))), M:tm-747, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82342
in-theory        82342
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-708 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82342.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H))), M:tm-708, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82343
in-theory        82343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-665 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82343.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-665, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82344
in-theory        82344
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E or ((C or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-623 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82344.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E or ((C or (B or C)) -> D))), M:tm-623, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82345
in-theory        82345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-622 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-50.           (((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-82345.        ((A -> (B -> (C or B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-622, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82346
in-theory        82346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-50.           (((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-82346.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82347
in-theory        82347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-605 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82347.        ((A -> ((B -> (C or B)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-605, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82348
in-theory        82348
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (F or E)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-595 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-82348.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (F or E)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))), M:tm-595, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82349
in-theory        82349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-550 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82349.        (((A -> (B or A)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-550, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82350
in-theory        82350
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-540 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82350.        ((A or (B -> (C or B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-540, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82351
in-theory        82351
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-530 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82351.        ((A or (B -> (B or C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-530, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82352
in-theory        82352
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-520 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82352.        ((A or (B -> (C -> (B and C)))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-520, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82353
in-theory        82353
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-510 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82353.        ((A or ((B and C) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-510, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82354
in-theory        82354
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-500 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82354.        ((A or ((B and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-500, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82355
in-theory        82355
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-490 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82355.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H))), M:tm-490, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82356
in-theory        82356
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-480 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82356.        ((A or (B -> (C -> B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-480, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82357
in-theory        82357
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((C or (B or C)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82357.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((C or (B or C)) -> D) or E)), M:tm-470, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82358
in-theory        82358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-469 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82358.        ((A -> (B -> (B or C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-469, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82359
in-theory        82359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-50.           (((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-82359.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82360
in-theory        82360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-453 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82360.        ((A -> ((B -> (B or C)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-453, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82361
in-theory        82361
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (E or F)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-443 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-50.           (((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-82361.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (E or F)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))), M:tm-443, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82362
in-theory        82362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-409 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82362.        (((A -> (A or B)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-409, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82363
in-theory        82363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-400 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82363.        (((A -> (B -> (A and B))) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-400, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82364
in-theory        82364
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-391 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-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-82364.        ((((A and B) -> B) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-391, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82365
in-theory        82365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-382 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82365.        ((((A and B) -> A) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-382, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82366
in-theory        82366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-373 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82366.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H))), M:tm-373, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82367
in-theory        82367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-364 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82367.        (((A -> (B -> A)) or C) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-364, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82368
in-theory        82368
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E -> (((C or (B or C)) -> D) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-50.           (((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-82368.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E -> (((C or (B or C)) -> D) and E))), M:tm-355, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82369
in-theory        82369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-354 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82369.        ((A -> (B -> (C -> (B and C)))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-354, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82370
in-theory        82370
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-50.           (((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-82370.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82371
in-theory        82371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-338 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82371.        (((A -> B) -> (A -> (A and B))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-338, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82372
in-theory        82372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) and ((C or (B or C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-328 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-50.           (((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-82372.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) and ((C or (B or C)) -> D)))), M:tm-328, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82373
in-theory        82373
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))))
theorem-size     51
proof            (modus-ponens tm-327 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-50.           (((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-82373.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))), M:tm-327, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82374
in-theory        82374
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((E and F) -> F) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-326 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-50.           (((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-82374.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((E and F) -> F) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))), M:tm-326, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82375
in-theory        82375
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((E and F) -> E) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-325 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-50.           (((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-82375.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((E and F) -> E) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))), M:tm-325, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82376
in-theory        82376
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-324 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82376.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))), M:tm-324, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82377
in-theory        82377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (F -> E)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-323 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-50.           (((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-82377.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (F -> E)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))), M:tm-323, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82378
in-theory        82378
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-50.           (((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-82378.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82379
in-theory        82379
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-50.           (((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-82379.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82380
in-theory        82380
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-50.           (((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-82380.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82381
in-theory        82381
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((A and ((B or C) -> D)) or ((B or C) -> D))))
theorem-size     49
proof            (modus-ponens tm-316 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-50.           (((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-82381.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((A and ((B or C) -> D)) or ((B or C) -> D)))), M:tm-316, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82382
in-theory        82382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-50.           (((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-82382.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82383
in-theory        82383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (not ((C or (B or C)) -> D))) -> (not ((A and ((B or C) -> D)) or ((B or C) -> D)))))
theorem-size     59
proof            (modus-ponens tm-313 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-50.           (((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-82383.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (not ((C or (B or C)) -> D))) -> (not ((A and ((B or C) -> D)) or ((B or C) -> D))))), M:tm-313, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82384
in-theory        82384
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((C or (B or C)) -> D) -> E) -> ((((A and ((B or C) -> D)) or ((B or C) -> D)) or ((C or (B or C)) -> D)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-82384.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((C or (B or C)) -> D) -> E) -> ((((A and ((B or C) -> D)) or ((B or C) -> D)) or ((C or (B or C)) -> D)) -> E))), M:tm-312, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82385
in-theory        82385
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E or (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-311 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (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-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-50.           (((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-82385.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E or (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))), M:tm-311, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82386
in-theory        82386
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-50.           (((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-82386.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) or E)), M:tm-310, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82387
in-theory        82387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-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-50.           (((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-82387.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and E))), M:tm-309, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82388
in-theory        82388
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (C or (B or C))) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> D)))
theorem-size     57
proof            (modus-ponens tm-306 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (or Cm (or Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-306.          ((A -> (B -> C)) -> ((A -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82388.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (C or (B or C))) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> D))), M:tm-306, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (or Cm (or Bm Cm))) (C Dm))
================================================================
tm-name          tm-82389
in-theory        82389
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-305 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-50.           (((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-82389.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and (E -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))), M:tm-305, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82390
in-theory        82390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-303 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82390.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-303, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82391
in-theory        82391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-270 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-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-82391.        ((A -> (((B and C) -> C) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-270, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82392
in-theory        82392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-239 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82392.        ((A -> (((B and C) -> B) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-239, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82393
in-theory        82393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-210 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-50.           (((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-82393.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H))), M:tm-210, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82394
in-theory        82394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-183 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82394.        ((A -> ((B -> (C -> B)) and A)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-183, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82395
in-theory        82395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-157 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-50.           (((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-82395.        ((A -> ((B and C) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-157, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82396
in-theory        82396
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-147 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-50.           (((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-82396.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-147, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82397
in-theory        82397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-134 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82397.        ((A -> ((B and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-134, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82398
in-theory        82398
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-125 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-50.           (((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-82398.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-125, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82399
in-theory        82399
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> (D -> E))) or ((B or C) -> (D -> E))) -> (((C or (B or C)) -> D) -> ((C or (B or C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-114 tm-915 ((A (or (and Am (-> (or Bm Cm) (-> C D))) (-> (or Bm Cm) (-> C D)))) (B (or Cm (or Bm Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82399.        (((A and ((B or C) -> (D -> E))) or ((B or C) -> (D -> E))) -> (((C or (B or C)) -> D) -> ((C or (B or C)) -> E))), M:tm-114, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) (-> C D))) (-> (or Bm Cm) (-> C D)))) (B (or Cm (or Bm Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-82400
in-theory        82400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-113 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82400.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H))), M:tm-113, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82401
in-theory        82401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-105 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82401.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-105, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82402
in-theory        82402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-95 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-50.           (((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-82402.        (((A -> B) -> (A -> A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-95, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82403
in-theory        82403
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E -> ((C or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-84 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82403.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (E -> ((C or (B or C)) -> D))), M:tm-84, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82404
in-theory        82404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-83 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82404.        ((A -> (B -> (C -> B))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-83, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82405
in-theory        82405
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-76 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82405.        (((not (not A)) -> A) and (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-76, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82406
in-theory        82406
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and ((B or C) -> D)) or ((B or C) -> D)))) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D))
theorem-size     37
proof            (modus-ponens tm-73 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82406.        (((not (not ((A and ((B or C) -> D)) or ((B or C) -> D)))) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D)), M:tm-73, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82407
in-theory        82407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-69 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82407.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-69, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82408
in-theory        82408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-54 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-82408.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-54, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82409
in-theory        82409
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((D and ((A or B) -> C)) or ((A or B) -> C))) -> ((B or (A or B)) -> C))
theorem-size     27
proof            (modus-ponens tm-50 tm-915 ((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-7 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-82409.        ((((A or B) -> C) or ((D and ((A or B) -> C)) or ((A or B) -> C))) -> ((B or (A or B)) -> C)), M:tm-50, m:tm-915, u:((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82410
in-theory        82410
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D))
theorem-size     29
proof            (modus-ponens tm-49 tm-915 ((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-6 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82410.        (((A and ((B or C) -> D)) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D)), M:tm-49, m:tm-915, u:((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82411
in-theory        82411
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and ((C or D) -> E)) or ((C or D) -> E))) or ((B and ((C or D) -> E)) or ((C or D) -> E))) -> ((D or (C or D)) -> E))
theorem-size     37
proof            (modus-ponens tm-47 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82411.        (((A and ((B and ((C or D) -> E)) or ((C or D) -> E))) or ((B and ((C or D) -> E)) or ((C or D) -> E))) -> ((D or (C or D)) -> E)), M:tm-47, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82412
in-theory        82412
times-derived    1
----------------------------------------------------------------
theorem          (((((A and ((B or C) -> D)) or ((B or C) -> D)) and E) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D))
theorem-size     37
proof            (modus-ponens tm-46 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82412.        (((((A and ((B or C) -> D)) or ((B or C) -> D)) and E) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D)), M:tm-46, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82413
in-theory        82413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-42 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82413.        ((A -> (B or A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-42, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82414
in-theory        82414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-32 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82414.        ((A -> (A or B)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-32, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82415
in-theory        82415
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) and ((C or (B or C)) -> D)))
theorem-size     35
proof            (modus-ponens tm-24 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-82415.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) and ((C or (B or C)) -> D))), M:tm-24, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82416
in-theory        82416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-23 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-82416.        ((A -> (B -> (A and B))) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-23, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82417
in-theory        82417
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-22 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-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-82417.        (((A and B) -> B) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-22, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82418
in-theory        82418
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-21 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82418.        (((A and B) -> A) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-21, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82419
in-theory        82419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-20 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-50.           (((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-82419.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-20, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82420
in-theory        82420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-19 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82420.        ((A -> (B -> A)) and (((C and ((D or E) -> F)) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-19, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82421
in-theory        82421
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (not ((C or (B or C)) -> D))) -> (not ((A and ((B or C) -> D)) or ((B or C) -> D))))
theorem-size     37
proof            (modus-ponens tm-9 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82421.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (not ((C or (B or C)) -> D))) -> (not ((A and ((B or C) -> D)) or ((B or C) -> D)))), M:tm-9, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82422
in-theory        82422
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> ((((E and ((B or A) -> C)) or ((B or A) -> C)) or ((A or (B or A)) -> C)) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-7)
proof-size       127
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-50.           (((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-82422.        ((((A or (B or A)) -> C) -> D) -> ((((E and ((B or A) -> C)) or ((B or A) -> C)) or ((A or (B or A)) -> C)) -> D)), M:tm-8, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82423
in-theory        82423
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-7 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82423.        (A or (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-7, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82424
in-theory        82424
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82424.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) or E), M:tm-6, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82425
in-theory        82425
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((D or (C or D)) -> E)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-82425.        (A -> ((((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((D or (C or D)) -> E)) and A)), M:tm-5, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82426
in-theory        82426
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (C or (B or C))) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> D))
theorem-size     35
proof            (modus-ponens tm-2 tm-915 ((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (or Cm (or Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-82426.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> (C or (B or C))) -> (((A and ((B or C) -> D)) or ((B or C) -> D)) -> D)), M:tm-2, m:tm-915, u:((A (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm))) (B (or Cm (or Bm Cm))) (C Dm))
================================================================
tm-name          tm-82427
in-theory        82427
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-1 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-7)
proof-size       109
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82427.        (A -> (((B and ((C or D) -> E)) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-1, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-82428
in-theory        82428
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-893 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 tm-7)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-82428.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-893, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82429
in-theory        82429
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C)))
theorem-size     51
proof            (modus-ponens tm-882 tm-916 ((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-82429.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C))), M:tm-882, m:tm-916, u:((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82430
in-theory        82430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     39
proof            (modus-ponens tm-855 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
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-82430.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-855, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82431
in-theory        82431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-808 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-82431.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-808, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82432
in-theory        82432
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((E and ((((A or B) -> C) and D) or ((A or B) -> C))) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C)))
theorem-size     59
proof            (modus-ponens tm-798 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3 tm-7)
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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-82432.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((E and ((((A or B) -> C) and D) or ((A or B) -> C))) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C))), M:tm-798, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82433
in-theory        82433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-757 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-82433.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-757, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82434
in-theory        82434
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((((((A or B) -> C) and D) or ((A or B) -> C)) and E) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C)))
theorem-size     59
proof            (modus-ponens tm-747 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82434.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((((((A or B) -> C) and D) or ((A or B) -> C)) and E) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C))), M:tm-747, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82435
in-theory        82435
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) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     47
proof            (modus-ponens tm-708 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82435.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-708, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82436
in-theory        82436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-665 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82436.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-665, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82437
in-theory        82437
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E or ((B or (A or B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-623 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or 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-50.           (((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-82437.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E or ((B or (A or B)) -> C))), M:tm-623, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82438
in-theory        82438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-622 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or 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-50.           (((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-82438.        ((A -> (B -> (C or B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-622, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82439
in-theory        82439
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or 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-50.           (((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-82439.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (F or E))), M:tm-609, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82440
in-theory        82440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-605 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
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-50.           (((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-82440.        ((A -> ((B -> (C or B)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-605, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82441
in-theory        82441
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (F or E)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-595 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-82441.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (F or E)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))), M:tm-595, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82442
in-theory        82442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-550 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-50.           (((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-82442.        (((A -> (B or A)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-550, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82443
in-theory        82443
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-540 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-50.           (((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-82443.        ((A or (B -> (C or B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-540, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82444
in-theory        82444
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-530 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-50.           (((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-82444.        ((A or (B -> (B or C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-530, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82445
in-theory        82445
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-520 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
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-50.           (((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-82445.        ((A or (B -> (C -> (B and C)))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-520, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82446
in-theory        82446
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-510 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-82446.        ((A or ((B and C) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-510, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82447
in-theory        82447
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-500 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-50.           (((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-82447.        ((A or ((B and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-500, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82448
in-theory        82448
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-490 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
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-50.           (((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-82448.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-490, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82449
in-theory        82449
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-480 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or 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-50.           (((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-82449.        ((A or (B -> (C -> B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-480, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82450
in-theory        82450
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((B or (A or B)) -> C) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82450.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((B or (A or B)) -> C) or E)), M:tm-470, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82451
in-theory        82451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-469 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82451.        ((A -> (B -> (B or C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-469, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82452
in-theory        82452
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-50.           (((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-82452.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (E or F))), M:tm-456, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82453
in-theory        82453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-453 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82453.        ((A -> ((B -> (B or C)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-453, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82454
in-theory        82454
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (E or F)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-443 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-50.           (((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-82454.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (E or F)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))), M:tm-443, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82455
in-theory        82455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-409 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82455.        (((A -> (A or B)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-409, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82456
in-theory        82456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-400 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82456.        (((A -> (B -> (A and B))) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-400, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82457
in-theory        82457
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-391 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82457.        ((((A and B) -> B) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-391, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82458
in-theory        82458
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-382 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82458.        ((((A and B) -> A) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-382, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82459
in-theory        82459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-373 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82459.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-373, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82460
in-theory        82460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-364 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82460.        (((A -> (B -> A)) or C) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-364, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82461
in-theory        82461
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E -> (((B or (A or B)) -> C) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-50.           (((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-82461.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E -> (((B or (A or B)) -> C) and E))), M:tm-355, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82462
in-theory        82462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-354 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82462.        ((A -> (B -> (C -> (B and C)))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-354, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82463
in-theory        82463
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-50.           (((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-82463.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82464
in-theory        82464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-338 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82464.        (((A -> B) -> (A -> (A and B))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-338, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82465
in-theory        82465
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((((A or B) -> C) and D) or ((A or B) -> C)) and ((B or (A or B)) -> C))))
theorem-size     57
proof            (modus-ponens tm-328 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82465.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((((A or B) -> C) and D) or ((A or B) -> C)) and ((B or (A or B)) -> C)))), M:tm-328, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82466
in-theory        82466
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (F -> (E and F))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))))
theorem-size     51
proof            (modus-ponens tm-327 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-50.           (((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-82466.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (F -> (E and F))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))), M:tm-327, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82467
in-theory        82467
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((E and F) -> F) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-326 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-50.           (((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-82467.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((E and F) -> F) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))), M:tm-326, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82468
in-theory        82468
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((E and F) -> E) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-325 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-50.           (((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-82468.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((E and F) -> E) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))), M:tm-325, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82469
in-theory        82469
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))))
theorem-size     57
proof            (modus-ponens tm-324 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82469.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))), M:tm-324, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82470
in-theory        82470
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (F -> E)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-323 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-50.           (((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-82470.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (F -> E)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))), M:tm-323, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82471
in-theory        82471
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-50.           (((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-82471.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82472
in-theory        82472
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82472.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82473
in-theory        82473
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-50.           (((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-82473.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82474
in-theory        82474
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((((A or B) -> C) and D) or ((A or B) -> C))))
theorem-size     49
proof            (modus-ponens tm-316 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-50.           (((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-82474.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((((A or B) -> C) and D) or ((A or B) -> C)))), M:tm-316, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82475
in-theory        82475
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-50.           (((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-82475.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82476
in-theory        82476
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (not ((B or (A or B)) -> C))) -> (not ((((A or B) -> C) and D) or ((A or B) -> C)))))
theorem-size     59
proof            (modus-ponens tm-313 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-50.           (((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-82476.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (not ((B or (A or B)) -> C))) -> (not ((((A or B) -> C) and D) or ((A or B) -> C))))), M:tm-313, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82477
in-theory        82477
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((((B or (A or B)) -> C) -> E) -> ((((((A or B) -> C) and D) or ((A or B) -> C)) or ((B or (A or B)) -> C)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82477.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((((B or (A or B)) -> C) -> E) -> ((((((A or B) -> C) and D) or ((A or B) -> C)) or ((B or (A or B)) -> C)) -> E))), M:tm-312, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82478
in-theory        82478
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E or (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-311 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
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-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-50.           (((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-82478.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E or (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))), M:tm-311, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82479
in-theory        82479
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((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)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-50.           (((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-82479.        ((((((A or B) -> C) and D) or ((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)) or E)), M:tm-310, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82480
in-theory        82480
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-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-50.           (((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-82480.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and E))), M:tm-309, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82481
in-theory        82481
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((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))) -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> C)))
theorem-size     57
proof            (modus-ponens tm-306 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (or Bm (or Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-306.          ((A -> (B -> C)) -> ((A -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82481.        ((((((A or B) -> C) and D) or ((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))) -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> C))), M:tm-306, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (or Bm (or Am Bm))) (C Cm))
================================================================
tm-name          tm-82482
in-theory        82482
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-305 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-50.           (((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-82482.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and (E -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))), M:tm-305, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82483
in-theory        82483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-303 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82483.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-303, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82484
in-theory        82484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-270 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82484.        ((A -> (((B and C) -> C) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-270, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82485
in-theory        82485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-239 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82485.        ((A -> (((B and C) -> B) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-239, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82486
in-theory        82486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-210 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-50.           (((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-82486.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-210, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82487
in-theory        82487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-183 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82487.        ((A -> ((B -> (C -> B)) and A)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-183, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82488
in-theory        82488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-157 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82488.        ((A -> ((B and C) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-157, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82489
in-theory        82489
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-147 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-50.           (((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-82489.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-147, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82490
in-theory        82490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-134 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-50.           (((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-82490.        ((A -> ((B and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-134, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82491
in-theory        82491
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-125 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-50.           (((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-82491.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-125, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82492
in-theory        82492
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> (C -> D)) and E) or ((A or B) -> (C -> D))) -> (((B or (A or B)) -> C) -> ((B or (A or B)) -> D)))
theorem-size     33
proof            (modus-ponens tm-114 tm-916 ((A (or (and (-> (or Am Bm) (-> C D)) Dm) (-> (or Am Bm) (-> C D)))) (B (or Bm (or Am Bm))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82492.        (((((A or B) -> (C -> D)) and E) or ((A or B) -> (C -> D))) -> (((B or (A or B)) -> C) -> ((B or (A or B)) -> D))), M:tm-114, m:tm-916, u:((A (or (and (-> (or Am Bm) (-> C D)) Dm) (-> (or Am Bm) (-> C D)))) (B (or Bm (or Am Bm))) (Cm (-> C D)))
================================================================
tm-name          tm-82493
in-theory        82493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-113 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82493.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-113, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82494
in-theory        82494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-105 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82494.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-105, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82495
in-theory        82495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-95 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-50.           (((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-82495.        (((A -> B) -> (A -> A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-95, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82496
in-theory        82496
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E -> ((B or (A or B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-84 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82496.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (E -> ((B or (A or B)) -> C))), M:tm-84, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82497
in-theory        82497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-83 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82497.        ((A -> (B -> (C -> B))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-83, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82498
in-theory        82498
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-76 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82498.        (((not (not A)) -> A) and (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((C or (B or C)) -> D))), M:tm-76, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82499
in-theory        82499
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A or B) -> C) and D) or ((A or B) -> C)))) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C))
theorem-size     37
proof            (modus-ponens tm-73 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-10 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82499.        (((not (not ((((A or B) -> C) and D) or ((A or B) -> C)))) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C)), M:tm-73, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82500
in-theory        82500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-69 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82500.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-69, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82501
in-theory        82501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-54 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-82501.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-54, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82502
in-theory        82502
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C))
theorem-size     27
proof            (modus-ponens tm-50 tm-916 ((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-7 tm-3)
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-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-82502.        ((((A or B) -> C) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C)), M:tm-50, m:tm-916, u:((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82503
in-theory        82503
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) 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-49 tm-916 ((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-6 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82503.        (((((A or B) -> C) and D) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C)), M:tm-49, m:tm-916, u:((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82504
in-theory        82504
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B or C) -> D) and E) or ((B or C) -> D))) or ((((B or C) -> D) and E) or ((B or C) -> D))) -> ((C or (B or C)) -> D))
theorem-size     37
proof            (modus-ponens tm-47 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82504.        (((A and ((((B or C) -> D) and E) or ((B or C) -> D))) or ((((B or C) -> D) and E) or ((B or C) -> D))) -> ((C or (B or C)) -> D)), M:tm-47, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82505
in-theory        82505
times-derived    1
----------------------------------------------------------------
theorem          (((((((A or B) -> C) and D) or ((A or B) -> C)) and E) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C))
theorem-size     37
proof            (modus-ponens tm-46 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82505.        (((((((A or B) -> C) and D) or ((A or B) -> C)) and E) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C)), M:tm-46, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82506
in-theory        82506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-42 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-50.           (((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-82506.        ((A -> (B or A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-42, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82507
in-theory        82507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-32 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82507.        ((A -> (A or B)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-32, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82508
in-theory        82508
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((((A or B) -> C) and D) or ((A or B) -> C)) and ((B or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-24 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (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       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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82508.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((((A or B) -> C) and D) or ((A or B) -> C)) and ((B or (A or B)) -> C))), M:tm-24, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82509
in-theory        82509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-23 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-50.           (((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-82509.        ((A -> (B -> (A and B))) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-23, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82510
in-theory        82510
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-22 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82510.        (((A and B) -> B) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-22, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82511
in-theory        82511
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-21 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82511.        (((A and B) -> A) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-21, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82512
in-theory        82512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-20 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-50.           (((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-82512.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-20, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82513
in-theory        82513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-19 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82513.        ((A -> (B -> A)) and (((((C or D) -> E) and F) or ((C or D) -> E)) -> ((D or (C or D)) -> E))), M:tm-19, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82514
in-theory        82514
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (not ((B or (A or B)) -> C))) -> (not ((((A or B) -> C) and D) or ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-9 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-9 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82514.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (not ((B or (A or B)) -> C))) -> (not ((((A or B) -> C) and D) or ((A or B) -> C)))), M:tm-9, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82515
in-theory        82515
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> ((((((B or A) -> C) and E) or ((B or A) -> C)) or ((A or (B or A)) -> C)) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82515.        ((((A or (B or A)) -> C) -> D) -> ((((((B or A) -> C) and E) or ((B or A) -> C)) or ((A or (B or A)) -> C)) -> D)), M:tm-8, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-82516
in-theory        82516
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-7 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-7 tm-8 tm-3)
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-50.           (((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-82516.        (A or (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((C or (B or C)) -> D))), M:tm-7, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82517
in-theory        82517
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-6 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82517.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) or E), M:tm-6, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82518
in-theory        82518
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B or C) -> D) and E) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
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-82518.        (A -> ((((((B or C) -> D) and E) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and A)), M:tm-5, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82519
in-theory        82519
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (B or (A or B))) -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> C))
theorem-size     35
proof            (modus-ponens tm-2 tm-916 ((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (or Bm (or Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82519.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> (B or (A or B))) -> (((((A or B) -> C) and D) or ((A or B) -> C)) -> C)), M:tm-2, m:tm-916, u:((A (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm))) (B (or Bm (or Am Bm))) (C Cm))
================================================================
tm-name          tm-82520
in-theory        82520
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((C or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-1 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-1 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82520.        (A -> (((((B or C) -> D) and E) or ((B or C) -> D)) -> ((C or (B or C)) -> D))), M:tm-1, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-82521
in-theory        82521
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-893 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-7)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-82521.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-893, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82522
in-theory        82522
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((A or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A)))
theorem-size     33
proof            (modus-ponens tm-882 tm-917 ((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-82522.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((A or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A))), M:tm-882, m:tm-917, u:((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82523
in-theory        82523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     33
proof            (modus-ponens tm-855 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-82523.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-855, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82524
in-theory        82524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     27
proof            (modus-ponens tm-808 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-7)
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-82524.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-808, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82525
in-theory        82525
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((D and (A or ((B or C) -> A))) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A)))
theorem-size     41
proof            (modus-ponens tm-798 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-82525.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((D and (A or ((B or C) -> A))) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A))), M:tm-798, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82526
in-theory        82526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82526.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-757, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82527
in-theory        82527
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((((A or ((B or C) -> A)) and D) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A)))
theorem-size     41
proof            (modus-ponens tm-747 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-50.           (((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-82527.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((((A or ((B or C) -> A)) and D) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A))), M:tm-747, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82528
in-theory        82528
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82528.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E))), M:tm-708, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82529
in-theory        82529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82529.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-665, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82530
in-theory        82530
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (D or ((C or (B or C)) -> A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or 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-50.           (((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-82530.        ((A or ((B or C) -> A)) -> (D or ((C or (B or C)) -> A))), M:tm-623, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82531
in-theory        82531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82531.        ((A -> (B -> (C or B))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-622, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82532
in-theory        82532
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82532.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (E or D))), M:tm-609, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82533
in-theory        82533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82533.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-605, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82534
in-theory        82534
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (E or D)) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82534.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (E or D)) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)))), M:tm-595, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82535
in-theory        82535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82535.        (((A -> (B or A)) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-550, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82536
in-theory        82536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82536.        ((A or (B -> (C or B))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-540, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82537
in-theory        82537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82537.        ((A or (B -> (B or C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-530, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82538
in-theory        82538
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82538.        ((A or (B -> (C -> (B and C)))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-520, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82539
in-theory        82539
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82539.        ((A or ((B and C) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-510, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82540
in-theory        82540
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82540.        ((A or ((B and C) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-500, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82541
in-theory        82541
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82541.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E))), M:tm-490, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82542
in-theory        82542
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82542.        ((A or (B -> (C -> B))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-480, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82543
in-theory        82543
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (((C or (B or C)) -> A) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-50.           (((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-82543.        ((A or ((B or C) -> A)) -> (((C or (B or C)) -> A) or D)), M:tm-470, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82544
in-theory        82544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82544.        ((A -> (B -> (B or C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-469, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82545
in-theory        82545
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-50.           (((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-82545.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (D or E))), M:tm-456, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82546
in-theory        82546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-50.           (((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-82546.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-453, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82547
in-theory        82547
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (D or E)) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-50.           (((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-82547.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (D or E)) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)))), M:tm-443, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82548
in-theory        82548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-50.           (((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-82548.        (((A -> (A or B)) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-409, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82549
in-theory        82549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-50.           (((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-82549.        (((A -> (B -> (A and B))) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-400, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82550
in-theory        82550
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-50.           (((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-82550.        ((((A and B) -> B) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-391, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82551
in-theory        82551
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-50.           (((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-82551.        ((((A and B) -> A) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-382, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82552
in-theory        82552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82552.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E))), M:tm-373, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82553
in-theory        82553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82553.        (((A -> (B -> A)) or C) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-364, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82554
in-theory        82554
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (D -> (((C or (B or C)) -> A) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-50.           (((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-82554.        ((A or ((B or C) -> A)) -> (D -> (((C or (B or C)) -> A) and D))), M:tm-355, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82555
in-theory        82555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82555.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-354, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82556
in-theory        82556
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-50.           (((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-82556.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82557
in-theory        82557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-50.           (((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-82557.        (((A -> B) -> (A -> (A and B))) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C))), M:tm-338, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82558
in-theory        82558
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((A or ((B or C) -> A)) -> ((A or ((B or C) -> A)) and ((C or (B or C)) -> A))))
theorem-size     39
proof            (modus-ponens tm-328 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-50.           (((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-82558.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((A or ((B or C) -> A)) -> ((A or ((B or C) -> A)) and ((C or (B or C)) -> A)))), M:tm-328, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82559
in-theory        82559
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (E -> (D and E))) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-50.           (((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-82559.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (E -> (D and E))) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)))), M:tm-327, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82560
in-theory        82560
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((D and E) -> E) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-50.           (((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-82560.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((D and E) -> E) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)))), M:tm-326, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82561
in-theory        82561
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((D and E) -> D) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-50.           (((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-82561.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((D and E) -> D) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)))), M:tm-325, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82562
in-theory        82562
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-50.           (((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-82562.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)))), M:tm-324, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82563
in-theory        82563
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (E -> D)) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-50.           (((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-82563.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (E -> D)) and ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)))), M:tm-323, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82564
in-theory        82564
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-50.           (((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-82564.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D and E) -> E)), M:tm-322, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82565
in-theory        82565
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-50.           (((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-82565.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D and E) -> D)), M:tm-320, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82566
in-theory        82566
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-50.           (((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-82566.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82567
in-theory        82567
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((A or ((B or C) -> A)) -> (A or ((B or C) -> A))))
theorem-size     31
proof            (modus-ponens tm-316 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-50.           (((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-82567.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((A or ((B or C) -> A)) -> (A or ((B or C) -> A)))), M:tm-316, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82568
in-theory        82568
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-50.           (((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-82568.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (E -> D))), M:tm-315, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82569
in-theory        82569
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> (not ((C or (B or C)) -> A))) -> (not (A or ((B or C) -> A)))))
theorem-size     41
proof            (modus-ponens tm-313 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-50.           (((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-82569.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> (not ((C or (B or C)) -> A))) -> (not (A or ((B or C) -> A))))), M:tm-313, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82570
in-theory        82570
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((((C or (B or C)) -> A) -> D) -> (((A or ((B or C) -> A)) or ((C or (B or C)) -> A)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
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-312.          ((A -> B) -> ((A -> B) and ((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-50.           (((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-82570.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((((C or (B or C)) -> A) -> D) -> (((A or ((B or C) -> A)) or ((C or (B or C)) -> A)) -> D))), M:tm-312, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82571
in-theory        82571
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D or ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82571.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D or ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)))), M:tm-311, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82572
in-theory        82572
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-50.           (((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-82572.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) or D)), M:tm-310, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82573
in-theory        82573
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
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-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-50.           (((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-82573.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and D))), M:tm-309, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82574
in-theory        82574
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> (C or (B or C))) -> ((A or ((B or C) -> A)) -> A)))
theorem-size     39
proof            (modus-ponens tm-306 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (or Cm (or Bm Cm))) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-50.           (((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-82574.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (((A or ((B or C) -> A)) -> (C or (B or C))) -> ((A or ((B or C) -> A)) -> A))), M:tm-306, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (or Cm (or Bm Cm))) (C Am))
================================================================
tm-name          tm-82575
in-theory        82575
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) 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-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-50.           (((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-82575.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and (D -> ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)))), M:tm-305, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82576
in-theory        82576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-50.           (((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-82576.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-303, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82577
in-theory        82577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82577.        ((A -> (((B and C) -> C) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-270, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82578
in-theory        82578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82578.        ((A -> (((B and C) -> B) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-239, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82579
in-theory        82579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-50.           (((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-82579.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E))), M:tm-210, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82580
in-theory        82580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82580.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-183, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82581
in-theory        82581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82581.        ((A -> ((B and C) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-157, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82582
in-theory        82582
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-50.           (((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-82582.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-147, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82583
in-theory        82583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82583.        ((A -> ((B and C) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-134, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82584
in-theory        82584
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-50.           (((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-82584.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-125, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82585
in-theory        82585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C or D) -> (A -> B))) -> (((D or (C or D)) -> A) -> ((D or (C or D)) -> B)))
theorem-size     27
proof            (modus-ponens tm-114 tm-917 ((A (or (-> C D) (-> (or Bm Cm) (-> C D)))) (B (or Cm (or Bm Cm))) (Am (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 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-14.           (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82585.        (((A -> B) or ((C or D) -> (A -> B))) -> (((D or (C or D)) -> A) -> ((D or (C or D)) -> B))), M:tm-114, m:tm-917, u:((A (or (-> C D) (-> (or Bm Cm) (-> C D)))) (B (or Cm (or Bm Cm))) (Am (-> C D)))
================================================================
tm-name          tm-82586
in-theory        82586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82586.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E))), M:tm-113, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82587
in-theory        82587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-50.           (((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-82587.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-105, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82588
in-theory        82588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-50.           (((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-82588.        (((A -> B) -> (A -> A)) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C))), M:tm-95, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82589
in-theory        82589
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (D -> ((C or (B or C)) -> A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-50.           (((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-82589.        ((A or ((B or C) -> A)) -> (D -> ((C or (B or C)) -> A))), M:tm-84, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82590
in-theory        82590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82590.        ((A -> (B -> (C -> B))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-83, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82591
in-theory        82591
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C or D) -> B)) -> ((D or (C or D)) -> B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82591.        (((not (not A)) -> A) and ((B or ((C or D) -> B)) -> ((D or (C or D)) -> B))), M:tm-76, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82592
in-theory        82592
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or ((B or C) -> A)))) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A))
theorem-size     25
proof            (modus-ponens tm-73 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82592.        (((not (not (A or ((B or C) -> A)))) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A)), M:tm-73, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82593
in-theory        82593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82593.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C))), M:tm-69, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82594
in-theory        82594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-82594.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-54, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82595
in-theory        82595
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or (C or ((A or B) -> C))) -> ((B or (A or B)) -> C))
theorem-size     21
proof            (modus-ponens tm-50 tm-917 ((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Cm (or 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-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-82595.        ((((A or B) -> C) or (C or ((A or B) -> C))) -> ((B or (A or B)) -> C)), M:tm-50, m:tm-917, u:((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82596
in-theory        82596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A))
theorem-size     17
proof            (modus-ponens tm-49 tm-917 ((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82596.        ((A or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A)), M:tm-49, m:tm-917, u:((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82597
in-theory        82597
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or ((C or D) -> B))) or (B or ((C or D) -> B))) -> ((D or (C or D)) -> B))
theorem-size     25
proof            (modus-ponens tm-47 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82597.        (((A and (B or ((C or D) -> B))) or (B or ((C or D) -> B))) -> ((D or (C or D)) -> B)), M:tm-47, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82598
in-theory        82598
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B or C) -> A)) and D) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A))
theorem-size     25
proof            (modus-ponens tm-46 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82598.        ((((A or ((B or C) -> A)) and D) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A)), M:tm-46, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82599
in-theory        82599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82599.        ((A -> (B or A)) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C))), M:tm-42, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82600
in-theory        82600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82600.        ((A -> (A or B)) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C))), M:tm-32, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82601
in-theory        82601
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> ((A or ((B or C) -> A)) and ((C or (B or C)) -> A)))
theorem-size     23
proof            (modus-ponens tm-24 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82601.        ((A or ((B or C) -> A)) -> ((A or ((B or C) -> A)) and ((C or (B or C)) -> A))), M:tm-24, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82602
in-theory        82602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-50.           (((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-82602.        ((A -> (B -> (A and B))) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C))), M:tm-23, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82603
in-theory        82603
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82603.        (((A and B) -> B) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C))), M:tm-22, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82604
in-theory        82604
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82604.        (((A and B) -> A) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C))), M:tm-21, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82605
in-theory        82605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-50.           (((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-82605.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-20, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82606
in-theory        82606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
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-19.           (A -> ((B -> (C -> B)) and 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-50.           (((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-82606.        ((A -> (B -> A)) and ((C or ((D or E) -> C)) -> ((E or (D or E)) -> C))), M:tm-19, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82607
in-theory        82607
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> (not ((C or (B or C)) -> A))) -> (not (A or ((B or C) -> A))))
theorem-size     25
proof            (modus-ponens tm-9 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-9 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82607.        (((A or ((B or C) -> A)) -> (not ((C or (B or C)) -> A))) -> (not (A or ((B or C) -> A)))), M:tm-9, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82608
in-theory        82608
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> (((C or ((B or A) -> C)) or ((A or (B or A)) -> C)) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82608.        ((((A or (B or A)) -> C) -> D) -> (((C or ((B or A) -> C)) or ((A or (B or A)) -> C)) -> D)), M:tm-8, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-82609
in-theory        82609
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or ((C or D) -> B)) -> ((D or (C or D)) -> B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or 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-50.           (((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-82609.        (A or ((B or ((C or D) -> B)) -> ((D or (C or D)) -> B))), M:tm-7, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82610
in-theory        82610
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-6 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82610.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) or D), M:tm-6, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82611
in-theory        82611
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C or D) -> B)) -> ((D or (C or D)) -> B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82611.        (A -> (((B or ((C or D) -> B)) -> ((D or (C or D)) -> B)) and A)), M:tm-5, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82612
in-theory        82612
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> (C or (B or C))) -> ((A or ((B or C) -> A)) -> A))
theorem-size     23
proof            (modus-ponens tm-2 tm-917 ((A (or Am (-> (or Bm Cm) Am))) (B (or Cm (or Bm Cm))) (C Am)))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82612.        (((A or ((B or C) -> A)) -> (C or (B or C))) -> ((A or ((B or C) -> A)) -> A)), M:tm-2, m:tm-917, u:((A (or Am (-> (or Bm Cm) Am))) (B (or Cm (or Bm Cm))) (C Am))
================================================================
tm-name          tm-82613
in-theory        82613
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or ((C or D) -> B)) -> ((D or (C or D)) -> B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82613.        (A -> ((B or ((C or D) -> B)) -> ((D or (C or D)) -> B))), M:tm-1, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-82614
in-theory        82614
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-50.           (((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-82614.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-893, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82615
in-theory        82615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-50.           (((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-82615.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-855, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82616
in-theory        82616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-50.           (((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-82616.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-808, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82617
in-theory        82617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-50.           (((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-82617.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-757, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82618
in-theory        82618
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 or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-50.           (((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-82618.        (((((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 or (G or H)) -> I)))), M:tm-708, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82619
in-theory        82619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82619.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-665, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82620
in-theory        82620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82620.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-622, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82621
in-theory        82621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82621.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82622
in-theory        82622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-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-82622.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-605, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82623
in-theory        82623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-82623.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-595, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82624
in-theory        82624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-50.           (((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-82624.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-550, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82625
in-theory        82625
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-82625.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-540, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82626
in-theory        82626
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-50.           (((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-82626.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-530, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82627
in-theory        82627
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-82627.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-520, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82628
in-theory        82628
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-82628.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-510, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82629
in-theory        82629
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-50.           (((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-82629.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-500, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82630
in-theory        82630
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-50.           (((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-82630.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-490, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82631
in-theory        82631
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82631.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-480, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82632
in-theory        82632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82632.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-469, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82633
in-theory        82633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82633.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82634
in-theory        82634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82634.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-453, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82635
in-theory        82635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-50.           (((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-82635.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-443, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82636
in-theory        82636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-50.           (((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-82636.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-409, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82637
in-theory        82637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82637.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-400, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82638
in-theory        82638
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-50.           (((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-82638.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-391, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82639
in-theory        82639
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-50.           (((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-82639.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-382, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82640
in-theory        82640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82640.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-373, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82641
in-theory        82641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82641.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-364, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82642
in-theory        82642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82642.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-354, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82643
in-theory        82643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82643.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82644
in-theory        82644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82644.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-338, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82645
in-theory        82645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82645.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-327, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82646
in-theory        82646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-50.           (((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-82646.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-326, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82647
in-theory        82647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-50.           (((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-82647.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-325, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82648
in-theory        82648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82648.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-324, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82649
in-theory        82649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82649.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-323, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82650
in-theory        82650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82650.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82651
in-theory        82651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82651.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82652
in-theory        82652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82652.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82653
in-theory        82653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82653.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82654
in-theory        82654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-50.           (((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-82654.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-311, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82655
in-theory        82655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-50.           (((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-82655.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)), M:tm-310, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82656
in-theory        82656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (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-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-50.           (((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-82656.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F))), M:tm-309, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82657
in-theory        82657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-918 ((A (-> Am (or Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82657.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-308, m:tm-918, u:((A (-> Am (or Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-82658
in-theory        82658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (A -> (B or A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-918 ((A (-> Am (or Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-50.           (((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-82658.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (A -> (B or A))), M:tm-307, m:tm-918, u:((A (-> Am (or Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-82659
in-theory        82659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82659.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-305, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82660
in-theory        82660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82660.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-303, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82661
in-theory        82661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82661.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-270, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82662
in-theory        82662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82662.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-239, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82663
in-theory        82663
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82663.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-210, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82664
in-theory        82664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82664.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-183, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82665
in-theory        82665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82665.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-157, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82666
in-theory        82666
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 or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82666.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-147, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82667
in-theory        82667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82667.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-134, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82668
in-theory        82668
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 or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82668.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-125, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82669
in-theory        82669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82669.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-113, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82670
in-theory        82670
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 or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-50.           (((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-82670.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-105, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82671
in-theory        82671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82671.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-95, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82672
in-theory        82672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82672.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-83, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82673
in-theory        82673
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82673.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-76, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82674
in-theory        82674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82674.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-69, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82675
in-theory        82675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-82675.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-54, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82676
in-theory        82676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-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-82676.        ((A -> (B or A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-42, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82677
in-theory        82677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82677.        ((A -> (A or B)) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-32, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82678
in-theory        82678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (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-23.           (A -> ((B -> (C -> (B and 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-50.           (((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-82678.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-23, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82679
in-theory        82679
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82679.        (((A and B) -> B) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-22, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82680
in-theory        82680
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82680.        (((A and B) -> A) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-21, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82681
in-theory        82681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-82681.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-20, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82682
in-theory        82682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82682.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-19, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82683
in-theory        82683
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-7 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-8)
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-50.           (((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-82683.        (A or ((B -> (C or B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-7, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82684
in-theory        82684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8)
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-50.           (((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-82684.        (((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F), M:tm-6, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82685
in-theory        82685
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-82685.        (A -> (((B -> (C or B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A)), M:tm-5, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82686
in-theory        82686
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-1 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82686.        (A -> ((B -> (C or B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-1, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82687
in-theory        82687
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-82687.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-893, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82688
in-theory        82688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-82688.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-855, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82689
in-theory        82689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-82689.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-808, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82690
in-theory        82690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-50.           (((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-82690.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-757, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82691
in-theory        82691
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 or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82691.        (((((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 or (G or H)) -> I)))), M:tm-708, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82692
in-theory        82692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-50.           (((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-82692.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-665, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82693
in-theory        82693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82693.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-622, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82694
in-theory        82694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82694.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82695
in-theory        82695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-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-82695.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-605, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82696
in-theory        82696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-82696.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-595, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82697
in-theory        82697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-50.           (((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-82697.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-550, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82698
in-theory        82698
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-50.           (((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-82698.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-540, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82699
in-theory        82699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-50.           (((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-82699.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-530, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82700
in-theory        82700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-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-82700.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-520, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82701
in-theory        82701
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-82701.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-510, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82702
in-theory        82702
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-50.           (((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-82702.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-500, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82703
in-theory        82703
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-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-82703.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-490, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82704
in-theory        82704
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-82704.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-480, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82705
in-theory        82705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82705.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-469, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82706
in-theory        82706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82706.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82707
in-theory        82707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82707.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-453, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82708
in-theory        82708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-82708.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-443, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82709
in-theory        82709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82709.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-409, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82710
in-theory        82710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82710.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-400, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82711
in-theory        82711
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82711.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-391, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82712
in-theory        82712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82712.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-382, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82713
in-theory        82713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82713.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-373, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82714
in-theory        82714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82714.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-364, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82715
in-theory        82715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82715.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-354, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82716
in-theory        82716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82716.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82717
in-theory        82717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82717.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-338, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82718
in-theory        82718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82718.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-327, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82719
in-theory        82719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82719.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-326, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82720
in-theory        82720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82720.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-325, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82721
in-theory        82721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82721.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-324, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82722
in-theory        82722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82722.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-323, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82723
in-theory        82723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82723.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82724
in-theory        82724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82724.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82725
in-theory        82725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82725.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82726
in-theory        82726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82726.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82727
in-theory        82727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-50.           (((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-82727.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-311, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82728
in-theory        82728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82728.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)), M:tm-310, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82729
in-theory        82729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82729.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F))), M:tm-309, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82730
in-theory        82730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-919 ((A (-> Am (or Am Bm))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-82730.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-308, m:tm-919, u:((A (-> Am (or Am Bm))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-82731
in-theory        82731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (A -> (A or B)))
theorem-size     25
proof            (modus-ponens tm-307 tm-919 ((A (-> Am (or Am Bm))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82731.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (A -> (A or B))), M:tm-307, m:tm-919, u:((A (-> Am (or Am Bm))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-82732
in-theory        82732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82732.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-305, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82733
in-theory        82733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82733.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-303, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82734
in-theory        82734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82734.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-270, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82735
in-theory        82735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82735.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-239, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82736
in-theory        82736
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82736.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-210, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82737
in-theory        82737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82737.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-183, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82738
in-theory        82738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82738.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-157, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82739
in-theory        82739
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 or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82739.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-147, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82740
in-theory        82740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82740.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-134, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82741
in-theory        82741
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 or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82741.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-125, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82742
in-theory        82742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82742.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-113, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82743
in-theory        82743
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 or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82743.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-105, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82744
in-theory        82744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82744.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-95, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82745
in-theory        82745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82745.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-83, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82746
in-theory        82746
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82746.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-76, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82747
in-theory        82747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82747.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-69, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82748
in-theory        82748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-82748.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-54, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82749
in-theory        82749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-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-82749.        ((A -> (B or A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-42, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82750
in-theory        82750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82750.        ((A -> (A or B)) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-32, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82751
in-theory        82751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-82751.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-23, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82752
in-theory        82752
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82752.        (((A and B) -> B) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-22, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82753
in-theory        82753
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82753.        (((A and B) -> A) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-21, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82754
in-theory        82754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-82754.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-20, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82755
in-theory        82755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82755.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-19, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82756
in-theory        82756
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-7 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8)
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-50.           (((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-82756.        (A or ((B -> (B or C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-7, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82757
in-theory        82757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82757.        (((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F), M:tm-6, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82758
in-theory        82758
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82758.        (A -> (((B -> (B or C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A)), M:tm-5, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82759
in-theory        82759
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-1 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82759.        (A -> ((B -> (B or C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-1, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-82760
in-theory        82760
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (A or B))) and ((B or (A or B)) -> (C -> (A or B))))
theorem-size     21
proof            (modus-ponens tm-920 tm-1 ((Am (or A B)) (C (-> Bm (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-82760.        (((A or B) -> (C -> (A or B))) and ((B or (A or B)) -> (C -> (A or B)))), M:tm-920, m:tm-1, u:((Am (or A B)) (C (-> Bm (or A B))))
================================================================
tm-name          tm-82761
in-theory        82761
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((A or B) and C))) and ((B or (A or B)) -> (C -> ((A or B) and C))))
theorem-size     25
proof            (modus-ponens tm-920 tm-5 ((Am (or A B)) (C (-> Bm (and (or A B) Bm)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82761.        (((A or B) -> (C -> ((A or B) and C))) and ((B or (A or B)) -> (C -> ((A or B) and C)))), M:tm-920, m:tm-5, u:((Am (or A B)) (C (-> Bm (and (or A B) Bm))))
================================================================
tm-name          tm-82762
in-theory        82762
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) or C)) and ((B or (A or B)) -> ((A or B) or C)))
theorem-size     21
proof            (modus-ponens tm-920 tm-6 ((Am (or A B)) (C (or (or A B) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-82762.        (((A or B) -> ((A or B) or C)) and ((B or (A or B)) -> ((A or B) or C))), M:tm-920, m:tm-6, u:((Am (or A B)) (C (or (or A B) Bm)))
================================================================
tm-name          tm-82763
in-theory        82763
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (A or B))) and ((B or (A or B)) -> (C or (A or B))))
theorem-size     21
proof            (modus-ponens tm-920 tm-7 ((Am (or A B)) (C (or Bm (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-82763.        (((A or B) -> (C or (A or B))) and ((B or (A or B)) -> (C or (A or B)))), M:tm-920, m:tm-7, u:((Am (or A B)) (C (or Bm (or A B))))
================================================================
tm-name          tm-82764
in-theory        82764
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> C))) and ((B or (A or B)) -> (C -> (D -> C))))
theorem-size     21
proof            (modus-ponens tm-920 tm-11 ((Am (or A B)) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82764.        (((A or B) -> (C -> (D -> C))) and ((B or (A or B)) -> (C -> (D -> C)))), M:tm-920, m:tm-11, u:((Am (or A B)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-82765
in-theory        82765
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((B or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-14 ((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-82765.        (((A or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((B or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-920, m:tm-14, u:((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-82766
in-theory        82766
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C and D) -> C)) and ((B or (A or B)) -> ((C and D) -> C)))
theorem-size     21
proof            (modus-ponens tm-920 tm-16 ((Am (or A B)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-82766.        (((A or B) -> ((C and D) -> C)) and ((B or (A or B)) -> ((C and D) -> C))), M:tm-920, m:tm-16, u:((Am (or A B)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-82767
in-theory        82767
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C and D) -> D)) and ((B or (A or B)) -> ((C and D) -> D)))
theorem-size     21
proof            (modus-ponens tm-920 tm-18 ((Am (or A B)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-82767.        (((A or B) -> ((C and D) -> D)) and ((B or (A or B)) -> ((C and D) -> D))), M:tm-920, m:tm-18, u:((Am (or A B)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-82768
in-theory        82768
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> C)) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> C)) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-920 tm-19 ((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82768.        (((A or B) -> ((C -> (D -> C)) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> C)) and (A or B)))), M:tm-920, m:tm-19, u:((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B))))
================================================================
tm-name          tm-82769
in-theory        82769
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((B or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-920 tm-20 ((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-82769.        (((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and ((B or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))), M:tm-920, m:tm-20, u:((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B))))
================================================================
tm-name          tm-82770
in-theory        82770
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and D) -> C) and (A or B))) and ((B or (A or B)) -> (((C and D) -> C) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-920 tm-21 ((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-82770.        (((A or B) -> (((C and D) -> C) and (A or B))) and ((B or (A or B)) -> (((C and D) -> C) and (A or B)))), M:tm-920, m:tm-21, u:((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B))))
================================================================
tm-name          tm-82771
in-theory        82771
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and D) -> D) and (A or B))) and ((B or (A or B)) -> (((C and D) -> D) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-920 tm-22 ((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-82771.        (((A or B) -> (((C and D) -> D) and (A or B))) and ((B or (A or B)) -> (((C and D) -> D) and (A or B)))), M:tm-920, m:tm-22, u:((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B))))
================================================================
tm-name          tm-82772
in-theory        82772
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (C and D))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-23 ((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-82772.        (((A or B) -> ((C -> (D -> (C and D))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))), M:tm-920, m:tm-23, u:((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-82773
in-theory        82773
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (C and D)))) and ((B or (A or B)) -> (C -> (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-920 tm-25 ((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-82773.        (((A or B) -> (C -> (D -> (C and D)))) and ((B or (A or B)) -> (C -> (D -> (C and D))))), M:tm-920, m:tm-25, u:((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-82774
in-theory        82774
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (C or D)) and (A or B))) and ((B or (A or B)) -> ((C -> (C or D)) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-920 tm-32 ((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-82774.        (((A or B) -> ((C -> (C or D)) and (A or B))) and ((B or (A or B)) -> ((C -> (C or D)) and (A or B)))), M:tm-920, m:tm-32, u:((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B))))
================================================================
tm-name          tm-82775
in-theory        82775
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (C or D))) and ((B or (A or B)) -> (C -> (C or D))))
theorem-size     21
proof            (modus-ponens tm-920 tm-33 ((Am (or A B)) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-82775.        (((A or B) -> (C -> (C or D))) and ((B or (A or B)) -> (C -> (C or D)))), M:tm-920, m:tm-33, u:((Am (or A B)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-82776
in-theory        82776
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D or C)) and (A or B))) and ((B or (A or B)) -> ((C -> (D or C)) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-920 tm-42 ((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-82776.        (((A or B) -> ((C -> (D or C)) and (A or B))) and ((B or (A or B)) -> ((C -> (D or C)) and (A or B)))), M:tm-920, m:tm-42, u:((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B))))
================================================================
tm-name          tm-82777
in-theory        82777
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D or C))) and ((B or (A or B)) -> (C -> (D or C))))
theorem-size     21
proof            (modus-ponens tm-920 tm-43 ((Am (or A B)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-82777.        (((A or B) -> (C -> (D or C))) and ((B or (A or B)) -> (C -> (D or C)))), M:tm-920, m:tm-43, u:((Am (or A B)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-82778
in-theory        82778
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-920 tm-54 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-82778.        (((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))), M:tm-920, m:tm-54, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B))))
================================================================
tm-name          tm-82779
in-theory        82779
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((B or (A or B)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-56 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82779.        (((A or B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((B or (A or B)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-920, m:tm-56, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-82780
in-theory        82780
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B))))
theorem-size     41
proof            (modus-ponens tm-920 tm-69 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-82780.        (((A or B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B)))), M:tm-920, m:tm-69, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B))))
================================================================
tm-name          tm-82781
in-theory        82781
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((B or (A or B)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     33
proof            (modus-ponens tm-920 tm-71 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82781.        (((A or B) -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((B or (A or B)) -> ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-920, m:tm-71, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-82782
in-theory        82782
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((not (not C)) -> C) and (A or B))) and ((B or (A or B)) -> (((not (not C)) -> C) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-920 tm-76 ((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-82782.        (((A or B) -> (((not (not C)) -> C) and (A or B))) and ((B or (A or B)) -> (((not (not C)) -> C) and (A or B)))), M:tm-920, m:tm-76, u:((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B))))
================================================================
tm-name          tm-82783
in-theory        82783
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((not (not C)) -> C)) and ((B or (A or B)) -> ((not (not C)) -> C)))
theorem-size     21
proof            (modus-ponens tm-920 tm-78 ((Am (or A B)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82783.        (((A or B) -> ((not (not C)) -> C)) and ((B or (A or B)) -> ((not (not C)) -> C))), M:tm-920, m:tm-78, u:((Am (or A B)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-82784
in-theory        82784
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (E -> D))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (E -> D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-83 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-82784.        (((A or B) -> ((C -> (D -> (E -> D))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (E -> D))) and (A or B)))), M:tm-920, m:tm-83, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-82785
in-theory        82785
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (E -> D)))) and ((B or (A or B)) -> (C -> (D -> (E -> D)))))
theorem-size     25
proof            (modus-ponens tm-920 tm-85 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82785.        (((A or B) -> (C -> (D -> (E -> D)))) and ((B or (A or B)) -> (C -> (D -> (E -> D))))), M:tm-920, m:tm-85, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-82786
in-theory        82786
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (A or B)) and ((B or (A or B)) -> (A or B)))
theorem-size     17
proof            (modus-ponens tm-920 tm-86 ((Am (or A B)) (C (or A B))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-82786.        (((A or B) -> (A or B)) and ((B or (A or B)) -> (A or B))), M:tm-920, m:tm-86, u:((Am (or A B)) (C (or A B)))
================================================================
tm-name          tm-82787
in-theory        82787
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> (C -> C)) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> (C -> C)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-95 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-82787.        (((A or B) -> (((C -> D) -> (C -> C)) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> (C -> C)) and (A or B)))), M:tm-920, m:tm-95, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B))))
================================================================
tm-name          tm-82788
in-theory        82788
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> (C -> C))) and ((B or (A or B)) -> ((C -> D) -> (C -> C))))
theorem-size     25
proof            (modus-ponens tm-920 tm-97 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-82788.        (((A or B) -> ((C -> D) -> (C -> C))) and ((B or (A or B)) -> ((C -> D) -> (C -> C)))), M:tm-920, m:tm-97, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-82789
in-theory        82789
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B))) and ((B or (A or B)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B))))
theorem-size     57
proof            (modus-ponens tm-920 tm-105 ((Am (or A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (or A B)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-82789.        (((A or B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B))) and ((B or (A or B)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B)))), M:tm-920, 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-82790
in-theory        82790
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((B or (A or B)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     49
proof            (modus-ponens tm-920 tm-107 ((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82790.        (((A or B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((B or (A or B)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-920, m:tm-107, u:((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-82791
in-theory        82791
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-920 tm-113 ((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-82791.        (((A or B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B)))), M:tm-920, m:tm-113, u:((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B))))
================================================================
tm-name          tm-82792
in-theory        82792
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A or B)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     41
proof            (modus-ponens tm-920 tm-115 ((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (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-82792.        (((A or B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A or B)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-920, m:tm-115, u:((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-82793
in-theory        82793
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B))) and ((B or (A or B)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-920 tm-125 ((Am (or A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-82793.        (((A or B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B))) and ((B or (A or B)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B)))), M:tm-920, 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-82794
in-theory        82794
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((B or (A or B)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-920 tm-127 ((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82794.        (((A or B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((B or (A or B)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-920, m:tm-127, u:((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-82795
in-theory        82795
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D and E) -> D)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D and E) -> D)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-134 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-82795.        (((A or B) -> ((C -> ((D and E) -> D)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D and E) -> D)) and (A or B)))), M:tm-920, m:tm-134, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-82796
in-theory        82796
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D and E) -> D))) and ((B or (A or B)) -> (C -> ((D and E) -> D))))
theorem-size     25
proof            (modus-ponens tm-920 tm-136 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-82796.        (((A or B) -> (C -> ((D and E) -> D))) and ((B or (A or B)) -> (C -> ((D and E) -> D)))), M:tm-920, m:tm-136, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-82797
in-theory        82797
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-920 tm-147 ((Am (or A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-82797.        (((A or B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B)))), M:tm-920, 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-82798
in-theory        82798
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((B or (A or B)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     41
proof            (modus-ponens tm-920 tm-149 ((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82798.        (((A or B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((B or (A or B)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-920, m:tm-149, u:((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-82799
in-theory        82799
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D and E) -> E)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D and E) -> E)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-157 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-82799.        (((A or B) -> ((C -> ((D and E) -> E)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D and E) -> E)) and (A or B)))), M:tm-920, m:tm-157, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-82800
in-theory        82800
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D and E) -> E))) and ((B or (A or B)) -> (C -> ((D and E) -> E))))
theorem-size     25
proof            (modus-ponens tm-920 tm-159 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-82800.        (((A or B) -> (C -> ((D and E) -> E))) and ((B or (A or B)) -> (C -> ((D and E) -> E)))), M:tm-920, m:tm-159, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-82801
in-theory        82801
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (E -> D)) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (E -> D)) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-920 tm-183 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-82801.        (((A or B) -> ((C -> ((D -> (E -> D)) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (E -> D)) and C)) and (A or B)))), M:tm-920, m:tm-183, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-82802
in-theory        82802
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (E -> D)) and C))) and ((B or (A or B)) -> (C -> ((D -> (E -> D)) and C))))
theorem-size     29
proof            (modus-ponens tm-920 tm-184 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-82802.        (((A or B) -> (C -> ((D -> (E -> D)) and C))) and ((B or (A or B)) -> (C -> ((D -> (E -> D)) and C)))), M:tm-920, m:tm-184, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-82803
in-theory        82803
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B))))
theorem-size     53
proof            (modus-ponens tm-920 tm-210 ((Am (or A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (or A B)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-82803.        (((A or B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B)))), M:tm-920, 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-82804
in-theory        82804
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((B or (A or B)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     45
proof            (modus-ponens tm-920 tm-211 ((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82804.        (((A or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((B or (A or B)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-920, m:tm-211, u:((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-82805
in-theory        82805
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (((D and E) -> D) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> (((D and E) -> D) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-920 tm-239 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-82805.        (((A or B) -> ((C -> (((D and E) -> D) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> (((D and E) -> D) and C)) and (A or B)))), M:tm-920, m:tm-239, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B))))
================================================================
tm-name          tm-82806
in-theory        82806
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (((D and E) -> D) and C))) and ((B or (A or B)) -> (C -> (((D and E) -> D) and C))))
theorem-size     29
proof            (modus-ponens tm-920 tm-240 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82806.        (((A or B) -> (C -> (((D and E) -> D) and C))) and ((B or (A or B)) -> (C -> (((D and E) -> D) and C)))), M:tm-920, m:tm-240, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-82807
in-theory        82807
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (((D and E) -> E) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> (((D and E) -> E) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-920 tm-270 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-82807.        (((A or B) -> ((C -> (((D and E) -> E) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> (((D and E) -> E) and C)) and (A or B)))), M:tm-920, m:tm-270, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B))))
================================================================
tm-name          tm-82808
in-theory        82808
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (((D and E) -> E) and C))) and ((B or (A or B)) -> (C -> (((D and E) -> E) and C))))
theorem-size     29
proof            (modus-ponens tm-920 tm-271 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82808.        (((A or B) -> (C -> (((D and E) -> E) and C))) and ((B or (A or B)) -> (C -> (((D and E) -> E) and C)))), M:tm-920, m:tm-271, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-82809
in-theory        82809
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B))))
theorem-size     41
proof            (modus-ponens tm-920 tm-303 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-82809.        (((A or B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B)))), M:tm-920, m:tm-303, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B))))
================================================================
tm-name          tm-82810
in-theory        82810
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (E -> (D and E))) and C))) and ((B or (A or B)) -> (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     33
proof            (modus-ponens tm-920 tm-304 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82810.        (((A or B) -> (C -> ((D -> (E -> (D and E))) and C))) and ((B or (A or B)) -> (C -> ((D -> (E -> (D and E))) and C)))), M:tm-920, m:tm-304, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-82811
in-theory        82811
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (A or B)))) and ((B or (A or B)) -> ((A or B) and (C -> (A or B)))))
theorem-size     29
proof            (modus-ponens tm-920 tm-305 ((Am (or A B)) (C (and (or A B) (-> Bm (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-82811.        (((A or B) -> ((A or B) and (C -> (A or B)))) and ((B or (A or B)) -> ((A or B) and (C -> (A or B))))), M:tm-920, m:tm-305, u:((Am (or A B)) (C (and (or A B) (-> Bm (or A B)))))
================================================================
tm-name          tm-82812
in-theory        82812
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> ((A or B) and C)))) and ((B or (A or B)) -> ((A or B) and (C -> ((A or B) and C)))))
theorem-size     33
proof            (modus-ponens tm-920 tm-309 ((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-82812.        (((A or B) -> ((A or B) and (C -> ((A or B) and C)))) and ((B or (A or B)) -> ((A or B) and (C -> ((A or B) and C))))), M:tm-920, m:tm-309, u:((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm)))))
================================================================
tm-name          tm-82813
in-theory        82813
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((A or B) or C))) and ((B or (A or B)) -> ((A or B) and ((A or B) or C))))
theorem-size     29
proof            (modus-ponens tm-920 tm-310 ((Am (or A B)) (C (and (or A B) (or (or A B) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-82813.        (((A or B) -> ((A or B) and ((A or B) or C))) and ((B or (A or B)) -> ((A or B) and ((A or B) or C)))), M:tm-920, m:tm-310, u:((Am (or A B)) (C (and (or A B) (or (or A B) Bm))))
================================================================
tm-name          tm-82814
in-theory        82814
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C or (A or B)))) and ((B or (A or B)) -> ((A or B) and (C or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-920 tm-311 ((Am (or A B)) (C (and (or A B) (or Bm (or A B))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-82814.        (((A or B) -> ((A or B) and (C or (A or B)))) and ((B or (A or B)) -> ((A or B) and (C or (A or B))))), M:tm-920, m:tm-311, u:((Am (or A B)) (C (and (or A B) (or Bm (or A B)))))
================================================================
tm-name          tm-82815
in-theory        82815
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (D -> C)))) and ((B or (A or B)) -> ((A or B) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-920 tm-315 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-82815.        (((A or B) -> ((A or B) and (C -> (D -> C)))) and ((B or (A or B)) -> ((A or B) and (C -> (D -> C))))), M:tm-920, m:tm-315, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-82816
in-theory        82816
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((B or (A or B)) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-920 tm-318 ((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-82816.        (((A or B) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((B or (A or B)) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-920, m:tm-318, u:((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-82817
in-theory        82817
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C and D) -> C))) and ((B or (A or B)) -> ((A or B) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-920 tm-320 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-82817.        (((A or B) -> ((A or B) and ((C and D) -> C))) and ((B or (A or B)) -> ((A or B) and ((C and D) -> C)))), M:tm-920, m:tm-320, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-82818
in-theory        82818
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C and D) -> D))) and ((B or (A or B)) -> ((A or B) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-920 tm-322 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-82818.        (((A or B) -> ((A or B) and ((C and D) -> D))) and ((B or (A or B)) -> ((A or B) and ((C and D) -> D)))), M:tm-920, m:tm-322, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-82819
in-theory        82819
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (D -> C)) and (A or B)))) and ((B or (A or B)) -> ((A or B) and ((C -> (D -> C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-323 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-82819.        (((A or B) -> ((A or B) and ((C -> (D -> C)) and (A or B)))) and ((B or (A or B)) -> ((A or B) and ((C -> (D -> C)) and (A or B))))), M:tm-920, m:tm-323, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B)))))
================================================================
tm-name          tm-82820
in-theory        82820
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))) and ((B or (A or B)) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-920 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-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-82820.        (((A or B) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))) and ((B or (A or B)) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))), M:tm-920, 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-82821
in-theory        82821
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (((C and D) -> C) and (A or B)))) and ((B or (A or B)) -> ((A or B) and (((C and D) -> C) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-325 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-82821.        (((A or B) -> ((A or B) and (((C and D) -> C) and (A or B)))) and ((B or (A or B)) -> ((A or B) and (((C and D) -> C) and (A or B))))), M:tm-920, m:tm-325, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B)))))
================================================================
tm-name          tm-82822
in-theory        82822
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (((C and D) -> D) and (A or B)))) and ((B or (A or B)) -> ((A or B) and (((C and D) -> D) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-326 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-82822.        (((A or B) -> ((A or B) and (((C and D) -> D) and (A or B)))) and ((B or (A or B)) -> ((A or B) and (((C and D) -> D) and (A or B))))), M:tm-920, m:tm-326, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B)))))
================================================================
tm-name          tm-82823
in-theory        82823
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B)))) and ((B or (A or B)) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B)))))
theorem-size     41
proof            (modus-ponens tm-920 tm-327 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-82823.        (((A or B) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B)))) and ((B or (A or B)) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B))))), M:tm-920, 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-82824
in-theory        82824
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> (C -> (C and D))) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> (C -> (C and D))) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-920 tm-338 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-82824.        (((A or B) -> (((C -> D) -> (C -> (C and D))) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> (C -> (C and D))) and (A or B)))), M:tm-920, m:tm-338, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-82825
in-theory        82825
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> (C -> (C and D)))) and ((B or (A or B)) -> ((C -> D) -> (C -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-920 tm-340 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82825.        (((A or B) -> ((C -> D) -> (C -> (C and D)))) and ((B or (A or B)) -> ((C -> D) -> (C -> (C and D))))), M:tm-920, m:tm-340, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-82826
in-theory        82826
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (D -> (C and D))))) and ((B or (A or B)) -> ((A or B) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-920 tm-341 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-82826.        (((A or B) -> ((A or B) and (C -> (D -> (C and D))))) and ((B or (A or B)) -> ((A or B) and (C -> (D -> (C and D)))))), M:tm-920, m:tm-341, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-82827
in-theory        82827
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (E -> (D and E)))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (E -> (D and E)))) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-920 tm-354 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-82827.        (((A or B) -> ((C -> (D -> (E -> (D and E)))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (E -> (D and E)))) and (A or B)))), M:tm-920, m:tm-354, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-82828
in-theory        82828
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (E -> (D and E))))) and ((B or (A or B)) -> (C -> (D -> (E -> (D and E))))))
theorem-size     29
proof            (modus-ponens tm-920 tm-356 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> 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-82828.        (((A or B) -> (C -> (D -> (E -> (D and E))))) and ((B or (A or B)) -> (C -> (D -> (E -> (D and E)))))), M:tm-920, m:tm-356, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-82829
in-theory        82829
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> C)) or E) and (A or B))) and ((B or (A or B)) -> (((C -> (D -> C)) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-364 ((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-82829.        (((A or B) -> (((C -> (D -> C)) or E) and (A or B))) and ((B or (A or B)) -> (((C -> (D -> C)) or E) and (A or B)))), M:tm-920, m:tm-364, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-82830
in-theory        82830
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> C)) or E)) and ((B or (A or B)) -> ((C -> (D -> C)) or E)))
theorem-size     25
proof            (modus-ponens tm-920 tm-365 ((Am (or A B)) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82830.        (((A or B) -> ((C -> (D -> C)) or E)) and ((B or (A or B)) -> ((C -> (D -> C)) or E))), M:tm-920, m:tm-365, u:((Am (or A B)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-82831
in-theory        82831
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B))) and ((B or (A or B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-920 tm-373 ((Am (or A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-82831.        (((A or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B))) and ((B or (A or B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B)))), M:tm-920, 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-82832
in-theory        82832
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((B or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     41
proof            (modus-ponens tm-920 tm-374 ((Am (or A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82832.        (((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((B or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-920, m:tm-374, u:((Am (or A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-82833
in-theory        82833
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C and D) -> C) or E) and (A or B))) and ((B or (A or B)) -> ((((C and D) -> C) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-382 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-82833.        (((A or B) -> ((((C and D) -> C) or E) and (A or B))) and ((B or (A or B)) -> ((((C and D) -> C) or E) and (A or B)))), M:tm-920, m:tm-382, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B))))
================================================================
tm-name          tm-82834
in-theory        82834
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and D) -> C) or E)) and ((B or (A or B)) -> (((C and D) -> C) or E)))
theorem-size     25
proof            (modus-ponens tm-920 tm-383 ((Am (or A B)) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82834.        (((A or B) -> (((C and D) -> C) or E)) and ((B or (A or B)) -> (((C and D) -> C) or E))), M:tm-920, m:tm-383, u:((Am (or A B)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-82835
in-theory        82835
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C and D) -> D) or E) and (A or B))) and ((B or (A or B)) -> ((((C and D) -> D) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-391 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-82835.        (((A or B) -> ((((C and D) -> D) or E) and (A or B))) and ((B or (A or B)) -> ((((C and D) -> D) or E) and (A or B)))), M:tm-920, m:tm-391, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B))))
================================================================
tm-name          tm-82836
in-theory        82836
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C and D) -> D) or E)) and ((B or (A or B)) -> (((C and D) -> D) or E)))
theorem-size     25
proof            (modus-ponens tm-920 tm-392 ((Am (or A B)) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82836.        (((A or B) -> (((C and D) -> D) or E)) and ((B or (A or B)) -> (((C and D) -> D) or E))), M:tm-920, m:tm-392, u:((Am (or A B)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-82837
in-theory        82837
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D -> (C and D))) or E) and (A or B))) and ((B or (A or B)) -> (((C -> (D -> (C and D))) or E) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-920 tm-400 ((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-82837.        (((A or B) -> (((C -> (D -> (C and D))) or E) and (A or B))) and ((B or (A or B)) -> (((C -> (D -> (C and D))) or E) and (A or B)))), M:tm-920, m:tm-400, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B))))
================================================================
tm-name          tm-82838
in-theory        82838
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (C and D))) or E)) and ((B or (A or B)) -> ((C -> (D -> (C and D))) or E)))
theorem-size     29
proof            (modus-ponens tm-920 tm-401 ((Am (or A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82838.        (((A or B) -> ((C -> (D -> (C and D))) or E)) and ((B or (A or B)) -> ((C -> (D -> (C and D))) or E))), M:tm-920, m:tm-401, u:((Am (or A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-82839
in-theory        82839
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (C or D)) or E) and (A or B))) and ((B or (A or B)) -> (((C -> (C or D)) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-409 ((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-82839.        (((A or B) -> (((C -> (C or D)) or E) and (A or B))) and ((B or (A or B)) -> (((C -> (C or D)) or E) and (A or B)))), M:tm-920, m:tm-409, u:((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B))))
================================================================
tm-name          tm-82840
in-theory        82840
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (C or D)) or E)) and ((B or (A or B)) -> ((C -> (C or D)) or E)))
theorem-size     25
proof            (modus-ponens tm-920 tm-410 ((Am (or A B)) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82840.        (((A or B) -> ((C -> (C or D)) or E)) and ((B or (A or B)) -> ((C -> (C or D)) or E))), M:tm-920, m:tm-410, u:((Am (or A B)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-82841
in-theory        82841
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (C or D)) and (A or B)))) and ((B or (A or B)) -> ((A or B) and ((C -> (C or D)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-443 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-82841.        (((A or B) -> ((A or B) and ((C -> (C or D)) and (A or B)))) and ((B or (A or B)) -> ((A or B) and ((C -> (C or D)) and (A or B))))), M:tm-920, m:tm-443, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B)))))
================================================================
tm-name          tm-82842
in-theory        82842
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (D or E)) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (D or E)) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-920 tm-453 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-82842.        (((A or B) -> ((C -> ((D -> (D or E)) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (D or E)) and C)) and (A or B)))), M:tm-920, m:tm-453, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B))))
================================================================
tm-name          tm-82843
in-theory        82843
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (D or E)) and C))) and ((B or (A or B)) -> (C -> ((D -> (D or E)) and C))))
theorem-size     29
proof            (modus-ponens tm-920 tm-454 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82843.        (((A or B) -> (C -> ((D -> (D or E)) and C))) and ((B or (A or B)) -> (C -> ((D -> (D or E)) and C)))), M:tm-920, m:tm-454, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-82844
in-theory        82844
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (C or D)))) and ((B or (A or B)) -> ((A or B) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-920 tm-456 ((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-82844.        (((A or B) -> ((A or B) and (C -> (C or D)))) and ((B or (A or B)) -> ((A or B) and (C -> (C or D))))), M:tm-920, m:tm-456, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-82845
in-theory        82845
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (D or E))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (D or E))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-469 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-82845.        (((A or B) -> ((C -> (D -> (D or E))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (D or E))) and (A or B)))), M:tm-920, m:tm-469, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-82846
in-theory        82846
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (D or E)))) and ((B or (A or B)) -> (C -> (D -> (D or E)))))
theorem-size     25
proof            (modus-ponens tm-920 tm-471 ((Am (or A B)) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-82846.        (((A or B) -> (C -> (D -> (D or E)))) and ((B or (A or B)) -> (C -> (D -> (D or E))))), M:tm-920, m:tm-471, u:((Am (or A B)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82847
in-theory        82847
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or (D -> (E -> D))) and (A or B))) and ((B or (A or B)) -> ((C or (D -> (E -> D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-480 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-82847.        (((A or B) -> ((C or (D -> (E -> D))) and (A or B))) and ((B or (A or B)) -> ((C or (D -> (E -> D))) and (A or B)))), M:tm-920, m:tm-480, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-82848
in-theory        82848
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (D -> (E -> D)))) and ((B or (A or B)) -> (C or (D -> (E -> D)))))
theorem-size     25
proof            (modus-ponens tm-920 tm-481 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82848.        (((A or B) -> (C or (D -> (E -> D)))) and ((B or (A or B)) -> (C or (D -> (E -> D))))), M:tm-920, m:tm-481, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-82849
in-theory        82849
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))) and ((B or (A or B)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-920 tm-490 ((Am (or A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-82849.        (((A or B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))) and ((B or (A or B)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B)))), M:tm-920, 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-82850
in-theory        82850
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A or B)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     41
proof            (modus-ponens tm-920 tm-491 ((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82850.        (((A or B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A or B)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-920, m:tm-491, u:((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-82851
in-theory        82851
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or ((D and E) -> D)) and (A or B))) and ((B or (A or B)) -> ((C or ((D and E) -> D)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-500 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-82851.        (((A or B) -> ((C or ((D and E) -> D)) and (A or B))) and ((B or (A or B)) -> ((C or ((D and E) -> D)) and (A or B)))), M:tm-920, m:tm-500, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-82852
in-theory        82852
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or ((D and E) -> D))) and ((B or (A or B)) -> (C or ((D and E) -> D))))
theorem-size     25
proof            (modus-ponens tm-920 tm-501 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82852.        (((A or B) -> (C or ((D and E) -> D))) and ((B or (A or B)) -> (C or ((D and E) -> D)))), M:tm-920, m:tm-501, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-82853
in-theory        82853
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or ((D and E) -> E)) and (A or B))) and ((B or (A or B)) -> ((C or ((D and E) -> E)) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-510 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-82853.        (((A or B) -> ((C or ((D and E) -> E)) and (A or B))) and ((B or (A or B)) -> ((C or ((D and E) -> E)) and (A or B)))), M:tm-920, m:tm-510, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-82854
in-theory        82854
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or ((D and E) -> E))) and ((B or (A or B)) -> (C or ((D and E) -> E))))
theorem-size     25
proof            (modus-ponens tm-920 tm-511 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82854.        (((A or B) -> (C or ((D and E) -> E))) and ((B or (A or B)) -> (C or ((D and E) -> E)))), M:tm-920, m:tm-511, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-82855
in-theory        82855
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or (D -> (E -> (D and E)))) and (A or B))) and ((B or (A or B)) -> ((C or (D -> (E -> (D and E)))) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-920 tm-520 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-82855.        (((A or B) -> ((C or (D -> (E -> (D and E)))) and (A or B))) and ((B or (A or B)) -> ((C or (D -> (E -> (D and E)))) and (A or B)))), M:tm-920, m:tm-520, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-82856
in-theory        82856
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (D -> (E -> (D and E))))) and ((B or (A or B)) -> (C or (D -> (E -> (D and E))))))
theorem-size     29
proof            (modus-ponens tm-920 tm-521 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82856.        (((A or B) -> (C or (D -> (E -> (D and E))))) and ((B or (A or B)) -> (C or (D -> (E -> (D and E)))))), M:tm-920, m:tm-521, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-82857
in-theory        82857
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or (D -> (D or E))) and (A or B))) and ((B or (A or B)) -> ((C or (D -> (D or E))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-530 ((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-82857.        (((A or B) -> ((C or (D -> (D or E))) and (A or B))) and ((B or (A or B)) -> ((C or (D -> (D or E))) and (A or B)))), M:tm-920, m:tm-530, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-82858
in-theory        82858
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (D -> (D or E)))) and ((B or (A or B)) -> (C or (D -> (D or E)))))
theorem-size     25
proof            (modus-ponens tm-920 tm-531 ((Am (or A B)) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82858.        (((A or B) -> (C or (D -> (D or E)))) and ((B or (A or B)) -> (C or (D -> (D or E))))), M:tm-920, m:tm-531, u:((Am (or A B)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-82859
in-theory        82859
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or (D -> (E or D))) and (A or B))) and ((B or (A or B)) -> ((C or (D -> (E or D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-540 ((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-82859.        (((A or B) -> ((C or (D -> (E or D))) and (A or B))) and ((B or (A or B)) -> ((C or (D -> (E or D))) and (A or B)))), M:tm-920, m:tm-540, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-82860
in-theory        82860
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or (D -> (E or D)))) and ((B or (A or B)) -> (C or (D -> (E or D)))))
theorem-size     25
proof            (modus-ponens tm-920 tm-541 ((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82860.        (((A or B) -> (C or (D -> (E or D)))) and ((B or (A or B)) -> (C or (D -> (E or D))))), M:tm-920, m:tm-541, u:((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82861
in-theory        82861
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D or C)) or E) and (A or B))) and ((B or (A or B)) -> (((C -> (D or C)) or E) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-550 ((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82861.        (((A or B) -> (((C -> (D or C)) or E) and (A or B))) and ((B or (A or B)) -> (((C -> (D or C)) or E) and (A or B)))), M:tm-920, m:tm-550, u:((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-82862
in-theory        82862
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D or C)) or E)) and ((B or (A or B)) -> ((C -> (D or C)) or E)))
theorem-size     25
proof            (modus-ponens tm-920 tm-551 ((Am (or A B)) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82862.        (((A or B) -> ((C -> (D or C)) or E)) and ((B or (A or B)) -> ((C -> (D or C)) or E))), M:tm-920, m:tm-551, u:((Am (or A B)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-82863
in-theory        82863
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and ((C -> (D or C)) and (A or B)))) and ((B or (A or B)) -> ((A or B) and ((C -> (D or C)) and (A or B)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-595 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-82863.        (((A or B) -> ((A or B) and ((C -> (D or C)) and (A or B)))) and ((B or (A or B)) -> ((A or B) and ((C -> (D or C)) and (A or B))))), M:tm-920, m:tm-595, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B)))))
================================================================
tm-name          tm-82864
in-theory        82864
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> ((D -> (E or D)) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (E or D)) and C)) and (A or B))))
theorem-size     37
proof            (modus-ponens tm-920 tm-605 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-82864.        (((A or B) -> ((C -> ((D -> (E or D)) and C)) and (A or B))) and ((B or (A or B)) -> ((C -> ((D -> (E or D)) and C)) and (A or B)))), M:tm-920, m:tm-605, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-82865
in-theory        82865
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> ((D -> (E or D)) and C))) and ((B or (A or B)) -> (C -> ((D -> (E or D)) and C))))
theorem-size     29
proof            (modus-ponens tm-920 tm-606 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82865.        (((A or B) -> (C -> ((D -> (E or D)) and C))) and ((B or (A or B)) -> (C -> ((D -> (E or D)) and C)))), M:tm-920, m:tm-606, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-82866
in-theory        82866
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((A or B) and (C -> (D or C)))) and ((B or (A or B)) -> ((A or B) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-920 tm-609 ((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-82866.        (((A or B) -> ((A or B) and (C -> (D or C)))) and ((B or (A or B)) -> ((A or B) and (C -> (D or C))))), M:tm-920, m:tm-609, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-82867
in-theory        82867
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> (D -> (E or D))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (E or D))) and (A or B))))
theorem-size     33
proof            (modus-ponens tm-920 tm-622 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-82867.        (((A or B) -> ((C -> (D -> (E or D))) and (A or B))) and ((B or (A or B)) -> ((C -> (D -> (E or D))) and (A or B)))), M:tm-920, m:tm-622, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-82868
in-theory        82868
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> (D -> (E or D)))) and ((B or (A or B)) -> (C -> (D -> (E or D)))))
theorem-size     25
proof            (modus-ponens tm-920 tm-624 ((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-82868.        (((A or B) -> (C -> (D -> (E or D)))) and ((B or (A or B)) -> (C -> (D -> (E or D))))), M:tm-920, m:tm-624, u:((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-82869
in-theory        82869
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (((B -> A) or (A or (B -> A))) -> (C -> (B -> A))))
theorem-size     27
proof            (modus-ponens tm-920 tm-625 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82869.        (((A or (B -> A)) -> (C -> (B -> A))) and (((B -> A) or (A or (B -> A))) -> (C -> (B -> A)))), M:tm-920, m:tm-625, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-82870
in-theory        82870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((C -> (A -> B)) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B))))
theorem-size     41
proof            (modus-ponens tm-920 tm-626 ((A (-> Am Bm)) (B (-> Cm (-> Am Bm))) (C (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82870.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((C -> (A -> B)) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B)))), M:tm-920, m:tm-626, u:((A (-> Am Bm)) (B (-> Cm (-> Am Bm))) (C (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-82871
in-theory        82871
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((B -> A) or (A or (B -> A))) -> (C -> ((B -> A) and C))))
theorem-size     31
proof            (modus-ponens tm-920 tm-627 ((A Am) (B (-> Bm Am)) (C (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82871.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((B -> A) or (A or (B -> A))) -> (C -> ((B -> A) and C)))), M:tm-920, m:tm-627, u:((A Am) (B (-> Bm Am)) (C (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-82872
in-theory        82872
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (((B -> A) or (A or (B -> A))) -> ((B -> A) or C)))
theorem-size     27
proof            (modus-ponens tm-920 tm-628 ((A Am) (B (-> Bm Am)) (C (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82872.        (((A or (B -> A)) -> ((B -> A) or C)) and (((B -> A) or (A or (B -> A))) -> ((B -> A) or C))), M:tm-920, m:tm-628, u:((A Am) (B (-> Bm Am)) (C (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-82873
in-theory        82873
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (((B -> A) or (A or (B -> A))) -> (C or (B -> A))))
theorem-size     27
proof            (modus-ponens tm-920 tm-629 ((A Am) (B (-> Bm Am)) (C (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82873.        (((A or (B -> A)) -> (C or (B -> A))) and (((B -> A) or (A or (B -> A))) -> (C or (B -> A)))), M:tm-920, m:tm-629, u:((A Am) (B (-> Bm Am)) (C (or Cm (-> Bm Am))))
================================================================
tm-name          tm-82874
in-theory        82874
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((B -> A) or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C))))
theorem-size     35
proof            (modus-ponens tm-920 tm-630 ((A Am) (B (-> Bm Am)) (C (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82874.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((B -> A) or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C)))), M:tm-920, m:tm-630, u:((A Am) (B (-> Bm Am)) (C (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-82875
in-theory        82875
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((B -> A) or (A or (B -> A))) -> ((B -> (not A)) -> (not B))))
theorem-size     31
proof            (modus-ponens tm-920 tm-631 ((A Am) (B (-> Bm Am)) (C (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82875.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((B -> A) or (A or (B -> A))) -> ((B -> (not A)) -> (not B)))), M:tm-920, m:tm-631, u:((A Am) (B (-> Bm Am)) (C (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-82876
in-theory        82876
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (((B -> A) or (A or (B -> A))) -> (C -> (D -> C))))
theorem-size     27
proof            (modus-ponens tm-920 tm-632 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82876.        (((A or (B -> A)) -> (C -> (D -> C))) and (((B -> A) or (A or (B -> A))) -> (C -> (D -> C)))), M:tm-920, m:tm-632, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-82877
in-theory        82877
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (((B -> A) or (A or (B -> A))) -> (B -> B)))
theorem-size     23
proof            (modus-ponens tm-920 tm-633 ((A Am) (B (-> Bm Am)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82877.        (((A or (B -> A)) -> (B -> B)) and (((B -> A) or (A or (B -> A))) -> (B -> B))), M:tm-920, m:tm-633, u:((A Am) (B (-> Bm Am)) (C (-> Bm Bm)))
================================================================
tm-name          tm-82878
in-theory        82878
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     57
proof            (modus-ponens tm-920 tm-634 ((A (-> Am Bm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82878.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-920, m:tm-634, u:((A (-> Am Bm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-82879
in-theory        82879
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((B -> A) or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     43
proof            (modus-ponens tm-920 tm-635 ((A Am) (B (-> Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82879.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((B -> A) or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-920, m:tm-635, u:((A Am) (B (-> Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-82880
in-theory        82880
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> A) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)))
theorem-size     43
proof            (modus-ponens tm-920 tm-636 ((A Am) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82880.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> A) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))), M:tm-920, m:tm-636, u:((A Am) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-82881
in-theory        82881
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (((B -> A) or (A or (B -> A))) -> ((C and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-920 tm-637 ((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82881.        (((A or (B -> A)) -> ((C and D) -> C)) and (((B -> A) or (A or (B -> A))) -> ((C and D) -> C))), M:tm-920, m:tm-637, u:((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-82882
in-theory        82882
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((((B and (A -> C)) -> A) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C)))
theorem-size     43
proof            (modus-ponens tm-920 tm-638 ((A Am) (B (-> (and Bm (-> Am Cm)) Am)) (C (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82882.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((((B and (A -> C)) -> A) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C))), M:tm-920, m:tm-638, u:((A Am) (B (-> (and Bm (-> Am Cm)) Am)) (C (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-82883
in-theory        82883
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (((B -> A) or (A or (B -> A))) -> ((C and D) -> D)))
theorem-size     27
proof            (modus-ponens tm-920 tm-639 ((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82883.        (((A or (B -> A)) -> ((C and D) -> D)) and (((B -> A) or (A or (B -> A))) -> ((C and D) -> D))), M:tm-920, m:tm-639, u:((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-82884
in-theory        82884
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-640 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82884.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A)))), M:tm-920, m:tm-640, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-82885
in-theory        82885
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))
theorem-size     51
proof            (modus-ponens tm-920 tm-641 ((A Am) (B (-> Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82885.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))), M:tm-920, m:tm-641, u:((A Am) (B (-> Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-82886
in-theory        82886
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> (((C and D) -> C) and (B -> A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-642 ((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82886.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> (((C and D) -> C) and (B -> A)))), M:tm-920, m:tm-642, u:((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-82887
in-theory        82887
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> (((C and D) -> D) and (B -> A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-643 ((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82887.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> (((C and D) -> D) and (B -> A)))), M:tm-920, m:tm-643, u:((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-82888
in-theory        82888
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-920 tm-644 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82888.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A)))), M:tm-920, m:tm-644, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-82889
in-theory        82889
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (((B -> A) or (A or (B -> A))) -> (B -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-920 tm-645 ((A Am) (B (-> Bm Am)) (C (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82889.        (((A or (B -> A)) -> (B -> (B and A))) and (((B -> A) or (A or (B -> A))) -> (B -> (B and A)))), M:tm-920, m:tm-645, u:((A Am) (B (-> Bm Am)) (C (-> Bm (and Bm Am))))
================================================================
tm-name          tm-82890
in-theory        82890
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((B -> A) or (A or (B -> A))) -> (C -> (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-920 tm-646 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82890.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((B -> A) or (A or (B -> A))) -> (C -> (D -> (C and D))))), M:tm-920, m:tm-646, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-82891
in-theory        82891
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-647 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82891.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A)))), M:tm-920, m:tm-647, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-82892
in-theory        82892
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (((B -> A) or (A or (B -> A))) -> (C -> (C or D))))
theorem-size     27
proof            (modus-ponens tm-920 tm-648 ((A Am) (B (-> Bm Am)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82892.        (((A or (B -> A)) -> (C -> (C or D))) and (((B -> A) or (A or (B -> A))) -> (C -> (C or D)))), M:tm-920, m:tm-648, u:((A Am) (B (-> Bm Am)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82893
in-theory        82893
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-649 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82893.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((B -> A) or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A)))), M:tm-920, m:tm-649, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-82894
in-theory        82894
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (((B -> A) or (A or (B -> A))) -> (C -> (D or C))))
theorem-size     27
proof            (modus-ponens tm-920 tm-650 ((A Am) (B (-> Bm Am)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82894.        (((A or (B -> A)) -> (C -> (D or C))) and (((B -> A) or (A or (B -> A))) -> (C -> (D or C)))), M:tm-920, m:tm-650, u:((A Am) (B (-> Bm Am)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82895
in-theory        82895
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((((B -> C) -> A) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A)))
theorem-size     37
proof            (modus-ponens tm-920 tm-651 ((A Am) (B (-> (-> Bm Cm) Am)) (C (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82895.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((((B -> C) -> A) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A))), M:tm-920, m:tm-651, u:((A Am) (B (-> (-> Bm Cm) Am)) (C (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-82896
in-theory        82896
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-920 tm-665 ((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-82896.        (((A or B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B)))), M:tm-920, m:tm-665, u:((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-82897
in-theory        82897
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((B or (A or B)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     37
proof            (modus-ponens tm-920 tm-667 ((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82897.        (((A or B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((B or (A or B)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-920, m:tm-667, u:((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-82898
in-theory        82898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-920 tm-668 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82898.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C))))), M:tm-920, m:tm-668, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-82899
in-theory        82899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C))))
theorem-size     59
proof            (modus-ponens tm-920 tm-669 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82899.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C)))), M:tm-920, m:tm-669, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-82900
in-theory        82900
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D))))
theorem-size     59
proof            (modus-ponens tm-920 tm-670 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82900.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D)))), M:tm-920, m:tm-670, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-82901
in-theory        82901
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D)))
theorem-size     55
proof            (modus-ponens tm-920 tm-671 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82901.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D))), M:tm-920, m:tm-671, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-82902
in-theory        82902
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-920 tm-672 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or Dm (-> (-> Am Bm) (-> Am Cm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82902.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C))))), M:tm-920, m:tm-672, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-82903
in-theory        82903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))
theorem-size     67
proof            (modus-ponens tm-920 tm-673 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82903.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))), M:tm-920, 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-82904
in-theory        82904
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))
theorem-size     63
proof            (modus-ponens tm-920 tm-674 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-9)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82904.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))), M:tm-920, 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-82905
in-theory        82905
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D))))
theorem-size     47
proof            (modus-ponens tm-920 tm-675 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82905.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D)))), M:tm-920, m:tm-675, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-82906
in-theory        82906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B))))
theorem-size     51
proof            (modus-ponens tm-920 tm-676 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82906.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B)))), M:tm-920, m:tm-676, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-82907
in-theory        82907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     65
proof            (modus-ponens tm-920 tm-677 ((A (-> Am (-> (-> Bm Cm) Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82907.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-920, m:tm-677, u:((A (-> Am (-> (-> Bm Cm) Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-82908
in-theory        82908
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 ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     63
proof            (modus-ponens tm-920 tm-678 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82908.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-920, m:tm-678, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-82909
in-theory        82909
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D)))
theorem-size     47
proof            (modus-ponens tm-920 tm-679 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82909.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D))), M:tm-920, m:tm-679, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-82910
in-theory        82910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E)))
theorem-size     47
proof            (modus-ponens tm-920 tm-680 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82910.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E))), M:tm-920, m:tm-680, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Em)))
================================================================
tm-name          tm-82911
in-theory        82911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-920 tm-681 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82911.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))), M:tm-920, 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-82912
in-theory        82912
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) -> (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     79
proof            (modus-ponens tm-920 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-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82912.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((((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-920, 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-82913
in-theory        82913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-920 tm-683 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82913.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))), M:tm-920, 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-82914
in-theory        82914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-920 tm-684 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82914.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))), M:tm-920, 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-82915
in-theory        82915
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) -> (A -> C)) or ((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-920 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-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82915.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((((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-920, 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-82916
in-theory        82916
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C)))))
theorem-size     59
proof            (modus-ponens tm-920 tm-686 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82916.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C))))), M:tm-920, m:tm-686, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-82917
in-theory        82917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E)))))
theorem-size     51
proof            (modus-ponens tm-920 tm-687 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82917.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E))))), M:tm-920, m:tm-687, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-82918
in-theory        82918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-920 tm-688 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82918.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))), M:tm-920, 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-82919
in-theory        82919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E))))
theorem-size     47
proof            (modus-ponens tm-920 tm-689 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-1 tm-6)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82919.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E)))), M:tm-920, m:tm-689, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Dm Em))))
================================================================
tm-name          tm-82920
in-theory        82920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-920 tm-690 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82920.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))), M:tm-920, 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-82921
in-theory        82921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D))))
theorem-size     47
proof            (modus-ponens tm-920 tm-691 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82921.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D)))), M:tm-920, m:tm-691, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Em Dm))))
================================================================
tm-name          tm-82922
in-theory        82922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C))))
theorem-size     55
proof            (modus-ponens tm-920 tm-692 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-82922.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C)))), M:tm-920, m:tm-692, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-82923
in-theory        82923
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)) -> ((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     101
proof            (modus-ponens tm-920 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-2 tm-5 tm-8 tm-7)
proof-size       325
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82923.        (((((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)) -> ((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-920, 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-82924
in-theory        82924
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((((B -> C) -> (B -> D)) -> A) or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))
theorem-size     65
proof            (modus-ponens tm-920 tm-694 ((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82924.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((((B -> C) -> (B -> D)) -> A) or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))), M:tm-920, 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-82925
in-theory        82925
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B))) and ((B or (A or B)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B))))
theorem-size     69
proof            (modus-ponens tm-920 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-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-82925.        (((A or B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B))) and ((B or (A or B)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B)))), M:tm-920, 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-82926
in-theory        82926
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((B or (A or B)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     61
proof            (modus-ponens tm-920 tm-710 ((Am (or 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82926.        (((A or B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((B or (A or B)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-920, 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-82927
in-theory        82927
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((A or ((A and B) or A)) -> (C -> A)))
theorem-size     21
proof            (modus-ponens tm-920 tm-711 ((A (and Am Bm)) (B Am) (C (-> Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82927.        ((((A and B) or A) -> (C -> A)) and ((A or ((A and B) or A)) -> (C -> A))), M:tm-920, m:tm-711, u:((A (and Am Bm)) (B Am) (C (-> Cm Am)))
================================================================
tm-name          tm-82928
in-theory        82928
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C))))
theorem-size     49
proof            (modus-ponens tm-920 tm-712 ((A (and (-> Am (-> Bm Cm)) Dm)) (B (-> Am (-> Bm Cm))) (C (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82928.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))), M:tm-920, m:tm-712, u:((A (and (-> Am (-> Bm Cm)) Dm)) (B (-> Am (-> Bm Cm))) (C (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-82929
in-theory        82929
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (((A and B) or (((A and B) and C) or (A and B))) -> A))
theorem-size     27
proof            (modus-ponens tm-920 tm-713 ((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82929.        (((((A and B) and C) or (A and B)) -> A) and (((A and B) or (((A and B) and C) or (A and B))) -> A)), M:tm-920, m:tm-713, u:((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Am))
================================================================
tm-name          tm-82930
in-theory        82930
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (((A and B) or (((A and B) and C) or (A and B))) -> B))
theorem-size     27
proof            (modus-ponens tm-920 tm-714 ((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82930.        (((((A and B) and C) or (A and B)) -> B) and (((A and B) or (((A and B) and C) or (A and B))) -> B)), M:tm-920, m:tm-714, u:((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Bm))
================================================================
tm-name          tm-82931
in-theory        82931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((A or ((A and B) or A)) -> (C -> (A and C))))
theorem-size     25
proof            (modus-ponens tm-920 tm-715 ((A (and Am Bm)) (B Am) (C (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82931.        ((((A and B) or A) -> (C -> (A and C))) and ((A or ((A and B) or A)) -> (C -> (A and C)))), M:tm-920, m:tm-715, u:((A (and Am Bm)) (B Am) (C (-> Cm (and Am Cm))))
================================================================
tm-name          tm-82932
in-theory        82932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((A or ((A and B) or A)) -> (A or C)))
theorem-size     21
proof            (modus-ponens tm-920 tm-716 ((A (and Am Bm)) (B Am) (C (or Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82932.        ((((A and B) or A) -> (A or C)) and ((A or ((A and B) or A)) -> (A or C))), M:tm-920, m:tm-716, u:((A (and Am Bm)) (B Am) (C (or Am Cm)))
================================================================
tm-name          tm-82933
in-theory        82933
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((A or ((A and B) or A)) -> (C or A)))
theorem-size     21
proof            (modus-ponens tm-920 tm-717 ((A (and Am Bm)) (B Am) (C (or Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82933.        ((((A and B) or A) -> (C or A)) and ((A or ((A and B) or A)) -> (C or A))), M:tm-920, m:tm-717, u:((A (and Am Bm)) (B Am) (C (or Cm Am)))
================================================================
tm-name          tm-82934
in-theory        82934
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D))))
theorem-size     43
proof            (modus-ponens tm-920 tm-718 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82934.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D)))), M:tm-920, m:tm-718, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-82935
in-theory        82935
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A))))
theorem-size     39
proof            (modus-ponens tm-920 tm-719 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82935.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A)))), M:tm-920, m:tm-719, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-82936
in-theory        82936
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (((not (not A)) or (((not (not A)) and B) or (not (not A)))) -> A))
theorem-size     27
proof            (modus-ponens tm-920 tm-720 ((A (and (not (not Am)) Bm)) (B (not (not Am))) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82936.        (((((not (not A)) and B) or (not (not A))) -> A) and (((not (not A)) or (((not (not A)) and B) or (not (not A)))) -> A)), M:tm-920, m:tm-720, u:((A (and (not (not Am)) Bm)) (B (not (not Am))) (C Am))
================================================================
tm-name          tm-82937
in-theory        82937
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((A or ((A and B) or A)) -> (C -> (D -> C))))
theorem-size     25
proof            (modus-ponens tm-920 tm-721 ((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82937.        ((((A and B) or A) -> (C -> (D -> C))) and ((A or ((A and B) or A)) -> (C -> (D -> C)))), M:tm-920, m:tm-721, u:((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-82938
in-theory        82938
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> (A -> A)))
theorem-size     31
proof            (modus-ponens tm-920 tm-722 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82938.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> (A -> A))), M:tm-920, m:tm-722, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am Am)))
================================================================
tm-name          tm-82939
in-theory        82939
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)) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     73
proof            (modus-ponens tm-920 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-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82939.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((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-920, 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-82940
in-theory        82940
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-920 tm-724 ((A (and Am Bm)) (B Am) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82940.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-920, m:tm-724, u:((A (and Am Bm)) (B Am) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-82941
in-theory        82941
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) or (((((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-920 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-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82941.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((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-920, 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-82942
in-theory        82942
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((A or ((A and B) or A)) -> ((C and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-920 tm-726 ((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82942.        ((((A and B) or A) -> ((C and D) -> C)) and ((A or ((A and B) or A)) -> ((C and D) -> C))), M:tm-920, m:tm-726, u:((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-82943
in-theory        82943
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) or ((((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-920 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-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82943.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((((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-920, 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-82944
in-theory        82944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((A or ((A and B) or A)) -> ((C and D) -> D)))
theorem-size     25
proof            (modus-ponens tm-920 tm-728 ((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82944.        ((((A and B) or A) -> ((C and D) -> D)) and ((A or ((A and B) or A)) -> ((C and D) -> D))), M:tm-920, m:tm-728, u:((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-82945
in-theory        82945
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((A or ((A and B) or A)) -> ((C -> (D -> C)) and A)))
theorem-size     29
proof            (modus-ponens tm-920 tm-729 ((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82945.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((A or ((A and B) or A)) -> ((C -> (D -> C)) and A))), M:tm-920, m:tm-729, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-82946
in-theory        82946
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((A or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))
theorem-size     45
proof            (modus-ponens tm-920 tm-730 ((A (and Am Bm)) (B Am) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82946.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((A or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))), M:tm-920, m:tm-730, u:((A (and Am Bm)) (B Am) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-82947
in-theory        82947
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((A or ((A and B) or A)) -> (((C and D) -> C) and A)))
theorem-size     29
proof            (modus-ponens tm-920 tm-731 ((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82947.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((A or ((A and B) or A)) -> (((C and D) -> C) and A))), M:tm-920, m:tm-731, u:((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-82948
in-theory        82948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((A or ((A and B) or A)) -> (((C and D) -> D) and A)))
theorem-size     29
proof            (modus-ponens tm-920 tm-732 ((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82948.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((A or ((A and B) or A)) -> (((C and D) -> D) and A))), M:tm-920, m:tm-732, u:((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-82949
in-theory        82949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((A or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A)))
theorem-size     33
proof            (modus-ponens tm-920 tm-733 ((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82949.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((A or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A))), M:tm-920, m:tm-733, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-82950
in-theory        82950
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B))))
theorem-size     35
proof            (modus-ponens tm-920 tm-734 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82950.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B)))), M:tm-920, m:tm-734, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am (and Am Bm))))
================================================================
tm-name          tm-82951
in-theory        82951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((A or ((A and B) or A)) -> (C -> (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-920 tm-735 ((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82951.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((A or ((A and B) or A)) -> (C -> (D -> (C and D))))), M:tm-920, m:tm-735, u:((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-82952
in-theory        82952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((A or ((A and B) or A)) -> ((C -> (C or D)) and A)))
theorem-size     29
proof            (modus-ponens tm-920 tm-736 ((A (and Am Bm)) (B Am) (C (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82952.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((A or ((A and B) or A)) -> ((C -> (C or D)) and A))), M:tm-920, m:tm-736, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-82953
in-theory        82953
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((A or ((A and B) or A)) -> (C -> (C or D))))
theorem-size     25
proof            (modus-ponens tm-920 tm-737 ((A (and Am Bm)) (B Am) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82953.        ((((A and B) or A) -> (C -> (C or D))) and ((A or ((A and B) or A)) -> (C -> (C or D)))), M:tm-920, m:tm-737, u:((A (and Am Bm)) (B Am) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82954
in-theory        82954
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((A or ((A and B) or A)) -> ((C -> (D or C)) and A)))
theorem-size     29
proof            (modus-ponens tm-920 tm-738 ((A (and Am Bm)) (B Am) (C (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82954.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((A or ((A and B) or A)) -> ((C -> (D or C)) and A))), M:tm-920, m:tm-738, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-82955
in-theory        82955
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((A or ((A and B) or A)) -> (C -> (D or C))))
theorem-size     25
proof            (modus-ponens tm-920 tm-739 ((A (and Am Bm)) (B Am) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82955.        ((((A and B) or A) -> (C -> (D or C))) and ((A or ((A and B) or A)) -> (C -> (D or C)))), M:tm-920, m:tm-739, u:((A (and Am Bm)) (B Am) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82956
in-theory        82956
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((A -> B) -> C) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C)))
theorem-size     49
proof            (modus-ponens tm-920 tm-740 ((A (and (-> (-> Am Bm) Cm) Dm)) (B (-> (-> Am Bm) Cm)) (C (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-82956.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((A -> B) -> C) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C))), M:tm-920, m:tm-740, u:((A (and (-> (-> Am Bm) Cm) Dm)) (B (-> (-> Am Bm) Cm)) (C (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-82957
in-theory        82957
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) 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     85
proof            (modus-ponens tm-920 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-2 tm-5 tm-8 tm-7 tm-3)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82957.        (((((((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) 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-920, 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-82958
in-theory        82958
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B)))
theorem-size     39
proof            (modus-ponens tm-920 tm-742 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82958.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B))), M:tm-920, m:tm-742, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-82959
in-theory        82959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))
theorem-size     63
proof            (modus-ponens tm-920 tm-743 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82959.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))), M:tm-920, 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-82960
in-theory        82960
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((B -> A) or (A or (B -> A))) -> (((B and C) or B) -> A)))
theorem-size     31
proof            (modus-ponens tm-920 tm-744 ((A Am) (B (-> Bm Am)) (C (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82960.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((B -> A) or (A or (B -> A))) -> (((B and C) or B) -> A))), M:tm-920, m:tm-744, u:((A Am) (B (-> Bm Am)) (C (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-82961
in-theory        82961
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B))))
theorem-size     41
proof            (modus-ponens tm-920 tm-757 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-82961.        (((A or B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B)))), M:tm-920, m:tm-757, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-82962
in-theory        82962
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> (((C and E) or C) -> D))) and ((B or (A or B)) -> ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     33
proof            (modus-ponens tm-920 tm-759 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-82962.        (((A or B) -> ((C -> D) -> (((C and E) or C) -> D))) and ((B or (A or B)) -> ((C -> D) -> (((C and E) or C) -> D)))), M:tm-920, m:tm-759, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-82963
in-theory        82963
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((B or ((A and B) or B)) -> (C -> B)))
theorem-size     21
proof            (modus-ponens tm-920 tm-760 ((A (and Am Bm)) (B Bm) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-82963.        ((((A and B) or B) -> (C -> B)) and ((B or ((A and B) or B)) -> (C -> B))), M:tm-920, m:tm-760, u:((A (and Am Bm)) (B Bm) (C (-> Cm Bm)))
================================================================
tm-name          tm-82964
in-theory        82964
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((B -> (C -> D)) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D))))
theorem-size     49
proof            (modus-ponens tm-920 tm-761 ((A (and Am (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82964.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((B -> (C -> D)) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))), M:tm-920, m:tm-761, u:((A (and Am (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-82965
in-theory        82965
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (((B and C) or ((A and (B and C)) or (B and C))) -> B))
theorem-size     27
proof            (modus-ponens tm-920 tm-762 ((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82965.        ((((A and (B and C)) or (B and C)) -> B) and (((B and C) or ((A and (B and C)) or (B and C))) -> B)), M:tm-920, m:tm-762, u:((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-82966
in-theory        82966
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (((B and C) or ((A and (B and C)) or (B and C))) -> C))
theorem-size     27
proof            (modus-ponens tm-920 tm-763 ((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82966.        ((((A and (B and C)) or (B and C)) -> C) and (((B and C) or ((A and (B and C)) or (B and C))) -> C)), M:tm-920, m:tm-763, u:((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-82967
in-theory        82967
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((B or ((A and B) or B)) -> (C -> (B and C))))
theorem-size     25
proof            (modus-ponens tm-920 tm-764 ((A (and Am Bm)) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82967.        ((((A and B) or B) -> (C -> (B and C))) and ((B or ((A and B) or B)) -> (C -> (B and C)))), M:tm-920, m:tm-764, u:((A (and Am Bm)) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-82968
in-theory        82968
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((B or ((A and B) or B)) -> (B or C)))
theorem-size     21
proof            (modus-ponens tm-920 tm-765 ((A (and Am Bm)) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82968.        ((((A and B) or B) -> (B or C)) and ((B or ((A and B) or B)) -> (B or C))), M:tm-920, m:tm-765, u:((A (and Am Bm)) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-82969
in-theory        82969
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((B or ((A and B) or B)) -> (C or B)))
theorem-size     21
proof            (modus-ponens tm-920 tm-766 ((A (and Am Bm)) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82969.        ((((A and B) or B) -> (C or B)) and ((B or ((A and B) or B)) -> (C or B))), M:tm-920, m:tm-766, u:((A (and Am Bm)) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-82970
in-theory        82970
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     43
proof            (modus-ponens tm-920 tm-767 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82970.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D)))), M:tm-920, m:tm-767, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-82971
in-theory        82971
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B))))
theorem-size     39
proof            (modus-ponens tm-920 tm-768 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82971.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B)))), M:tm-920, m:tm-768, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-82972
in-theory        82972
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (((not (not B)) or ((A and (not (not B))) or (not (not B)))) -> B))
theorem-size     27
proof            (modus-ponens tm-920 tm-769 ((A (and Am (not (not Bm)))) (B (not (not Bm))) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82972.        ((((A and (not (not B))) or (not (not B))) -> B) and (((not (not B)) or ((A and (not (not B))) or (not (not B)))) -> B)), M:tm-920, m:tm-769, u:((A (and Am (not (not Bm)))) (B (not (not Bm))) (C Bm))
================================================================
tm-name          tm-82973
in-theory        82973
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((B or ((A and B) or B)) -> (C -> (D -> C))))
theorem-size     25
proof            (modus-ponens tm-920 tm-770 ((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-82973.        ((((A and B) or B) -> (C -> (D -> C))) and ((B or ((A and B) or B)) -> (C -> (D -> C)))), M:tm-920, m:tm-770, u:((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-82974
in-theory        82974
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> (B -> B)))
theorem-size     31
proof            (modus-ponens tm-920 tm-771 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-82974.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> (B -> B))), M:tm-920, m:tm-771, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-82975
in-theory        82975
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 -> C)) or ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     73
proof            (modus-ponens tm-920 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-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82975.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) 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-920, 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-82976
in-theory        82976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((B or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-920 tm-773 ((A (and Am Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-82976.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((B or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-920, m:tm-773, u:((A (and Am Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-82977
in-theory        82977
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) -> B) or ((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-920 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-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82977.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) 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-920, 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-82978
in-theory        82978
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((B or ((A and B) or B)) -> ((C and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-920 tm-775 ((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-82978.        ((((A and B) or B) -> ((C and D) -> C)) and ((B or ((A and B) or B)) -> ((C and D) -> C))), M:tm-920, m:tm-775, u:((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-82979
in-theory        82979
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)) -> C) or ((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-920 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-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82979.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) 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-920, 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-82980
in-theory        82980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((B or ((A and B) or B)) -> ((C and D) -> D)))
theorem-size     25
proof            (modus-ponens tm-920 tm-777 ((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-82980.        ((((A and B) or B) -> ((C and D) -> D)) and ((B or ((A and B) or B)) -> ((C and D) -> D))), M:tm-920, m:tm-777, u:((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-82981
in-theory        82981
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((B or ((A and B) or B)) -> ((C -> (D -> C)) and B)))
theorem-size     29
proof            (modus-ponens tm-920 tm-778 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-82981.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((B or ((A and B) or B)) -> ((C -> (D -> C)) and B))), M:tm-920, m:tm-778, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-82982
in-theory        82982
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((B or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     45
proof            (modus-ponens tm-920 tm-779 ((A (and Am Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82982.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((B or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-920, m:tm-779, u:((A (and Am Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-82983
in-theory        82983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((B or ((A and B) or B)) -> (((C and D) -> C) and B)))
theorem-size     29
proof            (modus-ponens tm-920 tm-780 ((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82983.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((B or ((A and B) or B)) -> (((C and D) -> C) and B))), M:tm-920, m:tm-780, u:((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-82984
in-theory        82984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((B or ((A and B) or B)) -> (((C and D) -> D) and B)))
theorem-size     29
proof            (modus-ponens tm-920 tm-781 ((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82984.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((B or ((A and B) or B)) -> (((C and D) -> D) and B))), M:tm-920, m:tm-781, u:((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-82985
in-theory        82985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((B or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B)))
theorem-size     33
proof            (modus-ponens tm-920 tm-782 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82985.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((B or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B))), M:tm-920, m:tm-782, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-82986
in-theory        82986
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C))))
theorem-size     35
proof            (modus-ponens tm-920 tm-783 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82986.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C)))), M:tm-920, m:tm-783, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-82987
in-theory        82987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((B or ((A and B) or B)) -> (C -> (D -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-920 tm-784 ((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), 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-82987.        ((((A and B) or B) -> (C -> (D -> (C and D)))) and ((B or ((A and B) or B)) -> (C -> (D -> (C and D))))), M:tm-920, m:tm-784, u:((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-82988
in-theory        82988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((B or ((A and B) or B)) -> ((C -> (C or D)) and B)))
theorem-size     29
proof            (modus-ponens tm-920 tm-785 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-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-82988.        ((((A and B) or B) -> ((C -> (C or D)) and B)) and ((B or ((A and B) or B)) -> ((C -> (C or D)) and B))), M:tm-920, m:tm-785, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-82989
in-theory        82989
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (C or D))) and ((B or ((A and B) or B)) -> (C -> (C or D))))
theorem-size     25
proof            (modus-ponens tm-920 tm-786 ((A (and Am Bm)) (B Bm) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-82989.        ((((A and B) or B) -> (C -> (C or D))) and ((B or ((A and B) or B)) -> (C -> (C or D)))), M:tm-920, m:tm-786, u:((A (and Am Bm)) (B Bm) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-82990
in-theory        82990
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((B or ((A and B) or B)) -> ((C -> (D or C)) and B)))
theorem-size     29
proof            (modus-ponens tm-920 tm-787 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-82990.        ((((A and B) or B) -> ((C -> (D or C)) and B)) and ((B or ((A and B) or B)) -> ((C -> (D or C)) and B))), M:tm-920, m:tm-787, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-82991
in-theory        82991
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D or C))) and ((B or ((A and B) or B)) -> (C -> (D or C))))
theorem-size     25
proof            (modus-ponens tm-920 tm-788 ((A (and Am Bm)) (B Bm) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82991.        ((((A and B) or B) -> (C -> (D or C))) and ((B or ((A and B) or B)) -> (C -> (D or C)))), M:tm-920, m:tm-788, u:((A (and Am Bm)) (B Bm) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-82992
in-theory        82992
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((B -> C) -> D) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D)))
theorem-size     49
proof            (modus-ponens tm-920 tm-789 ((A (and Am (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-82992.        ((((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and ((((B -> C) -> D) or ((A and ((B -> C) -> D)) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D))), M:tm-920, m:tm-789, u:((A (and Am (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-82993
in-theory        82993
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((((B -> C) -> (B -> D)) -> E) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     85
proof            (modus-ponens tm-920 tm-790 ((A (and Am (-> (-> (-> 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-5 tm-8 tm-7 tm-4)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-82993.        ((((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and (((((B -> C) -> (B -> D)) -> E) or ((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-920, m:tm-790, u:((A (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-82994
in-theory        82994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C)))
theorem-size     39
proof            (modus-ponens tm-920 tm-791 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82994.        ((((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> (((B and D) or B) -> C))), M:tm-920, m:tm-791, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-82995
in-theory        82995
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C)))
theorem-size     39
proof            (modus-ponens tm-920 tm-792 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82995.        ((((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)) and (((B -> C) or ((A and (B -> C)) or (B -> C))) -> (((D and B) or B) -> C))), M:tm-920, m:tm-792, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Dm Bm) Bm) Cm)))
================================================================
tm-name          tm-82996
in-theory        82996
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B)))
theorem-size     39
proof            (modus-ponens tm-920 tm-793 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Dm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-82996.        (((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)) and (((A -> B) or (((A -> B) and C) or (A -> B))) -> (((D and A) or A) -> B))), M:tm-920, m:tm-793, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Dm Am) Am) Bm)))
================================================================
tm-name          tm-82997
in-theory        82997
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     63
proof            (modus-ponens tm-920 tm-794 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-82997.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-920, m:tm-794, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-82998
in-theory        82998
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((B -> A) or (A or (B -> A))) -> (((C and B) or B) -> A)))
theorem-size     31
proof            (modus-ponens tm-920 tm-795 ((A Am) (B (-> Bm Am)) (C (-> (or (and Cm Bm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-82998.        (((A or (B -> A)) -> (((C and B) or B) -> A)) and (((B -> A) or (A or (B -> A))) -> (((C and B) or B) -> A))), M:tm-920, m:tm-795, u:((A Am) (B (-> Bm Am)) (C (-> (or (and Cm Bm) Bm) Am)))
================================================================
tm-name          tm-82999
in-theory        82999
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B))))
theorem-size     41
proof            (modus-ponens tm-920 tm-808 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-82999.        (((A or B) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B))) and ((B or (A or B)) -> (((C -> D) -> (((E and C) or C) -> D)) and (A or B)))), M:tm-920, m:tm-808, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-83000
in-theory        83000
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C -> D) -> (((E and C) or C) -> D))) and ((B or (A or B)) -> ((C -> D) -> (((E and C) or C) -> D))))
theorem-size     33
proof            (modus-ponens tm-920 tm-810 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-83000.        (((A or B) -> ((C -> D) -> (((E and C) or C) -> D))) and ((B or (A or B)) -> ((C -> D) -> (((E and C) or C) -> D)))), M:tm-920, m:tm-810, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-83001
in-theory        83001
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (B -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-811 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83001.        (((A or (B -> (A and B))) -> (C -> (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (B -> (A and B))))), M:tm-920, m:tm-811, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-83002
in-theory        83002
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C))))
theorem-size     41
proof            (modus-ponens tm-920 tm-812 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83002.        (((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> ((B -> (A and B)) and C)))), M:tm-920, m:tm-812, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (and (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-83003
in-theory        83003
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C)))
theorem-size     37
proof            (modus-ponens tm-920 tm-813 ((A Am) (B (-> Bm (and Am Bm))) (C (or (-> Bm (and Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83003.        (((A or (B -> (A and B))) -> ((B -> (A and B)) or C)) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((B -> (A and B)) or C))), M:tm-920, m:tm-813, u:((A Am) (B (-> Bm (and Am Bm))) (C (or (-> Bm (and Am Bm)) Cm)))
================================================================
tm-name          tm-83004
in-theory        83004
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C or (B -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-814 ((A Am) (B (-> Bm (and Am Bm))) (C (or Cm (-> Bm (and Am Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-83004.        (((A or (B -> (A and B))) -> (C or (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C or (B -> (A and B))))), M:tm-920, m:tm-814, u:((A Am) (B (-> Bm (and Am Bm))) (C (or Cm (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-83005
in-theory        83005
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-920 tm-815 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83005.        (((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))), M:tm-920, m:tm-815, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-83006
in-theory        83006
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B))))
theorem-size     41
proof            (modus-ponens tm-920 tm-816 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83006.        (((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((B -> (not (A and B))) -> (not B)))), M:tm-920, m:tm-816, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-83007
in-theory        83007
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (D -> C))))
theorem-size     33
proof            (modus-ponens tm-920 tm-817 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83007.        (((A or (B -> (A and B))) -> (C -> (D -> C))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (D -> C)))), M:tm-920, m:tm-817, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-83008
in-theory        83008
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> B)) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (B -> B)))
theorem-size     29
proof            (modus-ponens tm-920 tm-818 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-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-83008.        (((A or (B -> (A and B))) -> (B -> B)) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (B -> B))), M:tm-920, m:tm-818, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm Bm)))
================================================================
tm-name          tm-83009
in-theory        83009
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     49
proof            (modus-ponens tm-920 tm-819 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-14.           (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-83009.        (((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-920, m:tm-819, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-83010
in-theory        83010
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C and D) -> C)))
theorem-size     33
proof            (modus-ponens tm-920 tm-820 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83010.        (((A or (B -> (A and B))) -> ((C and D) -> C)) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C and D) -> C))), M:tm-920, m:tm-820, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-83011
in-theory        83011
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C and D) -> D)))
theorem-size     33
proof            (modus-ponens tm-920 tm-821 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83011.        (((A or (B -> (A and B))) -> ((C and D) -> D)) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C and D) -> D))), M:tm-920, m:tm-821, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-83012
in-theory        83012
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B)))))
theorem-size     45
proof            (modus-ponens tm-920 tm-822 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83012.        (((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (D -> C)) and (B -> (A and B))))), M:tm-920, m:tm-822, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-83013
in-theory        83013
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))
theorem-size     61
proof            (modus-ponens tm-920 tm-823 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, 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-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-83013.        (((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))), M:tm-920, m:tm-823, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-83014
in-theory        83014
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B)))))
theorem-size     45
proof            (modus-ponens tm-920 tm-824 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83014.        (((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C and D) -> C) and (B -> (A and B))))), M:tm-920, m:tm-824, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-83015
in-theory        83015
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B)))))
theorem-size     45
proof            (modus-ponens tm-920 tm-825 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83015.        (((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C and D) -> D) and (B -> (A and B))))), M:tm-920, m:tm-825, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-83016
in-theory        83016
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))))
theorem-size     49
proof            (modus-ponens tm-920 tm-826 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83016.        (((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))), M:tm-920, m:tm-826, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-83017
in-theory        83017
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (B -> (B and (A and B)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-827 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-83017.        (((A or (B -> (A and B))) -> (B -> (B and (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (B -> (B and (A and B))))), M:tm-920, m:tm-827, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-83018
in-theory        83018
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (D -> (C and D)))))
theorem-size     37
proof            (modus-ponens tm-920 tm-828 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83018.        (((A or (B -> (A and B))) -> (C -> (D -> (C and D)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (D -> (C and D))))), M:tm-920, m:tm-828, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-83019
in-theory        83019
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B)))))
theorem-size     45
proof            (modus-ponens tm-920 tm-829 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83019.        (((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (C or D)) and (B -> (A and B))))), M:tm-920, m:tm-829, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-83020
in-theory        83020
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (C or D))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (C or D))))
theorem-size     33
proof            (modus-ponens tm-920 tm-830 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83020.        (((A or (B -> (A and B))) -> (C -> (C or D))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (C or D)))), M:tm-920, m:tm-830, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-83021
in-theory        83021
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B)))))
theorem-size     45
proof            (modus-ponens tm-920 tm-831 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-83021.        (((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> ((C -> (D or C)) and (B -> (A and B))))), M:tm-920, m:tm-831, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-83022
in-theory        83022
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (C -> (D or C))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (D or C))))
theorem-size     33
proof            (modus-ponens tm-920 tm-832 ((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-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-83022.        (((A or (B -> (A and B))) -> (C -> (D or C))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (C -> (D or C)))), M:tm-920, m:tm-832, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-83023
in-theory        83023
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((((B -> C) -> (A and (B -> C))) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C)))))
theorem-size     57
proof            (modus-ponens tm-920 tm-833 ((A Am) (B (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83023.        (((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))) and ((((B -> C) -> (A and (B -> C))) or (A or ((B -> C) -> (A and (B -> C))))) -> ((C or (B -> C)) -> (A and (B -> C))))), M:tm-920, m:tm-833, u:((A Am) (B (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-83024
in-theory        83024
times-derived    1
----------------------------------------------------------------
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))))) and (((((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))) or (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     105
proof            (modus-ponens tm-920 tm-834 ((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (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-5 tm-8 tm-7)
proof-size       315
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (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-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-83024.        (((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))))) and (((((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))) or (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-920, m:tm-834, u:((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-83025
in-theory        83025
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B))))
theorem-size     41
proof            (modus-ponens tm-920 tm-835 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Bm Cm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83025.        (((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((B and C) or B) -> (A and B)))), M:tm-920, m:tm-835, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Bm Cm) Bm) (and Am Bm))))
================================================================
tm-name          tm-83026
in-theory        83026
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B))))
theorem-size     41
proof            (modus-ponens tm-920 tm-836 ((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Cm Bm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83026.        (((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C and B) or B) -> (A and B)))), M:tm-920, m:tm-836, u:((A Am) (B (-> Bm (and Am Bm))) (C (-> (or (and Cm Bm) Bm) (and Am Bm))))
================================================================
tm-name          tm-83027
in-theory        83027
times-derived    1
----------------------------------------------------------------
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))))) and ((((B -> (C and B)) -> (A and (B -> (C and B)))) or (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     77
proof            (modus-ponens tm-920 tm-837 ((A Am) (B (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83027.        (((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))) and ((((B -> (C and B)) -> (A and (B -> (C and B)))) or (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-920, m:tm-837, u:((A Am) (B (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (C (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))
================================================================
tm-name          tm-83028
in-theory        83028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((B -> (C and B)) -> D) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D)))
theorem-size     63
proof            (modus-ponens tm-920 tm-838 ((A (and Am (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-83028.        ((((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)) and ((((B -> (C and B)) -> D) or ((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D))) -> ((C or (B -> (C and B))) -> D))), M:tm-920, m:tm-838, u:((A (and Am (-> (-> Bm (and Cm Bm)) Dm))) (B (-> (-> Bm (and Cm Bm)) Dm)) (C (-> (or Cm (-> Bm (and Cm Bm))) Dm)))
================================================================
tm-name          tm-83029
in-theory        83029
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((((A -> (B and A)) -> C) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C)))
theorem-size     63
proof            (modus-ponens tm-920 tm-839 ((A (and (-> (-> Am (and Bm Am)) Cm) Dm)) (B (-> (-> Am (and Bm Am)) Cm)) (C (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-83029.        ((((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)) and ((((A -> (B and A)) -> C) or ((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C))) -> ((B or (A -> (B and A))) -> C))), M:tm-920, m:tm-839, u:((A (and (-> (-> Am (and Bm Am)) Cm) Dm)) (B (-> (-> Am (and Bm Am)) Cm)) (C (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-83030
in-theory        83030
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((((A -> (B and A)) -> (A -> C)) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     69
proof            (modus-ponens tm-920 tm-840 ((A (-> Am (-> (and Bm Am) Cm))) (B (-> (-> Am (and Bm Am)) (-> Am Cm))) (C (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-83030.        ((((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))) and ((((A -> (B and A)) -> (A -> C)) or ((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C)))) -> ((B or (A -> (B and A))) -> (A -> C)))), M:tm-920, m:tm-840, u:((A (-> Am (-> (and Bm Am) Cm))) (B (-> (-> Am (and Bm Am)) (-> Am Cm))) (C (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))
================================================================
tm-name          tm-83031
in-theory        83031
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((((B -> (C and B)) -> A) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A)))
theorem-size     47
proof            (modus-ponens tm-920 tm-841 ((A Am) (B (-> (-> Bm (and Cm Bm)) Am)) (C (-> (or Cm (-> Bm (and Cm Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-83031.        (((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)) and ((((B -> (C and B)) -> A) or (A or ((B -> (C and B)) -> A))) -> ((C or (B -> (C and B))) -> A))), M:tm-920, m:tm-841, u:((A Am) (B (-> (-> Bm (and Cm Bm)) Am)) (C (-> (or Cm (-> Bm (and Cm Bm))) Am)))
================================================================
tm-name          tm-83032
in-theory        83032
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B))))
theorem-size     53
proof            (modus-ponens tm-920 tm-855 ((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83032.        (((A or B) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)) and (A or B)))), M:tm-920, m:tm-855, u:((Am (or A B)) (C (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (or A B))))
================================================================
tm-name          tm-83033
in-theory        83033
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((B or (A or B)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))))
theorem-size     45
proof            (modus-ponens tm-920 tm-857 ((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-83033.        (((A or B) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))) and ((B or (A or B)) -> (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))), M:tm-920, m:tm-857, u:((Am (or A B)) (C (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-83034
in-theory        83034
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (A or B))) and (((A or B) or (A or (A or B))) -> (C -> (A or B))))
theorem-size     27
proof            (modus-ponens tm-920 tm-858 ((A Am) (B (or Am Bm)) (C (-> Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-83034.        (((A or (A or B)) -> (C -> (A or B))) and (((A or B) or (A or (A or B))) -> (C -> (A or B)))), M:tm-920, m:tm-858, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Am Bm))))
================================================================
tm-name          tm-83035
in-theory        83035
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> ((A or B) and C))) and (((A or B) or (A or (A or B))) -> (C -> ((A or B) and C))))
theorem-size     31
proof            (modus-ponens tm-920 tm-859 ((A Am) (B (or Am Bm)) (C (-> Cm (and (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-83035.        (((A or (A or B)) -> (C -> ((A or B) and C))) and (((A or B) or (A or (A or B))) -> (C -> ((A or B) and C)))), M:tm-920, m:tm-859, u:((A Am) (B (or Am Bm)) (C (-> Cm (and (or Am Bm) Cm))))
================================================================
tm-name          tm-83036
in-theory        83036
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((A or B) or C)) and (((A or B) or (A or (A or B))) -> ((A or B) or C)))
theorem-size     27
proof            (modus-ponens tm-920 tm-860 ((A Am) (B (or Am Bm)) (C (or (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-83036.        (((A or (A or B)) -> ((A or B) or C)) and (((A or B) or (A or (A or B))) -> ((A or B) or C))), M:tm-920, m:tm-860, u:((A Am) (B (or Am Bm)) (C (or (or Am Bm) Cm)))
================================================================
tm-name          tm-83037
in-theory        83037
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C or (A or B))) and (((A or B) or (A or (A or B))) -> (C or (A or B))))
theorem-size     27
proof            (modus-ponens tm-920 tm-861 ((A Am) (B (or Am Bm)) (C (or Cm (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-83037.        (((A or (A or B)) -> (C or (A or B))) and (((A or B) or (A or (A or B))) -> (C or (A or B)))), M:tm-920, m:tm-861, u:((A Am) (B (or Am Bm)) (C (or Cm (or Am Bm))))
================================================================
tm-name          tm-83038
in-theory        83038
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> C))) and (((A or B) or (A or (A or B))) -> (C -> (D -> C))))
theorem-size     27
proof            (modus-ponens tm-920 tm-862 ((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-83038.        (((A or (A or B)) -> (C -> (D -> C))) and (((A or B) or (A or (A or B))) -> (C -> (D -> C)))), M:tm-920, m:tm-862, u:((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-83039
in-theory        83039
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or B) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     43
proof            (modus-ponens tm-920 tm-863 ((A Am) (B (or Am Bm)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-14.           (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-83039.        (((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or B) or (A or (A or B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-920, m:tm-863, u:((A Am) (B (or Am Bm)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-83040
in-theory        83040
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> C)) and (((A or B) or (A or (A or B))) -> ((C and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-920 tm-864 ((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-83040.        (((A or (A or B)) -> ((C and D) -> C)) and (((A or B) or (A or (A or B))) -> ((C and D) -> C))), M:tm-920, m:tm-864, u:((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-83041
in-theory        83041
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C and D) -> D)) and (((A or B) or (A or (A or B))) -> ((C and D) -> D)))
theorem-size     27
proof            (modus-ponens tm-920 tm-865 ((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-83041.        (((A or (A or B)) -> ((C and D) -> D)) and (((A or B) or (A or (A or B))) -> ((C and D) -> D))), M:tm-920, m:tm-865, u:((A Am) (B (or Am Bm)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-83042
in-theory        83042
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((A or B) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B))))
theorem-size     35
proof            (modus-ponens tm-920 tm-866 ((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-83042.        (((A or (A or B)) -> ((C -> (D -> C)) and (A or B))) and (((A or B) or (A or (A or B))) -> ((C -> (D -> C)) and (A or B)))), M:tm-920, m:tm-866, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-83043
in-theory        83043
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((A or B) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))
theorem-size     51
proof            (modus-ponens tm-920 tm-867 ((A Am) (B (or Am Bm)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-83043.        (((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))) and (((A or B) or (A or (A or B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))), M:tm-920, m:tm-867, u:((A Am) (B (or Am Bm)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))
================================================================
tm-name          tm-83044
in-theory        83044
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((A or B) or (A or (A or B))) -> (((C and D) -> C) and (A or B))))
theorem-size     35
proof            (modus-ponens tm-920 tm-868 ((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Cm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-83044.        (((A or (A or B)) -> (((C and D) -> C) and (A or B))) and (((A or B) or (A or (A or B))) -> (((C and D) -> C) and (A or B)))), M:tm-920, m:tm-868, u:((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Cm) (or Am Bm))))
================================================================
tm-name          tm-83045
in-theory        83045
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((A or B) or (A or (A or B))) -> (((C and D) -> D) and (A or B))))
theorem-size     35
proof            (modus-ponens tm-920 tm-869 ((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Dm) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-83045.        (((A or (A or B)) -> (((C and D) -> D) and (A or B))) and (((A or B) or (A or (A or B))) -> (((C and D) -> D) and (A or B)))), M:tm-920, m:tm-869, u:((A Am) (B (or Am Bm)) (C (and (-> (and Cm Dm) Dm) (or Am Bm))))
================================================================
tm-name          tm-83046
in-theory        83046
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((A or B) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B))))
theorem-size     39
proof            (modus-ponens tm-920 tm-870 ((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-83046.        (((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))) and (((A or B) or (A or (A or B))) -> ((C -> (D -> (C and D))) and (A or B)))), M:tm-920, m:tm-870, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))
================================================================
tm-name          tm-83047
in-theory        83047
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((A or B) or (A or (A or B))) -> (C -> (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-920 tm-871 ((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-83047.        (((A or (A or B)) -> (C -> (D -> (C and D)))) and (((A or B) or (A or (A or B))) -> (C -> (D -> (C and D))))), M:tm-920, m:tm-871, u:((A Am) (B (or Am Bm)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-83048
in-theory        83048
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((A or B) or (A or (A or B))) -> ((C -> (C or D)) and (A or B))))
theorem-size     35
proof            (modus-ponens tm-920 tm-872 ((A Am) (B (or Am Bm)) (C (and (-> Cm (or Cm Dm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-83048.        (((A or (A or B)) -> ((C -> (C or D)) and (A or B))) and (((A or B) or (A or (A or B))) -> ((C -> (C or D)) and (A or B)))), M:tm-920, m:tm-872, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (or Cm Dm)) (or Am Bm))))
================================================================
tm-name          tm-83049
in-theory        83049
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (C or D))) and (((A or B) or (A or (A or B))) -> (C -> (C or D))))
theorem-size     27
proof            (modus-ponens tm-920 tm-873 ((A Am) (B (or Am Bm)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-83049.        (((A or (A or B)) -> (C -> (C or D))) and (((A or B) or (A or (A or B))) -> (C -> (C or D)))), M:tm-920, m:tm-873, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-83050
in-theory        83050
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((A or B) or (A or (A or B))) -> ((C -> (D or C)) and (A or B))))
theorem-size     35
proof            (modus-ponens tm-920 tm-874 ((A Am) (B (or Am Bm)) (C (and (-> Cm (or Dm Cm)) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-83050.        (((A or (A or B)) -> ((C -> (D or C)) and (A or B))) and (((A or B) or (A or (A or B))) -> ((C -> (D or C)) and (A or B)))), M:tm-920, m:tm-874, u:((A Am) (B (or Am Bm)) (C (and (-> Cm (or Dm Cm)) (or Am Bm))))
================================================================
tm-name          tm-83051
in-theory        83051
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (C -> (D or C))) and (((A or B) or (A or (A or B))) -> (C -> (D or C))))
theorem-size     27
proof            (modus-ponens tm-920 tm-875 ((A Am) (B (or Am Bm)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-83051.        (((A or (A or B)) -> (C -> (D or C))) and (((A or B) or (A or (A or B))) -> (C -> (D or C)))), M:tm-920, m:tm-875, u:((A Am) (B (or Am Bm)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-83052
in-theory        83052
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((((B or C) -> (A and (B or C))) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C)))))
theorem-size     57
proof            (modus-ponens tm-920 tm-876 ((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-83052.        (((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))) and ((((B or C) -> (A and (B or C))) or (A or ((B or C) -> (A and (B or C))))) -> ((B or (B or C)) -> (A and (B or C))))), M:tm-920, m:tm-876, u:((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-83053
in-theory        83053
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((B or C) -> D) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D)))
theorem-size     49
proof            (modus-ponens tm-920 tm-877 ((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-83053.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)) and ((((B or C) -> D) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((B or (B or C)) -> D))), M:tm-920, m:tm-877, u:((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-83054
in-theory        83054
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((((A or B) -> C) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C)))
theorem-size     49
proof            (modus-ponens tm-920 tm-878 ((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-83054.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)) and ((((A or B) -> C) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((A or (A or B)) -> C))), M:tm-920, m:tm-878, u:((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-83055
in-theory        83055
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((((B or C) -> A) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A)))
theorem-size     37
proof            (modus-ponens tm-920 tm-879 ((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-83055.        (((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)) and ((((B or C) -> A) or (A or ((B or C) -> A))) -> ((B or (B or C)) -> A))), M:tm-920, m:tm-879, u:((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-83056
in-theory        83056
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-920 tm-893 ((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-83056.        (((A or B) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C or D) -> E) -> ((C or (C or D)) -> E)) and (A or B)))), M:tm-920, m:tm-893, u:((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-83057
in-theory        83057
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((B or (A or B)) -> (((C or D) -> E) -> ((C or (C or D)) -> E))))
theorem-size     37
proof            (modus-ponens tm-920 tm-895 ((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-83057.        (((A or B) -> (((C or D) -> E) -> ((C or (C or D)) -> E))) and ((B or (A or B)) -> (((C or D) -> E) -> ((C or (C or D)) -> E)))), M:tm-920, m:tm-895, u:((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-83058
in-theory        83058
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (B or A))) and (((B or A) or (A or (B or A))) -> (C -> (B or A))))
theorem-size     27
proof            (modus-ponens tm-920 tm-896 ((A Am) (B (or Bm Am)) (C (-> Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-83058.        (((A or (B or A)) -> (C -> (B or A))) and (((B or A) or (A or (B or A))) -> (C -> (B or A)))), M:tm-920, m:tm-896, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Bm Am))))
================================================================
tm-name          tm-83059
in-theory        83059
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> ((B or A) and C))) and (((B or A) or (A or (B or A))) -> (C -> ((B or A) and C))))
theorem-size     31
proof            (modus-ponens tm-920 tm-897 ((A Am) (B (or Bm Am)) (C (-> Cm (and (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-83059.        (((A or (B or A)) -> (C -> ((B or A) and C))) and (((B or A) or (A or (B or A))) -> (C -> ((B or A) and C)))), M:tm-920, m:tm-897, u:((A Am) (B (or Bm Am)) (C (-> Cm (and (or Bm Am) Cm))))
================================================================
tm-name          tm-83060
in-theory        83060
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((B or A) or C)) and (((B or A) or (A or (B or A))) -> ((B or A) or C)))
theorem-size     27
proof            (modus-ponens tm-920 tm-898 ((A Am) (B (or Bm Am)) (C (or (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-83060.        (((A or (B or A)) -> ((B or A) or C)) and (((B or A) or (A or (B or A))) -> ((B or A) or C))), M:tm-920, m:tm-898, u:((A Am) (B (or Bm Am)) (C (or (or Bm Am) Cm)))
================================================================
tm-name          tm-83061
in-theory        83061
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C or (B or A))) and (((B or A) or (A or (B or A))) -> (C or (B or A))))
theorem-size     27
proof            (modus-ponens tm-920 tm-899 ((A Am) (B (or Bm Am)) (C (or Cm (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-83061.        (((A or (B or A)) -> (C or (B or A))) and (((B or A) or (A or (B or A))) -> (C or (B or A)))), M:tm-920, m:tm-899, u:((A Am) (B (or Bm Am)) (C (or Cm (or Bm Am))))
================================================================
tm-name          tm-83062
in-theory        83062
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> C))) and (((B or A) or (A or (B or A))) -> (C -> (D -> C))))
theorem-size     27
proof            (modus-ponens tm-920 tm-900 ((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-83062.        (((A or (B or A)) -> (C -> (D -> C))) and (((B or A) or (A or (B or A))) -> (C -> (D -> C)))), M:tm-920, m:tm-900, u:((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-83063
in-theory        83063
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((B or A) or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     43
proof            (modus-ponens tm-920 tm-901 ((A Am) (B (or Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-14.           (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-83063.        (((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((B or A) or (A or (B or A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-920, m:tm-901, u:((A Am) (B (or Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-83064
in-theory        83064
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> C)) and (((B or A) or (A or (B or A))) -> ((C and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-920 tm-902 ((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-83064.        (((A or (B or A)) -> ((C and D) -> C)) and (((B or A) or (A or (B or A))) -> ((C and D) -> C))), M:tm-920, m:tm-902, u:((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-83065
in-theory        83065
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C and D) -> D)) and (((B or A) or (A or (B or A))) -> ((C and D) -> D)))
theorem-size     27
proof            (modus-ponens tm-920 tm-903 ((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-83065.        (((A or (B or A)) -> ((C and D) -> D)) and (((B or A) or (A or (B or A))) -> ((C and D) -> D))), M:tm-920, m:tm-903, u:((A Am) (B (or Bm Am)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-83066
in-theory        83066
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((B or A) or (A or (B or A))) -> ((C -> (D -> C)) and (B or A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-904 ((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-83066.        (((A or (B or A)) -> ((C -> (D -> C)) and (B or A))) and (((B or A) or (A or (B or A))) -> ((C -> (D -> C)) and (B or A)))), M:tm-920, m:tm-904, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-83067
in-theory        83067
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((B or A) or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))
theorem-size     51
proof            (modus-ponens tm-920 tm-905 ((A Am) (B (or Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-83067.        (((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))) and (((B or A) or (A or (B or A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))), M:tm-920, m:tm-905, u:((A Am) (B (or Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))
================================================================
tm-name          tm-83068
in-theory        83068
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((B or A) or (A or (B or A))) -> (((C and D) -> C) and (B or A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-906 ((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Cm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-83068.        (((A or (B or A)) -> (((C and D) -> C) and (B or A))) and (((B or A) or (A or (B or A))) -> (((C and D) -> C) and (B or A)))), M:tm-920, m:tm-906, u:((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Cm) (or Bm Am))))
================================================================
tm-name          tm-83069
in-theory        83069
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((B or A) or (A or (B or A))) -> (((C and D) -> D) and (B or A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-907 ((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Dm) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-83069.        (((A or (B or A)) -> (((C and D) -> D) and (B or A))) and (((B or A) or (A or (B or A))) -> (((C and D) -> D) and (B or A)))), M:tm-920, m:tm-907, u:((A Am) (B (or Bm Am)) (C (and (-> (and Cm Dm) Dm) (or Bm Am))))
================================================================
tm-name          tm-83070
in-theory        83070
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((B or A) or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A))))
theorem-size     39
proof            (modus-ponens tm-920 tm-908 ((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-83070.        (((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))) and (((B or A) or (A or (B or A))) -> ((C -> (D -> (C and D))) and (B or A)))), M:tm-920, m:tm-908, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))
================================================================
tm-name          tm-83071
in-theory        83071
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((B or A) or (A or (B or A))) -> (C -> (D -> (C and D)))))
theorem-size     31
proof            (modus-ponens tm-920 tm-909 ((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-83071.        (((A or (B or A)) -> (C -> (D -> (C and D)))) and (((B or A) or (A or (B or A))) -> (C -> (D -> (C and D))))), M:tm-920, m:tm-909, u:((A Am) (B (or Bm Am)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-83072
in-theory        83072
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((B or A) or (A or (B or A))) -> ((C -> (C or D)) and (B or A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-910 ((A Am) (B (or Bm Am)) (C (and (-> Cm (or Cm Dm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-83072.        (((A or (B or A)) -> ((C -> (C or D)) and (B or A))) and (((B or A) or (A or (B or A))) -> ((C -> (C or D)) and (B or A)))), M:tm-920, m:tm-910, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (or Cm Dm)) (or Bm Am))))
================================================================
tm-name          tm-83073
in-theory        83073
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (C or D))) and (((B or A) or (A or (B or A))) -> (C -> (C or D))))
theorem-size     27
proof            (modus-ponens tm-920 tm-911 ((A Am) (B (or Bm Am)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-83073.        (((A or (B or A)) -> (C -> (C or D))) and (((B or A) or (A or (B or A))) -> (C -> (C or D)))), M:tm-920, m:tm-911, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-83074
in-theory        83074
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((B or A) or (A or (B or A))) -> ((C -> (D or C)) and (B or A))))
theorem-size     35
proof            (modus-ponens tm-920 tm-912 ((A Am) (B (or Bm Am)) (C (and (-> Cm (or Dm Cm)) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-83074.        (((A or (B or A)) -> ((C -> (D or C)) and (B or A))) and (((B or A) or (A or (B or A))) -> ((C -> (D or C)) and (B or A)))), M:tm-920, m:tm-912, u:((A Am) (B (or Bm Am)) (C (and (-> Cm (or Dm Cm)) (or Bm Am))))
================================================================
tm-name          tm-83075
in-theory        83075
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (C -> (D or C))) and (((B or A) or (A or (B or A))) -> (C -> (D or C))))
theorem-size     27
proof            (modus-ponens tm-920 tm-913 ((A Am) (B (or Bm Am)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-83075.        (((A or (B or A)) -> (C -> (D or C))) and (((B or A) or (A or (B or A))) -> (C -> (D or C)))), M:tm-920, m:tm-913, u:((A Am) (B (or Bm Am)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-83076
in-theory        83076
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((((B or C) -> (A and (B or C))) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C)))))
theorem-size     57
proof            (modus-ponens tm-920 tm-914 ((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-83076.        (((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))) and ((((B or C) -> (A and (B or C))) or (A or ((B or C) -> (A and (B or C))))) -> ((C or (B or C)) -> (A and (B or C))))), M:tm-920, m:tm-914, u:((A Am) (B (-> (or Bm Cm) (and Am (or Bm Cm)))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-83077
in-theory        83077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((B or C) -> D) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D)))
theorem-size     49
proof            (modus-ponens tm-920 tm-915 ((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-83077.        ((((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)) and ((((B or C) -> D) or ((A and ((B or C) -> D)) or ((B or C) -> D))) -> ((C or (B or C)) -> D))), M:tm-920, m:tm-915, u:((A (and Am (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-83078
in-theory        83078
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((((A or B) -> C) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C)))
theorem-size     49
proof            (modus-ponens tm-920 tm-916 ((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B 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-83078.        ((((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)) and ((((A or B) -> C) or ((((A or B) -> C) and D) or ((A or B) -> C))) -> ((B or (A or B)) -> C))), M:tm-920, m:tm-916, u:((A (and (-> (or Am Bm) Cm) Dm)) (B (-> (or Am Bm) Cm)) (C (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-83079
in-theory        83079
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((((B or C) -> A) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A)))
theorem-size     37
proof            (modus-ponens tm-920 tm-917 ((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> 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-83079.        (((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)) and ((((B or C) -> A) or (A or ((B or C) -> A))) -> ((C or (B or C)) -> A))), M:tm-920, m:tm-917, u:((A Am) (B (-> (or Bm Cm) Am)) (C (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-83080
in-theory        83080
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-893 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83080.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-893, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83081
in-theory        83081
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((A or B) or (A or (A or B))) -> C)))
theorem-size     33
proof            (modus-ponens tm-890 tm-920 ((A Am) (Bm (or Am B)) (C Cm) (D (and (-> (or Am (or Am B)) Cm) (-> (or (or Am B) (or Am (or Am B))) Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83081.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((A or (A or B)) -> C) and (((A or B) or (A or (A or B))) -> C))), M:tm-890, m:tm-920, u:((A Am) (Bm (or Am B)) (C Cm) (D (and (-> (or Am (or Am B)) Cm) (-> (or (or Am B) (or Am (or Am B))) Cm))))
================================================================
tm-name          tm-83082
in-theory        83082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     37
proof            (modus-ponens tm-855 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83082.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-855, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83083
in-theory        83083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((A -> (B and A)) or (B or (A -> (B and A)))) -> C)))
theorem-size     43
proof            (modus-ponens tm-852 tm-920 ((A Am) (Bm (-> B (and Am B))) (C Cm) (D (and (-> (or Am (-> B (and Am B))) Cm) (-> (or (-> B (and Am B)) (or Am (-> B (and Am B)))) Cm)))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83083.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((B or (A -> (B and A))) -> C) and (((A -> (B and A)) or (B or (A -> (B and A)))) -> C))), M:tm-852, m:tm-920, u:((A Am) (Bm (-> B (and Am B))) (C Cm) (D (and (-> (or Am (-> B (and Am B))) Cm) (-> (or (-> B (and Am B)) (or Am (-> B (and Am B)))) Cm))))
================================================================
tm-name          tm-83084
in-theory        83084
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C and (A or B))) -> (((A or B) -> (C and (A or B))) and ((B or (A or B)) -> (C and (A or B)))))
theorem-size     31
proof            (modus-ponens tm-850 tm-920 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Bm (or Am Bm)) (and B (or Am Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       187
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83084.        (((A or B) -> (C and (A or B))) -> (((A or B) -> (C and (A or B))) and ((B or (A or B)) -> (C and (A or B))))), M:tm-850, m:tm-920, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Bm (or Am Bm)) (and B (or Am Bm))))))
================================================================
tm-name          tm-83085
in-theory        83085
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and (A or B))) -> (((A or B) -> (C and (A or B))) and ((B or (A or B)) -> (C and (A or B))))) and ((C or ((A or B) -> (C and (A or B)))) -> (((A or B) -> (C and (A or B))) and ((B or (A or B)) -> (C and (A or B))))))
theorem-size     65
proof            (modus-ponens tm-844 tm-920 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Bm (or Am Bm)) (and B (or Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83085.        ((((A or B) -> (C and (A or B))) -> (((A or B) -> (C and (A or B))) and ((B or (A or B)) -> (C and (A or B))))) and ((C or ((A or B) -> (C and (A or B)))) -> (((A or B) -> (C and (A or B))) and ((B or (A or B)) -> (C and (A or B)))))), M:tm-844, m:tm-920, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Bm (or Am Bm)) (and B (or Am Bm))))))
================================================================
tm-name          tm-83086
in-theory        83086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-808 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-7)
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83086.        (((A -> B) -> (((C and A) or A) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-808, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83087
in-theory        83087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((A or ((C and A) or A)) -> B)))
theorem-size     29
proof            (modus-ponens tm-805 tm-920 ((Am (and A Bm)) (B Bm) (C Cm) (D (and (-> (or (and A Bm) Bm) Cm) (-> (or Bm (or (and A Bm) Bm)) Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83087.        (((A -> B) or (((C and A) or A) -> B)) -> ((((C and A) or A) -> B) and ((A or ((C and A) or A)) -> B))), M:tm-805, m:tm-920, u:((Am (and A Bm)) (B Bm) (C Cm) (D (and (-> (or (and A Bm) Bm) Cm) (-> (or Bm (or (and A Bm) Bm)) Cm))))
================================================================
tm-name          tm-83088
in-theory        83088
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C))))
theorem-size     47
proof            (modus-ponens tm-798 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83088.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((D and ((A or B) -> C)) or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C)))), M:tm-798, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83089
in-theory        83089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-757 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83089.        (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-757, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83090
in-theory        83090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((A or ((A and C) or A)) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-920 ((Am (and Bm B)) (A Bm) (C Cm) (D (and (-> (or (and Bm B) Bm) Cm) (-> (or Bm (or (and Bm B) Bm)) Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83090.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((A or ((A and C) or A)) -> B))), M:tm-754, m:tm-920, u:((Am (and Bm B)) (A Bm) (C Cm) (D (and (-> (or (and Bm B) Bm) Cm) (-> (or Bm (or (and Bm B) Bm)) Cm))))
================================================================
tm-name          tm-83091
in-theory        83091
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C))))
theorem-size     47
proof            (modus-ponens tm-747 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-83091.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C)))), M:tm-747, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83092
in-theory        83092
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 F) -> G) and ((F or (E or F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-708 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83092.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G)))), M:tm-708, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83093
in-theory        83093
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) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)))
theorem-size     65
proof            (modus-ponens tm-705 tm-920 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D Cm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm) (-> (or (-> (-> A B) (-> A C)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       253
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-50.           (((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-83093.        (((((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) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))), M:tm-705, m:tm-920, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D Cm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm) (-> (or (-> (-> A B) (-> A C)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm))))
================================================================
tm-name          tm-83094
in-theory        83094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-665 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-50.           (((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-83094.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-665, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83095
in-theory        83095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((A -> B) or (B or (A -> B))) -> C)))
theorem-size     33
proof            (modus-ponens tm-662 tm-920 ((A Am) (Bm (-> B Am)) (C Cm) (D (and (-> (or Am (-> B Am)) Cm) (-> (or (-> B Am) (or Am (-> B Am))) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83095.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((A -> B) or (B or (A -> B))) -> C))), M:tm-662, m:tm-920, u:((A Am) (Bm (-> B Am)) (C Cm) (D (and (-> (or Am (-> B Am)) Cm) (-> (or (-> B Am) (or Am (-> B Am))) Cm))))
================================================================
tm-name          tm-83096
in-theory        83096
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((C or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-654 tm-920 ((A (or Am Bm)) (B Cm) (C (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-83096.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((C or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C)))), M:tm-654, m:tm-920, u:((A (or Am Bm)) (B Cm) (C (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83097
in-theory        83097
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D or (((A or B) -> C) and ((B or (A or B)) -> C))))
theorem-size     21
proof            (modus-ponens tm-623 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or 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-50.           (((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-83097.        (((A or B) -> C) -> (D or (((A or B) -> C) and ((B or (A or B)) -> C)))), M:tm-623, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83098
in-theory        83098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-622 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or 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-50.           (((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-83098.        ((A -> (B -> (C or B))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-622, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83099
in-theory        83099
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D or (B or C)))) -> (((B or C) -> (D or (B or C))) and ((C or (B or C)) -> (D or (B or C)))))
theorem-size     33
proof            (modus-ponens tm-619 tm-920 ((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (and (-> (or Am Bm) (or B (or Am Bm))) (-> (or Bm (or Am Bm)) (or B (or 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-50.           (((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-83099.        ((A or ((B or C) -> (D or (B or C)))) -> (((B or C) -> (D or (B or C))) and ((C or (B or C)) -> (D or (B or C))))), M:tm-619, m:tm-920, u:((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (and (-> (or Am Bm) (or B (or Am Bm))) (-> (or Bm (or Am Bm)) (or B (or Am Bm))))))
================================================================
tm-name          tm-83100
in-theory        83100
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or 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-50.           (((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-83100.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (E or D))), M:tm-609, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83101
in-theory        83101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-605 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-83101.        ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-605, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83102
in-theory        83102
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (E or D)) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-83102.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (E or D)) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-595, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83103
in-theory        83103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-550 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-50.           (((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-83103.        (((A -> (B or A)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-550, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83104
in-theory        83104
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-540 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-50.           (((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-83104.        ((A or (B -> (C or B))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-540, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83105
in-theory        83105
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-530 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-50.           (((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-83105.        ((A or (B -> (B or C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-530, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83106
in-theory        83106
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-520 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-83106.        ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-520, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83107
in-theory        83107
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-510 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-83107.        ((A or ((B and C) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-510, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83108
in-theory        83108
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-500 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-50.           (((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-83108.        ((A or ((B and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-500, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83109
in-theory        83109
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-490 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-83109.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G)))), M:tm-490, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83110
in-theory        83110
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-480 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or 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-50.           (((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-83110.        ((A or (B -> (C -> B))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-480, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83111
in-theory        83111
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> ((((A or B) -> C) and ((B or (A or B)) -> C)) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83111.        (((A or B) -> C) -> ((((A or B) -> C) and ((B or (A or B)) -> C)) or D)), M:tm-470, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83112
in-theory        83112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-469 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83112.        ((A -> (B -> (B or C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-469, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83113
in-theory        83113
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> ((B or C) or D))) -> (((B or C) -> ((B or C) or D)) and ((C or (B or C)) -> ((B or C) or D))))
theorem-size     33
proof            (modus-ponens tm-466 tm-920 ((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (and (-> (or Am Bm) (or (or Am Bm) B)) (-> (or Bm (or Am Bm)) (or (or Am Bm) B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83113.        ((A or ((B or C) -> ((B or C) or D))) -> (((B or C) -> ((B or C) or D)) and ((C or (B or C)) -> ((B or C) or D)))), M:tm-466, m:tm-920, u:((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (and (-> (or Am Bm) (or (or Am Bm) B)) (-> (or Bm (or Am Bm)) (or (or Am Bm) B)))))
================================================================
tm-name          tm-83114
in-theory        83114
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (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       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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83114.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (D or E))), M:tm-456, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83115
in-theory        83115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-453 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83115.        ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-453, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83116
in-theory        83116
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (D or E)) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83116.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (D or E)) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-443, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83117
in-theory        83117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-409 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83117.        (((A -> (A or B)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-409, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83118
in-theory        83118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-400 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83118.        (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-400, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83119
in-theory        83119
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-391 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83119.        ((((A and B) -> B) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-391, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83120
in-theory        83120
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-382 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83120.        ((((A and B) -> A) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-382, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83121
in-theory        83121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-373 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83121.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G)))), M:tm-373, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83122
in-theory        83122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-364 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83122.        (((A -> (B -> A)) or C) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-364, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83123
in-theory        83123
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> ((((A or B) -> C) and ((B or (A or B)) -> C)) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83123.        (((A or B) -> C) -> (D -> ((((A or B) -> C) and ((B or (A or B)) -> C)) and D))), M:tm-355, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83124
in-theory        83124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-354 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83124.        ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-354, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83125
in-theory        83125
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> ((B or C) and D)))) -> (((B or C) -> (D -> ((B or C) and D))) and ((C or (B or C)) -> (D -> ((B or C) and D)))))
theorem-size     39
proof            (modus-ponens tm-351 tm-920 ((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (and (-> (or Am Bm) (-> B (and (or Am Bm) B))) (-> (or Bm (or Am Bm)) (-> B (and (or Am Bm) B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83125.        ((A or ((B or C) -> (D -> ((B or C) and D)))) -> (((B or C) -> (D -> ((B or C) and D))) and ((C or (B or C)) -> (D -> ((B or C) and D))))), M:tm-351, m:tm-920, u:((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (and (-> (or Am Bm) (-> B (and (or Am Bm) B))) (-> (or Bm (or Am Bm)) (-> B (and (or Am Bm) B))))))
================================================================
tm-name          tm-83126
in-theory        83126
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-83126.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83127
in-theory        83127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E))))
theorem-size     29
proof            (modus-ponens tm-338 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-83127.        (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E)))), M:tm-338, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83128
in-theory        83128
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> (((A or B) -> ((A or B) and C)) and ((B or (A or B)) -> ((A or B) and C))))
theorem-size     37
proof            (modus-ponens tm-335 tm-920 ((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (and (-> (or Am Bm) (and (or Am Bm) B)) (-> (or Bm (or Am Bm)) (and (or Am Bm) B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83128.        ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> (((A or B) -> ((A or B) and C)) and ((B or (A or B)) -> ((A or B) and C)))), M:tm-335, m:tm-920, u:((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (and (-> (or Am Bm) (and (or Am Bm) B)) (-> (or Bm (or Am Bm)) (and (or Am Bm) B)))))
================================================================
tm-name          tm-83129
in-theory        83129
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((A or B) -> C) -> (((A or B) -> C) and (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-328 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-83129.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((A or B) -> C) -> (((A or B) -> C) and (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-328, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83130
in-theory        83130
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-83130.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-327, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83131
in-theory        83131
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((D and E) -> E) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83131.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((D and E) -> E) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-326, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83132
in-theory        83132
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((D and E) -> D) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83132.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((D and E) -> D) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-325, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83133
in-theory        83133
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83133.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-324, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83134
in-theory        83134
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (E -> D)) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83134.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (E -> D)) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-323, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83135
in-theory        83135
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (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       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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83135.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83136
in-theory        83136
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (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       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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83136.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83137
in-theory        83137
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-83137.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83138
in-theory        83138
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((A or B) -> C) -> ((A or B) -> C)))
theorem-size     31
proof            (modus-ponens tm-316 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-83138.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((A or B) -> C) -> ((A or B) -> C))), M:tm-316, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83139
in-theory        83139
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-83139.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83140
in-theory        83140
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((((A or B) -> C) -> (not (((A or B) -> C) and ((B or (A or B)) -> C)))) -> (not ((A or B) -> C))))
theorem-size     47
proof            (modus-ponens tm-313 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-83140.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((((A or B) -> C) -> (not (((A or B) -> C) and ((B or (A or B)) -> C)))) -> (not ((A or B) -> C)))), M:tm-313, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83141
in-theory        83141
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((((A or B) -> C) and ((B or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or (((A or B) -> C) and ((B or (A or B)) -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-312 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-83141.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (((((A or B) -> C) and ((B or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or (((A or B) -> C) and ((B or (A or B)) -> C))) -> D))), M:tm-312, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83142
in-theory        83142
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D or (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (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-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-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-83142.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D or (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-311, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83143
in-theory        83143
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-83143.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) or D)), M:tm-310, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83144
in-theory        83144
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83144.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and D))), M:tm-309, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83145
in-theory        83145
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
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-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-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-83145.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) and (D -> (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))), M:tm-305, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83146
in-theory        83146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-303 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83146.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-303, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83147
in-theory        83147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-270 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83147.        ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-270, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83148
in-theory        83148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-239 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83148.        ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-239, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83149
in-theory        83149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-210 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83149.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G)))), M:tm-210, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83150
in-theory        83150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-183 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83150.        ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-183, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83151
in-theory        83151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-157 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83151.        ((A -> ((B and C) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-157, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83152
in-theory        83152
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-147 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83152.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-147, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83153
in-theory        83153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-134 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83153.        ((A -> ((B and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-134, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83154
in-theory        83154
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-125 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83154.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-125, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83155
in-theory        83155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-113 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83155.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G)))), M:tm-113, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83156
in-theory        83156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-105 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83156.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-105, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83157
in-theory        83157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-95 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83157.        (((A -> B) -> (A -> A)) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E)))), M:tm-95, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83158
in-theory        83158
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> (A or B))) -> (((A or B) -> (A or B)) and ((B or (A or B)) -> (A or B))))
theorem-size     31
proof            (modus-ponens tm-92 tm-920 ((Cm (or Am Bm)) (A (or Am Bm)) (B (and (-> (or Am Bm) (or Am Bm)) (-> (or Bm (or Am Bm)) (or Am Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83158.        ((((A or B) -> C) or ((A or B) -> (A or B))) -> (((A or B) -> (A or B)) and ((B or (A or B)) -> (A or B)))), M:tm-92, m:tm-920, u:((Cm (or Am Bm)) (A (or Am Bm)) (B (and (-> (or Am Bm) (or Am Bm)) (-> (or Bm (or Am Bm)) (or Am Bm)))))
================================================================
tm-name          tm-83159
in-theory        83159
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> (((A or B) -> C) and ((B or (A or B)) -> C))))
theorem-size     21
proof            (modus-ponens tm-84 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83159.        (((A or B) -> C) -> (D -> (((A or B) -> C) and ((B or (A or B)) -> C)))), M:tm-84, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83160
in-theory        83160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-83 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83160.        ((A -> (B -> (C -> B))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-83, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83161
in-theory        83161
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> (B or C)))) -> (((B or C) -> (D -> (B or C))) and ((C or (B or C)) -> (D -> (B or C)))))
theorem-size     33
proof            (modus-ponens tm-80 tm-920 ((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (and (-> (or Am Bm) (-> B (or Am Bm))) (-> (or Bm (or Am Bm)) (-> B (or Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83161.        ((A or ((B or C) -> (D -> (B or C)))) -> (((B or C) -> (D -> (B or C))) and ((C or (B or C)) -> (D -> (B or C))))), M:tm-80, m:tm-920, u:((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (and (-> (or Am Bm) (-> B (or Am Bm))) (-> (or Bm (or Am Bm)) (-> B (or Am Bm))))))
================================================================
tm-name          tm-83162
in-theory        83162
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B or C) -> D) -> (((B or C) -> D) and ((C or (B or C)) -> D))))
theorem-size     25
proof            (modus-ponens tm-76 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83162.        (((not (not A)) -> A) and (((B or C) -> D) -> (((B or C) -> D) and ((C or (B or C)) -> D)))), M:tm-76, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83163
in-theory        83163
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-73 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83163.        (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C))), M:tm-73, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83164
in-theory        83164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E))))
theorem-size     31
proof            (modus-ponens tm-69 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83164.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E)))), M:tm-69, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83165
in-theory        83165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-54 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-83165.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-54, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83166
in-theory        83166
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> (((B or C) -> (A and (B or C))) and ((C or (B or C)) -> (A and (B or C)))))
theorem-size     33
proof            (modus-ponens tm-48 tm-920 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Bm (or Am Bm)) (and B (or Am Bm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83166.        ((A or ((B or C) -> (A and (B or C)))) -> (((B or C) -> (A and (B or C))) and ((C or (B or C)) -> (A and (B or C))))), M:tm-48, m:tm-920, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (and (-> (or Am Bm) (and B (or Am Bm))) (-> (or Bm (or Am Bm)) (and B (or Am Bm))))))
================================================================
tm-name          tm-83167
in-theory        83167
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((B or C) -> D) and ((C or (B or C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-47 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83167.        (((A and ((B or C) -> D)) or ((B or C) -> D)) -> (((B or C) -> D) and ((C or (B or C)) -> D))), M:tm-47, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83168
in-theory        83168
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-46 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83168.        (((((A or B) -> C) and D) or ((A or B) -> C)) -> (((A or B) -> C) and ((B or (A or B)) -> C))), M:tm-46, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83169
in-theory        83169
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> (((B or C) -> A) and ((C or (B or C)) -> A)))
theorem-size     21
proof            (modus-ponens tm-44 tm-920 ((A (or Am Bm)) (B Cm) (C (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83169.        ((A or ((B or C) -> A)) -> (((B or C) -> A) and ((C or (B or C)) -> A))), M:tm-44, m:tm-920, u:((A (or Am Bm)) (B Cm) (C (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83170
in-theory        83170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-42 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and 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-50.           (((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-83170.        ((A -> (B or A)) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E)))), M:tm-42, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83171
in-theory        83171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-32 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83171.        ((A -> (A or B)) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E)))), M:tm-32, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83172
in-theory        83172
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (((A or B) -> C) and (((A or B) -> C) and ((B or (A or B)) -> C))))
theorem-size     25
proof            (modus-ponens tm-24 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83172.        (((A or B) -> C) -> (((A or B) -> C) and (((A or B) -> C) and ((B or (A or B)) -> C)))), M:tm-24, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83173
in-theory        83173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-23 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83173.        ((A -> (B -> (A and B))) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E)))), M:tm-23, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83174
in-theory        83174
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-22 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83174.        (((A and B) -> B) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E)))), M:tm-22, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83175
in-theory        83175
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-21 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83175.        (((A and B) -> A) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E)))), M:tm-21, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83176
in-theory        83176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-20 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83176.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-20, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83177
in-theory        83177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-19 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83177.        ((A -> (B -> A)) and (((C or D) -> E) -> (((C or D) -> E) and ((D or (C or D)) -> E)))), M:tm-19, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83178
in-theory        83178
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not (((A or B) -> C) and ((B or (A or B)) -> C)))) -> (not ((A or B) -> C)))
theorem-size     27
proof            (modus-ponens tm-9 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83178.        ((((A or B) -> C) -> (not (((A or B) -> C) and ((B or (A or B)) -> C)))) -> (not ((A or B) -> C))), M:tm-9, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83179
in-theory        83179
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) and ((B or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or (((A or B) -> C) and ((B or (A or B)) -> C))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-920 ((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83179.        (((((A or B) -> C) and ((B or (A or B)) -> C)) -> D) -> ((((A or B) -> C) or (((A or B) -> C) and ((B or (A or B)) -> C))) -> D)), M:tm-8, m:tm-920, u:((A (-> (or Am Bm) Cm)) (B (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-83180
in-theory        83180
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B or C) -> D) -> (((B or C) -> D) and ((C or (B or C)) -> D))))
theorem-size     21
proof            (modus-ponens tm-7 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-8)
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-50.           (((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-83180.        (A or (((B or C) -> D) -> (((B or C) -> D) and ((C or (B or C)) -> D)))), M:tm-7, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83181
in-theory        83181
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83181.        ((((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))) or D), M:tm-6, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83182
in-theory        83182
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> (((B or C) -> D) and ((C or (B or C)) -> D))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-83182.        (A -> ((((B or C) -> D) -> (((B or C) -> D) and ((C or (B or C)) -> D))) and A)), M:tm-5, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83183
in-theory        83183
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or C) -> D) -> (((B or C) -> D) and ((C or (B or C)) -> D))))
theorem-size     21
proof            (modus-ponens tm-1 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83183.        (A -> (((B or C) -> D) -> (((B or C) -> D) and ((C or (B or C)) -> D)))), M:tm-1, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83184
in-theory        83184
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-893 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-83184.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-893, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83185
in-theory        83185
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-83185.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-855, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83186
in-theory        83186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-808 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-83186.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-808, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83187
in-theory        83187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83187.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-757, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83188
in-theory        83188
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 or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83188.        (((((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 or (G or H)) -> I)))), M:tm-708, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83189
in-theory        83189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-50.           (((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-83189.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-665, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83190
in-theory        83190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83190.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-622, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83191
in-theory        83191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83191.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83192
in-theory        83192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-83192.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-605, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83193
in-theory        83193
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-83193.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-595, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83194
in-theory        83194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-50.           (((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-83194.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-550, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83195
in-theory        83195
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-83195.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-540, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83196
in-theory        83196
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-50.           (((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-83196.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-530, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83197
in-theory        83197
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-83197.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-520, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83198
in-theory        83198
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-50.           (((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-83198.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-510, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83199
in-theory        83199
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-50.           (((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-83199.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-500, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83200
in-theory        83200
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-83200.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-490, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83201
in-theory        83201
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83201.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-480, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83202
in-theory        83202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83202.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-469, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83203
in-theory        83203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83203.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83204
in-theory        83204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83204.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-453, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83205
in-theory        83205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83205.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-443, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83206
in-theory        83206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83206.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-409, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83207
in-theory        83207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83207.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-400, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83208
in-theory        83208
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83208.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-391, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83209
in-theory        83209
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83209.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-382, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83210
in-theory        83210
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83210.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-373, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83211
in-theory        83211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83211.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-364, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83212
in-theory        83212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83212.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-354, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83213
in-theory        83213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83213.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83214
in-theory        83214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83214.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-338, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83215
in-theory        83215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-83215.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-327, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83216
in-theory        83216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83216.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-326, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83217
in-theory        83217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83217.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-325, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83218
in-theory        83218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83218.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-324, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83219
in-theory        83219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83219.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-323, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83220
in-theory        83220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83220.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83221
in-theory        83221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83221.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83222
in-theory        83222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83222.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83223
in-theory        83223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83223.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83224
in-theory        83224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-50.           (((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-83224.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-311, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83225
in-theory        83225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83225.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)), M:tm-310, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83226
in-theory        83226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83226.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F))), M:tm-309, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83227
in-theory        83227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     35
proof            (modus-ponens tm-308 tm-921 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-83227.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-308, m:tm-921, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-83228
in-theory        83228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (A -> (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-307 tm-921 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83228.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-921, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-83229
in-theory        83229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83229.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-305, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83230
in-theory        83230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83230.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-303, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83231
in-theory        83231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83231.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-270, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83232
in-theory        83232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83232.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-239, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83233
in-theory        83233
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 or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83233.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-210, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83234
in-theory        83234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83234.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-183, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83235
in-theory        83235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83235.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-157, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83236
in-theory        83236
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 or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83236.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-147, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83237
in-theory        83237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83237.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-134, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83238
in-theory        83238
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 or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83238.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-125, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83239
in-theory        83239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83239.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-113, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83240
in-theory        83240
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 or (F or G)) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83240.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-105, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83241
in-theory        83241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83241.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-95, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83242
in-theory        83242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83242.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-83, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83243
in-theory        83243
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83243.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-76, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83244
in-theory        83244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83244.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-69, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83245
in-theory        83245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-83245.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-54, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83246
in-theory        83246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-83246.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-42, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83247
in-theory        83247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83247.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-32, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83248
in-theory        83248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-83248.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-23, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83249
in-theory        83249
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83249.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-22, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83250
in-theory        83250
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83250.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-21, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83251
in-theory        83251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83251.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-20, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83252
in-theory        83252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83252.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-19, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83253
in-theory        83253
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-7 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-8)
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-50.           (((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-83253.        (A or ((B -> (C -> (B and C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-7, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83254
in-theory        83254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83254.        (((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F), M:tm-6, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83255
in-theory        83255
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
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-50.           (((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-83255.        (A -> (((B -> (C -> (B and C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A)), M:tm-5, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83256
in-theory        83256
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-1 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83256.        (A -> ((B -> (C -> (B and C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-1, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83257
in-theory        83257
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-83257.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-893, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83258
in-theory        83258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-83258.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-855, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83259
in-theory        83259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-83259.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-808, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83260
in-theory        83260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-50.           (((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-83260.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-757, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83261
in-theory        83261
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 or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83261.        (((((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 or (G or H)) -> I)))), M:tm-708, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83262
in-theory        83262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-83262.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-665, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83263
in-theory        83263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83263.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-622, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83264
in-theory        83264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83264.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83265
in-theory        83265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-83265.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-605, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83266
in-theory        83266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-83266.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-595, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83267
in-theory        83267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-50.           (((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-83267.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-550, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83268
in-theory        83268
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-50.           (((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-83268.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-540, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83269
in-theory        83269
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-50.           (((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-83269.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-530, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83270
in-theory        83270
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-83270.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-520, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83271
in-theory        83271
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-83271.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-510, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83272
in-theory        83272
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-50.           (((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-83272.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-500, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83273
in-theory        83273
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-83273.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-490, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83274
in-theory        83274
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83274.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-480, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83275
in-theory        83275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83275.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-469, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83276
in-theory        83276
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83276.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83277
in-theory        83277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83277.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-453, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83278
in-theory        83278
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83278.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-443, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83279
in-theory        83279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83279.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-409, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83280
in-theory        83280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83280.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-400, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83281
in-theory        83281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83281.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-391, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83282
in-theory        83282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83282.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-382, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83283
in-theory        83283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83283.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-373, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83284
in-theory        83284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83284.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-364, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83285
in-theory        83285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83285.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-354, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83286
in-theory        83286
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83286.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83287
in-theory        83287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83287.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-338, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83288
in-theory        83288
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83288.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-327, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83289
in-theory        83289
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-83289.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-326, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83290
in-theory        83290
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83290.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-325, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83291
in-theory        83291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83291.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-324, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83292
in-theory        83292
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83292.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-323, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83293
in-theory        83293
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83293.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83294
in-theory        83294
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83294.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83295
in-theory        83295
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83295.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83296
in-theory        83296
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83296.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83297
in-theory        83297
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-50.           (((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-83297.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-311, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83298
in-theory        83298
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8 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-6.            (A -> (A or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83298.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)), M:tm-310, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83299
in-theory        83299
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83299.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F))), M:tm-309, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83300
in-theory        83300
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-922 ((A (-> (and Am Bm) Bm)) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-22.           (A -> (((B and C) -> C) and A)), 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-83300.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-308, m:tm-922, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-83301
in-theory        83301
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((A and B) -> B))
theorem-size     25
proof            (modus-ponens tm-307 tm-922 ((A (-> (and Am Bm) Bm)) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83301.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((A and B) -> B)), M:tm-307, m:tm-922, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-83302
in-theory        83302
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83302.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-305, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83303
in-theory        83303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83303.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-303, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83304
in-theory        83304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83304.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-270, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83305
in-theory        83305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83305.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-239, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83306
in-theory        83306
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83306.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-210, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83307
in-theory        83307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83307.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-183, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83308
in-theory        83308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83308.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-157, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83309
in-theory        83309
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 or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83309.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-147, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83310
in-theory        83310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83310.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-134, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83311
in-theory        83311
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 or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83311.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-125, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83312
in-theory        83312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83312.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-113, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83313
in-theory        83313
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 or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83313.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-105, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83314
in-theory        83314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83314.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-95, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83315
in-theory        83315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83315.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-83, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83316
in-theory        83316
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83316.        (((not (not A)) -> A) and (((B and C) -> C) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-76, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83317
in-theory        83317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83317.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-69, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83318
in-theory        83318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-83318.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-54, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83319
in-theory        83319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-83319.        ((A -> (B or A)) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-42, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83320
in-theory        83320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83320.        ((A -> (A or B)) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-32, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83321
in-theory        83321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-83321.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-23, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83322
in-theory        83322
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83322.        (((A and B) -> B) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-22, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83323
in-theory        83323
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83323.        (((A and B) -> A) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-21, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83324
in-theory        83324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-83324.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-20, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83325
in-theory        83325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83325.        ((A -> (B -> A)) and (((C and D) -> D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-19, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83326
in-theory        83326
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-7 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8)
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-50.           (((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-83326.        (A or (((B and C) -> C) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-7, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83327
in-theory        83327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83327.        ((((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F), M:tm-6, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83328
in-theory        83328
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83328.        (A -> ((((B and C) -> C) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A)), M:tm-5, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83329
in-theory        83329
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-1 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83329.        (A -> (((B and C) -> C) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-1, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83330
in-theory        83330
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-83330.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-893, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83331
in-theory        83331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-83331.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-855, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83332
in-theory        83332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-83332.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-808, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83333
in-theory        83333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-50.           (((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-83333.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-757, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83334
in-theory        83334
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 or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83334.        (((((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 or (G or H)) -> I)))), M:tm-708, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83335
in-theory        83335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-83335.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-665, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83336
in-theory        83336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83336.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-622, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83337
in-theory        83337
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83337.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83338
in-theory        83338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-83338.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-605, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83339
in-theory        83339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-83339.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-595, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83340
in-theory        83340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-50.           (((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-83340.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-550, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83341
in-theory        83341
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-50.           (((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-83341.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-540, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83342
in-theory        83342
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-50.           (((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-83342.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-530, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83343
in-theory        83343
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-83343.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-520, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83344
in-theory        83344
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-83344.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-510, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83345
in-theory        83345
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-50.           (((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-83345.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-500, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83346
in-theory        83346
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-83346.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-490, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83347
in-theory        83347
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83347.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-480, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83348
in-theory        83348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83348.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-469, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83349
in-theory        83349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83349.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83350
in-theory        83350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83350.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-453, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83351
in-theory        83351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83351.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-443, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83352
in-theory        83352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83352.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-409, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83353
in-theory        83353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83353.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-400, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83354
in-theory        83354
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83354.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-391, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83355
in-theory        83355
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83355.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-382, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83356
in-theory        83356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83356.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-373, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83357
in-theory        83357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83357.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-364, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83358
in-theory        83358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83358.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-354, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83359
in-theory        83359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83359.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83360
in-theory        83360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83360.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-338, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83361
in-theory        83361
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83361.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-327, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83362
in-theory        83362
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83362.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-326, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83363
in-theory        83363
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-83363.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-325, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83364
in-theory        83364
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83364.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-324, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83365
in-theory        83365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83365.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-323, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83366
in-theory        83366
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83366.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83367
in-theory        83367
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83367.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83368
in-theory        83368
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83368.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83369
in-theory        83369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83369.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83370
in-theory        83370
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-50.           (((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-83370.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-311, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83371
in-theory        83371
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8 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-6.            (A -> (A or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83371.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)), M:tm-310, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83372
in-theory        83372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83372.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F))), M:tm-309, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83373
in-theory        83373
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-923 ((A (-> (and Am Bm) Am)) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-83373.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-308, m:tm-923, u:((A (-> (and Am Bm) Am)) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-83374
in-theory        83374
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((A and B) -> A))
theorem-size     25
proof            (modus-ponens tm-307 tm-923 ((A (-> (and Am Bm) Am)) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83374.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((A and B) -> A)), M:tm-307, m:tm-923, u:((A (-> (and Am Bm) Am)) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-83375
in-theory        83375
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83375.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-305, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83376
in-theory        83376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83376.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-303, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83377
in-theory        83377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83377.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-270, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83378
in-theory        83378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83378.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-239, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83379
in-theory        83379
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83379.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-210, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83380
in-theory        83380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83380.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-183, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83381
in-theory        83381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83381.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-157, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83382
in-theory        83382
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 or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83382.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-147, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83383
in-theory        83383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83383.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-134, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83384
in-theory        83384
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 or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83384.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-125, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83385
in-theory        83385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83385.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-113, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83386
in-theory        83386
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 or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83386.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-105, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83387
in-theory        83387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83387.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-95, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83388
in-theory        83388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83388.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-83, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83389
in-theory        83389
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83389.        (((not (not A)) -> A) and (((B and C) -> B) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-76, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83390
in-theory        83390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83390.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-69, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83391
in-theory        83391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-83391.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-54, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83392
in-theory        83392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-83392.        ((A -> (B or A)) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-42, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83393
in-theory        83393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83393.        ((A -> (A or B)) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-32, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83394
in-theory        83394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-83394.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-23, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83395
in-theory        83395
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83395.        (((A and B) -> B) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-22, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83396
in-theory        83396
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83396.        (((A and B) -> A) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-21, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83397
in-theory        83397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-83397.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-20, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83398
in-theory        83398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83398.        ((A -> (B -> A)) and (((C and D) -> C) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-19, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83399
in-theory        83399
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-7 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8)
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-50.           (((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-83399.        (A or (((B and C) -> B) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-7, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83400
in-theory        83400
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83400.        ((((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F), M:tm-6, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83401
in-theory        83401
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83401.        (A -> ((((B and C) -> B) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A)), M:tm-5, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83402
in-theory        83402
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-1 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83402.        (A -> (((B and C) -> B) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-1, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83403
in-theory        83403
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-893 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-83403.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-893, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83404
in-theory        83404
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 (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-855 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-83404.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-855, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83405
in-theory        83405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-808 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-83405.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-808, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83406
in-theory        83406
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 or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-757 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-50.           (((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-83406.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-757, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83407
in-theory        83407
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 or (H or I)) -> J))))
theorem-size     53
proof            (modus-ponens tm-708 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83407.        (((((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 or (H or I)) -> J)))), M:tm-708, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83408
in-theory        83408
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 or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-665 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-50.           (((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-83408.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-665, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83409
in-theory        83409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-622 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or 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-50.           (((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-83409.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-622, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83410
in-theory        83410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or 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-50.           (((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-83410.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H or G))), M:tm-609, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83411
in-theory        83411
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-605 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-83411.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-605, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83412
in-theory        83412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-83412.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-595, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83413
in-theory        83413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-550 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-50.           (((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-83413.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-550, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83414
in-theory        83414
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-540 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-50.           (((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-83414.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-540, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83415
in-theory        83415
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-530 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-50.           (((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-83415.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-530, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83416
in-theory        83416
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-520 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-83416.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-520, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83417
in-theory        83417
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-510 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-83417.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-510, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83418
in-theory        83418
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-500 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-50.           (((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-83418.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-500, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83419
in-theory        83419
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 or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-490 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-83419.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-490, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83420
in-theory        83420
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-480 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or 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-50.           (((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-83420.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-480, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83421
in-theory        83421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-469 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83421.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-469, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83422
in-theory        83422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83422.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (G or H))), M:tm-456, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83423
in-theory        83423
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-453 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83423.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-453, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83424
in-theory        83424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83424.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-443, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83425
in-theory        83425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-409 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83425.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-409, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83426
in-theory        83426
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-400 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83426.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-400, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83427
in-theory        83427
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-391 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83427.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-391, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83428
in-theory        83428
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-382 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83428.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-382, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83429
in-theory        83429
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 or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-373 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83429.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-373, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83430
in-theory        83430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-364 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83430.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-364, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83431
in-theory        83431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-354 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83431.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-354, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83432
in-theory        83432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H -> (G and H))))
theorem-size     35
proof            (modus-ponens tm-341 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83432.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83433
in-theory        83433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-338 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83433.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-338, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83434
in-theory        83434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83434.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-327, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83435
in-theory        83435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83435.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-326, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83436
in-theory        83436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83436.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-325, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83437
in-theory        83437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-83437.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-324, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83438
in-theory        83438
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83438.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-323, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83439
in-theory        83439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83439.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83440
in-theory        83440
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83440.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83441
in-theory        83441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     41
proof            (modus-ponens tm-318 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83441.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83442
in-theory        83442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83442.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83443
in-theory        83443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
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-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-50.           (((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-83443.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-311, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83444
in-theory        83444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83444.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) or G)), M:tm-310, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83445
in-theory        83445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83445.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and G))), M:tm-309, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83446
in-theory        83446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-308 tm-924 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83446.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-308, m:tm-924, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))
================================================================
tm-name          tm-83447
in-theory        83447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-307 tm-924 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83447.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-924, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))
================================================================
tm-name          tm-83448
in-theory        83448
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83448.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-305, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83449
in-theory        83449
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 or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-303 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83449.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-303, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83450
in-theory        83450
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-270 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83450.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-270, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83451
in-theory        83451
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 or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-239 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83451.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-239, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83452
in-theory        83452
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 or (H or I)) -> J))))
theorem-size     45
proof            (modus-ponens tm-210 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83452.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-210, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83453
in-theory        83453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-183 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83453.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-183, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83454
in-theory        83454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-157 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83454.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-157, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83455
in-theory        83455
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 or (G or H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-147 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83455.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-147, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83456
in-theory        83456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-134 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83456.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-134, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83457
in-theory        83457
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 or (G or H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-125 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83457.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-125, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83458
in-theory        83458
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 or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-113 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83458.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-113, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83459
in-theory        83459
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 or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-105 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83459.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-105, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83460
in-theory        83460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-95 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83460.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-95, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83461
in-theory        83461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-83 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83461.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-83, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83462
in-theory        83462
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-76 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83462.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-76, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83463
in-theory        83463
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 or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-69 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83463.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-69, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83464
in-theory        83464
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 or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-54 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83464.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-54, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83465
in-theory        83465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-42 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-83465.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-42, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83466
in-theory        83466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-32 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83466.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-32, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83467
in-theory        83467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-23 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83467.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-23, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83468
in-theory        83468
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-22 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83468.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-22, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83469
in-theory        83469
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-21 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83469.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-21, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83470
in-theory        83470
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 or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-20 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-83470.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-20, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83471
in-theory        83471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-19 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83471.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-19, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83472
in-theory        83472
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-7 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8)
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-50.           (((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-83472.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-7, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83473
in-theory        83473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) or G)
theorem-size     29
proof            (modus-ponens tm-6 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83473.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) or G), M:tm-6, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83474
in-theory        83474
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83474.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))) and A)), M:tm-5, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83475
in-theory        83475
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-1 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83475.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-1, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-83476
in-theory        83476
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-83476.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-893, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83477
in-theory        83477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-83477.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-855, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83478
in-theory        83478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-83478.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-808, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83479
in-theory        83479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-50.           (((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-83479.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-757, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83480
in-theory        83480
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 or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83480.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-708, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83481
in-theory        83481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-83481.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-665, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83482
in-theory        83482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83482.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-622, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83483
in-theory        83483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83483.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83484
in-theory        83484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83484.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-605, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83485
in-theory        83485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83485.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-595, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83486
in-theory        83486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83486.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-550, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83487
in-theory        83487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83487.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-540, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83488
in-theory        83488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83488.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-530, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83489
in-theory        83489
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83489.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-520, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83490
in-theory        83490
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83490.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-510, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83491
in-theory        83491
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83491.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-500, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83492
in-theory        83492
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83492.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-490, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83493
in-theory        83493
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83493.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-480, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83494
in-theory        83494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83494.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-469, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83495
in-theory        83495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83495.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83496
in-theory        83496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83496.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-453, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83497
in-theory        83497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83497.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-443, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83498
in-theory        83498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83498.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-409, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83499
in-theory        83499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83499.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-400, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83500
in-theory        83500
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83500.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-391, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83501
in-theory        83501
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83501.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-382, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83502
in-theory        83502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83502.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-373, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83503
in-theory        83503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83503.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-364, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83504
in-theory        83504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83504.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-354, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83505
in-theory        83505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83505.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83506
in-theory        83506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83506.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-338, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83507
in-theory        83507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83507.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-327, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83508
in-theory        83508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83508.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-326, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83509
in-theory        83509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83509.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-325, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83510
in-theory        83510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83510.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-324, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83511
in-theory        83511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-83511.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-323, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83512
in-theory        83512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83512.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83513
in-theory        83513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83513.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83514
in-theory        83514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83514.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83515
in-theory        83515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83515.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83516
in-theory        83516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83516.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F or ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-311, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83517
in-theory        83517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8 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-6.            (A -> (A or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83517.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)), M:tm-310, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83518
in-theory        83518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83518.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and F))), M:tm-309, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83519
in-theory        83519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-925 ((A (-> Am (-> Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-83519.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-308, m:tm-925, u:((A (-> Am (-> Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-83520
in-theory        83520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (A -> (B -> A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-925 ((A (-> Am (-> Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83520.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (A -> (B -> A))), M:tm-307, m:tm-925, u:((A (-> Am (-> Bm Am))) (B (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))
================================================================
tm-name          tm-83521
in-theory        83521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83521.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) and (F -> ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))))), M:tm-305, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83522
in-theory        83522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83522.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-303, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83523
in-theory        83523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83523.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-270, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83524
in-theory        83524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83524.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-239, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83525
in-theory        83525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83525.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-210, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83526
in-theory        83526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83526.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-183, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83527
in-theory        83527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83527.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-157, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83528
in-theory        83528
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83528.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-147, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83529
in-theory        83529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83529.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-134, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83530
in-theory        83530
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83530.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-125, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83531
in-theory        83531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83531.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-113, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83532
in-theory        83532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83532.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-105, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83533
in-theory        83533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83533.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-95, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83534
in-theory        83534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83534.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-83, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83535
in-theory        83535
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83535.        (((not (not A)) -> A) and ((B -> (C -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-76, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83536
in-theory        83536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83536.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-69, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83537
in-theory        83537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-83537.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-54, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83538
in-theory        83538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83538.        ((A -> (B or A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-42, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83539
in-theory        83539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83539.        ((A -> (A or B)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-32, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83540
in-theory        83540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-83540.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-23, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83541
in-theory        83541
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83541.        (((A and B) -> B) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-22, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83542
in-theory        83542
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83542.        (((A and B) -> A) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-21, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83543
in-theory        83543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-83543.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-20, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83544
in-theory        83544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83544.        ((A -> (B -> A)) and ((C -> (D -> C)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-19, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83545
in-theory        83545
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-7 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or 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-50.           (((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-83545.        (A or ((B -> (C -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-7, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83546
in-theory        83546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83546.        (((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))) or F), M:tm-6, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83547
in-theory        83547
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83547.        (A -> (((B -> (C -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and A)), M:tm-5, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83548
in-theory        83548
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-1 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83548.        (A -> ((B -> (C -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-1, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-83549
in-theory        83549
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-893 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83549.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-893, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83550
in-theory        83550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-855 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-9 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-48.           (((A -> (B and 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83550.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-855, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83551
in-theory        83551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-808 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83551.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-808, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83552
in-theory        83552
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C))))
theorem-size     60
proof            (modus-ponens tm-798 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9 tm-7)
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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-83552.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C)))), M:tm-798, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83553
in-theory        83553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-757 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-50.           (((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-83553.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-757, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83554
in-theory        83554
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((((A or B) -> C) -> (not ((B or (A or B)) -> C))) and D) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C))))
theorem-size     60
proof            (modus-ponens tm-747 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83554.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((((A or B) -> C) -> (not ((B or (A or B)) -> C))) and D) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C)))), M:tm-747, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83555
in-theory        83555
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     47
proof            (modus-ponens tm-708 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83555.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-708, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83556
in-theory        83556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-665 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-50.           (((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-83556.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-665, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83557
in-theory        83557
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((not ((B or (A or B)) -> C)) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C))))
theorem-size     52
proof            (modus-ponens tm-654 tm-926 ((A (-> (or Am Bm) Cm)) (B (not (-> (or Bm (or Am Bm)) Cm))) (C (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83557.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((not ((B or (A or B)) -> C)) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C)))), M:tm-654, m:tm-926, u:((A (-> (or Am Bm) Cm)) (B (not (-> (or Bm (or Am Bm)) Cm))) (C (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83558
in-theory        83558
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (D or (not ((A or B) -> C))))
theorem-size     23
proof            (modus-ponens tm-623 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or 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-50.           (((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-83558.        ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (D or (not ((A or B) -> C)))), M:tm-623, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83559
in-theory        83559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-622 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or 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-50.           (((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-83559.        ((A -> (B -> (C or B))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-622, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83560
in-theory        83560
times-derived    1
----------------------------------------------------------------
theorem          (not (((A or B) -> (C or (A or B))) -> (not ((B or (A or B)) -> (C or (A or B))))))
theorem-size     23
proof            (modus-ponens tm-618 tm-926 ((A (-> (-> (or Am Bm) (or C (or Am Bm))) (not (-> (or Bm (or Am Bm)) (or C (or Am Bm)))))) (B (or Am Bm)) (Cm (or C (or 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-50.           (((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-83560.        (not (((A or B) -> (C or (A or B))) -> (not ((B or (A or B)) -> (C or (A or B)))))), M:tm-618, m:tm-926, u:((A (-> (-> (or Am Bm) (or C (or Am Bm))) (not (-> (or Bm (or Am Bm)) (or C (or Am Bm)))))) (B (or Am Bm)) (Cm (or C (or Am Bm))))
================================================================
tm-name          tm-83561
in-theory        83561
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-609 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or 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-50.           (((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-83561.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E or D))), M:tm-609, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83562
in-theory        83562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-605 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
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-50.           (((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-83562.        ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-605, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83563
in-theory        83563
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E or D)) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-83563.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E or D)) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-595, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83564
in-theory        83564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-550 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-50.           (((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-83564.        (((A -> (B or A)) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-550, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83565
in-theory        83565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-540 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-50.           (((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-83565.        ((A or (B -> (C or B))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-540, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83566
in-theory        83566
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-530 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-50.           (((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-83566.        ((A or (B -> (B or C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-530, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83567
in-theory        83567
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-520 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
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-50.           (((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-83567.        ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-520, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83568
in-theory        83568
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-510 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-83568.        ((A or ((B and C) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-510, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83569
in-theory        83569
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-500 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-50.           (((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-83569.        ((A or ((B and C) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-500, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83570
in-theory        83570
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-490 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-8)
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-50.           (((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-83570.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-490, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83571
in-theory        83571
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-480 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or 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-50.           (((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-83571.        ((A or (B -> (C -> B))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-480, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83572
in-theory        83572
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> ((not ((A or B) -> C)) or D))
theorem-size     23
proof            (modus-ponens tm-470 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83572.        ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> ((not ((A or B) -> C)) or D)), M:tm-470, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83573
in-theory        83573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-469 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83573.        ((A -> (B -> (B or C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-469, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83574
in-theory        83574
times-derived    1
----------------------------------------------------------------
theorem          (not (((A or B) -> ((A or B) or C)) -> (not ((B or (A or B)) -> ((A or B) or C)))))
theorem-size     23
proof            (modus-ponens tm-465 tm-926 ((A (-> (-> (or Am Bm) (or (or Am Bm) C)) (not (-> (or Bm (or Am Bm)) (or (or Am Bm) C))))) (B (or Am Bm)) (Cm (or (or Am Bm) C))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83574.        (not (((A or B) -> ((A or B) or C)) -> (not ((B or (A or B)) -> ((A or B) or C))))), M:tm-465, m:tm-926, u:((A (-> (-> (or Am Bm) (or (or Am Bm) C)) (not (-> (or Bm (or Am Bm)) (or (or Am Bm) C))))) (B (or Am Bm)) (Cm (or (or Am Bm) C)))
================================================================
tm-name          tm-83575
in-theory        83575
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-456 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83575.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (D or E))), M:tm-456, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83576
in-theory        83576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-453 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83576.        ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-453, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83577
in-theory        83577
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (D or E)) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83577.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (D or E)) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-443, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83578
in-theory        83578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-409 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83578.        (((A -> (A or B)) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-409, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83579
in-theory        83579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-400 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83579.        (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-400, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83580
in-theory        83580
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-391 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83580.        ((((A and B) -> B) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-391, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83581
in-theory        83581
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-382 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83581.        ((((A and B) -> A) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-382, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83582
in-theory        83582
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-373 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83582.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-373, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83583
in-theory        83583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-364 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83583.        (((A -> (B -> A)) or C) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-364, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83584
in-theory        83584
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (D -> ((not ((A or B) -> C)) and D)))
theorem-size     25
proof            (modus-ponens tm-355 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83584.        ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (D -> ((not ((A or B) -> C)) and D))), M:tm-355, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83585
in-theory        83585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-354 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83585.        ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-354, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83586
in-theory        83586
times-derived    1
----------------------------------------------------------------
theorem          (not (((A or B) -> (C -> ((A or B) and C))) -> (not ((B or (A or B)) -> (C -> ((A or B) and C))))))
theorem-size     27
proof            (modus-ponens tm-350 tm-926 ((A (-> (-> (or Am Bm) (-> C (and (or Am Bm) C))) (not (-> (or Bm (or Am Bm)) (-> C (and (or Am Bm) C)))))) (B (or Am Bm)) (Cm (-> C (and (or Am Bm) C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83586.        (not (((A or B) -> (C -> ((A or B) and C))) -> (not ((B or (A or B)) -> (C -> ((A or B) and C)))))), M:tm-350, m:tm-926, u:((A (-> (-> (or Am Bm) (-> C (and (or Am Bm) C))) (not (-> (or Bm (or Am Bm)) (-> C (and (or Am Bm) C)))))) (B (or Am Bm)) (Cm (-> C (and (or Am Bm) C))))
================================================================
tm-name          tm-83587
in-theory        83587
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-341 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83587.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83588
in-theory        83588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-338 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83588.        (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-338, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83589
in-theory        83589
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) and (not ((A or B) -> C)))))
theorem-size     58
proof            (modus-ponens tm-328 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83589.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) and (not ((A or B) -> C))))), M:tm-328, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83590
in-theory        83590
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83590.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-327, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83591
in-theory        83591
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and E) -> E) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83591.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and E) -> E) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-326, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83592
in-theory        83592
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and E) -> D) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83592.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D and E) -> D) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-325, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83593
in-theory        83593
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83593.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-324, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83594
in-theory        83594
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> D)) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83594.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> D)) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-323, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83595
in-theory        83595
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-322 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83595.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83596
in-theory        83596
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-320 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83596.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83597
in-theory        83597
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-318 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83597.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83598
in-theory        83598
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (((A or B) -> C) -> (not ((B or (A or B)) -> C)))))
theorem-size     51
proof            (modus-ponens tm-316 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83598.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (((A or B) -> C) -> (not ((B or (A or B)) -> C))))), M:tm-316, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83599
in-theory        83599
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-315 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83599.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83600
in-theory        83600
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not (not ((A or B) -> C)))) -> (not (((A or B) -> C) -> (not ((B or (A or B)) -> C))))))
theorem-size     60
proof            (modus-ponens tm-313 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83600.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not (not ((A or B) -> C)))) -> (not (((A or B) -> C) -> (not ((B or (A or B)) -> C)))))), M:tm-313, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83601
in-theory        83601
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((not ((A or B) -> C)) -> D) -> (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) or (not ((A or B) -> C))) -> D)))
theorem-size     54
proof            (modus-ponens tm-312 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83601.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((not ((A or B) -> C)) -> D) -> (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) or (not ((A or B) -> C))) -> D))), M:tm-312, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83602
in-theory        83602
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D or ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
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-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-50.           (((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-83602.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D or ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-311, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83603
in-theory        83603
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) or D))
theorem-size     45
proof            (modus-ponens tm-310 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-8 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-6.            (A -> (A or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83603.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) or D)), M:tm-310, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83604
in-theory        83604
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and D)))
theorem-size     47
proof            (modus-ponens tm-309 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83604.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and D))), M:tm-309, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83605
in-theory        83605
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 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-1.            (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83605.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) and (D -> ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))), M:tm-305, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83606
in-theory        83606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-303 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83606.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-303, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83607
in-theory        83607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-270 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83607.        ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-270, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83608
in-theory        83608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-239 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83608.        ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-239, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83609
in-theory        83609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-210 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 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-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83609.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-210, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83610
in-theory        83610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-183 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83610.        ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-183, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83611
in-theory        83611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-157 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83611.        ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-157, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83612
in-theory        83612
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-147 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83612.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-147, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83613
in-theory        83613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-134 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83613.        ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-134, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83614
in-theory        83614
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-125 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83614.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-125, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83615
in-theory        83615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-113 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83615.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-113, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83616
in-theory        83616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-105 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83616.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-105, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83617
in-theory        83617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-95 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83617.        (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-95, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83618
in-theory        83618
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (D -> (not ((A or B) -> C))))
theorem-size     23
proof            (modus-ponens tm-84 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-9 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83618.        ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (D -> (not ((A or B) -> C)))), M:tm-84, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83619
in-theory        83619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-83 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83619.        ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-83, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83620
in-theory        83620
times-derived    1
----------------------------------------------------------------
theorem          (not (((A or B) -> (C -> (A or B))) -> (not ((B or (A or B)) -> (C -> (A or B))))))
theorem-size     23
proof            (modus-ponens tm-79 tm-926 ((A (-> (-> (or Am Bm) (-> C (or Am Bm))) (not (-> (or Bm (or Am Bm)) (-> C (or Am Bm)))))) (B (or Am Bm)) (Cm (-> C (or Am Bm)))))
axioms-used      (tm-9 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83620.        (not (((A or B) -> (C -> (A or B))) -> (not ((B or (A or B)) -> (C -> (A or B)))))), M:tm-79, m:tm-926, u:((A (-> (-> (or Am Bm) (-> C (or Am Bm))) (not (-> (or Bm (or Am Bm)) (-> C (or Am Bm)))))) (B (or Am Bm)) (Cm (-> C (or Am Bm))))
================================================================
tm-name          tm-83621
in-theory        83621
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or C) -> D) -> (not ((C or (B or C)) -> D))) -> (not ((B or C) -> D))))
theorem-size     27
proof            (modus-ponens tm-76 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83621.        (((not (not A)) -> A) and ((((B or C) -> D) -> (not ((C or (B or C)) -> D))) -> (not ((B or C) -> D)))), M:tm-76, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83622
in-theory        83622
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A or B) -> C) -> (not ((B or (A or B)) -> C))))) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C)))
theorem-size     38
proof            (modus-ponens tm-73 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83622.        (((not (not (((A or B) -> C) -> (not ((B or (A or B)) -> C))))) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C))), M:tm-73, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83623
in-theory        83623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-69 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83623.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-69, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83624
in-theory        83624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-54 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83624.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-54, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83625
in-theory        83625
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B or C) -> D) -> (not ((C or (B or C)) -> D)))) or (((B or C) -> D) -> (not ((C or (B or C)) -> D)))) -> (not ((B or C) -> D)))
theorem-size     38
proof            (modus-ponens tm-47 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83625.        (((A and (((B or C) -> D) -> (not ((C or (B or C)) -> D)))) or (((B or C) -> D) -> (not ((C or (B or C)) -> D)))) -> (not ((B or C) -> D))), M:tm-47, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83626
in-theory        83626
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> (not ((B or (A or B)) -> C))) and D) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C)))
theorem-size     38
proof            (modus-ponens tm-46 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83626.        ((((((A or B) -> C) -> (not ((B or (A or B)) -> C))) and D) or (((A or B) -> C) -> (not ((B or (A or B)) -> C)))) -> (not ((A or B) -> C))), M:tm-46, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83627
in-theory        83627
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A or (B or A)) -> C)) or (((B or A) -> C) -> (not ((A or (B or A)) -> C)))) -> (not ((B or A) -> C)))
theorem-size     30
proof            (modus-ponens tm-44 tm-926 ((A (-> (or Am Bm) Cm)) (B (not (-> (or Bm (or Am Bm)) Cm))) (C (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83627.        (((not ((A or (B or A)) -> C)) or (((B or A) -> C) -> (not ((A or (B or A)) -> C)))) -> (not ((B or A) -> C))), M:tm-44, m:tm-926, u:((A (-> (or Am Bm) Cm)) (B (not (-> (or Bm (or Am Bm)) Cm))) (C (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83628
in-theory        83628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-42 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not 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-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-83628.        ((A -> (B or A)) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-42, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83629
in-theory        83629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-32 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83629.        ((A -> (A or B)) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-32, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83630
in-theory        83630
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) and (not ((A or B) -> C))))
theorem-size     36
proof            (modus-ponens tm-24 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83630.        ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) and (not ((A or B) -> C)))), M:tm-24, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83631
in-theory        83631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-23 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83631.        ((A -> (B -> (A and B))) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-23, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83632
in-theory        83632
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-22 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83632.        (((A and B) -> B) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-22, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83633
in-theory        83633
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-21 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83633.        (((A and B) -> A) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-21, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83634
in-theory        83634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-20 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83634.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-20, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83635
in-theory        83635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-19 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83635.        ((A -> (B -> A)) and ((((C or D) -> E) -> (not ((D or (C or D)) -> E))) -> (not ((C or D) -> E)))), M:tm-19, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83636
in-theory        83636
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (((A or B) -> C) -> (not ((B or (A or B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-12 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-9 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-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-83636.        ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (((A or B) -> C) -> (not ((B or (A or B)) -> C)))), M:tm-12, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83637
in-theory        83637
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not (not ((A or B) -> C)))) -> (not (((A or B) -> C) -> (not ((B or (A or B)) -> C)))))
theorem-size     38
proof            (modus-ponens tm-9 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83637.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not (not ((A or B) -> C)))) -> (not (((A or B) -> C) -> (not ((B or (A or B)) -> C))))), M:tm-9, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83638
in-theory        83638
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A or B) -> C)) -> D) -> (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) or (not ((A or B) -> C))) -> D))
theorem-size     32
proof            (modus-ponens tm-8 tm-926 ((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83638.        (((not ((A or B) -> C)) -> D) -> (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) or (not ((A or B) -> C))) -> D)), M:tm-8, m:tm-926, u:((A (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm)))) (B (not (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-83639
in-theory        83639
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B or C) -> D) -> (not ((C or (B or C)) -> D))) -> (not ((B or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-7 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-7 tm-9 tm-8)
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-50.           (((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-83639.        (A or ((((B or C) -> D) -> (not ((C or (B or C)) -> D))) -> (not ((B or C) -> D)))), M:tm-7, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83640
in-theory        83640
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) or D)
theorem-size     23
proof            (modus-ponens tm-6 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-6 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83640.        (((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))) or D), M:tm-6, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83641
in-theory        83641
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) -> (not ((C or (B or C)) -> D))) -> (not ((B or C) -> D))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83641.        (A -> (((((B or C) -> D) -> (not ((C or (B or C)) -> D))) -> (not ((B or C) -> D))) and A)), M:tm-5, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83642
in-theory        83642
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> (not ((C or (B or C)) -> D))) -> (not ((B or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-1 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-1 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83642.        (A -> ((((B or C) -> D) -> (not ((C or (B or C)) -> D))) -> (not ((B or C) -> D)))), M:tm-1, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-83643
in-theory        83643
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((B or (A or B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-927 tm-1 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       97
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-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-1.            (A -> (B -> A)), axiom
tm-83643.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((B or (A or B)) -> C))), M:tm-927, m:tm-1, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83644
in-theory        83644
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> D)) or ((B or (A or B)) -> (C -> D))) -> (((B or (A or B)) -> C) -> ((B or (A or B)) -> D)))
theorem-size     33
proof            (modus-ponens tm-927 tm-2 ((Am (or A (or B A))) (C (-> Bm Cm)) (D (-> (-> (or A (or B A)) Bm) (-> (or A (or B A)) Cm)))))
axioms-used      (tm-8 tm-7 tm-2)
proof-size       115
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-83644.        ((((A or B) -> (C -> D)) or ((B or (A or B)) -> (C -> D))) -> (((B or (A or B)) -> C) -> ((B or (A or B)) -> D))), M:tm-927, m:tm-2, u:((Am (or A (or B A))) (C (-> Bm Cm)) (D (-> (-> (or A (or B A)) Bm) (-> (or A (or B A)) Cm))))
================================================================
tm-name          tm-83645
in-theory        83645
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (((B or (A or B)) -> C) and D)))
theorem-size     25
proof            (modus-ponens tm-927 tm-5 ((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> (or A (or B A)) C) Bm)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       101
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-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-5.            (A -> (B -> (A and B))), axiom
tm-83645.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (((B or (A or B)) -> C) and D))), M:tm-927, m:tm-5, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> (or A (or B A)) C) Bm))))
================================================================
tm-name          tm-83646
in-theory        83646
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) or D))
theorem-size     23
proof            (modus-ponens tm-927 tm-6 ((Am (-> (or A (or B A)) C)) (D (or (-> (or A (or B A)) C) Bm))))
axioms-used      (tm-8 tm-7 tm-6)
proof-size       97
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-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-6.            (A -> (A or B)), axiom
tm-83646.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) or D)), M:tm-927, m:tm-6, u:((Am (-> (or A (or B A)) C)) (D (or (-> (or A (or B A)) C) Bm)))
================================================================
tm-name          tm-83647
in-theory        83647
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((B or (A or B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-927 tm-7 ((Am (-> (or A (or B A)) C)) (D (or Bm (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7)
proof-size       97
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-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-83647.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((B or (A or B)) -> C))), M:tm-927, m:tm-7, u:((Am (-> (or A (or B A)) C)) (D (or Bm (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83648
in-theory        83648
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((C -> D) -> (((B or (A or B)) or C) -> D)))
theorem-size     27
proof            (modus-ponens tm-927 tm-8 ((Am (or A (or B A))) (C Bm) (D (-> (-> Bm Cm) (-> (or (or A (or B A)) Bm) Cm)))))
axioms-used      (tm-8 tm-7)
proof-size       109
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-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-83648.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((C -> D) -> (((B or (A or B)) or C) -> D))), M:tm-927, m:tm-8, u:((Am (or A (or B A))) (C Bm) (D (-> (-> Bm Cm) (-> (or (or A (or B A)) Bm) Cm))))
================================================================
tm-name          tm-83649
in-theory        83649
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> (not C)) -> (not (B or (A or B)))))
theorem-size     29
proof            (modus-ponens tm-927 tm-9 ((Am (or A (or B A))) (C Bm) (D (-> (-> (or A (or B A)) (not Bm)) (not (or A (or B A)))))))
axioms-used      (tm-8 tm-7 tm-9)
proof-size       109
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-83649.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> (not C)) -> (not (B or (A or B))))), M:tm-927, m:tm-9, u:((Am (or A (or B A))) (C Bm) (D (-> (-> (or A (or B A)) (not Bm)) (not (or A (or B A))))))
================================================================
tm-name          tm-83650
in-theory        83650
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-927 tm-11 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83650.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> D))), M:tm-927, m:tm-11, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-83651
in-theory        83651
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (B or (A or B))))
theorem-size     25
proof            (modus-ponens tm-927 tm-12 ((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       119
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-83651.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (B or (A or B)))), M:tm-927, m:tm-12, u:((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (or A (or B A)))))
================================================================
tm-name          tm-83652
in-theory        83652
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-927 tm-14 ((Am (-> (or A (or B A)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       129
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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-83652.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-927, m:tm-14, u:((Am (-> (or A (or B A)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-83653
in-theory        83653
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-927 tm-16 ((Am (-> (or A (or B A)) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-83653.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D and E) -> D)), M:tm-927, m:tm-16, u:((Am (-> (or A (or B A)) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-83654
in-theory        83654
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-927 tm-18 ((Am (-> (or A (or B A)) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-83654.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D and E) -> E)), M:tm-927, m:tm-18, u:((Am (-> (or A (or B A)) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-83655
in-theory        83655
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> D)) and ((B or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-927 tm-19 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       117
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83655.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-19, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83656
in-theory        83656
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-927 tm-20 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-83656.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-20, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83657
in-theory        83657
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and E) -> D) and ((B or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-927 tm-21 ((Am (-> (or A (or B A)) C)) (D (and (-> (and Bm Cm) Bm) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
proof-size       117
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-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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-83657.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and E) -> D) and ((B or (A or B)) -> C))), M:tm-927, m:tm-21, u:((Am (-> (or A (or B A)) C)) (D (and (-> (and Bm Cm) Bm) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83658
in-theory        83658
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and E) -> E) and ((B or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-927 tm-22 ((Am (-> (or A (or B A)) C)) (D (and (-> (and Bm Cm) Cm) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
proof-size       117
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-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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-83658.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and E) -> E) and ((B or (A or B)) -> C))), M:tm-927, m:tm-22, u:((Am (-> (or A (or B A)) C)) (D (and (-> (and Bm Cm) Cm) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83659
in-theory        83659
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (D and E))) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-23 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-83659.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (D and E))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-23, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83660
in-theory        83660
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> ((B or (A or B)) and C)))
theorem-size     27
proof            (modus-ponens tm-927 tm-24 ((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (and (or A (or B A)) Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       125
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-83660.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> ((B or (A or B)) and C))), M:tm-927, m:tm-24, u:((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (and (or A (or B A)) Bm))))
================================================================
tm-name          tm-83661
in-theory        83661
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-927 tm-25 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       111
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-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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-83661.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (D and E)))), M:tm-927, m:tm-25, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-83662
in-theory        83662
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (D or E)) and ((B or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-927 tm-32 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (or Bm Cm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
proof-size       117
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-83662.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (D or E)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-32, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (or Bm Cm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83663
in-theory        83663
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-927 tm-33 ((Am (-> (or A (or B A)) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-83663.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (D or E))), M:tm-927, m:tm-33, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-83664
in-theory        83664
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E or D)) and ((B or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-927 tm-42 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (or Cm Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       117
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-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-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-83664.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E or D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-42, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (or Cm Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83665
in-theory        83665
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-927 tm-43 ((Am (-> (or A (or B A)) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       105
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-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-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-83665.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E or D))), M:tm-927, m:tm-43, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-83666
in-theory        83666
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((B or (A or B)) and D) or (B or (A or B))) -> C))
theorem-size     29
proof            (modus-ponens tm-927 tm-46 ((Am (or A (or B A))) (C Bm) (D (-> (or (and (or A (or B A)) Cm) (or A (or B A))) Bm))))
axioms-used      (tm-8 tm-7 tm-3)
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-83666.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((B or (A or B)) and D) or (B or (A or B))) -> C)), M:tm-927, m:tm-46, u:((Am (or A (or B A))) (C Bm) (D (-> (or (and (or A (or B A)) Cm) (or A (or B A))) Bm)))
================================================================
tm-name          tm-83667
in-theory        83667
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and (B or (A or B))) or (B or (A or B))) -> C))
theorem-size     29
proof            (modus-ponens tm-927 tm-47 ((Am (or A (or B A))) (C Bm) (D (-> (or (and Cm (or A (or B A))) (or A (or B A))) Bm))))
axioms-used      (tm-8 tm-7 tm-4)
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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-83667.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and (B or (A or B))) or (B or (A or B))) -> C)), M:tm-927, m:tm-47, u:((Am (or A (or B A))) (C Bm) (D (-> (or (and Cm (or A (or B A))) (or A (or B A))) Bm)))
================================================================
tm-name          tm-83668
in-theory        83668
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (B or (A or B))) -> C))
theorem-size     23
proof            (modus-ponens tm-927 tm-49 ((A Am) (Bm (or B Am)) (C Cm) (D (-> (or Am (or Am (or B Am))) Cm))))
axioms-used      (tm-8 tm-7 tm-6)
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-83668.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (B or (A or B))) -> C)), M:tm-927, m:tm-49, u:((A Am) (Bm (or B Am)) (C Cm) (D (-> (or Am (or Am (or B Am))) Cm)))
================================================================
tm-name          tm-83669
in-theory        83669
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((A or B) or (B or (A or B))) -> C))
theorem-size     25
proof            (modus-ponens tm-927 tm-50 ((A Am) (Bm (or B Am)) (C Cm) (D (-> (or (or B Am) (or Am (or B Am))) Cm))))
axioms-used      (tm-8 tm-7)
proof-size       125
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-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-83669.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((A or B) or (B or (A or B))) -> C)), M:tm-927, m:tm-50, u:((A Am) (Bm (or B Am)) (C Cm) (D (-> (or (or B Am) (or Am (or B Am))) Cm)))
================================================================
tm-name          tm-83670
in-theory        83670
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-927 tm-54 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-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-83670.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-54, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83671
in-theory        83671
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-927 tm-56 ((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       129
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-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-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-83671.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-927, m:tm-56, u:((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-83672
in-theory        83672
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (B or (A or B))))) or ((B or (A or B)) -> (not (C -> (B or (A or B)))))) -> (not (B or (A or B))))
theorem-size     34
proof            (modus-ponens tm-927 tm-57 ((Am (or A (or B A))) (C (not (-> Bm (or A (or B A))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-1)
proof-size       128
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-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-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-83672.        ((((A or B) -> (not (C -> (B or (A or B))))) or ((B or (A or B)) -> (not (C -> (B or (A or B)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-57, u:((Am (or A (or B A))) (C (not (-> Bm (or A (or B A))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83673
in-theory        83673
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> ((B or (A or B)) and C)))) or ((B or (A or B)) -> (not (C -> ((B or (A or B)) and C))))) -> (not (B or (A or B))))
theorem-size     38
proof            (modus-ponens tm-927 tm-61 ((Am (or A (or B A))) (C (not (-> Bm (and (or A (or B A)) Bm)))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-5)
proof-size       136
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-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-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-83673.        ((((A or B) -> (not (C -> ((B or (A or B)) and C)))) or ((B or (A or B)) -> (not (C -> ((B or (A or B)) and C))))) -> (not (B or (A or B)))), M:tm-927, m:tm-61, u:((Am (or A (or B A))) (C (not (-> Bm (and (or A (or B A)) Bm)))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83674
in-theory        83674
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((B or (A or B)) or C))) or ((B or (A or B)) -> (not ((B or (A or B)) or C)))) -> (not (B or (A or B))))
theorem-size     34
proof            (modus-ponens tm-927 tm-62 ((Am (or A (or B A))) (C (not (or (or A (or B A)) Bm))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-6)
proof-size       128
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-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-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-83674.        ((((A or B) -> (not ((B or (A or B)) or C))) or ((B or (A or B)) -> (not ((B or (A or B)) or C)))) -> (not (B or (A or B)))), M:tm-927, m:tm-62, u:((Am (or A (or B A))) (C (not (or (or A (or B A)) Bm))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83675
in-theory        83675
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C or (B or (A or B))))) or ((B or (A or B)) -> (not (C or (B or (A or B)))))) -> (not (B or (A or B))))
theorem-size     34
proof            (modus-ponens tm-927 tm-63 ((Am (or A (or B A))) (C (not (or Bm (or A (or B A))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9)
proof-size       128
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-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-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-83675.        ((((A or B) -> (not (C or (B or (A or B))))) or ((B or (A or B)) -> (not (C or (B or (A or B)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-63, u:((Am (or A (or B A))) (C (not (or Bm (or A (or B A))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83676
in-theory        83676
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B or (A or B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-927 tm-69 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-9)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-83676.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-69, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83677
in-theory        83677
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-927 tm-71 ((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-9)
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-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-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-83677.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-927, m:tm-71, u:((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-83678
in-theory        83678
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((not (not (B or (A or B)))) or (B or (A or B))) -> C))
theorem-size     29
proof            (modus-ponens tm-927 tm-73 ((Am (or A (or B A))) (C Bm) (D (-> (or (not (not (or A (or B A)))) (or A (or B A))) Bm))))
axioms-used      (tm-8 tm-7 tm-10)
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-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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-83678.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((not (not (B or (A or B)))) or (B or (A or B))) -> C)), M:tm-927, m:tm-73, u:((Am (or A (or B A))) (C Bm) (D (-> (or (not (not (or A (or B A)))) (or A (or B A))) Bm)))
================================================================
tm-name          tm-83679
in-theory        83679
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((not (not D)) -> D) and ((B or (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-927 tm-76 ((Am (-> (or A (or B A)) C)) (D (and (-> (not (not Bm)) Bm) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-10)
proof-size       117
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-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-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-83679.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((not (not D)) -> D) and ((B or (A or B)) -> C))), M:tm-927, m:tm-76, u:((Am (-> (or A (or B A)) C)) (D (and (-> (not (not Bm)) Bm) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83680
in-theory        83680
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-927 tm-78 ((Am (-> (or A (or B A)) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-7 tm-1 tm-10)
proof-size       105
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-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-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-83680.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((not (not D)) -> D)), M:tm-927, m:tm-78, u:((Am (-> (or A (or B A)) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-83681
in-theory        83681
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (D -> C)))) or ((B or (A or B)) -> (not (C -> (D -> C))))) -> (not (B or (A or B))))
theorem-size     30
proof            (modus-ponens tm-927 tm-79 ((Am (or A (or B A))) (C (not (-> Bm (-> Cm Bm)))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-1)
proof-size       138
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-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-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-83681.        ((((A or B) -> (not (C -> (D -> C)))) or ((B or (A or B)) -> (not (C -> (D -> C))))) -> (not (B or (A or B)))), M:tm-927, m:tm-79, u:((Am (or A (or B A))) (C (not (-> Bm (-> Cm Bm)))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83682
in-theory        83682
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (F -> E))) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-83 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-83682.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (F -> E))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-83, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83683
in-theory        83683
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (D -> C)))
theorem-size     23
proof            (modus-ponens tm-927 tm-84 ((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (-> Cm Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       131
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-83683.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (D -> C))), M:tm-927, m:tm-84, u:((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (-> Cm Bm))))
================================================================
tm-name          tm-83684
in-theory        83684
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-927 tm-85 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-7 tm-1)
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-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-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-83684.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (F -> E)))), M:tm-927, m:tm-85, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-83685
in-theory        83685
times-derived    3
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> C))
theorem-size     21
proof            (modus-ponens tm-927 tm-86 ((Am (-> (or A (or B A)) C)) (D (-> (or A (or B A)) C))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-83685.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> C)), M:tm-927, m:tm-86, u:((Am (-> (or A (or B A)) C)) (D (-> (or A (or B A)) C)))
================================================================
tm-name          tm-83686
in-theory        83686
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> D)) or ((B or (A or B)) -> (C -> D))) -> ((B or (A or B)) -> (C -> D)))
theorem-size     27
proof            (modus-ponens tm-927 tm-87 ((Am (or A (or B A))) (C (-> Bm Cm)) (D (-> (or A (or B A)) (-> Bm Cm)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-83686.        ((((A or B) -> (C -> D)) or ((B or (A or B)) -> (C -> D))) -> ((B or (A or B)) -> (C -> D))), M:tm-927, m:tm-87, u:((Am (or A (or B A))) (C (-> Bm Cm)) (D (-> (or A (or B A)) (-> Bm Cm))))
================================================================
tm-name          tm-83687
in-theory        83687
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> (D -> D)) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-95 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2 tm-1)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-83687.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> (D -> D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-95, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83688
in-theory        83688
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-927 tm-97 ((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
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-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-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-83688.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> (D -> D))), M:tm-927, m:tm-97, u:((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-83689
in-theory        83689
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> ((C -> (B or (A or B))) -> D)) or ((B or (A or B)) -> ((C -> (B or (A or B))) -> D))) -> ((B or (A or B)) -> D))
theorem-size     37
proof            (modus-ponens tm-927 tm-98 ((Am (or A (or B A))) (C (-> (-> Bm (or A (or B A))) Cm)) (D (-> (or A (or B A)) Cm))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-83689.        ((((A or B) -> ((C -> (B or (A or B))) -> D)) or ((B or (A or B)) -> ((C -> (B or (A or B))) -> D))) -> ((B or (A or B)) -> D)), M:tm-927, m:tm-98, u:((Am (or A (or B A))) (C (-> (-> Bm (or A (or B A))) Cm)) (D (-> (or A (or B A)) Cm)))
================================================================
tm-name          tm-83690
in-theory        83690
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> ((B or (A or B)) -> C)) or ((B or (A or B)) -> ((B or (A or B)) -> C))) -> ((B or (A or B)) -> C))
theorem-size     33
proof            (modus-ponens tm-927 tm-99 ((Am (or A (or B A))) (C (-> (or A (or B A)) Bm)) (D (-> (or A (or B A)) Bm))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-83690.        ((((A or B) -> ((B or (A or B)) -> C)) or ((B or (A or B)) -> ((B or (A or B)) -> C))) -> ((B or (A or B)) -> C)), M:tm-927, m:tm-99, u:((Am (or A (or B A))) (C (-> (or A (or B A)) Bm)) (D (-> (or A (or B A)) Bm)))
================================================================
tm-name          tm-83691
in-theory        83691
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B or (A or B)) -> C)))
theorem-size     41
proof            (modus-ponens tm-927 tm-105 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       185
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-83691.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-105, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83692
in-theory        83692
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-927 tm-107 ((Am (-> (or A (or B A)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
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-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-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-83692.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-927, m:tm-107, u:((Am (-> (or A (or B A)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-83693
in-theory        83693
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or ((B or (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (B or (A or B))))
theorem-size     46
proof            (modus-ponens tm-927 tm-109 ((Am (or A (or B A))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-1 tm-2)
proof-size       178
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-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-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-83693.        ((((A or B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or ((B or (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-109, u:((Am (or A (or B A))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83694
in-theory        83694
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-927 tm-113 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 tm-2)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-83694.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-113, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83695
in-theory        83695
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> (D -> E))) or ((B or (A or B)) -> (C -> (D -> E)))) -> ((B or (A or B)) -> ((C -> D) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-927 tm-114 ((Am (or A (or B A))) (C (-> Bm (-> Cm Dm))) (D (-> (or A (or B A)) (-> (-> Bm Cm) (-> Bm Dm))))))
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-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-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-83695.        ((((A or B) -> (C -> (D -> E))) or ((B or (A or B)) -> (C -> (D -> E)))) -> ((B or (A or B)) -> ((C -> D) -> (C -> E)))), M:tm-927, m:tm-114, u:((Am (or A (or B A))) (C (-> Bm (-> Cm Dm))) (D (-> (or A (or B A)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-83696
in-theory        83696
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-927 tm-115 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-83696.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-927, m:tm-115, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-83697
in-theory        83697
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-927 tm-125 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2 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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-83697.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-125, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83698
in-theory        83698
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-927 tm-127 ((Am (-> (or A (or B A)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2 tm-3)
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-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-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-83698.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-927, m:tm-127, u:((Am (-> (or A (or B A)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-83699
in-theory        83699
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C and D) -> C))) or ((B or (A or B)) -> (not ((C and D) -> C)))) -> (not (B or (A or B))))
theorem-size     30
proof            (modus-ponens tm-927 tm-130 ((Am (or A (or B A))) (C (not (-> (and Bm Cm) Bm))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-1 tm-3)
proof-size       138
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-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-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-83699.        ((((A or B) -> (not ((C and D) -> C))) or ((B or (A or B)) -> (not ((C and D) -> C)))) -> (not (B or (A or B)))), M:tm-927, m:tm-130, u:((Am (or A (or B A))) (C (not (-> (and Bm Cm) Bm))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83700
in-theory        83700
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E and F) -> E)) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-134 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 tm-3)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-83700.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E and F) -> E)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-134, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83701
in-theory        83701
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and D)) or ((B or (A or B)) -> (C and D))) -> ((B or (A or B)) -> C))
theorem-size     25
proof            (modus-ponens tm-927 tm-135 ((Am (or A (or B A))) (C (and Bm Cm)) (D (-> (or A (or B A)) Bm))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-3)
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-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-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-83701.        ((((A or B) -> (C and D)) or ((B or (A or B)) -> (C and D))) -> ((B or (A or B)) -> C)), M:tm-927, m:tm-135, u:((Am (or A (or B A))) (C (and Bm Cm)) (D (-> (or A (or B A)) Bm)))
================================================================
tm-name          tm-83702
in-theory        83702
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-927 tm-136 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-83702.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E and F) -> E))), M:tm-927, m:tm-136, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-83703
in-theory        83703
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-927 tm-147 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2 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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-83703.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-147, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83704
in-theory        83704
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-927 tm-149 ((Am (-> (or A (or B A)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2 tm-4)
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-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-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-83704.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-927, m:tm-149, u:((Am (-> (or A (or B A)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-83705
in-theory        83705
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C and D) -> D))) or ((B or (A or B)) -> (not ((C and D) -> D)))) -> (not (B or (A or B))))
theorem-size     30
proof            (modus-ponens tm-927 tm-153 ((Am (or A (or B A))) (C (not (-> (and Bm Cm) Cm))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-1 tm-4)
proof-size       138
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-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-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-83705.        ((((A or B) -> (not ((C and D) -> D))) or ((B or (A or B)) -> (not ((C and D) -> D)))) -> (not (B or (A or B)))), M:tm-927, m:tm-153, u:((Am (or A (or B A))) (C (not (-> (and Bm Cm) Cm))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83706
in-theory        83706
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E and F) -> F)) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-157 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 tm-4)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-83706.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E and F) -> F)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-157, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83707
in-theory        83707
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C and D)) or ((B or (A or B)) -> (C and D))) -> ((B or (A or B)) -> D))
theorem-size     25
proof            (modus-ponens tm-927 tm-158 ((Am (or A (or B A))) (C (and Bm Cm)) (D (-> (or A (or B A)) Cm))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-4)
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-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-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-83707.        ((((A or B) -> (C and D)) or ((B or (A or B)) -> (C and D))) -> ((B or (A or B)) -> D)), M:tm-927, m:tm-158, u:((Am (or A (or B A))) (C (and Bm Cm)) (D (-> (or A (or B A)) Cm)))
================================================================
tm-name          tm-83708
in-theory        83708
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-927 tm-159 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-83708.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E and F) -> F))), M:tm-927, m:tm-159, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-83709
in-theory        83709
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (D -> C)) and (B or (A or B))))) or ((B or (A or B)) -> (not ((C -> (D -> C)) and (B or (A or B)))))) -> (not (B or (A or B))))
theorem-size     42
proof            (modus-ponens tm-927 tm-179 ((Am (or A (or B A))) (C (not (and (-> Bm (-> Cm Bm)) (or A (or B A))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-5 tm-1)
proof-size       156
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-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-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-83709.        ((((A or B) -> (not ((C -> (D -> C)) and (B or (A or B))))) or ((B or (A or B)) -> (not ((C -> (D -> C)) and (B or (A or B)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-179, u:((Am (or A (or B A))) (C (not (and (-> Bm (-> Cm Bm)) (or A (or B A))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83710
in-theory        83710
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-183 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-83710.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-183, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83711
in-theory        83711
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-927 tm-184 ((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
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-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-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-83711.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (F -> E)) and D))), M:tm-927, m:tm-184, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-83712
in-theory        83712
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A or B))))) or ((B or (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A or B)))))) -> (not (B or (A or B))))
theorem-size     58
proof            (modus-ponens tm-927 tm-206 ((Am (or A (or B A))) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A (or B A))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-5 tm-2)
proof-size       196
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-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-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-83712.        ((((A or B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A or B))))) or ((B or (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A or B)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-206, u:((Am (or A (or B A))) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A (or B A))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83713
in-theory        83713
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B or (A or B)) -> C)))
theorem-size     39
proof            (modus-ponens tm-927 tm-210 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-83713.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-210, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83714
in-theory        83714
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-927 tm-211 ((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-2)
proof-size       161
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-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-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-83714.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-927, m:tm-211, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-83715
in-theory        83715
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (((C and D) -> C) and (B or (A or B))))) or ((B or (A or B)) -> (not (((C and D) -> C) and (B or (A or B)))))) -> (not (B or (A or B))))
theorem-size     42
proof            (modus-ponens tm-927 tm-235 ((Am (or A (or B A))) (C (not (and (-> (and Bm Cm) Bm) (or A (or B A))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-5 tm-3)
proof-size       156
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-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-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-83715.        ((((A or B) -> (not (((C and D) -> C) and (B or (A or B))))) or ((B or (A or B)) -> (not (((C and D) -> C) and (B or (A or B)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-235, u:((Am (or A (or B A))) (C (not (and (-> (and Bm Cm) Bm) (or A (or B A))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83716
in-theory        83716
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-239 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-83716.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-239, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83717
in-theory        83717
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-927 tm-240 ((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-3)
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-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-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-83717.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (((E and F) -> E) and D))), M:tm-927, m:tm-240, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-83718
in-theory        83718
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (((C and D) -> D) and (B or (A or B))))) or ((B or (A or B)) -> (not (((C and D) -> D) and (B or (A or B)))))) -> (not (B or (A or B))))
theorem-size     42
proof            (modus-ponens tm-927 tm-266 ((Am (or A (or B A))) (C (not (and (-> (and Bm Cm) Cm) (or A (or B A))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-5 tm-4)
proof-size       156
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-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-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-83718.        ((((A or B) -> (not (((C and D) -> D) and (B or (A or B))))) or ((B or (A or B)) -> (not (((C and D) -> D) and (B or (A or B)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-266, u:((Am (or A (or B A))) (C (not (and (-> (and Bm Cm) Cm) (or A (or B A))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83719
in-theory        83719
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-270 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-83719.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-270, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83720
in-theory        83720
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-927 tm-271 ((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-4)
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-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-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-83720.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (((E and F) -> F) and D))), M:tm-927, m:tm-271, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-83721
in-theory        83721
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (D -> (C and D))) and (B or (A or B))))) or ((B or (A or B)) -> (not ((C -> (D -> (C and D))) and (B or (A or B)))))) -> (not (B or (A or B))))
theorem-size     46
proof            (modus-ponens tm-927 tm-299 ((Am (or A (or B A))) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or A (or B A))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-5)
proof-size       166
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-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-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-83721.        ((((A or B) -> (not ((C -> (D -> (C and D))) and (B or (A or B))))) or ((B or (A or B)) -> (not ((C -> (D -> (C and D))) and (B or (A or B)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-299, u:((Am (or A (or B A))) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or A (or B A))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83722
in-theory        83722
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B or (A or B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-927 tm-303 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-83722.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-303, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83723
in-theory        83723
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-927 tm-304 ((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
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-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-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-83723.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-927, m:tm-304, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-83724
in-theory        83724
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> ((B or (A or B)) -> C))))
theorem-size     31
proof            (modus-ponens tm-927 tm-305 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (-> (or A (or B A)) C))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-83724.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> ((B or (A or B)) -> C)))), M:tm-927, m:tm-305, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (-> (or A (or B A)) C)))))
================================================================
tm-name          tm-83725
in-theory        83725
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> D)) or ((B or (A or B)) -> (C -> D))) -> (((B or (A or B)) -> (C -> D)) and (((B or (A or B)) -> C) -> ((B or (A or B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-927 tm-306 ((Am (or A (or B A))) (C (-> Bm Cm)) (D (and (-> (or A (or B A)) (-> Bm Cm)) (-> (-> (or A (or B A)) Bm) (-> (or A (or B A)) 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-83725.        ((((A or B) -> (C -> D)) or ((B or (A or B)) -> (C -> D))) -> (((B or (A or B)) -> (C -> D)) and (((B or (A or B)) -> C) -> ((B or (A or B)) -> D)))), M:tm-927, m:tm-306, u:((Am (or A (or B A))) (C (-> Bm Cm)) (D (and (-> (or A (or B A)) (-> Bm Cm)) (-> (-> (or A (or B A)) Bm) (-> (or A (or B A)) Cm)))))
================================================================
tm-name          tm-83726
in-theory        83726
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (((B or (A or B)) -> C) and D))))
theorem-size     33
proof            (modus-ponens tm-927 tm-309 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (and (-> (or A (or B A)) C) Bm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       147
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-83726.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (((B or (A or B)) -> C) and D)))), M:tm-927, m:tm-309, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (and (-> (or A (or B A)) C) Bm)))))
================================================================
tm-name          tm-83727
in-theory        83727
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((B or (A or B)) -> C) or D)))
theorem-size     31
proof            (modus-ponens tm-927 tm-310 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (or (-> (or A (or B A)) C) Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-6)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-83727.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((B or (A or B)) -> C) or D))), M:tm-927, m:tm-310, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (or (-> (or A (or B A)) C) Bm))))
================================================================
tm-name          tm-83728
in-theory        83728
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D or ((B or (A or B)) -> C))))
theorem-size     31
proof            (modus-ponens tm-927 tm-311 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (or Bm (-> (or A (or B A)) C))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-83728.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D or ((B or (A or B)) -> C)))), M:tm-927, m:tm-311, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (or Bm (-> (or A (or B A)) C)))))
================================================================
tm-name          tm-83729
in-theory        83729
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((C -> D) -> (((B or (A or B)) or C) -> D))))
theorem-size     35
proof            (modus-ponens tm-927 tm-312 ((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (-> Bm Cm) (-> (or (or A (or B A)) Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-83729.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((C -> D) -> (((B or (A or B)) or C) -> D)))), M:tm-927, m:tm-312, u:((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (-> Bm Cm) (-> (or (or A (or B A)) Bm) Cm)))))
================================================================
tm-name          tm-83730
in-theory        83730
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((B or (A or B)) -> (not C)) -> (not (B or (A or B))))))
theorem-size     37
proof            (modus-ponens tm-927 tm-313 ((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (-> (or A (or B A)) (not Bm)) (not (or A (or B A))))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-9)
proof-size       161
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-83730.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((B or (A or B)) -> (not C)) -> (not (B or (A or B)))))), M:tm-927, m:tm-313, u:((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (-> (or A (or B A)) (not Bm)) (not (or A (or B A)))))))
================================================================
tm-name          tm-83731
in-theory        83731
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (E -> D))))
theorem-size     27
proof            (modus-ponens tm-927 tm-315 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-83731.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (E -> D)))), M:tm-927, m:tm-315, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-83732
in-theory        83732
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((B or (A or B)) -> (B or (A or B)))))
theorem-size     33
proof            (modus-ponens tm-927 tm-316 ((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (or A (or B A)) (or A (or B A)))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-83732.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((B or (A or B)) -> (B or (A or B))))), M:tm-927, m:tm-316, u:((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (or A (or B A)) (or A (or B A))))))
================================================================
tm-name          tm-83733
in-theory        83733
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-927 tm-318 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-83733.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-927, m:tm-318, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-83734
in-theory        83734
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-927 tm-320 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-83734.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D and E) -> D))), M:tm-927, m:tm-320, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-83735
in-theory        83735
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D and E) -> E)))
theorem-size     27
proof            (modus-ponens tm-927 tm-322 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-83735.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D and E) -> E))), M:tm-927, m:tm-322, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-83736
in-theory        83736
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (E -> D)) and ((B or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-927 tm-323 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> Bm (-> Cm Bm)) (-> (or A (or B A)) C))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-83736.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (E -> D)) and ((B or (A or B)) -> C)))), M:tm-927, m:tm-323, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> Bm (-> Cm Bm)) (-> (or A (or B A)) C)))))
================================================================
tm-name          tm-83737
in-theory        83737
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A or B)) -> C))))
theorem-size     43
proof            (modus-ponens tm-927 tm-324 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (or B A)) C))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-83737.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A or B)) -> C)))), M:tm-927, m:tm-324, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (or B A)) C)))))
================================================================
tm-name          tm-83738
in-theory        83738
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((D and E) -> D) and ((B or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-927 tm-325 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> (and Bm Cm) Bm) (-> (or A (or B A)) C))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-83738.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((D and E) -> D) and ((B or (A or B)) -> C)))), M:tm-927, m:tm-325, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> (and Bm Cm) Bm) (-> (or A (or B A)) C)))))
================================================================
tm-name          tm-83739
in-theory        83739
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((D and E) -> E) and ((B or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-927 tm-326 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> (and Bm Cm) Cm) (-> (or A (or B A)) C))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-83739.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((D and E) -> E) and ((B or (A or B)) -> C)))), M:tm-927, m:tm-326, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> (and Bm Cm) Cm) (-> (or A (or B A)) C)))))
================================================================
tm-name          tm-83740
in-theory        83740
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (E -> (D and E))) and ((B or (A or B)) -> C))))
theorem-size     37
proof            (modus-ponens tm-927 tm-327 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (or B A)) C))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-83740.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (E -> (D and E))) and ((B or (A or B)) -> C)))), M:tm-927, m:tm-327, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (or B A)) C)))))
================================================================
tm-name          tm-83741
in-theory        83741
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((B or (A or B)) -> ((B or (A or B)) and C))))
theorem-size     35
proof            (modus-ponens tm-927 tm-328 ((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (or A (or B A)) (and (or A (or B A)) Bm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-83741.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((B or (A or B)) -> ((B or (A or B)) and C)))), M:tm-927, m:tm-328, u:((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (or A (or B A)) (and (or A (or B A)) Bm)))))
================================================================
tm-name          tm-83742
in-theory        83742
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-338 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-83742.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-338, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83743
in-theory        83743
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-927 tm-340 ((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2 tm-5)
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-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-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-83743.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> (D -> (D and E)))), M:tm-927, m:tm-340, u:((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-83744
in-theory        83744
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-927 tm-341 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-83744.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (E -> (D and E))))), M:tm-927, m:tm-341, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-83745
in-theory        83745
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> ((C -> ((B or (A or B)) and C)) -> D)) or ((B or (A or B)) -> ((C -> ((B or (A or B)) and C)) -> D))) -> ((B or (A or B)) -> D))
theorem-size     41
proof            (modus-ponens tm-927 tm-349 ((Am (or A (or B A))) (C (-> (-> Bm (and (or A (or B A)) Bm)) Cm)) (D (-> (or A (or B A)) Cm))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-83745.        ((((A or B) -> ((C -> ((B or (A or B)) and C)) -> D)) or ((B or (A or B)) -> ((C -> ((B or (A or B)) and C)) -> D))) -> ((B or (A or B)) -> D)), M:tm-927, m:tm-349, u:((Am (or A (or B A))) (C (-> (-> Bm (and (or A (or B A)) Bm)) Cm)) (D (-> (or A (or B A)) Cm)))
================================================================
tm-name          tm-83746
in-theory        83746
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (D -> (C and D))))) or ((B or (A or B)) -> (not (C -> (D -> (C and D)))))) -> (not (B or (A or B))))
theorem-size     34
proof            (modus-ponens tm-927 tm-350 ((Am (or A (or B A))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-1 tm-5)
proof-size       148
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-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-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-83746.        ((((A or B) -> (not (C -> (D -> (C and D))))) or ((B or (A or B)) -> (not (C -> (D -> (C and D)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-350, u:((Am (or A (or B A))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83747
in-theory        83747
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-354 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-83747.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-354, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83748
in-theory        83748
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (D -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-927 tm-355 ((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-5)
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-83748.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (D -> (C and D)))), M:tm-927, m:tm-355, u:((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-83749
in-theory        83749
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-927 tm-356 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
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-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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-83749.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (F -> (E and F))))), M:tm-927, m:tm-356, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-83750
in-theory        83750
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> D)) or F) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-364 ((Am (-> (or A (or B A)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6 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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-83750.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> D)) or F) and ((B or (A or B)) -> C))), M:tm-927, m:tm-364, u:((Am (-> (or A (or B A)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83751
in-theory        83751
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-927 tm-365 ((Am (-> (or A (or B A)) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-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-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-83751.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> D)) or F)), M:tm-927, m:tm-365, u:((Am (-> (or A (or B A)) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-83752
in-theory        83752
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-927 tm-373 ((Am (-> (or A (or B A)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6 tm-2)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-83752.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B or (A or B)) -> C))), M:tm-927, m:tm-373, u:((Am (-> (or A (or B A)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83753
in-theory        83753
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-927 tm-374 ((Am (-> (or A (or B A)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-7 tm-1 tm-6 tm-2)
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-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-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-83753.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-927, m:tm-374, u:((Am (-> (or A (or B A)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-83754
in-theory        83754
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D and E) -> D) or F) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-382 ((Am (-> (or A (or B A)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6 tm-3)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-83754.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D and E) -> D) or F) and ((B or (A or B)) -> C))), M:tm-927, m:tm-382, u:((Am (-> (or A (or B A)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83755
in-theory        83755
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-927 tm-383 ((Am (-> (or A (or B A)) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6 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-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-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-83755.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and E) -> D) or F)), M:tm-927, m:tm-383, u:((Am (-> (or A (or B A)) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-83756
in-theory        83756
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D and E) -> E) or F) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-391 ((Am (-> (or A (or B A)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6 tm-4)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-83756.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D and E) -> E) or F) and ((B or (A or B)) -> C))), M:tm-927, m:tm-391, u:((Am (-> (or A (or B A)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83757
in-theory        83757
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-927 tm-392 ((Am (-> (or A (or B A)) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6 tm-4)
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-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-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-83757.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D and E) -> E) or F)), M:tm-927, m:tm-392, u:((Am (-> (or A (or B A)) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-83758
in-theory        83758
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> (D and E))) or F) and ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-400 ((Am (-> (or A (or B A)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-83758.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E -> (D and E))) or F) and ((B or (A or B)) -> C))), M:tm-927, m:tm-400, u:((Am (-> (or A (or B A)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83759
in-theory        83759
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-927 tm-401 ((Am (-> (or A (or B A)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6 tm-5)
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-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-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-83759.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (D and E))) or F)), M:tm-927, m:tm-401, u:((Am (-> (or A (or B A)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-83760
in-theory        83760
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (D or E)) or F) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-409 ((Am (-> (or A (or B A)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-83760.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (D or E)) or F) and ((B or (A or B)) -> C))), M:tm-927, m:tm-409, u:((Am (-> (or A (or B A)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83761
in-theory        83761
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-927 tm-410 ((Am (-> (or A (or B A)) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-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-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-83761.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (D or E)) or F)), M:tm-927, m:tm-410, u:((Am (-> (or A (or B A)) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-83762
in-theory        83762
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (D or E)) and ((B or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-927 tm-443 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> Bm (or Bm Cm)) (-> (or A (or B A)) C))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-83762.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (D or E)) and ((B or (A or B)) -> C)))), M:tm-927, m:tm-443, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> Bm (or Bm Cm)) (-> (or A (or B A)) C)))))
================================================================
tm-name          tm-83763
in-theory        83763
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (C or D)) and (B or (A or B))))) or ((B or (A or B)) -> (not ((C -> (C or D)) and (B or (A or B)))))) -> (not (B or (A or B))))
theorem-size     42
proof            (modus-ponens tm-927 tm-449 ((Am (or A (or B A))) (C (not (and (-> Bm (or Bm Cm)) (or A (or B A))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-5 tm-6)
proof-size       156
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-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-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-83763.        ((((A or B) -> (not ((C -> (C or D)) and (B or (A or B))))) or ((B or (A or B)) -> (not ((C -> (C or D)) and (B or (A or B)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-449, u:((Am (or A (or B A))) (C (not (and (-> Bm (or Bm Cm)) (or A (or B A))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83764
in-theory        83764
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-453 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-83764.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-453, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83765
in-theory        83765
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-927 tm-454 ((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-6)
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-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-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-83765.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (E or F)) and D))), M:tm-927, m:tm-454, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-83766
in-theory        83766
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (D or E))))
theorem-size     27
proof            (modus-ponens tm-927 tm-456 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-83766.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (D or E)))), M:tm-927, m:tm-456, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-83767
in-theory        83767
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (((B or (A or B)) or C) -> D)) or ((B or (A or B)) -> (((B or (A or B)) or C) -> D))) -> ((B or (A or B)) -> D))
theorem-size     37
proof            (modus-ponens tm-927 tm-464 ((Am (or A (or B A))) (C (-> (or (or A (or B A)) Bm) Cm)) (D (-> (or A (or B A)) Cm))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-83767.        ((((A or B) -> (((B or (A or B)) or C) -> D)) or ((B or (A or B)) -> (((B or (A or B)) or C) -> D))) -> ((B or (A or B)) -> D)), M:tm-927, m:tm-464, u:((Am (or A (or B A))) (C (-> (or (or A (or B A)) Bm) Cm)) (D (-> (or A (or B A)) Cm)))
================================================================
tm-name          tm-83768
in-theory        83768
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (C or D)))) or ((B or (A or B)) -> (not (C -> (C or D))))) -> (not (B or (A or B))))
theorem-size     30
proof            (modus-ponens tm-927 tm-465 ((Am (or A (or B A))) (C (not (-> Bm (or Bm Cm)))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-1 tm-6)
proof-size       138
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-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-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-83768.        ((((A or B) -> (not (C -> (C or D)))) or ((B or (A or B)) -> (not (C -> (C or D))))) -> (not (B or (A or B)))), M:tm-927, m:tm-465, u:((Am (or A (or B A))) (C (not (-> Bm (or Bm Cm)))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83769
in-theory        83769
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (E or F))) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-469 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-83769.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (E or F))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-469, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83770
in-theory        83770
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (C or D)))
theorem-size     23
proof            (modus-ponens tm-927 tm-470 ((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (or Bm Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-6)
proof-size       131
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-83770.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (C or D))), M:tm-927, m:tm-470, u:((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (or Bm Cm))))
================================================================
tm-name          tm-83771
in-theory        83771
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-927 tm-471 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-83771.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (E or F)))), M:tm-927, m:tm-471, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-83772
in-theory        83772
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or (E -> (F -> E))) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-480 ((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 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-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-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-83772.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or (E -> (F -> E))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-480, u:((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83773
in-theory        83773
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-927 tm-481 ((Am (-> (or A (or B A)) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-7 tm-1)
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-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-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-83773.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or (E -> (F -> E)))), M:tm-927, m:tm-481, u:((Am (-> (or A (or B A)) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-83774
in-theory        83774
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-927 tm-490 ((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
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-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-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-83774.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-490, u:((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83775
in-theory        83775
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-927 tm-491 ((Am (-> (or A (or B A)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
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-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-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-83775.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-927, m:tm-491, u:((Am (-> (or A (or B A)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-83776
in-theory        83776
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or ((E and F) -> E)) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-500 ((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
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-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-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-83776.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or ((E and F) -> E)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-500, u:((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83777
in-theory        83777
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-927 tm-501 ((Am (-> (or A (or B A)) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
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-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-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-83777.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((E and F) -> E))), M:tm-927, m:tm-501, u:((Am (-> (or A (or B A)) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-83778
in-theory        83778
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or ((E and F) -> F)) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-510 ((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
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-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-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-83778.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or ((E and F) -> F)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-510, u:((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83779
in-theory        83779
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-927 tm-511 ((Am (-> (or A (or B A)) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
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-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-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-83779.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((E and F) -> F))), M:tm-927, m:tm-511, u:((Am (-> (or A (or B A)) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-83780
in-theory        83780
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-520 ((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-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-83780.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-520, u:((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83781
in-theory        83781
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-927 tm-521 ((Am (-> (or A (or B A)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
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-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-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-83781.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or (E -> (F -> (E and F))))), M:tm-927, m:tm-521, u:((Am (-> (or A (or B A)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-83782
in-theory        83782
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or (E -> (E or F))) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-530 ((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-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-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-83782.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or (E -> (E or F))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-530, u:((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83783
in-theory        83783
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-927 tm-531 ((Am (-> (or A (or B A)) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-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-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-83783.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or (E -> (E or F)))), M:tm-927, m:tm-531, u:((Am (-> (or A (or B A)) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-83784
in-theory        83784
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or (E -> (F or E))) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-540 ((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-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-83784.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or (E -> (F or E))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-540, u:((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83785
in-theory        83785
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-927 tm-541 ((Am (-> (or A (or B A)) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-7 tm-1)
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-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-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-83785.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or (E -> (F or E)))), M:tm-927, m:tm-541, u:((Am (-> (or A (or B A)) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-83786
in-theory        83786
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E or D)) or F) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-550 ((Am (-> (or A (or B A)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-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-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-83786.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E or D)) or F) and ((B or (A or B)) -> C))), M:tm-927, m:tm-550, u:((Am (-> (or A (or B A)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83787
in-theory        83787
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-927 tm-551 ((Am (-> (or A (or B A)) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-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-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-83787.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E or D)) or F)), M:tm-927, m:tm-551, u:((Am (-> (or A (or B A)) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-83788
in-theory        83788
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (E or D)) and ((B or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-927 tm-595 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> Bm (or Cm Bm)) (-> (or A (or B A)) C))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-83788.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((D -> (E or D)) and ((B or (A or B)) -> C)))), M:tm-927, m:tm-595, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (and (-> Bm (or Cm Bm)) (-> (or A (or B A)) C)))))
================================================================
tm-name          tm-83789
in-theory        83789
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not ((C -> (D or C)) and (B or (A or B))))) or ((B or (A or B)) -> (not ((C -> (D or C)) and (B or (A or B)))))) -> (not (B or (A or B))))
theorem-size     42
proof            (modus-ponens tm-927 tm-601 ((Am (or A (or B A))) (C (not (and (-> Bm (or Cm Bm)) (or A (or B A))))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-5)
proof-size       156
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-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-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-83789.        ((((A or B) -> (not ((C -> (D or C)) and (B or (A or B))))) or ((B or (A or B)) -> (not ((C -> (D or C)) and (B or (A or B)))))) -> (not (B or (A or B)))), M:tm-927, m:tm-601, u:((Am (or A (or B A))) (C (not (and (-> Bm (or Cm Bm)) (or A (or B A))))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83790
in-theory        83790
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-605 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-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-83790.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-605, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83791
in-theory        83791
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-927 tm-606 ((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
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-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-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-83791.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> ((E -> (F or E)) and D))), M:tm-927, m:tm-606, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-83792
in-theory        83792
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (E or D))))
theorem-size     27
proof            (modus-ponens tm-927 tm-609 ((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-83792.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (D -> (E or D)))), M:tm-927, m:tm-609, u:((Am (-> (or A (or B A)) C)) (D (and (-> (or A (or B A)) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-83793
in-theory        83793
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> ((C or (B or (A or B))) -> D)) or ((B or (A or B)) -> ((C or (B or (A or B))) -> D))) -> ((B or (A or B)) -> D))
theorem-size     37
proof            (modus-ponens tm-927 tm-617 ((Am (or A (or B A))) (C (-> (or Bm (or A (or B A))) Cm)) (D (-> (or A (or B A)) Cm))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-83793.        ((((A or B) -> ((C or (B or (A or B))) -> D)) or ((B or (A or B)) -> ((C or (B or (A or B))) -> D))) -> ((B or (A or B)) -> D)), M:tm-927, m:tm-617, u:((Am (or A (or B A))) (C (-> (or Bm (or A (or B A))) Cm)) (D (-> (or A (or B A)) Cm)))
================================================================
tm-name          tm-83794
in-theory        83794
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (C -> (D or C)))) or ((B or (A or B)) -> (not (C -> (D or C))))) -> (not (B or (A or B))))
theorem-size     30
proof            (modus-ponens tm-927 tm-618 ((Am (or A (or B A))) (C (not (-> Bm (or Cm Bm)))) (D (not (or A (or B A))))))
axioms-used      (tm-8 tm-7 tm-9 tm-1)
proof-size       138
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-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-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-83794.        ((((A or B) -> (not (C -> (D or C)))) or ((B or (A or B)) -> (not (C -> (D or C))))) -> (not (B or (A or B)))), M:tm-927, m:tm-618, u:((Am (or A (or B A))) (C (not (-> Bm (or Cm Bm)))) (D (not (or A (or B A)))))
================================================================
tm-name          tm-83795
in-theory        83795
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (F or E))) and ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-927 tm-622 ((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 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-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-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-83795.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> (E -> (F or E))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-622, u:((Am (-> (or A (or B A)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83796
in-theory        83796
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (D or C)))
theorem-size     23
proof            (modus-ponens tm-927 tm-623 ((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (or Cm Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       131
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-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-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-83796.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((B or (A or B)) -> (D or C))), M:tm-927, m:tm-623, u:((Am (or A (or B A))) (C Bm) (D (-> (or A (or B A)) (or Cm Bm))))
================================================================
tm-name          tm-83797
in-theory        83797
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-927 tm-624 ((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-7 tm-1)
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-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-1.            (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-83797.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D -> (E -> (F or E)))), M:tm-927, m:tm-624, u:((Am (-> (or A (or B A)) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-83798
in-theory        83798
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-927 tm-665 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       159
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-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-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-83798.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-665, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83799
in-theory        83799
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-927 tm-667 ((Am (-> (or A (or B A)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       147
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-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-1.            (A -> (B -> A)), 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-83799.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-927, m:tm-667, u:((Am (-> (or A (or B A)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-83800
in-theory        83800
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B or (A or B)) -> C)))
theorem-size     47
proof            (modus-ponens tm-927 tm-708 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       203
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-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-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-83800.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-708, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83801
in-theory        83801
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (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-927 tm-710 ((Am (-> (or 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-7 tm-1 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-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-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-83801.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-927, m:tm-710, u:((Am (-> (or A (or B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-83802
in-theory        83802
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((((B or (A or B)) and D) or (B or (A or B))) -> C)))
theorem-size     37
proof            (modus-ponens tm-927 tm-747 ((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (or (and (or A (or B A)) Cm) (or A (or B A))) Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-83802.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((((B or (A or B)) and D) or (B or (A or B))) -> C))), M:tm-927, m:tm-747, u:((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (or (and (or A (or B A)) Cm) (or A (or B A))) Bm))))
================================================================
tm-name          tm-83803
in-theory        83803
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B or (A or B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-927 tm-757 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
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-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-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-83803.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-757, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83804
in-theory        83804
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-927 tm-759 ((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
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-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-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-83804.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-927, m:tm-759, u:((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-83805
in-theory        83805
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((D and (B or (A or B))) or (B or (A or B))) -> C)))
theorem-size     37
proof            (modus-ponens tm-927 tm-798 ((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (or (and Cm (or A (or B A))) (or A (or B A))) Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83805.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((D and (B or (A or B))) or (B or (A or B))) -> C))), M:tm-927, m:tm-798, u:((Am (or A (or B A))) (C Bm) (D (and (-> (or A (or B A)) Bm) (-> (or (and Cm (or A (or B A))) (or A (or B A))) Bm))))
================================================================
tm-name          tm-83806
in-theory        83806
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B or (A or B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-927 tm-808 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-83806.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-808, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83807
in-theory        83807
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-927 tm-810 ((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-83807.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-927, m:tm-810, u:((Am (-> (or A (or B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-83808
in-theory        83808
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B or (A or B)) -> C)))
theorem-size     39
proof            (modus-ponens tm-927 tm-855 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 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-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-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-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-83808.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-855, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83809
in-theory        83809
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-927 tm-857 ((Am (-> (or A (or B A)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       161
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-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-1.            (A -> (B -> A)), 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-83809.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-927, m:tm-857, u:((Am (-> (or A (or B A)) C)) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-83810
in-theory        83810
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((B or (B or (A or B))) -> C)))
theorem-size     31
proof            (modus-ponens tm-927 tm-882 ((A Am) (Bm (or B Am)) (C Cm) (D (and (-> (or Am (or B Am)) Cm) (-> (or Am (or Am (or B Am))) Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-83810.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and ((B or (B or (A or B))) -> C))), M:tm-927, m:tm-882, u:((A Am) (Bm (or B Am)) (C Cm) (D (and (-> (or Am (or B Am)) Cm) (-> (or Am (or Am (or B Am))) Cm))))
================================================================
tm-name          tm-83811
in-theory        83811
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-927 tm-893 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
proof-size       159
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-83811.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-893, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-83812
in-theory        83812
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-927 tm-895 ((Am (-> (or A (or B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       147
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-83812.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-927, m:tm-895, u:((Am (-> (or A (or B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-83813
in-theory        83813
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((A or B) or (B or (A or B))) -> C)))
theorem-size     33
proof            (modus-ponens tm-927 tm-920 ((A Am) (Bm (or B Am)) (C Cm) (D (and (-> (or Am (or B Am)) Cm) (-> (or (or B Am) (or Am (or B Am))) Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
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-83813.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((B or (A or B)) -> C) and (((A or B) or (B or (A or B))) -> C))), M:tm-927, m:tm-920, u:((A Am) (Bm (or B Am)) (C Cm) (D (and (-> (or Am (or B Am)) Cm) (-> (or (or B Am) (or Am (or B Am))) Cm))))
================================================================
tm-name          tm-83814
in-theory        83814
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-893 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83814.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-893, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83815
in-theory        83815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-855 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83815.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-855, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83816
in-theory        83816
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> (D and ((A or (B or A)) -> C))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> (D and ((A or (B or A)) -> C))))
theorem-size     41
proof            (modus-ponens tm-850 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (Dm (and B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (and B (-> (or Am (or Bm Am)) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83816.        ((((A or (B or A)) -> C) -> (D and ((A or (B or A)) -> C))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> (D and ((A or (B or A)) -> C)))), M:tm-850, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (Dm (and B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (and B (-> (or Am (or Bm Am)) Cm)))))
================================================================
tm-name          tm-83817
in-theory        83817
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> (D and ((A or (B or A)) -> C))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> (D and ((A or (B or A)) -> C)))) and ((D or (((A or (B or A)) -> C) -> (D and ((A or (B or A)) -> C)))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> (D and ((A or (B or A)) -> C)))))
theorem-size     85
proof            (modus-ponens tm-844 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (Dm (and B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (and B (-> (or Am (or Bm Am)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83817.        (((((A or (B or A)) -> C) -> (D and ((A or (B or A)) -> C))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> (D and ((A or (B or A)) -> C)))) and ((D or (((A or (B or A)) -> C) -> (D and ((A or (B or A)) -> C)))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> (D and ((A or (B or A)) -> C))))), M:tm-844, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (Dm (and B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (and B (-> (or Am (or Bm Am)) Cm)))))
================================================================
tm-name          tm-83818
in-theory        83818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-808 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83818.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-808, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83819
in-theory        83819
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((E and (((A or (B or A)) -> C) -> D)) or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))
theorem-size     63
proof            (modus-ponens tm-798 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83819.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((E and (((A or (B or A)) -> C) -> D)) or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))), M:tm-798, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83820
in-theory        83820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-757 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-83820.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-757, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83821
in-theory        83821
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((((((A or (B or A)) -> C) -> D) and E) or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))
theorem-size     63
proof            (modus-ponens tm-747 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-83821.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((((((A or (B or A)) -> C) -> D) and E) or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))), M:tm-747, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83822
in-theory        83822
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-708 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83822.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H))), M:tm-708, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83823
in-theory        83823
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> ((A or (B or A)) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> D)))
theorem-size     37
proof            (modus-ponens tm-703 tm-927 ((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or Am (or Bm Am)) C)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or Am (or Bm Am)) C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83823.        ((((A or (B or A)) -> C) -> ((A or (B or A)) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> D))), M:tm-703, m:tm-927, u:((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or Am (or Bm Am)) C)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or Am (or Bm Am)) C))))
================================================================
tm-name          tm-83824
in-theory        83824
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> ((A or (B or A)) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> D))) and ((((A or (B or A)) -> (C -> D)) or (((A or (B or A)) -> C) -> ((A or (B or A)) -> D))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> D))))
theorem-size     85
proof            (modus-ponens tm-697 tm-927 ((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or Am (or Bm Am)) C)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or Am (or Bm Am)) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83824.        (((((A or (B or A)) -> C) -> ((A or (B or A)) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> D))) and ((((A or (B or A)) -> (C -> D)) or (((A or (B or A)) -> C) -> ((A or (B or A)) -> D))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> D)))), M:tm-697, m:tm-927, u:((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or Am (or Bm Am)) C)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or Am (or Bm Am)) C))))
================================================================
tm-name          tm-83825
in-theory        83825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-665 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-83825.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-665, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83826
in-theory        83826
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((D or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))
theorem-size     53
proof            (modus-ponens tm-654 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (B Dm) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-83826.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((D or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))), M:tm-654, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (B Dm) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83827
in-theory        83827
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> (E or ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-623 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or 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-50.           (((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-83827.        ((((A or (B or A)) -> C) -> D) -> (E or ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))), M:tm-623, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83828
in-theory        83828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-622 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or 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-50.           (((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-83828.        ((A -> (B -> (C or B))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-622, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83829
in-theory        83829
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C or B)) -> D) -> (E or ((B or (C or B)) -> D)))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (E or ((B or (C or B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-619 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (Dm (or B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (or B (-> (or Am (or 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-50.           (((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-83829.        ((A or (((B or (C or B)) -> D) -> (E or ((B or (C or B)) -> D)))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (E or ((B or (C or B)) -> D)))), M:tm-619, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (Dm (or B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (or B (-> (or Am (or Bm Am)) Cm)))))
================================================================
tm-name          tm-83830
in-theory        83830
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or 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-50.           (((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-83830.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83831
in-theory        83831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-605 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-83831.        ((A -> ((B -> (C or B)) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-605, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83832
in-theory        83832
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (F or E)) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-595 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-83832.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (F or E)) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-595, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83833
in-theory        83833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-550 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-50.           (((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-83833.        (((A -> (B or A)) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-550, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83834
in-theory        83834
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-540 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-83834.        ((A or (B -> (C or B))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-540, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83835
in-theory        83835
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-530 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-50.           (((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-83835.        ((A or (B -> (B or C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-530, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83836
in-theory        83836
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-520 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-83836.        ((A or (B -> (C -> (B and C)))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-520, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83837
in-theory        83837
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-510 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-50.           (((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-83837.        ((A or ((B and C) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-510, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83838
in-theory        83838
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-500 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-50.           (((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-83838.        ((A or ((B and C) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-500, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83839
in-theory        83839
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-490 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-83839.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H))), M:tm-490, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83840
in-theory        83840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-480 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or 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-50.           (((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-83840.        ((A or (B -> (C -> B))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-480, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83841
in-theory        83841
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> (((((B or A) -> C) or ((A or (B or A)) -> C)) -> D) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83841.        ((((A or (B or A)) -> C) -> D) -> (((((B or A) -> C) or ((A or (B or A)) -> C)) -> D) or E)), M:tm-470, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83842
in-theory        83842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-469 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83842.        ((A -> (B -> (B or C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-469, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83843
in-theory        83843
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C or B)) -> D) -> (((B or (C or B)) -> D) or E))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (((B or (C or B)) -> D) or E)))
theorem-size     43
proof            (modus-ponens tm-466 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (Dm (or (-> (or Am (or Bm Am)) Cm) B)) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (or (-> (or Am (or Bm Am)) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 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-6.            (A -> (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-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-83843.        ((A or (((B or (C or B)) -> D) -> (((B or (C or B)) -> D) or E))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (((B or (C or B)) -> D) or E))), M:tm-466, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (Dm (or (-> (or Am (or Bm Am)) Cm) B)) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (or (-> (or Am (or Bm Am)) Cm) B))))
================================================================
tm-name          tm-83844
in-theory        83844
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-83844.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83845
in-theory        83845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-453 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83845.        ((A -> ((B -> (B or C)) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-453, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83846
in-theory        83846
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (E or F)) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-443 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-83846.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (E or F)) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-443, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83847
in-theory        83847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-409 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83847.        (((A -> (A or B)) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-409, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83848
in-theory        83848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-400 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83848.        (((A -> (B -> (A and B))) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-400, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83849
in-theory        83849
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-391 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83849.        ((((A and B) -> B) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-391, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83850
in-theory        83850
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-382 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83850.        ((((A and B) -> A) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-382, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83851
in-theory        83851
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-373 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83851.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H))), M:tm-373, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83852
in-theory        83852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-364 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83852.        (((A -> (B -> A)) or C) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-364, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83853
in-theory        83853
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> (E -> (((((B or A) -> C) or ((A or (B or A)) -> C)) -> D) and E)))
theorem-size     29
proof            (modus-ponens tm-355 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-83853.        ((((A or (B or A)) -> C) -> D) -> (E -> (((((B or A) -> C) or ((A or (B or A)) -> C)) -> D) and E))), M:tm-355, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83854
in-theory        83854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-354 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83854.        ((A -> (B -> (C -> (B and C)))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-354, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83855
in-theory        83855
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C or B)) -> D) -> (E -> (((B or (C or B)) -> D) and E)))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (E -> (((B or (C or B)) -> D) and E))))
theorem-size     47
proof            (modus-ponens tm-351 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (Dm (-> B (and (-> (or Am (or Bm Am)) Cm) B))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> B (and (-> (or Am (or Bm Am)) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83855.        ((A or (((B or (C or B)) -> D) -> (E -> (((B or (C or B)) -> D) and E)))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (E -> (((B or (C or B)) -> D) and E)))), M:tm-351, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (Dm (-> B (and (-> (or Am (or Bm Am)) Cm) B))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> B (and (-> (or Am (or Bm Am)) Cm) B)))))
================================================================
tm-name          tm-83856
in-theory        83856
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-83856.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83857
in-theory        83857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-338 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-83857.        (((A -> B) -> (A -> (A and B))) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F))), M:tm-338, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83858
in-theory        83858
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) or (((A or (B or A)) -> C) -> (((A or (B or A)) -> C) and D))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> (((A or (B or A)) -> C) and D)))
theorem-size     51
proof            (modus-ponens tm-335 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (Dm (and (-> (or Am (or Bm Am)) Cm) B)) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (and (-> (or Am (or Bm Am)) Cm) B)))))
axioms-used      (tm-8 tm-2 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-5.            (A -> (B -> (A and B))), axiom
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-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-83858.        (((((A or (B or A)) -> C) -> D) or (((A or (B or A)) -> C) -> (((A or (B or A)) -> C) and D))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> (((A or (B or A)) -> C) and D))), M:tm-335, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (Dm (and (-> (or Am (or Bm Am)) Cm) B)) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (and (-> (or Am (or Bm Am)) Cm) B))))
================================================================
tm-name          tm-83859
in-theory        83859
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((((A or (B or A)) -> C) -> D) -> ((((A or (B or A)) -> C) -> D) and ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-328 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
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-328.          ((A -> 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-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-83859.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((((A or (B or A)) -> C) -> D) -> ((((A or (B or A)) -> C) -> D) and ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-328, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83860
in-theory        83860
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     59
proof            (modus-ponens tm-327 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-83860.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-327, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83861
in-theory        83861
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((E and F) -> F) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-326 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-83861.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((E and F) -> F) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-326, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83862
in-theory        83862
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((E and F) -> E) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-325 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-83862.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((E and F) -> E) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-325, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83863
in-theory        83863
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     65
proof            (modus-ponens tm-324 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83863.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-324, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83864
in-theory        83864
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (F -> E)) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-323 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-83864.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (F -> E)) and ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-323, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83865
in-theory        83865
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-83865.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83866
in-theory        83866
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-83866.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83867
in-theory        83867
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-83867.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83868
in-theory        83868
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((((A or (B or A)) -> C) -> D) -> (((A or (B or A)) -> C) -> D)))
theorem-size     45
proof            (modus-ponens tm-316 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-83868.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((((A or (B or A)) -> C) -> D) -> (((A or (B or A)) -> C) -> D))), M:tm-316, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83869
in-theory        83869
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-83869.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83870
in-theory        83870
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((((A or (B or A)) -> C) -> D) -> (not ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))) -> (not (((A or (B or A)) -> C) -> D))))
theorem-size     63
proof            (modus-ponens tm-313 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83870.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((((A or (B or A)) -> C) -> D) -> (not ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))) -> (not (((A or (B or A)) -> C) -> D)))), M:tm-313, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83871
in-theory        83871
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((((((B or A) -> C) or ((A or (B or A)) -> C)) -> D) -> E) -> (((((A or (B or A)) -> C) -> D) or ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) -> E)))
theorem-size     71
proof            (modus-ponens tm-312 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83871.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and ((((((B or A) -> C) or ((A or (B or A)) -> C)) -> D) -> E) -> (((((A or (B or A)) -> C) -> D) or ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) -> E))), M:tm-312, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83872
in-theory        83872
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E or ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-311 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) 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-7.            (A -> (B or 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-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-83872.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E or ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-311, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83873
in-theory        83873
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-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-83873.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) or E)), M:tm-310, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83874
in-theory        83874
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) 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-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-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-83874.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and E))), M:tm-309, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83875
in-theory        83875
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((((A or (B or A)) -> C) -> D) -> (((B or A) -> C) or ((A or (B or A)) -> C))) -> ((((A or (B or A)) -> C) -> D) -> D)))
theorem-size     61
proof            (modus-ponens tm-306 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83875.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (((((A or (B or A)) -> C) -> D) -> (((B or A) -> C) or ((A or (B or A)) -> C))) -> ((((A or (B or A)) -> C) -> D) -> D))), M:tm-306, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (C Dm))
================================================================
tm-name          tm-83876
in-theory        83876
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-305 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-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-83876.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) and (E -> ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))), M:tm-305, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83877
in-theory        83877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-303 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83877.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-303, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83878
in-theory        83878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-270 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83878.        ((A -> (((B and C) -> C) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-270, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83879
in-theory        83879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-239 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83879.        ((A -> (((B and C) -> B) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-239, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83880
in-theory        83880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H)))
theorem-size     43
proof            (modus-ponens tm-210 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
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-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-83880.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H))), M:tm-210, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83881
in-theory        83881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-183 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83881.        ((A -> ((B -> (C -> B)) and A)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-183, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83882
in-theory        83882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-157 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83882.        ((A -> ((B and C) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-157, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83883
in-theory        83883
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-147 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83883.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-147, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83884
in-theory        83884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-134 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83884.        ((A -> ((B and C) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-134, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83885
in-theory        83885
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-125 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83885.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-125, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83886
in-theory        83886
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> (D -> E)) -> (((((B or A) -> C) or ((A or (B or A)) -> C)) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> E)))
theorem-size     43
proof            (modus-ponens tm-114 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) (-> C D))) (B (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83886.        ((((A or (B or A)) -> C) -> (D -> E)) -> (((((B or A) -> C) or ((A or (B or A)) -> C)) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> E))), M:tm-114, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) (-> C D))) (B (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-83887
in-theory        83887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-113 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83887.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H))), M:tm-113, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83888
in-theory        83888
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C or B)) -> (D -> E)) -> (((B or (C or B)) -> D) -> ((B or (C or B)) -> E)))) -> ((((C or B) -> (D -> E)) or ((B or (C or B)) -> (D -> E))) -> (((B or (C or B)) -> D) -> ((B or (C or B)) -> E))))
theorem-size     61
proof            (modus-ponens tm-110 tm-927 ((A (or Am (or Bm Am))) (Cm (-> B C)) (Dm (-> (-> (or Am (or Bm Am)) B) (-> (or Am (or Bm Am)) C))) (D (-> (or (-> (or Bm Am) (-> B C)) (-> (or Am (or Bm Am)) (-> B C))) (-> (-> (or Am (or Bm Am)) B) (-> (or Am (or Bm Am)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83888.        ((A or (((B or (C or B)) -> (D -> E)) -> (((B or (C or B)) -> D) -> ((B or (C or B)) -> E)))) -> ((((C or B) -> (D -> E)) or ((B or (C or B)) -> (D -> E))) -> (((B or (C or B)) -> D) -> ((B or (C or B)) -> E)))), M:tm-110, m:tm-927, u:((A (or Am (or Bm Am))) (Cm (-> B C)) (Dm (-> (-> (or Am (or Bm Am)) B) (-> (or Am (or Bm Am)) C))) (D (-> (or (-> (or Bm Am) (-> B C)) (-> (or Am (or Bm Am)) (-> B C))) (-> (-> (or Am (or Bm Am)) B) (-> (or Am (or Bm Am)) C)))))
================================================================
tm-name          tm-83889
in-theory        83889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-105 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83889.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-105, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83890
in-theory        83890
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> (C -> D)) -> ((A or (B or A)) -> C)) or (((A or (B or A)) -> (C -> D)) -> ((A or (B or A)) -> D))) -> ((((B or A) -> (C -> D)) or ((A or (B or A)) -> (C -> D))) -> ((A or (B or A)) -> D)))
theorem-size     61
proof            (modus-ponens tm-102 tm-927 ((A (or Am (or Bm Am))) (Cm (-> B C)) (Dm (-> (or Am (or Bm Am)) C)) (D (-> (or (-> (or Bm Am) (-> B C)) (-> (or Am (or Bm Am)) (-> B C))) (-> (or Am (or Bm Am)) C)))))
axioms-used      (tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83890.        (((((A or (B or A)) -> (C -> D)) -> ((A or (B or A)) -> C)) or (((A or (B or A)) -> (C -> D)) -> ((A or (B or A)) -> D))) -> ((((B or A) -> (C -> D)) or ((A or (B or A)) -> (C -> D))) -> ((A or (B or A)) -> D))), M:tm-102, m:tm-927, u:((A (or Am (or Bm Am))) (Cm (-> B C)) (Dm (-> (or Am (or Bm Am)) C)) (D (-> (or (-> (or Bm Am) (-> B C)) (-> (or Am (or Bm Am)) (-> B C))) (-> (or Am (or Bm Am)) C))))
================================================================
tm-name          tm-83891
in-theory        83891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-95 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-83891.        (((A -> B) -> (A -> A)) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F))), M:tm-95, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83892
in-theory        83892
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) or (((A or (B or A)) -> C) -> ((A or (B or A)) -> C))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> C)))
theorem-size     47
proof            (modus-ponens tm-92 tm-927 ((Dm (-> (or Am (or Bm Am)) Cm)) (A (-> (or Am (or Bm Am)) Cm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or Am (or Bm Am)) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 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-1.            (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-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-83892.        (((((A or (B or A)) -> C) -> D) or (((A or (B or A)) -> C) -> ((A or (B or A)) -> C))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> C))), M:tm-92, m:tm-927, u:((Dm (-> (or Am (or Bm Am)) Cm)) (A (-> (or Am (or Bm Am)) Cm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or Am (or Bm Am)) Cm))))
================================================================
tm-name          tm-83893
in-theory        83893
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> (E -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-84 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83893.        ((((A or (B or A)) -> C) -> D) -> (E -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))), M:tm-84, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83894
in-theory        83894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-83 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83894.        ((A -> (B -> (C -> B))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-83, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83895
in-theory        83895
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C or B)) -> D) -> (E -> ((B or (C or B)) -> D)))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (E -> ((B or (C or B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-80 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (Dm (-> B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> B (-> (or Am (or 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-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-83895.        ((A or (((B or (C or B)) -> D) -> (E -> ((B or (C or B)) -> D)))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (E -> ((B or (C or B)) -> D)))), M:tm-80, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (Dm (-> B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> B (-> (or Am (or Bm Am)) Cm)))))
================================================================
tm-name          tm-83896
in-theory        83896
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or (C or B)) -> D) -> E) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-76 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83896.        (((not (not A)) -> A) and ((((B or (C or B)) -> D) -> E) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E))), M:tm-76, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83897
in-theory        83897
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A or (B or A)) -> C) -> D))) or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-73 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83897.        (((not (not (((A or (B or A)) -> C) -> D))) or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)), M:tm-73, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83898
in-theory        83898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-69 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83898.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F))), M:tm-69, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83899
in-theory        83899
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) or (((A or (B or A)) -> (not C)) -> (not (A or (B or A))))) -> ((((B or A) -> (not C)) or ((A or (B or A)) -> (not C))) -> (not (A or (B or A)))))
theorem-size     46
proof            (modus-ponens tm-66 tm-927 ((A (or Am (or Bm Am))) (Cm (not B)) (Dm (not (or Am (or Bm Am)))) (C (-> (or (-> (or Bm Am) (not B)) (-> (or Am (or Bm Am)) (not B))) (not (or Am (or Bm Am)))))))
axioms-used      (tm-8 tm-9 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83899.        ((((A or (B or A)) -> C) or (((A or (B or A)) -> (not C)) -> (not (A or (B or A))))) -> ((((B or A) -> (not C)) or ((A or (B or A)) -> (not C))) -> (not (A or (B or A))))), M:tm-66, m:tm-927, u:((A (or Am (or Bm Am))) (Cm (not B)) (Dm (not (or Am (or Bm Am)))) (C (-> (or (-> (or Bm Am) (not B)) (-> (or Am (or Bm Am)) (not B))) (not (or Am (or Bm Am))))))
================================================================
tm-name          tm-83900
in-theory        83900
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> (((B or A) -> C) or ((A or (B or A)) -> C))) -> ((((A or (B or A)) -> C) or (((B or A) -> C) or ((A or (B or A)) -> C))) -> (((B or A) -> C) or ((A or (B or A)) -> C))))
theorem-size     57
proof            (modus-ponens tm-55 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (Dm (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (B (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (C (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)))))
axioms-used      (tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83900.        ((((A or (B or A)) -> C) -> (((B or A) -> C) or ((A or (B or A)) -> C))) -> ((((A or (B or A)) -> C) or (((B or A) -> C) or ((A or (B or A)) -> C))) -> (((B or A) -> C) or ((A or (B or A)) -> C)))), M:tm-55, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (Dm (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (B (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (C (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))))
================================================================
tm-name          tm-83901
in-theory        83901
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-54 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83901.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-54, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83902
in-theory        83902
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or (C or B))) or (((B or (C or B)) -> D) -> ((A or (B or (C or B))) -> D))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> ((A or (B or (C or B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-51 tm-927 ((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or C (or Am (or Bm Am))) Cm)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or C (or Am (or Bm Am))) Cm)))))
axioms-used      (tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83902.        (((A -> (B or (C or B))) or (((B or (C or B)) -> D) -> ((A or (B or (C or B))) -> D))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> ((A or (B or (C or B))) -> D))), M:tm-51, m:tm-927, u:((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or C (or Am (or Bm Am))) Cm)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or C (or Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-83903
in-theory        83903
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or (C or B)) -> D) -> (A and ((B or (C or B)) -> D)))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (A and ((B or (C or B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-48 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (Dm (and B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (and B (-> (or Am (or Bm Am)) Cm))))))
axioms-used      (tm-8 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83903.        ((A or (((B or (C or B)) -> D) -> (A and ((B or (C or B)) -> D)))) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> (A and ((B or (C or B)) -> D)))), M:tm-48, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (Dm (and B (-> (or Am (or Bm Am)) Cm))) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (and B (-> (or Am (or Bm Am)) Cm)))))
================================================================
tm-name          tm-83904
in-theory        83904
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B or (C or B)) -> D) -> E)) or (((B or (C or B)) -> D) -> E)) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-47 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83904.        (((A and (((B or (C or B)) -> D) -> E)) or (((B or (C or B)) -> D) -> E)) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E)), M:tm-47, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83905
in-theory        83905
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or (B or A)) -> C) -> D) and E) or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-46 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83905.        ((((((A or (B or A)) -> C) -> D) and E) or (((A or (B or A)) -> C) -> D)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)), M:tm-46, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83906
in-theory        83906
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> (C -> D)) or (((A or (B or A)) -> C) -> ((A or (B or A)) -> D))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> D)))
theorem-size     47
proof            (modus-ponens tm-45 tm-927 ((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or Am (or Bm Am)) C)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or Am (or Bm Am)) C)))))
axioms-used      (tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83906.        ((((A or (B or A)) -> (C -> D)) or (((A or (B or A)) -> C) -> ((A or (B or A)) -> D))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((A or (B or A)) -> D))), M:tm-45, m:tm-927, u:((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or Am (or Bm Am)) C)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or Am (or Bm Am)) C))))
================================================================
tm-name          tm-83907
in-theory        83907
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or (C or B)) -> D) -> A)) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> A))
theorem-size     27
proof            (modus-ponens tm-44 tm-927 ((A (-> (or Am (or Bm Am)) Cm)) (B Dm) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83907.        ((A or (((B or (C or B)) -> D) -> A)) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> A)), M:tm-44, m:tm-927, u:((A (-> (or Am (or Bm Am)) Cm)) (B Dm) (C (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83908
in-theory        83908
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-42 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-83908.        ((A -> (B or A)) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F))), M:tm-42, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83909
in-theory        83909
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-32 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83909.        ((A -> (A or B)) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F))), M:tm-32, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83910
in-theory        83910
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> ((((A or (B or A)) -> C) -> D) and ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)))
theorem-size     35
proof            (modus-ponens tm-24 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83910.        ((((A or (B or A)) -> C) -> D) -> ((((A or (B or A)) -> C) -> D) and ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))), M:tm-24, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83911
in-theory        83911
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-23 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-83911.        ((A -> (B -> (A and B))) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F))), M:tm-23, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83912
in-theory        83912
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-22 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83912.        (((A and B) -> B) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F))), M:tm-22, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83913
in-theory        83913
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-21 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83913.        (((A and B) -> A) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F))), M:tm-21, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83914
in-theory        83914
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-20 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83914.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-20, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83915
in-theory        83915
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-19 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83915.        ((A -> (B -> A)) and ((((C or (D or C)) -> E) -> F) -> ((((D or C) -> E) or ((C or (D or C)) -> E)) -> F))), M:tm-19, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83916
in-theory        83916
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> (((A or (B or A)) -> C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83916.        ((((A or (B or A)) -> C) -> D) -> (((A or (B or A)) -> C) -> D)), M:tm-12, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83917
in-theory        83917
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> (not ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))) -> (not (((A or (B or A)) -> C) -> D)))
theorem-size     37
proof            (modus-ponens tm-9 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83917.        (((((A or (B or A)) -> C) -> D) -> (not ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))) -> (not (((A or (B or A)) -> C) -> D))), M:tm-9, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83918
in-theory        83918
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or B) -> C) or ((B or (A or B)) -> C)) -> D) -> E) -> (((((B or (A or B)) -> C) -> D) or ((((A or B) -> C) or ((B or (A or B)) -> C)) -> D)) -> E))
theorem-size     45
proof            (modus-ponens tm-8 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-7)
proof-size       127
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-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-83918.        ((((((A or B) -> C) or ((B or (A or B)) -> C)) -> D) -> E) -> (((((B or (A or B)) -> C) -> D) or ((((A or B) -> C) or ((B or (A or B)) -> C)) -> D)) -> E)), M:tm-8, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-83919
in-theory        83919
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B or (C or B)) -> D) -> E) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-7 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-7 tm-8)
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-50.           (((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-83919.        (A or ((((B or (C or B)) -> D) -> E) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E))), M:tm-7, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83920
in-theory        83920
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83920.        (((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)) or E), M:tm-6, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83921
in-theory        83921
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B or (C or B)) -> D) -> E) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83921.        (A -> (((((B or (C or B)) -> D) -> E) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E)) and A)), M:tm-5, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83922
in-theory        83922
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> D) -> (((B or A) -> C) or ((A or (B or A)) -> C))) -> ((((A or (B or A)) -> C) -> D) -> D))
theorem-size     35
proof            (modus-ponens tm-2 tm-927 ((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83922.        (((((A or (B or A)) -> C) -> D) -> (((B or A) -> C) or ((A or (B or A)) -> C))) -> ((((A or (B or A)) -> C) -> D) -> D)), M:tm-2, m:tm-927, u:((A (-> (-> (or Am (or Bm Am)) Cm) Dm)) (B (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm))) (C Dm))
================================================================
tm-name          tm-83923
in-theory        83923
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B or (C or B)) -> D) -> E) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-1 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-7)
proof-size       101
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-50.           (((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-83923.        (A -> ((((B or (C or B)) -> D) -> E) -> ((((C or B) -> D) or ((B or (C or B)) -> D)) -> E))), M:tm-1, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-83924
in-theory        83924
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-893 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83924.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-893, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83925
in-theory        83925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-855 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83925.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-855, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83926
in-theory        83926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-808 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83926.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-808, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83927
in-theory        83927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-757 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
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-50.           (((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-83927.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-757, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83928
in-theory        83928
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 or (F or G)) -> H))))
theorem-size     41
proof            (modus-ponens tm-708 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-83928.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-708, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83929
in-theory        83929
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-665 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83929.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-665, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83930
in-theory        83930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-622 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83930.        ((A -> (B -> (C or B))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-622, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83931
in-theory        83931
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83931.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83932
in-theory        83932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-605 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 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-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-83932.        ((A -> ((B -> (C or B)) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-605, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83933
in-theory        83933
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F or E)) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-83933.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F or E)) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-595, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83934
in-theory        83934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-550 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-83934.        (((A -> (B or A)) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-550, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83935
in-theory        83935
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-540 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 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-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-83935.        ((A or (B -> (C or B))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-540, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83936
in-theory        83936
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-530 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-83936.        ((A or (B -> (B or C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-530, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83937
in-theory        83937
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-520 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 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-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-83937.        ((A or (B -> (C -> (B and C)))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-520, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83938
in-theory        83938
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-510 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 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-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-83938.        ((A or ((B and C) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-510, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83939
in-theory        83939
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-500 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-50.           (((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-83939.        ((A or ((B and C) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-500, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83940
in-theory        83940
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-490 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 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-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-83940.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-490, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83941
in-theory        83941
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-480 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83941.        ((A or (B -> (C -> B))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-480, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83942
in-theory        83942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-469 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83942.        ((A -> (B -> (B or C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-469, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83943
in-theory        83943
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83943.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83944
in-theory        83944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-453 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-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-83944.        ((A -> ((B -> (B or C)) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-453, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83945
in-theory        83945
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (E or F)) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-50.           (((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-83945.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (E or F)) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-443, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83946
in-theory        83946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-409 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-50.           (((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-83946.        (((A -> (A or B)) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-409, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83947
in-theory        83947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-400 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-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-83947.        (((A -> (B -> (A and B))) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-400, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83948
in-theory        83948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-391 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-50.           (((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-83948.        ((((A and B) -> B) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-391, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83949
in-theory        83949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-382 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-50.           (((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-83949.        ((((A and B) -> A) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-382, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83950
in-theory        83950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-373 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 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-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-83950.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-373, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83951
in-theory        83951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-364 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83951.        (((A -> (B -> A)) or C) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-364, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83952
in-theory        83952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-354 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83952.        ((A -> (B -> (C -> (B and C)))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-354, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83953
in-theory        83953
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83953.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83954
in-theory        83954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-338 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-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-83954.        (((A -> B) -> (A -> (A and B))) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-338, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83955
in-theory        83955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> (E and F))) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-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-83955.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> (E and F))) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-327, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83956
in-theory        83956
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and F) -> F) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-50.           (((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-83956.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and F) -> F) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-326, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83957
in-theory        83957
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and F) -> E) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-50.           (((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-83957.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and F) -> E) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-325, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83958
in-theory        83958
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-50.           (((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-83958.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-324, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83959
in-theory        83959
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> E)) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83959.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> E)) and (A or (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-323, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83960
in-theory        83960
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83960.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83961
in-theory        83961
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83961.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83962
in-theory        83962
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83962.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83963
in-theory        83963
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83963.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83964
in-theory        83964
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E or (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-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-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-83964.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E or (A or (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-311, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83965
in-theory        83965
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-50.           (((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-83965.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) or E)), M:tm-310, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83966
in-theory        83966
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (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-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-50.           (((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-83966.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and E))), M:tm-309, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83967
in-theory        83967
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83967.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (A or (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-305, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83968
in-theory        83968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-303 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 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-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-83968.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-303, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83969
in-theory        83969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-270 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 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-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-83969.        ((A -> (((B and C) -> C) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-270, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83970
in-theory        83970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-239 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 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-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-83970.        ((A -> (((B and C) -> B) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-239, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83971
in-theory        83971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-210 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 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-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-83971.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-210, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83972
in-theory        83972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-183 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83972.        ((A -> ((B -> (C -> B)) and A)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-183, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83973
in-theory        83973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-157 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83973.        ((A -> ((B and C) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-157, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83974
in-theory        83974
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-147 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 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-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-83974.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-147, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83975
in-theory        83975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-134 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83975.        ((A -> ((B and C) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-134, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83976
in-theory        83976
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-125 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-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-83976.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-125, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83977
in-theory        83977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-113 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83977.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-113, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83978
in-theory        83978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-105 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-50.           (((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-83978.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-105, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83979
in-theory        83979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-95 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83979.        (((A -> B) -> (A -> A)) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-95, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83980
in-theory        83980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-83 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83980.        ((A -> (B -> (C -> B))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-83, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83981
in-theory        83981
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     21
proof            (modus-ponens tm-76 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 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-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-83981.        (((not (not A)) -> A) and (B or (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-76, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83982
in-theory        83982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-69 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 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-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-83982.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-69, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83983
in-theory        83983
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-54 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-83983.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-54, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83984
in-theory        83984
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-42 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-50.           (((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-83984.        ((A -> (B or A)) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-42, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83985
in-theory        83985
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-32 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-50.           (((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-83985.        ((A -> (A or B)) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-32, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83986
in-theory        83986
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-23 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (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-23.           (A -> ((B -> (C -> (B and 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-50.           (((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-83986.        ((A -> (B -> (A and B))) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-23, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83987
in-theory        83987
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-22 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-50.           (((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-83987.        (((A and B) -> B) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-22, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83988
in-theory        83988
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-21 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 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-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-83988.        (((A and B) -> A) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-21, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83989
in-theory        83989
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-20 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-50.           (((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-83989.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-20, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83990
in-theory        83990
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-19 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83990.        ((A -> (B -> A)) and (C or (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-19, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83991
in-theory        83991
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-7 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-7 tm-8)
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-50.           (((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-83991.        (A or (B or (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-7, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83992
in-theory        83992
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-6 tm-7 tm-8)
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-50.           (((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-83992.        ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) or E), M:tm-6, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83993
in-theory        83993
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C or D) -> E) -> ((D or (C or D)) -> E))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-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-83993.        (A -> ((B or (((C or D) -> E) -> ((D or (C or D)) -> E))) and A)), M:tm-5, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83994
in-theory        83994
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-1 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-83994.        (A -> (B or (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-1, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-83995
in-theory        83995
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-917 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (or B C) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
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-83995.        ((A or (B or A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-917, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (or B C) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83996
in-theory        83996
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-914 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (or B C) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (or B C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-83996.        ((A or (B or A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (B or A))), M:tm-914, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (or B C) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (or B C)))))
================================================================
tm-name          tm-83997
in-theory        83997
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-893 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83997.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-893, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-83998
in-theory        83998
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-879 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (or B C) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-6 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83998.        ((A or (A or B)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-879, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (or B C) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-83999
in-theory        83999
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-876 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (or B C) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (or B C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-83999.        ((A or (A or B)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B))), M:tm-876, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (or B C) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (or B C)))))
================================================================
tm-name          tm-84000
in-theory        84000
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-874 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-50.           (((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-84000.        ((A -> (B or A)) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F)), M:tm-874, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84001
in-theory        84001
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-872 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84001.        ((A -> (A or B)) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F)), M:tm-872, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84002
in-theory        84002
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-870 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84002.        ((A -> (B -> (A and B))) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F)), M:tm-870, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84003
in-theory        84003
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-869 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84003.        (((A and B) -> B) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F)), M:tm-869, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84004
in-theory        84004
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-868 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84004.        (((A and B) -> A) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F)), M:tm-868, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84005
in-theory        84005
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-867 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84005.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-867, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84006
in-theory        84006
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-866 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84006.        ((A -> (B -> A)) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F)), M:tm-866, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84007
in-theory        84007
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B or C) -> D) -> ((C or (B or C)) -> D)) or E))
theorem-size     17
proof            (modus-ponens tm-861 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 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-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-50.           (((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-84007.        (A or ((((B or C) -> D) -> ((C or (B or C)) -> D)) or E)), M:tm-861, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84008
in-theory        84008
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) or E)
theorem-size     17
proof            (modus-ponens tm-860 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84008.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) or E), M:tm-860, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84009
in-theory        84009
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) -> ((C or (B or C)) -> D)) or E) and A))
theorem-size     19
proof            (modus-ponens tm-859 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       121
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84009.        (A -> (((((B or C) -> D) -> ((C or (B or C)) -> D)) or E) and A)), M:tm-859, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84010
in-theory        84010
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) or E))
theorem-size     17
proof            (modus-ponens tm-858 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
axioms-used      (tm-8 tm-6 tm-1 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84010.        (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) or E)), M:tm-858, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))
================================================================
tm-name          tm-84011
in-theory        84011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-855 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84011.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-855, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84012
in-theory        84012
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-841 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> B (and C B)) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
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-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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84012.        ((A or (B -> (A and B))) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-841, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> B (and C B)) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84013
in-theory        84013
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (B -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-837 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> B (and C B)) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (-> B (and C B)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84013.        ((A or (B -> (A and B))) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (B -> (A and B)))), M:tm-837, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> B (and C B)) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (-> B (and C B))))))
================================================================
tm-name          tm-84014
in-theory        84014
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B))
theorem-size     21
proof            (modus-ponens tm-836 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84014.        (((A and B) or B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B)), M:tm-836, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84015
in-theory        84015
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and A))
theorem-size     21
proof            (modus-ponens tm-835 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84015.        (((A and B) or A) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and A)), M:tm-835, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84016
in-theory        84016
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-834 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-7)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84016.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> (A -> C)))), M:tm-834, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-84017
in-theory        84017
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-833 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> B C) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (-> B C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84017.        ((A or (B -> A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (B -> A))), M:tm-833, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> B C) (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) (-> B C)))))
================================================================
tm-name          tm-84018
in-theory        84018
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-831 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-50.           (((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-84018.        ((A -> (B or A)) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C))), M:tm-831, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84019
in-theory        84019
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-829 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84019.        ((A -> (A or B)) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C))), M:tm-829, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84020
in-theory        84020
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))
theorem-size     19
proof            (modus-ponens tm-827 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84020.        (A -> (A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))), M:tm-827, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84021
in-theory        84021
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-826 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84021.        ((A -> (B -> (A and B))) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C))), M:tm-826, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84022
in-theory        84022
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-825 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84022.        (((A and B) -> B) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C))), M:tm-825, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84023
in-theory        84023
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-824 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84023.        (((A and B) -> A) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C))), M:tm-824, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84024
in-theory        84024
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-823 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84024.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-823, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84025
in-theory        84025
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-822 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84025.        ((A -> (B -> A)) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C))), M:tm-822, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84026
in-theory        84026
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-816 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-9 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84026.        ((A -> (not ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))) -> (not A)), M:tm-816, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84027
in-theory        84027
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> ((B or (A or B)) -> C)) and D) -> E) -> ((D or ((((A or B) -> C) -> ((B or (A or B)) -> C)) and D)) -> E))
theorem-size     37
proof            (modus-ponens tm-815 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84027.        ((((((A or B) -> C) -> ((B or (A or B)) -> C)) and D) -> E) -> ((D or ((((A or B) -> C) -> ((B or (A or B)) -> C)) and D)) -> E)), M:tm-815, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84028
in-theory        84028
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B)))
theorem-size     19
proof            (modus-ponens tm-814 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-50.           (((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-84028.        (A or (B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B))), M:tm-814, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84029
in-theory        84029
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) or E)
theorem-size     19
proof            (modus-ponens tm-813 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84029.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) or E), M:tm-813, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84030
in-theory        84030
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B)) and A))
theorem-size     21
proof            (modus-ponens tm-812 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84030.        (A -> ((B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B)) and A)), M:tm-812, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84031
in-theory        84031
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B)))
theorem-size     19
proof            (modus-ponens tm-811 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B)))))
axioms-used      (tm-8 tm-5 tm-1 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84031.        (A -> (B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B))), M:tm-811, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (and (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B))))
================================================================
tm-name          tm-84032
in-theory        84032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-808 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-7)
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84032.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-808, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84033
in-theory        84033
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-795 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-6 tm-7)
proof-size       143
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84033.        (((A and B) or B) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-795, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84034
in-theory        84034
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B or C) -> D) -> (C or (B or C)))) or (((B or C) -> D) -> (C or (B or C)))) -> (((B or C) -> D) -> D))
theorem-size     33
proof            (modus-ponens tm-794 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-6 tm-7)
proof-size       191
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84034.        (((A and (((B or C) -> D) -> (C or (B or C)))) or (((B or C) -> D) -> (C or (B or C)))) -> (((B or C) -> D) -> D)), M:tm-794, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84035
in-theory        84035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-757 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84035.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-757, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84036
in-theory        84036
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-744 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-6 tm-7)
proof-size       143
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84036.        (((A and B) or A) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-744, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84037
in-theory        84037
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> (B or (A or B))) and D) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-743 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-6 tm-7)
proof-size       191
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84037.        ((((((A or B) -> C) -> (B or (A or B))) and D) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C)), M:tm-743, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84038
in-theory        84038
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)) or H))
theorem-size     41
proof            (modus-ponens tm-708 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-50.           (((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-84038.        (((((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)) or H)), M:tm-708, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84039
in-theory        84039
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-694 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-7)
proof-size       187
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84039.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-694, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84040
in-theory        84040
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B or A)) or (((B or A) -> C) -> (A or (B or A)))) -> (((B or A) -> C) -> C))
theorem-size     25
proof            (modus-ponens tm-692 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 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-1.            (A -> (B -> A)), 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84040.        (((A or (B or A)) or (((B or A) -> C) -> (A or (B or A)))) -> (((B or A) -> C) -> C)), M:tm-692, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84041
in-theory        84041
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-690 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6)
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-7.            (A -> (B or 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-50.           (((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-84041.        ((A -> (B or A)) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E))), M:tm-690, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84042
in-theory        84042
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-688 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7)
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-6.            (A -> (A or 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-50.           (((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-84042.        ((A -> (A or B)) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E))), M:tm-688, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84043
in-theory        84043
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (B or (A or B))) -> ((((A or B) -> C) -> (B or (A or B))) and (((A or B) -> C) -> C)))
theorem-size     31
proof            (modus-ponens tm-686 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7)
proof-size       187
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84043.        ((((A or B) -> C) -> (B or (A or B))) -> ((((A or B) -> C) -> (B or (A or B))) and (((A or B) -> C) -> C))), M:tm-686, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84044
in-theory        84044
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-685 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 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-5.            (A -> (B -> (A and B))), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84044.        ((A -> (B -> (A and B))) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E))), M:tm-685, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84045
in-theory        84045
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-684 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-6 tm-7)
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-4.            ((A and B) -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84045.        (((A and B) -> B) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E))), M:tm-684, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84046
in-theory        84046
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-683 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-6 tm-7)
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-3.            ((A and B) -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84046.        (((A and B) -> A) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E))), M:tm-683, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84047
in-theory        84047
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-682 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7)
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84047.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-682, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84048
in-theory        84048
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-681 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6 tm-7)
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-1.            (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84048.        ((A -> (B -> A)) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E))), M:tm-681, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84049
in-theory        84049
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> (B or (A or B))))
theorem-size     23
proof            (modus-ponens tm-676 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84049.        ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> (B or (A or B)))), M:tm-676, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84050
in-theory        84050
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (not (((A or B) -> C) -> C))) -> (not (((A or B) -> C) -> (B or (A or B)))))
theorem-size     33
proof            (modus-ponens tm-674 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-9 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84050.        (((((A or B) -> C) -> (B or (A or B))) -> (not (((A or B) -> C) -> C))) -> (not (((A or B) -> C) -> (B or (A or B))))), M:tm-674, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84051
in-theory        84051
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> C) -> D) -> (((((A or B) -> C) -> (B or (A or B))) or (((A or B) -> C) -> C)) -> D))
theorem-size     31
proof            (modus-ponens tm-673 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-6 tm-7)
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84051.        (((((A or B) -> C) -> C) -> D) -> (((((A or B) -> C) -> (B or (A or B))) or (((A or B) -> C) -> C)) -> D)), M:tm-673, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84052
in-theory        84052
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B or C) -> D) -> (C or (B or C))) -> (((B or C) -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-672 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-7 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-50.           (((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-84052.        (A or ((((B or C) -> D) -> (C or (B or C))) -> (((B or C) -> D) -> D))), M:tm-672, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84053
in-theory        84053
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) or D)
theorem-size     21
proof            (modus-ponens tm-671 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-50.           (((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-84053.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) or D), M:tm-671, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84054
in-theory        84054
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) -> (C or (B or C))) -> (((B or C) -> D) -> D)) and A))
theorem-size     23
proof            (modus-ponens tm-670 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84054.        (A -> (((((B or C) -> D) -> (C or (B or C))) -> (((B or C) -> D) -> D)) and A)), M:tm-670, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84055
in-theory        84055
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> ((A or B) -> C)) -> ((((A or B) -> C) -> (B or (A or B))) -> C))
theorem-size     31
proof            (modus-ponens tm-669 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84055.        (((((A or B) -> C) -> (B or (A or B))) -> ((A or B) -> C)) -> ((((A or B) -> C) -> (B or (A or B))) -> C)), M:tm-669, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84056
in-theory        84056
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> (C or (B or C))) -> (((B or C) -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-668 tm-929 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84056.        (A -> ((((B or C) -> D) -> (C or (B or C))) -> (((B or C) -> D) -> D))), M:tm-668, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm) (Dm (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84057
in-theory        84057
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-665 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-84057.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-665, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84058
in-theory        84058
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-651 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> B C) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-6 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84058.        ((A or (B -> A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-651, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (-> B C) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84059
in-theory        84059
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-649 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or 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-50.           (((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-84059.        ((A -> (B or A)) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-649, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84060
in-theory        84060
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-647 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84060.        ((A -> (A or B)) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-647, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84061
in-theory        84061
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B or C) -> D) -> ((C or (B or C)) -> D))))
theorem-size     17
proof            (modus-ponens tm-645 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84061.        (A -> (A and (((B or C) -> D) -> ((C or (B or C)) -> D)))), M:tm-645, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84062
in-theory        84062
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-644 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84062.        ((A -> (B -> (A and B))) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-644, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84063
in-theory        84063
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-643 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84063.        (((A and B) -> B) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-643, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84064
in-theory        84064
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-642 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84064.        (((A and B) -> A) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-642, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84065
in-theory        84065
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-641 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84065.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-641, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84066
in-theory        84066
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-640 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84066.        ((A -> (B -> A)) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-640, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84067
in-theory        84067
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E)) -> E)
theorem-size     19
proof            (modus-ponens tm-638 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (and B (-> (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) C)) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84067.        ((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E)) -> E), M:tm-638, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (and B (-> (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) C)) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84068
in-theory        84068
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) and E) -> D)
theorem-size     19
proof            (modus-ponens tm-636 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (and (-> (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B) C) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84068.        ((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) and E) -> D), M:tm-636, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> (and (-> (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) B) C) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84069
in-theory        84069
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((B or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> D))
theorem-size     23
proof            (modus-ponens tm-634 tm-929 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)) (Dm (-> (-> (-> (or Am Bm) Cm) (-> (-> (or Bm (or Am Bm)) Cm) C)) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84069.        ((((A or B) -> C) -> (((B or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> D)), M:tm-634, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)) (Dm (-> (-> (-> (or Am Bm) Cm) (-> (-> (or Bm (or Am Bm)) Cm) C)) (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84070
in-theory        84070
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B or C) -> D) -> ((C or (B or C)) -> D)))) -> (not A))
theorem-size     19
proof            (modus-ponens tm-631 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-9 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84070.        ((A -> (not (((B or C) -> D) -> ((C or (B or C)) -> D)))) -> (not A)), M:tm-631, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84071
in-theory        84071
times-derived    2
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) -> ((E or (((A or B) -> C) -> ((B or (A or B)) -> C))) -> D))
theorem-size     33
proof            (modus-ponens tm-630 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84071.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) -> ((E or (((A or B) -> C) -> ((B or (A or B)) -> C))) -> D)), M:tm-630, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84072
in-theory        84072
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-629 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or 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-50.           (((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-84072.        (A or (B -> (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-629, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84073
in-theory        84073
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) or E)
theorem-size     17
proof            (modus-ponens tm-628 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84073.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) or E), M:tm-628, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84074
in-theory        84074
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and A))
theorem-size     19
proof            (modus-ponens tm-627 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84074.        (A -> ((B -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and A)), M:tm-627, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84075
in-theory        84075
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or C) -> D)) -> (A -> ((C or (B or C)) -> D)))
theorem-size     17
proof            (modus-ponens tm-626 tm-929 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)) (Dm (-> C (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84075.        ((A -> ((B or C) -> D)) -> (A -> ((C or (B or C)) -> D))), M:tm-626, m:tm-929, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)) (Dm (-> C (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84076
in-theory        84076
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-625 tm-929 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84076.        (A -> (B -> (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-625, m:tm-929, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))) (Dm (-> B (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-84077
in-theory        84077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-622 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or 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-50.           (((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-84077.        ((A -> (B -> (C or B))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-622, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84078
in-theory        84078
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or 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-50.           (((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-84078.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (F or E))), M:tm-609, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84079
in-theory        84079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-605 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), 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-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-84079.        ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-605, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84080
in-theory        84080
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (F or E)) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-595 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-84080.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (F or E)) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))), M:tm-595, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84081
in-theory        84081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-550 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-84081.        (((A -> (B or A)) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-550, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84082
in-theory        84082
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-540 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-50.           (((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-84082.        ((A or (B -> (C or B))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-540, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84083
in-theory        84083
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-530 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-84083.        ((A or (B -> (B or C))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-530, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84084
in-theory        84084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-520 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), 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-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-84084.        ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-520, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84085
in-theory        84085
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-510 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-84085.        ((A or ((B and C) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-510, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84086
in-theory        84086
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-500 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-50.           (((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-84086.        ((A or ((B and C) -> B)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-500, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84087
in-theory        84087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-490 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 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-6.            (A -> (A or B)), 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-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-84087.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H)), M:tm-490, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84088
in-theory        84088
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-480 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or 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-50.           (((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-84088.        ((A or (B -> (C -> B))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-480, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84089
in-theory        84089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-469 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-84089.        ((A -> (B -> (B or C))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-469, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84090
in-theory        84090
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-84090.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (E or F))), M:tm-456, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84091
in-theory        84091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-453 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84091.        ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-453, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84092
in-theory        84092
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (E or F)) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-443 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-84092.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (E or F)) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))), M:tm-443, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84093
in-theory        84093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-409 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84093.        (((A -> (A or B)) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-409, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84094
in-theory        84094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-400 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84094.        (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-400, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84095
in-theory        84095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-391 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84095.        ((((A and B) -> B) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-391, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84096
in-theory        84096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-382 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84096.        ((((A and B) -> A) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-382, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84097
in-theory        84097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-373 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84097.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H)), M:tm-373, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84098
in-theory        84098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-364 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84098.        (((A -> (B -> A)) or C) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-364, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84099
in-theory        84099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-354 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84099.        ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-354, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84100
in-theory        84100
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84100.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84101
in-theory        84101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-338 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84101.        (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F)), M:tm-338, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84102
in-theory        84102
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)))
theorem-size     39
proof            (modus-ponens tm-327 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84102.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))), M:tm-327, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84103
in-theory        84103
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (((E and F) -> F) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-326 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84103.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (((E and F) -> F) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))), M:tm-326, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84104
in-theory        84104
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (((E and F) -> E) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-325 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84104.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (((E and F) -> E) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))), M:tm-325, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84105
in-theory        84105
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)))
theorem-size     45
proof            (modus-ponens tm-324 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-84105.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))), M:tm-324, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84106
in-theory        84106
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (F -> E)) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-323 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-84106.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (F -> E)) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))), M:tm-323, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84107
in-theory        84107
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84107.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E and F) -> F)), M:tm-322, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84108
in-theory        84108
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84108.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E and F) -> E)), M:tm-320, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84109
in-theory        84109
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84109.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84110
in-theory        84110
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84110.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (F -> E))), M:tm-315, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84111
in-theory        84111
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E or ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)))
theorem-size     33
proof            (modus-ponens tm-311 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-50.           (((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-84111.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E or ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))), M:tm-311, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84112
in-theory        84112
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
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-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-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-84112.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) or E)), M:tm-310, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84113
in-theory        84113
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84113.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and E))), M:tm-309, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84114
in-theory        84114
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)))
theorem-size     33
proof            (modus-ponens tm-305 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84114.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) or D) and (E -> ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))), M:tm-305, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84115
in-theory        84115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-303 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84115.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-303, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84116
in-theory        84116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-270 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84116.        ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-270, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84117
in-theory        84117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-239 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84117.        ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-239, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84118
in-theory        84118
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)) or H))
theorem-size     33
proof            (modus-ponens tm-210 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84118.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H)), M:tm-210, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84119
in-theory        84119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-183 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84119.        ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-183, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84120
in-theory        84120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-157 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84120.        ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-157, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84121
in-theory        84121
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)) or G))
theorem-size     31
proof            (modus-ponens tm-147 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84121.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-147, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84122
in-theory        84122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-134 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84122.        ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-134, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84123
in-theory        84123
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)) or G))
theorem-size     31
proof            (modus-ponens tm-125 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84123.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-125, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84124
in-theory        84124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-113 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84124.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H)), M:tm-113, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84125
in-theory        84125
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)) or G))
theorem-size     35
proof            (modus-ponens tm-105 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84125.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-105, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84126
in-theory        84126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-95 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84126.        (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F)), M:tm-95, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84127
in-theory        84127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-83 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84127.        ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-83, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84128
in-theory        84128
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or C) -> D) -> ((C or (B or C)) -> D)) or E))
theorem-size     21
proof            (modus-ponens tm-76 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84128.        (((not (not A)) -> A) and ((((B or C) -> D) -> ((C or (B or C)) -> D)) or E)), M:tm-76, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84129
in-theory        84129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F))
theorem-size     27
proof            (modus-ponens tm-69 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-8 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-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-84129.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> ((D or (C or D)) -> E)) or F)), M:tm-69, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84130
in-theory        84130
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-54 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-84130.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-54, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84131
in-theory        84131
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84131.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-930, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-84132
in-theory        84132
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-84132.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-930, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-84133
in-theory        84133
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-930 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-10.           ((not (not A)) -> A), axiom
tm-84133.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((not (not D)) -> D)), M:tm-930, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-84134
in-theory        84134
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-930 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84134.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> E)))), M:tm-930, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-84135
in-theory        84135
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-930 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-84135.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> D))), M:tm-930, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-84136
in-theory        84136
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-930 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-84136.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-930, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-84137
in-theory        84137
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-84137.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-930, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-84138
in-theory        84138
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-930 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-84138.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-930, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-84139
in-theory        84139
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-930 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-84139.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E and F) -> E))), M:tm-930, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-84140
in-theory        84140
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-930 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-84140.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-930, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-84141
in-theory        84141
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-930 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-84141.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E and F) -> F))), M:tm-930, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-84142
in-theory        84142
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84142.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> E)) and D))), M:tm-930, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-84143
in-theory        84143
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-930 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-84143.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-930, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-84144
in-theory        84144
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-84144.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and F) -> E) and D))), M:tm-930, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-84145
in-theory        84145
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-84145.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and F) -> F) and D))), M:tm-930, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-84146
in-theory        84146
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-84146.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-930, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-84147
in-theory        84147
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-930 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-84147.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (D and E)))), M:tm-930, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-84148
in-theory        84148
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-84148.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (E and F))))), M:tm-930, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-84149
in-theory        84149
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-930 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84149.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) or F)), M:tm-930, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-84150
in-theory        84150
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-930 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-84150.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-930, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-84151
in-theory        84151
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-930 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-84151.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) or F)), M:tm-930, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-84152
in-theory        84152
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-930 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-84152.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) or F)), M:tm-930, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-84153
in-theory        84153
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-930 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-84153.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) or F)), M:tm-930, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-84154
in-theory        84154
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-930 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-84154.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) or F)), M:tm-930, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-84155
in-theory        84155
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-84155.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (E or F)) and D))), M:tm-930, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-84156
in-theory        84156
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-930 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-84156.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (E or F)))), M:tm-930, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-84157
in-theory        84157
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-930 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84157.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> E)))), M:tm-930, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-84158
in-theory        84158
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-84158.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-930, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-84159
in-theory        84159
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-930 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-84159.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E and F) -> E))), M:tm-930, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-84160
in-theory        84160
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-930 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-84160.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E and F) -> F))), M:tm-930, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-84161
in-theory        84161
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-84161.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (E and F))))), M:tm-930, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-84162
in-theory        84162
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-930 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-84162.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (E or F)))), M:tm-930, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-84163
in-theory        84163
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-930 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-84163.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F or E)))), M:tm-930, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-84164
in-theory        84164
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-930 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84164.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) or F)), M:tm-930, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-84165
in-theory        84165
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-84165.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F or E)) and D))), M:tm-930, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-84166
in-theory        84166
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-930 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-84166.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F or E)))), M:tm-930, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-84167
in-theory        84167
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-930 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-84167.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-930, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-84168
in-theory        84168
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-84168.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-930, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-84169
in-theory        84169
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-930 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-84169.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-930, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-84170
in-theory        84170
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-930 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-84170.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-930, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-84171
in-theory        84171
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-930 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-84171.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-930, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-84172
in-theory        84172
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-930 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-84172.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-930, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-84173
in-theory        84173
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-930 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-84173.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-930, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-84174
in-theory        84174
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-84174.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-930, 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-84175
in-theory        84175
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84175.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-930, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-84176
in-theory        84176
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-930 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84176.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-930, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-84177
in-theory        84177
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-930 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-84177.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-930, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-84178
in-theory        84178
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-930 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84178.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-930, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-84179
in-theory        84179
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84179.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-930, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-84180
in-theory        84180
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84180.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> D))) -> (not D))), M:tm-930, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-84181
in-theory        84181
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84181.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-930, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-84182
in-theory        84182
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84182.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-930, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-84183
in-theory        84183
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84183.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-930, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-84184
in-theory        84184
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84184.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-930, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-84185
in-theory        84185
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84185.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (D or E))) -> (not D))), M:tm-930, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-84186
in-theory        84186
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84186.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E or D))) -> (not D))), M:tm-930, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-84187
in-theory        84187
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-930 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84187.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-930, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-84188
in-theory        84188
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-930 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84188.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-930, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-84189
in-theory        84189
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84189.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-930, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-84190
in-theory        84190
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84190.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-930, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-84191
in-theory        84191
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     27
proof            (modus-ponens tm-930 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84191.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-930, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-84192
in-theory        84192
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-84192.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-930, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-84193
in-theory        84193
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84193.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-930, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-84194
in-theory        84194
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84194.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-930, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-84195
in-theory        84195
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     25
proof            (modus-ponens tm-930 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84195.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-930, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-84196
in-theory        84196
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-930 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-84196.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-930, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-84197
in-theory        84197
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-930 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84197.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((not (not E)) -> E))), M:tm-930, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-84198
in-theory        84198
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((not (not D)) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-930 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84198.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((not (not D)) -> D) or E)), M:tm-930, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-84199
in-theory        84199
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-84199.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((not (not E)) -> E) and D))), M:tm-930, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-84200
in-theory        84200
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     29
proof            (modus-ponens tm-930 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84200.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-930, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-84201
in-theory        84201
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-930 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84201.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((not (not E)) -> E))), M:tm-930, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-84202
in-theory        84202
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84202.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-930, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-84203
in-theory        84203
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-930 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84203.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-930, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-84204
in-theory        84204
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84204.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (G -> F))))), M:tm-930, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-84205
in-theory        84205
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84205.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (F -> E))) or G)), M:tm-930, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-84206
in-theory        84206
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-84206.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-930, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-84207
in-theory        84207
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-930 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-84207.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (F -> E)))), M:tm-930, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-84208
in-theory        84208
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84208.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (G -> F))))), M:tm-930, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-84209
in-theory        84209
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> D))
theorem-size     17
proof            (modus-ponens tm-930 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84209.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> D)), M:tm-930, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-84210
in-theory        84210
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84210.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-930, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-84211
in-theory        84211
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> (D and E)))
theorem-size     21
proof            (modus-ponens tm-930 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84211.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> (D and E))), M:tm-930, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-84212
in-theory        84212
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-930 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84212.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> E))), M:tm-930, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-84213
in-theory        84213
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((not (not D)) -> (not (not D))))
theorem-size     21
proof            (modus-ponens tm-930 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84213.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((not (not D)) -> (not (not D)))), M:tm-930, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-84214
in-theory        84214
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-930 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84214.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-930, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-84215
in-theory        84215
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-930 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84215.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-930, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-84216
in-theory        84216
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-930 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84216.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> (E -> E)))), M:tm-930, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-84217
in-theory        84217
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (D -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-930 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84217.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (D -> D)) or F)), M:tm-930, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-84218
in-theory        84218
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-84218.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-930, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-84219
in-theory        84219
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84219.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-930, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-84220
in-theory        84220
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-930 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84220.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> (E -> E)))), M:tm-930, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-84221
in-theory        84221
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-84221.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-930, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-84222
in-theory        84222
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-930 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-84222.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D -> E)) -> (D -> E))), M:tm-930, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-84223
in-theory        84223
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     33
proof            (modus-ponens tm-930 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84223.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-930, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-84224
in-theory        84224
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84224.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-930, 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-84225
in-theory        84225
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-84225.        ((((A or B) -> C) -> ((B or (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-930, 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-84226
in-theory        84226
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-930 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       161
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-84226.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-930, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-84227
in-theory        84227
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     35
proof            (modus-ponens tm-930 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84227.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-930, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-84228
in-theory        84228
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-84228.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-930, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-84229
in-theory        84229
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-84229.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-930, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-84230
in-theory        84230
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84230.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-930, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-84231
in-theory        84231
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-930 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-84231.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-930, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-84232
in-theory        84232
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-930 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84232.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-930, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-84233
in-theory        84233
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-84233.        ((((A or B) -> C) -> ((B or (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-930, 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-84234
in-theory        84234
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-930 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       141
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-84234.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-930, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-84235
in-theory        84235
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-930 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84235.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-930, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-84236
in-theory        84236
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-930 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-84236.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-930, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-84237
in-theory        84237
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-930 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84237.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-930, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-84238
in-theory        84238
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-930 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-84238.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-930, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-84239
in-theory        84239
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) and D) -> E))
theorem-size     21
proof            (modus-ponens tm-930 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-84239.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) and D) -> E)), M:tm-930, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-84240
in-theory        84240
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-930 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-84240.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-930, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-84241
in-theory        84241
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     33
proof            (modus-ponens tm-930 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-3 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-84241.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-930, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-84242
in-theory        84242
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-84242.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-930, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-84243
in-theory        84243
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84243.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-930, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-84244
in-theory        84244
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84244.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-930, 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-84245
in-theory        84245
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-84245.        ((((A or B) -> C) -> ((B or (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-930, 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-84246
in-theory        84246
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-930 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       141
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-84246.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-930, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-84247
in-theory        84247
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     31
proof            (modus-ponens tm-930 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84247.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-930, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-84248
in-theory        84248
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-84248.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-930, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-84249
in-theory        84249
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-84249.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-930, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-84250
in-theory        84250
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-930 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84250.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-930, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-84251
in-theory        84251
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-930 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-84251.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-930, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-84252
in-theory        84252
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-930 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-84252.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-930, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-84253
in-theory        84253
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84253.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-930, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-84254
in-theory        84254
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     31
proof            (modus-ponens tm-930 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-84254.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-930, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-84255
in-theory        84255
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-930 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-84255.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F and G) -> F)))), M:tm-930, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-84256
in-theory        84256
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84256.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E and F) -> E)) or G)), M:tm-930, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-84257
in-theory        84257
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-84257.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-930, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-84258
in-theory        84258
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-930 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84258.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E and F)) -> (D -> E))), M:tm-930, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-84259
in-theory        84259
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-930 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-84259.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F and G) -> F)))), M:tm-930, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-84260
in-theory        84260
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and (D -> E)) -> E))
theorem-size     21
proof            (modus-ponens tm-930 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-84260.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and (D -> E)) -> E)), M:tm-930, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-84261
in-theory        84261
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-930 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-84261.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-930, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-84262
in-theory        84262
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     33
proof            (modus-ponens tm-930 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-84262.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-930, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-84263
in-theory        84263
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-930 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-84263.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-930, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-84264
in-theory        84264
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-84264.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-930, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-84265
in-theory        84265
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     29
proof            (modus-ponens tm-930 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84265.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-930, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-84266
in-theory        84266
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84266.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-930, 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-84267
in-theory        84267
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-84267.        ((((A or B) -> C) -> ((B or (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-930, 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-84268
in-theory        84268
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-930 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       141
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-84268.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-930, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-84269
in-theory        84269
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     31
proof            (modus-ponens tm-930 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84269.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-930, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-84270
in-theory        84270
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-84270.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-930, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-84271
in-theory        84271
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-84271.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-930, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-84272
in-theory        84272
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-930 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84272.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-930, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-84273
in-theory        84273
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-930 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-84273.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-930, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-84274
in-theory        84274
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-930 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-84274.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-930, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-84275
in-theory        84275
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-930 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-84275.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-930, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-84276
in-theory        84276
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84276.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-930, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-84277
in-theory        84277
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-930 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-84277.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-930, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-84278
in-theory        84278
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-930 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-84278.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F and G) -> G)))), M:tm-930, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-84279
in-theory        84279
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84279.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E and F) -> F)) or G)), M:tm-930, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-84280
in-theory        84280
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-84280.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-930, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-84281
in-theory        84281
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-930 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84281.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E and F)) -> (D -> F))), M:tm-930, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-84282
in-theory        84282
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-930 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-84282.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F and G) -> G)))), M:tm-930, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-84283
in-theory        84283
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84283.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-930, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84284
in-theory        84284
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84284.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84285
in-theory        84285
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84285.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-930, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84286
in-theory        84286
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84286.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-930, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84287
in-theory        84287
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84287.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-930, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84288
in-theory        84288
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84288.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-930, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84289
in-theory        84289
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84289.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-930, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84290
in-theory        84290
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84290.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-930, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-84291
in-theory        84291
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-930 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84291.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-930, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-84292
in-theory        84292
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84292.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-930, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-84293
in-theory        84293
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84293.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-930, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84294
in-theory        84294
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84294.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-930, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-84295
in-theory        84295
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84295.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-930, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-84296
in-theory        84296
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-930 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84296.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84297
in-theory        84297
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84297.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-930, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-84298
in-theory        84298
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84298.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-930, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84299
in-theory        84299
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84299.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-930, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-84300
in-theory        84300
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84300.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-930, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84301
in-theory        84301
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84301.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-930, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-84302
in-theory        84302
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84302.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-930, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-84303
in-theory        84303
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84303.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-930, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-84304
in-theory        84304
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84304.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-930, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-84305
in-theory        84305
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-930 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84305.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-930, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-84306
in-theory        84306
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-84306.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-930, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-84307
in-theory        84307
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84307.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-930, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-84308
in-theory        84308
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84308.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-930, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-84309
in-theory        84309
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84309.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-930, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-84310
in-theory        84310
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-930 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84310.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-930, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-84311
in-theory        84311
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-930 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84311.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-930, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-84312
in-theory        84312
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84312.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-930, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-84313
in-theory        84313
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84313.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-930, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-84314
in-theory        84314
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84314.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-930, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-84315
in-theory        84315
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84315.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-930, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-84316
in-theory        84316
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84316.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-930, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-84317
in-theory        84317
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-930 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84317.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-930, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-84318
in-theory        84318
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84318.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-930, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-84319
in-theory        84319
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-930 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84319.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-930, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-84320
in-theory        84320
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84320.        ((((A or B) -> C) -> ((B or (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-930, 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-84321
in-theory        84321
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84321.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-930, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-84322
in-theory        84322
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84322.        ((((A or B) -> C) -> ((B or (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-930, 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-84323
in-theory        84323
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84323.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-930, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-84324
in-theory        84324
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84324.        ((((A or B) -> C) -> ((B or (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-930, 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-84325
in-theory        84325
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84325.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-930, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-84326
in-theory        84326
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84326.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-930, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-84327
in-theory        84327
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84327.        ((((A or B) -> C) -> ((B or (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-930, 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-84328
in-theory        84328
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84328.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-930, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-84329
in-theory        84329
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84329.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-930, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-84330
in-theory        84330
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84330.        ((((A or B) -> C) -> ((B or (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-930, 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-84331
in-theory        84331
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-930 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       149
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84331.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-930, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-84332
in-theory        84332
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     33
proof            (modus-ponens tm-930 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84332.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-930, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-84333
in-theory        84333
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-84333.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-930, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-84334
in-theory        84334
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-930 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84334.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-930, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-84335
in-theory        84335
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84335.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-930, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84336
in-theory        84336
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-84336.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84337
in-theory        84337
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84337.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-930, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84338
in-theory        84338
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84338.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-930, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84339
in-theory        84339
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84339.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-930, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84340
in-theory        84340
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84340.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-930, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84341
in-theory        84341
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84341.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-930, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84342
in-theory        84342
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84342.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-930, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-84343
in-theory        84343
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-930 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84343.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-930, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-84344
in-theory        84344
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84344.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-930, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-84345
in-theory        84345
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84345.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-930, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84346
in-theory        84346
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-84346.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-930, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-84347
in-theory        84347
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-84347.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-930, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-84348
in-theory        84348
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84348.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84349
in-theory        84349
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-84349.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-930, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-84350
in-theory        84350
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84350.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-930, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84351
in-theory        84351
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-84351.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-930, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-84352
in-theory        84352
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84352.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-930, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84353
in-theory        84353
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84353.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-930, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-84354
in-theory        84354
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-84354.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-930, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-84355
in-theory        84355
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84355.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-930, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-84356
in-theory        84356
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84356.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-930, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-84357
in-theory        84357
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84357.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-930, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-84358
in-theory        84358
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84358.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-930, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-84359
in-theory        84359
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84359.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-930, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-84360
in-theory        84360
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84360.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-930, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-84361
in-theory        84361
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-930 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84361.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-930, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-84362
in-theory        84362
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-84362.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-930, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-84363
in-theory        84363
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84363.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-930, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-84364
in-theory        84364
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84364.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-930, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84365
in-theory        84365
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-84365.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84366
in-theory        84366
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84366.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-930, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84367
in-theory        84367
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84367.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-930, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84368
in-theory        84368
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84368.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-930, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84369
in-theory        84369
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84369.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-930, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84370
in-theory        84370
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84370.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-930, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84371
in-theory        84371
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84371.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-930, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-84372
in-theory        84372
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-930 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84372.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-930, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-84373
in-theory        84373
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84373.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-930, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-84374
in-theory        84374
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84374.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-930, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84375
in-theory        84375
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-84375.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-930, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-84376
in-theory        84376
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-84376.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-930, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-84377
in-theory        84377
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84377.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84378
in-theory        84378
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-84378.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-930, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-84379
in-theory        84379
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84379.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-930, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84380
in-theory        84380
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-84380.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-930, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-84381
in-theory        84381
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84381.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-930, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84382
in-theory        84382
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84382.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-930, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-84383
in-theory        84383
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-84383.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-930, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-84384
in-theory        84384
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84384.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-930, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-84385
in-theory        84385
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84385.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-930, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-84386
in-theory        84386
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84386.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-930, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-84387
in-theory        84387
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84387.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-930, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-84388
in-theory        84388
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84388.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-930, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-84389
in-theory        84389
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84389.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-930, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-84390
in-theory        84390
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84390.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-930, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-84391
in-theory        84391
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84391.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-930, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-84392
in-theory        84392
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-930 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84392.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-930, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-84393
in-theory        84393
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-84393.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-930, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-84394
in-theory        84394
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84394.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-930, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-84395
in-theory        84395
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84395.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-930, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84396
in-theory        84396
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-84396.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84397
in-theory        84397
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-930 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84397.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-930, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84398
in-theory        84398
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-930 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84398.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-930, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84399
in-theory        84399
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84399.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-930, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84400
in-theory        84400
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and 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-84400.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-930, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84401
in-theory        84401
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84401.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-930, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84402
in-theory        84402
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84402.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-930, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-84403
in-theory        84403
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84403.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-930, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-84404
in-theory        84404
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-930 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84404.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-930, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-84405
in-theory        84405
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84405.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-930, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84406
in-theory        84406
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-84406.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-930, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-84407
in-theory        84407
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-84407.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-930, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-84408
in-theory        84408
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84408.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84409
in-theory        84409
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-84409.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-930, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-84410
in-theory        84410
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-930 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84410.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-930, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84411
in-theory        84411
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-84411.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-930, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-84412
in-theory        84412
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-930 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84412.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-930, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84413
in-theory        84413
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-930 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84413.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-930, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-84414
in-theory        84414
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-84414.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-930, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-84415
in-theory        84415
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84415.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-930, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-84416
in-theory        84416
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84416.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-930, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-84417
in-theory        84417
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84417.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-930, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-84418
in-theory        84418
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84418.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-930, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-84419
in-theory        84419
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84419.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-930, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-84420
in-theory        84420
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84420.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-930, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-84421
in-theory        84421
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-930 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84421.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-930, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-84422
in-theory        84422
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84422.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-930, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-84423
in-theory        84423
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84423.        ((((A or B) -> C) -> ((B or (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-930, 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-84424
in-theory        84424
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-930 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84424.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-930, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-84425
in-theory        84425
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-930 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84425.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-930, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-84426
in-theory        84426
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-84426.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-930, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-84427
in-theory        84427
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-930 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84427.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-930, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-84428
in-theory        84428
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> D))))
theorem-size     21
proof            (modus-ponens tm-930 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-84428.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> D)))), M:tm-930, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-84429
in-theory        84429
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-84429.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-930, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-84430
in-theory        84430
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> ((D and E) and D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-84430.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> ((D and E) and D))), M:tm-930, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-84431
in-theory        84431
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> ((D and E) and E)))
theorem-size     23
proof            (modus-ponens tm-930 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-84431.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> ((D and E) and E))), M:tm-930, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-84432
in-theory        84432
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-84432.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (D and E))))), M:tm-930, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84433
in-theory        84433
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (D or E))))
theorem-size     21
proof            (modus-ponens tm-930 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-84433.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (D or E)))), M:tm-930, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-84434
in-theory        84434
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E or D))))
theorem-size     21
proof            (modus-ponens tm-930 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-84434.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E or D)))), M:tm-930, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-84435
in-theory        84435
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     31
proof            (modus-ponens tm-930 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-84435.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-84436
in-theory        84436
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-84436.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-930, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-84437
in-theory        84437
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-84437.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-930, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-84438
in-theory        84438
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (F -> E)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-84438.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (F -> E))))), M:tm-930, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-84439
in-theory        84439
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-84439.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-930, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-84440
in-theory        84440
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-84440.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-930, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-84441
in-theory        84441
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     31
proof            (modus-ponens tm-930 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-84441.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-930, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-84442
in-theory        84442
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-84442.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-930, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-84443
in-theory        84443
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-930 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-84443.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E and F) -> E)))), M:tm-930, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-84444
in-theory        84444
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-84444.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-930, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-84445
in-theory        84445
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E and F) -> F))))
theorem-size     23
proof            (modus-ponens tm-930 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-84445.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E and F) -> F)))), M:tm-930, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-84446
in-theory        84446
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-84446.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-930, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-84447
in-theory        84447
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     33
proof            (modus-ponens tm-930 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-84447.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-930, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-84448
in-theory        84448
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-84448.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-930, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-84449
in-theory        84449
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-84449.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-930, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-84450
in-theory        84450
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     27
proof            (modus-ponens tm-930 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-84450.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-930, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-84451
in-theory        84451
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-84451.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-930, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-84452
in-theory        84452
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-930 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-84452.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-930, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-84453
in-theory        84453
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-84453.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-930, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-84454
in-theory        84454
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-84454.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-930, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-84455
in-theory        84455
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84455.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-930, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-84456
in-theory        84456
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84456.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-930, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-84457
in-theory        84457
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-930 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84457.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-930, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-84458
in-theory        84458
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-84458.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-930, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-84459
in-theory        84459
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-930 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-84459.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-930, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-84460
in-theory        84460
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     25
proof            (modus-ponens tm-930 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84460.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-930, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-84461
in-theory        84461
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-84461.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-930, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-84462
in-theory        84462
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-930 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-84462.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-930, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-84463
in-theory        84463
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-930 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84463.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-930, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-84464
in-theory        84464
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     25
proof            (modus-ponens tm-930 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-84464.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-930, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-84465
in-theory        84465
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-930 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84465.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-930, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84466
in-theory        84466
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84466.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-930, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84467
in-theory        84467
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84467.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-930, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84468
in-theory        84468
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84468.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-930, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-84469
in-theory        84469
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84469.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-930, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84470
in-theory        84470
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-930 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-84470.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-930, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-84471
in-theory        84471
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-930 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-84471.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-930, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-84472
in-theory        84472
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-930 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-84472.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-930, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-84473
in-theory        84473
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84473.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-930, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-84474
in-theory        84474
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> 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-84474.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-930, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-84475
in-theory        84475
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-930 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> 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-84475.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-930, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-84476
in-theory        84476
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-930 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84476.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-930, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-84477
in-theory        84477
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-84477.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-930, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-84478
in-theory        84478
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-930 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84478.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-930, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-84479
in-theory        84479
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-930 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> 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-84479.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-930, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-84480
in-theory        84480
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-930 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and 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-84480.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-930, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-84481
in-theory        84481
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84481.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-930, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-84482
in-theory        84482
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84482.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-930, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-84483
in-theory        84483
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84483.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-930, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-84484
in-theory        84484
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84484.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-930, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-84485
in-theory        84485
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-930 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-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-84485.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (F -> E)) or G))), M:tm-930, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-84486
in-theory        84486
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-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-84486.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> D)) or F) or G)), M:tm-930, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-84487
in-theory        84487
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-84487.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-930, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-84488
in-theory        84488
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-930 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84488.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> E)) or G))), M:tm-930, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-84489
in-theory        84489
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and 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-84489.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-930, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-84490
in-theory        84490
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84490.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-930, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-84491
in-theory        84491
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84491.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-930, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-84492
in-theory        84492
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84492.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-930, 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-84493
in-theory        84493
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84493.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-930, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-84494
in-theory        84494
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-930 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       141
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-84494.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-930, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-84495
in-theory        84495
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-930 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-84495.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-930, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-84496
in-theory        84496
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-930 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-84496.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-930, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-84497
in-theory        84497
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-930 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84497.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-930, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-84498
in-theory        84498
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-930 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and 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-84498.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-930, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-84499
in-theory        84499
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84499.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-930, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-84500
in-theory        84500
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84500.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-930, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-84501
in-theory        84501
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84501.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-930, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-84502
in-theory        84502
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84502.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-930, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-84503
in-theory        84503
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-930 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       109
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-84503.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E and F) -> E) or G))), M:tm-930, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-84504
in-theory        84504
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) -> D) or F) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-84504.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) -> D) or F) or G)), M:tm-930, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-84505
in-theory        84505
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-84505.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-930, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-84506
in-theory        84506
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-930 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84506.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and F) -> E) or G))), M:tm-930, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-84507
in-theory        84507
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-930 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and 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-84507.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-930, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-84508
in-theory        84508
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84508.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-930, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-84509
in-theory        84509
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84509.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-930, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-84510
in-theory        84510
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84510.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-930, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-84511
in-theory        84511
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84511.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-930, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-84512
in-theory        84512
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-930 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       109
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-84512.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E and F) -> F) or G))), M:tm-930, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-84513
in-theory        84513
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) -> E) or F) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-84513.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) -> E) or F) or G)), M:tm-930, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-84514
in-theory        84514
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-84514.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-930, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-84515
in-theory        84515
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-930 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84515.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E and F) -> F) or G))), M:tm-930, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-84516
in-theory        84516
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and 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-84516.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-930, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-84517
in-theory        84517
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-930 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84517.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-930, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-84518
in-theory        84518
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-930 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84518.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-930, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-84519
in-theory        84519
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84519.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-930, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-84520
in-theory        84520
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-930 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84520.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-930, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-84521
in-theory        84521
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), 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-84521.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-930, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-84522
in-theory        84522
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     25
proof            (modus-ponens tm-930 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), 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-84522.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-930, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-84523
in-theory        84523
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-84523.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-930, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-84524
in-theory        84524
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84524.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-930, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-84525
in-theory        84525
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-930 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and 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-84525.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-930, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-84526
in-theory        84526
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84526.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-930, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-84527
in-theory        84527
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84527.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-930, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-84528
in-theory        84528
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84528.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-930, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-84529
in-theory        84529
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84529.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-930, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-84530
in-theory        84530
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-930 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A 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-84530.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (E or F)) or G))), M:tm-930, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-84531
in-theory        84531
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (D or E)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A 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-84531.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (D or E)) or F) or G)), M:tm-930, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-84532
in-theory        84532
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-84532.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-930, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-84533
in-theory        84533
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-930 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84533.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (E or F)) or G))), M:tm-930, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-84534
in-theory        84534
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84534.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-930, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84535
in-theory        84535
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84535.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84536
in-theory        84536
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84536.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-930, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84537
in-theory        84537
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84537.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-930, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84538
in-theory        84538
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84538.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-930, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84539
in-theory        84539
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84539.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-930, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84540
in-theory        84540
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84540.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-930, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84541
in-theory        84541
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84541.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-930, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-84542
in-theory        84542
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-930 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84542.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-930, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-84543
in-theory        84543
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84543.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-930, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-84544
in-theory        84544
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84544.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-930, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84545
in-theory        84545
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84545.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-930, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-84546
in-theory        84546
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84546.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-930, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-84547
in-theory        84547
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84547.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84548
in-theory        84548
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84548.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-930, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-84549
in-theory        84549
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84549.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-930, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84550
in-theory        84550
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84550.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-930, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-84551
in-theory        84551
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84551.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-930, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84552
in-theory        84552
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84552.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-930, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-84553
in-theory        84553
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84553.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-930, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-84554
in-theory        84554
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84554.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-930, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-84555
in-theory        84555
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84555.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-930, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-84556
in-theory        84556
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84556.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-930, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-84557
in-theory        84557
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84557.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-930, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-84558
in-theory        84558
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84558.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-930, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84559
in-theory        84559
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84559.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-930, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-84560
in-theory        84560
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84560.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-930, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-84561
in-theory        84561
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84561.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-930, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-84562
in-theory        84562
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84562.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-930, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-84563
in-theory        84563
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-930 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84563.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-930, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-84564
in-theory        84564
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84564.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-930, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-84565
in-theory        84565
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84565.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-930, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-84566
in-theory        84566
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-84566.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-930, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-84567
in-theory        84567
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and 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-84567.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-930, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-84568
in-theory        84568
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84568.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-930, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-84569
in-theory        84569
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84569.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-930, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-84570
in-theory        84570
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84570.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-930, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-84571
in-theory        84571
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84571.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-930, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-84572
in-theory        84572
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84572.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-930, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-84573
in-theory        84573
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84573.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-930, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-84574
in-theory        84574
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84574.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-930, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-84575
in-theory        84575
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-930 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84575.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-930, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-84576
in-theory        84576
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-84576.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-930, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-84577
in-theory        84577
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84577.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-930, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-84578
in-theory        84578
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84578.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-930, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84579
in-theory        84579
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (E or F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-84579.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (E or F))))), M:tm-930, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-84580
in-theory        84580
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84580.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-930, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84581
in-theory        84581
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84581.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-930, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84582
in-theory        84582
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84582.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-930, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84583
in-theory        84583
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84583.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-930, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-84584
in-theory        84584
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84584.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-930, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84585
in-theory        84585
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-930 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-84585.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-930, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-84586
in-theory        84586
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-930 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-84586.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-930, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-84587
in-theory        84587
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-84587.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-930, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-84588
in-theory        84588
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84588.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-930, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-84589
in-theory        84589
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-930 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-84589.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-930, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-84590
in-theory        84590
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-84590.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (F or G))))), M:tm-930, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-84591
in-theory        84591
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84591.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (E or F))) or G)), M:tm-930, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-84592
in-theory        84592
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-84592.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-930, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-84593
in-theory        84593
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-930 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-84593.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (E or F)))), M:tm-930, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-84594
in-theory        84594
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-84594.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (F or G))))), M:tm-930, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-84595
in-theory        84595
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84595.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-930, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84596
in-theory        84596
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-84596.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-930, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84597
in-theory        84597
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84597.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-930, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84598
in-theory        84598
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84598.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-930, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84599
in-theory        84599
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84599.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-930, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-84600
in-theory        84600
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84600.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-930, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84601
in-theory        84601
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84601.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or (F -> (G -> F))))), M:tm-930, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-84602
in-theory        84602
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84602.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (F -> E))) or G)), M:tm-930, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-84603
in-theory        84603
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-84603.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-930, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-84604
in-theory        84604
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84604.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or (F -> (G -> F))))), M:tm-930, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-84605
in-theory        84605
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84605.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84606
in-theory        84606
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       173
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-84606.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84607
in-theory        84607
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-84607.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84608
in-theory        84608
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-84608.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84609
in-theory        84609
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84609.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-930, 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-84610
in-theory        84610
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84610.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84611
in-theory        84611
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-930 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       141
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-84611.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-930, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-84612
in-theory        84612
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-930 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84612.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-930, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-84613
in-theory        84613
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-930 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       147
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-84613.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-930, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-84614
in-theory        84614
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-930 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84614.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-930, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-84615
in-theory        84615
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84615.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-930, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84616
in-theory        84616
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-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-84616.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-930, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84617
in-theory        84617
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84617.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-930, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84618
in-theory        84618
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84618.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-930, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84619
in-theory        84619
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84619.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-930, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-84620
in-theory        84620
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84620.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-930, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84621
in-theory        84621
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-930 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and 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-84621.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or ((F and G) -> F)))), M:tm-930, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-84622
in-theory        84622
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84622.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E and F) -> E)) or G)), M:tm-930, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-84623
in-theory        84623
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-84623.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-930, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-84624
in-theory        84624
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-930 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84624.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or ((F and G) -> F)))), M:tm-930, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-84625
in-theory        84625
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84625.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-930, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84626
in-theory        84626
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-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-84626.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-930, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84627
in-theory        84627
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84627.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-930, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84628
in-theory        84628
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84628.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-930, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84629
in-theory        84629
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84629.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-930, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-84630
in-theory        84630
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84630.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-930, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84631
in-theory        84631
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-930 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and 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-84631.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or ((F and G) -> G)))), M:tm-930, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-84632
in-theory        84632
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84632.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E and F) -> F)) or G)), M:tm-930, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-84633
in-theory        84633
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-84633.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-930, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-84634
in-theory        84634
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-930 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84634.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or ((F and G) -> G)))), M:tm-930, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-84635
in-theory        84635
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84635.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-930, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84636
in-theory        84636
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       149
proof-steps      13
----------------------------------------------------------------
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-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-84636.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-930, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84637
in-theory        84637
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84637.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-930, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84638
in-theory        84638
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84638.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-930, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84639
in-theory        84639
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84639.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-930, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-84640
in-theory        84640
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84640.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-930, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84641
in-theory        84641
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-930 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84641.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-930, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-84642
in-theory        84642
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-930 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84642.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-930, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-84643
in-theory        84643
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-84643.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-930, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-84644
in-theory        84644
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-930 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84644.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-930, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-84645
in-theory        84645
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84645.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-930, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84646
in-theory        84646
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-84646.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-930, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84647
in-theory        84647
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84647.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-930, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84648
in-theory        84648
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84648.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-930, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84649
in-theory        84649
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84649.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-930, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-84650
in-theory        84650
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84650.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-930, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84651
in-theory        84651
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A 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-84651.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or (F -> (F or G))))), M:tm-930, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-84652
in-theory        84652
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A 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-84652.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (E or F))) or G)), M:tm-930, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-84653
in-theory        84653
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-84653.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-930, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-84654
in-theory        84654
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84654.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or (F -> (F or G))))), M:tm-930, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-84655
in-theory        84655
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84655.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-930, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84656
in-theory        84656
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-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-84656.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-930, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84657
in-theory        84657
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84657.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-930, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84658
in-theory        84658
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84658.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-930, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84659
in-theory        84659
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84659.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-930, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-84660
in-theory        84660
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84660.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-930, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84661
in-theory        84661
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84661.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or (F -> (G or F))))), M:tm-930, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-84662
in-theory        84662
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84662.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (F or E))) or G)), M:tm-930, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-84663
in-theory        84663
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-84663.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-930, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-84664
in-theory        84664
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84664.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or (F -> (G or F))))), M:tm-930, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-84665
in-theory        84665
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84665.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-930, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-84666
in-theory        84666
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-930 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and 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-84666.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-930, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-84667
in-theory        84667
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-84667.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-930, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-84668
in-theory        84668
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-84668.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-930, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-84669
in-theory        84669
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84669.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-930, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-84670
in-theory        84670
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-84670.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-930, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-84671
in-theory        84671
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-930 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84671.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> (F or E)) or G))), M:tm-930, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-84672
in-theory        84672
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E or D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84672.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E or D)) or F) or G)), M:tm-930, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-84673
in-theory        84673
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84673.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-930, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-84674
in-theory        84674
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-930 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84674.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F or E)) or G))), M:tm-930, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-84675
in-theory        84675
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (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-84675.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-930, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84676
in-theory        84676
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 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       141
proof-steps      11
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-84676.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84677
in-theory        84677
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C 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-84677.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-930, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84678
in-theory        84678
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C 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-84678.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-930, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84679
in-theory        84679
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84679.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-930, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84680
in-theory        84680
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C 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-84680.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-930, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84681
in-theory        84681
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84681.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-930, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84682
in-theory        84682
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       141
proof-steps      11
----------------------------------------------------------------
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-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-84682.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-930, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-84683
in-theory        84683
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-930 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       135
proof-steps      11
----------------------------------------------------------------
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-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-84683.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-930, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-84684
in-theory        84684
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84684.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-930, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-84685
in-theory        84685
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (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-84685.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-930, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84686
in-theory        84686
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-84686.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-930, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-84687
in-theory        84687
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       185
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-84687.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-930, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-84688
in-theory        84688
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       165
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-84688.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84689
in-theory        84689
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       165
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-84689.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-930, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-84690
in-theory        84690
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-84690.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-930, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84691
in-theory        84691
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       165
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-84691.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-930, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-84692
in-theory        84692
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-84692.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-930, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84693
in-theory        84693
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-84693.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-930, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-84694
in-theory        84694
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       173
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-84694.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-930, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-84695
in-theory        84695
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84695.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-930, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-84696
in-theory        84696
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84696.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-930, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-84697
in-theory        84697
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       149
proof-steps      13
----------------------------------------------------------------
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-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-84697.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-930, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-84698
in-theory        84698
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-930 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       149
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-84698.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-930, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-84699
in-theory        84699
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-84699.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-930, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84700
in-theory        84700
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84700.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-930, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-84701
in-theory        84701
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       165
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84701.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-930, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-84702
in-theory        84702
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84702.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-930, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-84703
in-theory        84703
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84703.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-930, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-84704
in-theory        84704
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84704.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-930, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-84705
in-theory        84705
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84705.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-930, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-84706
in-theory        84706
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84706.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-930, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-84707
in-theory        84707
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-84707.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-930, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84708
in-theory        84708
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-84708.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-930, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-84709
in-theory        84709
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       165
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-84709.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-930, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-84710
in-theory        84710
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84710.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-930, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-84711
in-theory        84711
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84711.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-930, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-84712
in-theory        84712
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-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-84712.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-930, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-84713
in-theory        84713
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84713.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-930, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-84714
in-theory        84714
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84714.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-930, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84715
in-theory        84715
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84715.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-930, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-84716
in-theory        84716
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 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       141
proof-steps      13
----------------------------------------------------------------
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-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-84716.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-930, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-84717
in-theory        84717
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84717.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-930, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-84718
in-theory        84718
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-84718.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-930, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-84719
in-theory        84719
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       149
proof-steps      13
----------------------------------------------------------------
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-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-84719.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-930, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-84720
in-theory        84720
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84720.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-930, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-84721
in-theory        84721
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84721.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-930, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-84722
in-theory        84722
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84722.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-930, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-84723
in-theory        84723
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84723.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-930, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-84724
in-theory        84724
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84724.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-930, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-84725
in-theory        84725
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       145
proof-steps      11
----------------------------------------------------------------
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-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-84725.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-930, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-84726
in-theory        84726
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84726.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-930, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-84727
in-theory        84727
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-930 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84727.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-930, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-84728
in-theory        84728
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-84728.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-930, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-84729
in-theory        84729
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84729.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-930, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-84730
in-theory        84730
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 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       133
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-84730.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-930, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84731
in-theory        84731
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84731.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-930, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84732
in-theory        84732
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (F or E)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-84732.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D and (E -> (F or E))))), M:tm-930, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-84733
in-theory        84733
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84733.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-930, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84734
in-theory        84734
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84734.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-930, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84735
in-theory        84735
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84735.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-930, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84736
in-theory        84736
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84736.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-930, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-84737
in-theory        84737
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84737.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-930, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-84738
in-theory        84738
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-930 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-84738.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-930, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-84739
in-theory        84739
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-930 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-84739.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-930, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-84740
in-theory        84740
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-84740.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-930, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-84741
in-theory        84741
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84741.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-930, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-84742
in-theory        84742
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-930 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84742.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-930, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-84743
in-theory        84743
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84743.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E -> (F -> (G or F))))), M:tm-930, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-84744
in-theory        84744
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-930 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84744.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (F or E))) or G)), M:tm-930, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-84745
in-theory        84745
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-930 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84745.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-930, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-84746
in-theory        84746
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-930 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84746.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> (D -> (F or E)))), M:tm-930, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-84747
in-theory        84747
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-930 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84747.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (F -> (G or F))))), M:tm-930, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-84748
in-theory        84748
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84748.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-930, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-84749
in-theory        84749
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     31
proof            (modus-ponens tm-930 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-84749.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-930, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-84750
in-theory        84750
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84750.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-930, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-84751
in-theory        84751
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84751.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-930, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-84752
in-theory        84752
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84752.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-930, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-84753
in-theory        84753
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84753.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-930, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-84754
in-theory        84754
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-930 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84754.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-930, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-84755
in-theory        84755
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84755.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-930, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84756
in-theory        84756
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-930 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-84756.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (E -> E))), M:tm-930, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-84757
in-theory        84757
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-84757.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-930, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-84758
in-theory        84758
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-84758.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84759
in-theory        84759
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-930 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-84759.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-930, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-84760
in-theory        84760
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84760.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-930, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84761
in-theory        84761
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-930 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-84761.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-930, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-84762
in-theory        84762
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84762.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-930, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84763
in-theory        84763
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84763.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-930, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-84764
in-theory        84764
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-84764.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-930, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-84765
in-theory        84765
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84765.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-930, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-84766
in-theory        84766
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84766.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-930, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-84767
in-theory        84767
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-930 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84767.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-930, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-84768
in-theory        84768
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-84768.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-930, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-84769
in-theory        84769
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84769.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-930, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84770
in-theory        84770
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84770.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-930, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-84771
in-theory        84771
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84771.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-930, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84772
in-theory        84772
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84772.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-930, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-84773
in-theory        84773
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84773.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-930, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84774
in-theory        84774
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84774.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-930, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-84775
in-theory        84775
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       159
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-84775.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-930, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-84776
in-theory        84776
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-84776.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-930, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-84777
in-theory        84777
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-930 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-84777.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-930, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-84778
in-theory        84778
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B 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-84778.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-930, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-84779
in-theory        84779
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-84779.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-930, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-84780
in-theory        84780
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-84780.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-930, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-84781
in-theory        84781
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-84781.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-930, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-84782
in-theory        84782
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84782.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-930, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-84783
in-theory        84783
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84783.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-930, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-84784
in-theory        84784
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84784.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-930, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-84785
in-theory        84785
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-84785.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-930, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-84786
in-theory        84786
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-930 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       135
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-84786.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-930, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-84787
in-theory        84787
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-930 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84787.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-930, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-84788
in-theory        84788
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-930 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-84788.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-930, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-84789
in-theory        84789
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-930 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84789.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-930, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-84790
in-theory        84790
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-930 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84790.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-930, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-84791
in-theory        84791
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84791.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-930, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-84792
in-theory        84792
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84792.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-930, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-84793
in-theory        84793
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84793.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-930, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-84794
in-theory        84794
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84794.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-930, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-84795
in-theory        84795
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84795.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-930, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-84796
in-theory        84796
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84796.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-930, 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-84797
in-theory        84797
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84797.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-930, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-84798
in-theory        84798
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84798.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-930, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-84799
in-theory        84799
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     35
proof            (modus-ponens tm-930 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84799.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-930, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-84800
in-theory        84800
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84800.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-930, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-84801
in-theory        84801
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 tm-2 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84801.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-930, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-84802
in-theory        84802
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-930 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84802.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-930, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-84803
in-theory        84803
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-930 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84803.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-930, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-84804
in-theory        84804
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84804.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-930, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-84805
in-theory        84805
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84805.        ((((A or B) -> C) -> ((B or (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-930, 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-84806
in-theory        84806
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84806.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-930, 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-84807
in-theory        84807
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84807.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-930, 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-84808
in-theory        84808
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84808.        ((((A or B) -> C) -> ((B or (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-930, 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-84809
in-theory        84809
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84809.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-930, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-84810
in-theory        84810
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84810.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-930, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-84811
in-theory        84811
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84811.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-930, 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-84812
in-theory        84812
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84812.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-930, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-84813
in-theory        84813
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84813.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-930, 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-84814
in-theory        84814
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84814.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-930, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-84815
in-theory        84815
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-84815.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-930, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-84816
in-theory        84816
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84816.        ((((A or B) -> C) -> ((B or (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-930, 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-84817
in-theory        84817
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-84817.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-930, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-84818
in-theory        84818
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       203
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-84818.        ((((A or B) -> C) -> ((B or (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-930, 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-84819
in-theory        84819
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-84819.        ((((A or B) -> C) -> ((B or (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-930, 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-84820
in-theory        84820
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-84820.        ((((A or B) -> C) -> ((B or (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-930, 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-84821
in-theory        84821
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-84821.        ((((A or B) -> C) -> ((B or (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-930, 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-84822
in-theory        84822
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-84822.        ((((A or B) -> C) -> ((B or (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-930, 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-84823
in-theory        84823
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-84823.        ((((A or B) -> C) -> ((B or (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-930, 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-84824
in-theory        84824
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-84824.        ((((A or B) -> C) -> ((B or (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-930, 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-84825
in-theory        84825
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-84825.        ((((A or B) -> C) -> ((B or (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-930, 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-84826
in-theory        84826
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-930 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-84826.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-930, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-84827
in-theory        84827
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84827.        ((((A or B) -> C) -> ((B or (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-930, 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-84828
in-theory        84828
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-84828.        ((((A or B) -> C) -> ((B or (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-930, 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-84829
in-theory        84829
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       179
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84829.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-930, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-84830
in-theory        84830
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84830.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-930, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-84831
in-theory        84831
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-84831.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-930, 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-84832
in-theory        84832
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84832.        ((((A or B) -> C) -> ((B or (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-930, 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-84833
in-theory        84833
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84833.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-930, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-84834
in-theory        84834
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84834.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> D))), M:tm-930, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-84835
in-theory        84835
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-84835.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-930, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-84836
in-theory        84836
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     25
proof            (modus-ponens tm-930 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84836.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-930, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-84837
in-theory        84837
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     25
proof            (modus-ponens tm-930 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84837.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-930, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-84838
in-theory        84838
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84838.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-930, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-84839
in-theory        84839
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (D or F)))
theorem-size     23
proof            (modus-ponens tm-930 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84839.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (D or F))), M:tm-930, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-84840
in-theory        84840
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F or D)))
theorem-size     23
proof            (modus-ponens tm-930 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84840.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F or D))), M:tm-930, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-84841
in-theory        84841
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84841.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-930, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-84842
in-theory        84842
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     31
proof            (modus-ponens tm-930 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84842.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-930, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-84843
in-theory        84843
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     25
proof            (modus-ponens tm-930 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84843.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-930, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-84844
in-theory        84844
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84844.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-930, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84845
in-theory        84845
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-84845.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-930, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-84846
in-theory        84846
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-84846.        ((((A or B) -> C) -> ((B or (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-930, 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-84847
in-theory        84847
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84847.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84848
in-theory        84848
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-84848.        ((((A or B) -> C) -> ((B or (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-930, 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-84849
in-theory        84849
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84849.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-930, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84850
in-theory        84850
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-84850.        ((((A or B) -> C) -> ((B or (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-930, 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-84851
in-theory        84851
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84851.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-930, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84852
in-theory        84852
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84852.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-930, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-84853
in-theory        84853
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-84853.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-930, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-84854
in-theory        84854
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84854.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-930, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-84855
in-theory        84855
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84855.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-930, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-84856
in-theory        84856
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84856.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-930, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-84857
in-theory        84857
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-930 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-84857.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-930, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-84858
in-theory        84858
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84858.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-930, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84859
in-theory        84859
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84859.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-930, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-84860
in-theory        84860
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84860.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-930, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84861
in-theory        84861
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84861.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-930, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-84862
in-theory        84862
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84862.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-930, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84863
in-theory        84863
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-84863.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-930, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-84864
in-theory        84864
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-84864.        ((((A or B) -> C) -> ((B or (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-930, 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-84865
in-theory        84865
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84865.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-930, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-84866
in-theory        84866
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84866.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-930, 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-84867
in-theory        84867
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84867.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-930, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-84868
in-theory        84868
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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       153
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-84868.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-930, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-84869
in-theory        84869
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84869.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-930, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-84870
in-theory        84870
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-930 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-84870.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-930, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-84871
in-theory        84871
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84871.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-930, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-84872
in-theory        84872
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-84872.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-930, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-84873
in-theory        84873
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-84873.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-930, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-84874
in-theory        84874
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-84874.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-930, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-84875
in-theory        84875
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-930 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-84875.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-930, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-84876
in-theory        84876
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-930 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84876.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-930, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-84877
in-theory        84877
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-84877.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-930, 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-84878
in-theory        84878
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-930 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       129
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-84878.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-930, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-84879
in-theory        84879
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-930 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84879.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-930, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-84880
in-theory        84880
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-84880.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-930, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-84881
in-theory        84881
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-930 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84881.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-930, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-84882
in-theory        84882
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-84882.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-930, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-84883
in-theory        84883
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-930 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-84883.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> E))), M:tm-930, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-84884
in-theory        84884
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-84884.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-930, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-84885
in-theory        84885
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     25
proof            (modus-ponens tm-930 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84885.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-930, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-84886
in-theory        84886
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     25
proof            (modus-ponens tm-930 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84886.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-930, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-84887
in-theory        84887
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84887.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-930, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-84888
in-theory        84888
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-930 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84888.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (E or F))), M:tm-930, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-84889
in-theory        84889
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-930 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84889.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F or E))), M:tm-930, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-84890
in-theory        84890
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84890.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-930, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-84891
in-theory        84891
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-930 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84891.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-930, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-84892
in-theory        84892
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     25
proof            (modus-ponens tm-930 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84892.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-930, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-84893
in-theory        84893
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-84893.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-930, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84894
in-theory        84894
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     27
proof            (modus-ponens tm-930 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-84894.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-930, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-84895
in-theory        84895
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-84895.        ((((A or B) -> C) -> ((B or (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-930, 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-84896
in-theory        84896
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-84896.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84897
in-theory        84897
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-84897.        ((((A or B) -> C) -> ((B or (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-930, 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-84898
in-theory        84898
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-84898.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-930, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84899
in-theory        84899
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 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-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-84899.        ((((A or B) -> C) -> ((B or (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-930, 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-84900
in-theory        84900
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-84900.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-930, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84901
in-theory        84901
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-930 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-84901.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-930, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-84902
in-theory        84902
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (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-930 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-84902.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-930, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-84903
in-theory        84903
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     27
proof            (modus-ponens tm-930 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84903.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-930, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-84904
in-theory        84904
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     27
proof            (modus-ponens tm-930 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84904.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-930, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-84905
in-theory        84905
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-930 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84905.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-930, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-84906
in-theory        84906
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-930 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-84906.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-930, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-84907
in-theory        84907
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), 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-84907.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G -> (F and G))))), M:tm-930, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84908
in-theory        84908
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E)))
theorem-size     27
proof            (modus-ponens tm-930 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-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-84908.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (F or G)) and E))), M:tm-930, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-84909
in-theory        84909
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-84909.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (F or G)))), M:tm-930, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84910
in-theory        84910
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E)))
theorem-size     27
proof            (modus-ponens tm-930 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-84910.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> ((F -> (G or F)) and E))), M:tm-930, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-84911
in-theory        84911
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-84911.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) or E) -> (F -> (G or F)))), M:tm-930, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84912
in-theory        84912
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-930 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-84912.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((E -> F) -> G)) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-930, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-84913
in-theory        84913
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     51
proof            (modus-ponens tm-930 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-84913.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (((E -> F) -> (E -> G)) -> H)) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-930, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-84914
in-theory        84914
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-930 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84914.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((E and G) or E) -> F))), M:tm-930, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-84915
in-theory        84915
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F)))
theorem-size     31
proof            (modus-ponens tm-930 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84915.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (((G and E) or E) -> F))), M:tm-930, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-84916
in-theory        84916
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-930 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-84916.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((G and D) or D) -> E))), M:tm-930, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-84917
in-theory        84917
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-930 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-84917.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and (D -> E)) or (D -> E)) -> (D -> F)))), M:tm-930, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-84918
in-theory        84918
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-930 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-4)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84918.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> D)) -> (((F and E) or E) -> D))), M:tm-930, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-84919
in-theory        84919
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-930 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (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-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-84919.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-930, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-84920
in-theory        84920
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-930 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-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-84920.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-930, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-84921
in-theory        84921
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-930 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-84921.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> E) -> ((D -> E) and (((F and D) or D) -> E)))), M:tm-930, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-84922
in-theory        84922
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-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-84922.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-930, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-84923
in-theory        84923
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-930 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-84923.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-930, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-84924
in-theory        84924
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-930 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-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-84924.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-930, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-84925
in-theory        84925
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-930 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-84925.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-930, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-84926
in-theory        84926
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-930 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-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-84926.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-930, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-84927
in-theory        84927
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-930 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
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-84927.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (not (((F and D) or D) -> E))) -> (not (D -> E)))), M:tm-930, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-84928
in-theory        84928
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-930 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84928.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D and E) or E) -> F) -> G) -> (((E -> F) or (((D and E) or E) -> F)) -> G))), M:tm-930, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-84929
in-theory        84929
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84929.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((E -> F) -> (((G and E) or E) -> F)))), M:tm-930, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-84930
in-theory        84930
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-930 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 tm-4)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
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-84930.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> (((F and D) or D) -> E)) or G)), M:tm-930, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-84931
in-theory        84931
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-84931.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> (((G and E) or E) -> F)) and D))), M:tm-930, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-84932
in-theory        84932
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-930 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-84932.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((F and D) or D)) -> ((D -> E) -> E))), M:tm-930, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-84933
in-theory        84933
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-4)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-84933.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E -> F) -> (((G and E) or E) -> F)))), M:tm-930, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-84934
in-theory        84934
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84934.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (E -> (D and E))))), M:tm-930, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84935
in-theory        84935
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F))))
theorem-size     31
proof            (modus-ponens tm-930 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84935.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> ((E -> (D and E)) and F)))), M:tm-930, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-84936
in-theory        84936
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F)))
theorem-size     29
proof            (modus-ponens tm-930 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84936.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (D and E)) or F))), M:tm-930, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-84937
in-theory        84937
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-84937.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F or (E -> (D and E))))), M:tm-930, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84938
in-theory        84938
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-930 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84938.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((D and E) -> F) -> ((E or (D and E)) -> F)))), M:tm-930, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-84939
in-theory        84939
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-930 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84939.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((E -> (not (D and E))) -> (not E)))), M:tm-930, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-84940
in-theory        84940
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84940.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> F)))), M:tm-930, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84941
in-theory        84941
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-930 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84941.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (E -> E))), M:tm-930, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-84942
in-theory        84942
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84942.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84943
in-theory        84943
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-930 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84943.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> F))), M:tm-930, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84944
in-theory        84944
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-930 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84944.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F and G) -> G))), M:tm-930, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84945
in-theory        84945
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84945.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> F)) and (E -> (D and E))))), M:tm-930, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84946
in-theory        84946
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-930 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84946.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> (D and E))))), M:tm-930, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84947
in-theory        84947
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84947.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> F) and (E -> (D and E))))), M:tm-930, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84948
in-theory        84948
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84948.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and G) -> G) and (E -> (D and E))))), M:tm-930, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84949
in-theory        84949
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84949.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G -> (F and G))) and (E -> (D and E))))), M:tm-930, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84950
in-theory        84950
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84950.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (E -> (E and (D and E))))), M:tm-930, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-84951
in-theory        84951
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-930 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84951.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G -> (F and G))))), M:tm-930, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84952
in-theory        84952
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84952.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (F or G)) and (E -> (D and E))))), M:tm-930, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84953
in-theory        84953
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-930 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84953.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (F or G)))), M:tm-930, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84954
in-theory        84954
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-84954.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> ((F -> (G or F)) and (E -> (D and E))))), M:tm-930, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-84955
in-theory        84955
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-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-84955.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (F -> (G or F)))), M:tm-930, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84956
in-theory        84956
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-930 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84956.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> F) -> (D and (E -> F)))) -> ((F or (E -> F)) -> (D and (E -> F))))), M:tm-930, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-84957
in-theory        84957
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G))))))
theorem-size     57
proof            (modus-ponens tm-930 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84957.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> (D and ((E -> F) -> (E -> G))))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (D and ((E -> F) -> (E -> G)))))), M:tm-930, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-84958
in-theory        84958
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-930 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84958.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((E and F) or E) -> (D and E)))), M:tm-930, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-84959
in-theory        84959
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-930 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84959.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F and E) or E) -> (D and E)))), M:tm-930, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-84960
in-theory        84960
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E))))))
theorem-size     45
proof            (modus-ponens tm-930 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84960.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> (F and E)) -> (D and (E -> (F and E))))) -> ((F or (E -> (F and E))) -> (D and (E -> (F and E)))))), M:tm-930, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-84961
in-theory        84961
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-930 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-84961.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((E -> (F and E)) -> G)) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-930, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-84962
in-theory        84962
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F)))
theorem-size     41
proof            (modus-ponens tm-930 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-84962.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> (E and D)) -> F) and G) or ((D -> (E and D)) -> F)) -> ((E or (D -> (E and D))) -> F))), M:tm-930, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-84963
in-theory        84963
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-930 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-84963.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> ((E and D) -> F)) or ((D -> (E and D)) -> (D -> F))) -> ((E or (D -> (E and D))) -> (D -> F)))), M:tm-930, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-84964
in-theory        84964
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D)))
theorem-size     33
proof            (modus-ponens tm-930 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-84964.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> (F and E)) -> D)) -> ((F or (E -> (F and E))) -> D))), M:tm-930, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-84965
in-theory        84965
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-930 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48.           (((A -> (B and 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-84965.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-930, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-84966
in-theory        84966
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-930 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-84966.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-930, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-84967
in-theory        84967
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F))))
theorem-size     39
proof            (modus-ponens tm-930 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-84967.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> (((D -> (E and D)) -> F) and ((E or (D -> (E and D))) -> F)))), M:tm-930, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-84968
in-theory        84968
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-930 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (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-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-84968.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-930, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-84969
in-theory        84969
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-930 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-84969.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-930, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-84970
in-theory        84970
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-930 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48.           (((A -> (B and 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-84970.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-930, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-84971
in-theory        84971
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-930 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-84971.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-930, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-84972
in-theory        84972
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-930 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48.           (((A -> (B and 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-84972.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-930, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-84973
in-theory        84973
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-930 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-84973.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E and D)) -> F) -> ((D -> (E and D)) -> F))), M:tm-930, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-84974
in-theory        84974
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F))))
theorem-size     41
proof            (modus-ponens tm-930 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-84974.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> (not ((E or (D -> (E and D))) -> F))) -> (not ((D -> (E and D)) -> F)))), M:tm-930, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-84975
in-theory        84975
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-930 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84975.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or (E -> (D and E))) -> F) -> G) -> ((((E -> (D and E)) -> F) or ((D or (E -> (D and E))) -> F)) -> G))), M:tm-930, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-84976
in-theory        84976
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84976.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-930, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-84977
in-theory        84977
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-930 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-84977.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) or G)), M:tm-930, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-84978
in-theory        84978
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-930 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84978.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and D))), M:tm-930, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-84979
in-theory        84979
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F)))
theorem-size     39
proof            (modus-ponens tm-930 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-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-84979.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> (E and D)) -> F) -> (E or (D -> (E and D)))) -> (((D -> (E and D)) -> F) -> F))), M:tm-930, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-84980
in-theory        84980
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-84980.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-930, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-84981
in-theory        84981
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (D or E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-84981.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (D or E)))), M:tm-930, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-84982
in-theory        84982
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-84982.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> ((D or E) and F)))), M:tm-930, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-84983
in-theory        84983
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((D or E) or F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-84983.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((D or E) or F))), M:tm-930, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-84984
in-theory        84984
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F or (D or E))))
theorem-size     25
proof            (modus-ponens tm-930 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-84984.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F or (D or E)))), M:tm-930, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-84985
in-theory        84985
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-84985.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G -> F)))), M:tm-930, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-84986
in-theory        84986
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-84986.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-84987
in-theory        84987
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-84987.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F and G) -> F))), M:tm-930, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-84988
in-theory        84988
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-84988.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F and G) -> G))), M:tm-930, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-84989
in-theory        84989
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-930 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-84989.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> F)) and (D or E)))), M:tm-930, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-84990
in-theory        84990
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-930 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-84990.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (D or E)))), M:tm-930, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-84991
in-theory        84991
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-930 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-84991.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (((F and G) -> F) and (D or E)))), M:tm-930, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-84992
in-theory        84992
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-930 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-84992.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (((F and G) -> G) and (D or E)))), M:tm-930, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-84993
in-theory        84993
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-930 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-84993.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G -> (F and G))) and (D or E)))), M:tm-930, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-84994
in-theory        84994
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-84994.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G -> (F and G))))), M:tm-930, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-84995
in-theory        84995
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-930 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-84995.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (F or G)) and (D or E)))), M:tm-930, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-84996
in-theory        84996
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-84996.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (F or G)))), M:tm-930, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-84997
in-theory        84997
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E))))
theorem-size     29
proof            (modus-ponens tm-930 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-84997.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> ((F -> (G or F)) and (D or E)))), M:tm-930, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-84998
in-theory        84998
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-84998.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (F -> (G or F)))), M:tm-930, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-84999
in-theory        84999
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-930 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-84999.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((E or (E or F)) -> (D and (E or F))))), M:tm-930, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-85000
in-theory        85000
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-930 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 tm-6)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-85000.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-930, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85001
in-theory        85001
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-930 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 tm-6)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-85001.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((D or (D or E)) -> F))), M:tm-930, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-85002
in-theory        85002
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-6)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-85002.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E or F) -> D)) -> ((E or (E or F)) -> D))), M:tm-930, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-85003
in-theory        85003
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-85003.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-930, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85004
in-theory        85004
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-49.           (((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-85004.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-930, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85005
in-theory        85005
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-930 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-85005.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((D or (D or E)) -> F)))), M:tm-930, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-85006
in-theory        85006
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-930 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-85006.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-930, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85007
in-theory        85007
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-85007.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-930, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85008
in-theory        85008
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-85008.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-930, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85009
in-theory        85009
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-930 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-85009.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-930, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-85010
in-theory        85010
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-85010.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-930, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85011
in-theory        85011
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> ((D or E) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-85011.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> ((D or E) -> F))), M:tm-930, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-85012
in-theory        85012
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-930 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-85012.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> (not ((D or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-930, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85013
in-theory        85013
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-930 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-85013.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or (D or E)) -> F) -> G) -> ((((D or E) -> F) or ((D or (D or E)) -> F)) -> G))), M:tm-930, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-85014
in-theory        85014
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-930 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-85014.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-930, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85015
in-theory        85015
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-930 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-85015.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> ((D or (D or E)) -> F)) or G)), M:tm-930, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-85016
in-theory        85016
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-930 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-85016.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and D))), M:tm-930, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85017
in-theory        85017
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-930 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-6)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-85017.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> (D or (D or E))) -> (((D or E) -> F) -> F))), M:tm-930, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85018
in-theory        85018
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-930 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-85018.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-930, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85019
in-theory        85019
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (E or D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85019.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (E or D)))), M:tm-930, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-85020
in-theory        85020
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F))))
theorem-size     27
proof            (modus-ponens tm-930 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85020.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> ((E or D) and F)))), M:tm-930, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-85021
in-theory        85021
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((E or D) or F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85021.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((E or D) or F))), M:tm-930, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-85022
in-theory        85022
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F or (E or D))))
theorem-size     25
proof            (modus-ponens tm-930 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85022.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F or (E or D)))), M:tm-930, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-85023
in-theory        85023
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85023.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G -> F)))), M:tm-930, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-85024
in-theory        85024
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-930 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-85024.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-930, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-85025
in-theory        85025
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-930 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-85025.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F and G) -> F))), M:tm-930, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-85026
in-theory        85026
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-930 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-85026.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F and G) -> G))), M:tm-930, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-85027
in-theory        85027
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-85027.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> F)) and (E or D)))), M:tm-930, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-85028
in-theory        85028
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-930 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-85028.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E or D)))), M:tm-930, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-85029
in-theory        85029
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> 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-85029.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (((F and G) -> F) and (E or D)))), M:tm-930, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-85030
in-theory        85030
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> 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-85030.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (((F and G) -> G) and (E or D)))), M:tm-930, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-85031
in-theory        85031
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-930 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85031.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G -> (F and G))) and (E or D)))), M:tm-930, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-85032
in-theory        85032
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-930 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-85032.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G -> (F and G))))), M:tm-930, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-85033
in-theory        85033
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or 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-85033.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (F or G)) and (E or D)))), M:tm-930, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-85034
in-theory        85034
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-930 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-85034.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (F or G)))), M:tm-930, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-85035
in-theory        85035
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D))))
theorem-size     29
proof            (modus-ponens tm-930 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85035.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> ((F -> (G or F)) and (E or D)))), M:tm-930, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-85036
in-theory        85036
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-930 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (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-85036.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (F -> (G or F)))), M:tm-930, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-85037
in-theory        85037
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F)))))
theorem-size     37
proof            (modus-ponens tm-930 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-85037.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E or F) -> (D and (E or F)))) -> ((F or (E or F)) -> (D and (E or F))))), M:tm-930, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-85038
in-theory        85038
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-930 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-85038.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and ((E or F) -> G)) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-930, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85039
in-theory        85039
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-930 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B 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-85039.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D or E) -> F) and G) or ((D or E) -> F)) -> ((E or (D or E)) -> F))), M:tm-930, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-85040
in-theory        85040
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-930 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> 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-85040.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E or F) -> D)) -> ((F or (E or F)) -> D))), M:tm-930, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-85041
in-theory        85041
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (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-85041.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-930, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85042
in-theory        85042
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-85042.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-930, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85043
in-theory        85043
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-930 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
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-85043.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D or E) -> F) -> (((D or E) -> F) and ((E or (D or E)) -> F)))), M:tm-930, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-85044
in-theory        85044
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-930 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
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-85044.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-930, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85045
in-theory        85045
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-85045.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-930, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85046
in-theory        85046
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-85046.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-930, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85047
in-theory        85047
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-930 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
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-85047.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-930, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-85048
in-theory        85048
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-85048.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-930, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-85049
in-theory        85049
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-930 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
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-85049.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> (not ((E or (D or E)) -> F))) -> (not ((D or E) -> F)))), M:tm-930, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85050
in-theory        85050
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-930 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85050.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or (E or D)) -> F) -> G) -> ((((E or D) -> F) or ((D or (E or D)) -> F)) -> G))), M:tm-930, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-85051
in-theory        85051
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-930 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85051.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-930, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85052
in-theory        85052
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-930 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
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-85052.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> ((E or (D or E)) -> F)) or G)), M:tm-930, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-85053
in-theory        85053
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-930 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85053.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-930, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85054
in-theory        85054
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-927 tm-930 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       159
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-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-5.            (A -> (B -> (A and B))), axiom
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-85054.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-930, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-85055
in-theory        85055
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-920 tm-930 ((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (or A B)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85055.        (((A or B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B))) and ((B or (A or B)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B)))), M:tm-920, m:tm-930, u:((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-85056
in-theory        85056
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-893 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85056.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-893, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85057
in-theory        85057
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-890 tm-930 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       159
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85057.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-930, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-85058
in-theory        85058
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-888 tm-930 ((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-5 tm-7)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85058.        ((A or B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B))), M:tm-888, m:tm-930, u:((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-85059
in-theory        85059
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B))))
theorem-size     45
proof            (modus-ponens tm-882 tm-930 ((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85059.        (((A or B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B))) and ((A or (A or B)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A or B)))), M:tm-882, m:tm-930, u:((Am (or A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-85060
in-theory        85060
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-855 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85060.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-855, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85061
in-theory        85061
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B or (A -> (B and A))) -> C)))
theorem-size     41
proof            (modus-ponens tm-852 tm-930 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85061.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-930, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-85062
in-theory        85062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> (B and A))))
theorem-size     25
proof            (modus-ponens tm-850 tm-930 ((Am (-> A (and B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85062.        ((A -> (B and A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> (B and A)))), M:tm-850, m:tm-930, u:((Am (-> A (and B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-85063
in-theory        85063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> (B and A)))))
theorem-size     53
proof            (modus-ponens tm-844 tm-930 ((Am (-> A (and B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85063.        (((A -> (B and A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> (B and A))))), M:tm-844, m:tm-930, u:((Am (-> A (and B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-85064
in-theory        85064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-808 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85064.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-808, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85065
in-theory        85065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((C and A) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-805 tm-930 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85065.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((C and A) or A) -> B))), M:tm-805, m:tm-930, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-85066
in-theory        85066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((E and A) or A) -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))
theorem-size     39
proof            (modus-ponens tm-798 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85066.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((E and A) or A) -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))), M:tm-798, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85067
in-theory        85067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-757 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-50.           (((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-85067.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-757, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85068
in-theory        85068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((A and C) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-754 tm-930 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85068.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((A and C) or A) -> B))), M:tm-754, m:tm-930, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-85069
in-theory        85069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((A and E) or A) -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))
theorem-size     39
proof            (modus-ponens tm-747 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-85069.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((A and E) or A) -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))), M:tm-747, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85070
in-theory        85070
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 or (F or G)) -> H)) and E)))
theorem-size     43
proof            (modus-ponens tm-708 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-50.           (((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-85070.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E))), M:tm-708, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85071
in-theory        85071
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     55
proof            (modus-ponens tm-705 tm-930 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85071.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-930, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-85072
in-theory        85072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-703 tm-930 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85072.        (((A -> B) -> (A -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-930, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-85073
in-theory        85073
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-697 tm-930 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85073.        ((((A -> B) -> (A -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-930, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-85074
in-theory        85074
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-665 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-50.           (((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-85074.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-665, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85075
in-theory        85075
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B or (A -> B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-662 tm-930 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((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-50.           (((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-85075.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-930, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-85076
in-theory        85076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> B)))
theorem-size     21
proof            (modus-ponens tm-660 tm-930 ((Am (-> A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85076.        ((A -> B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> B))), M:tm-660, m:tm-930, u:((Am (-> A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A B))))
================================================================
tm-name          tm-85077
in-theory        85077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> B))))
theorem-size     45
proof            (modus-ponens tm-654 tm-930 ((Am (-> A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A B)))))
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-50.           (((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-85077.        (((A -> B) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> B)))), M:tm-654, m:tm-930, u:((Am (-> A B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A B))))
================================================================
tm-name          tm-85078
in-theory        85078
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C or D) -> E) -> ((D or (C or D)) -> E)) and A)))
theorem-size     19
proof            (modus-ponens tm-623 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85078.        (A -> (B or ((((C or D) -> E) -> ((D or (C or D)) -> E)) and A))), M:tm-623, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85079
in-theory        85079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-622 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85079.        ((A -> (B -> (C or B))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-622, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85080
in-theory        85080
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (B -> (C or B))))
theorem-size     27
proof            (modus-ponens tm-619 tm-930 ((Am (-> A (or B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85080.        ((A or (B -> (C or B))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (B -> (C or B)))), M:tm-619, m:tm-930, u:((Am (-> A (or B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (or B A)))))
================================================================
tm-name          tm-85081
in-theory        85081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85081.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (F or E))), M:tm-609, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85082
in-theory        85082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-605 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-50.           (((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-85082.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-605, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85083
in-theory        85083
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> (C or B)) and A)))
theorem-size     31
proof            (modus-ponens tm-602 tm-930 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-50.           (((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-85083.        ((A or ((B -> (C or B)) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-930, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-85084
in-theory        85084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-595 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-85084.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-595, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85085
in-theory        85085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-550 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-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-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-85085.        (((A -> (B or A)) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-550, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85086
in-theory        85086
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-540 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-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-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-85086.        ((A or (B -> (C or B))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-540, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85087
in-theory        85087
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-530 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-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-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-85087.        ((A or (B -> (B or C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-530, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85088
in-theory        85088
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-520 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-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-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-85088.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-520, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85089
in-theory        85089
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-510 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-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-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-85089.        ((A or ((B and C) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-510, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85090
in-theory        85090
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-500 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-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-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-85090.        ((A or ((B and C) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-500, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85091
in-theory        85091
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-490 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-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-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-85091.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E))), M:tm-490, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85092
in-theory        85092
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-480 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85092.        ((A or (B -> (C -> B))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-480, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85093
in-theory        85093
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B or C) -> D) -> ((C or (B or C)) -> D)) and A) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85093.        (A -> (((((B or C) -> D) -> ((C or (B or C)) -> D)) and A) or E)), M:tm-470, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85094
in-theory        85094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-469 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85094.        ((A -> (B -> (B or C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-469, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85095
in-theory        85095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (B -> (B or C))))
theorem-size     27
proof            (modus-ponens tm-466 tm-930 ((Am (-> A (or A B))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 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-6.            (A -> (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-50.           (((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-85095.        ((A or (B -> (B or C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (B -> (B or C)))), M:tm-466, m:tm-930, u:((Am (-> A (or A B))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (or A B)))))
================================================================
tm-name          tm-85096
in-theory        85096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85096.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (E or F))), M:tm-456, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85097
in-theory        85097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-453 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-453.          (A -> ((B -> ((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-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-85097.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-453, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85098
in-theory        85098
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> (B or C)) and A)))
theorem-size     31
proof            (modus-ponens tm-450 tm-930 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85098.        ((A or ((B -> (B or C)) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-930, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-85099
in-theory        85099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-443 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-85099.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-443, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85100
in-theory        85100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-409 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85100.        (((A -> (A or B)) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-409, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85101
in-theory        85101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-400 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85101.        (((A -> (B -> (A and B))) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-400, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85102
in-theory        85102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-391 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85102.        ((((A and B) -> B) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-391, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85103
in-theory        85103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-382 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85103.        ((((A and B) -> A) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-382, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85104
in-theory        85104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-373 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85104.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E))), M:tm-373, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85105
in-theory        85105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-364 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85105.        (((A -> (B -> A)) or C) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-364, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85106
in-theory        85106
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C or D) -> E) -> ((D or (C or D)) -> E)) and A) and B)))
theorem-size     21
proof            (modus-ponens tm-355 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-85106.        (A -> (B -> (((((C or D) -> E) -> ((D or (C or D)) -> E)) and A) and B))), M:tm-355, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85107
in-theory        85107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-354 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85107.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-354, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85108
in-theory        85108
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (B -> (C -> (B and C)))))
theorem-size     31
proof            (modus-ponens tm-351 tm-930 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (-> B (and A B)))))))
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-5.            (A -> (B -> (A and 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-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-85108.        ((A or (B -> (C -> (B and C)))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-930, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-85109
in-theory        85109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-85109.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85110
in-theory        85110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-338 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85110.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C))), M:tm-338, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85111
in-theory        85111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-335 tm-930 ((Am (-> A (and A B))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (and A B))))))
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-5.            (A -> (B -> (A and B))), axiom
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-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-85111.        (((A -> B) or (A -> (A and B))) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> (A and B)))), M:tm-335, m:tm-930, u:((Am (-> A (and A B))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (and A B)))))
================================================================
tm-name          tm-85112
in-theory        85112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (A -> (A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-328 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-85112.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (A -> (A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-328, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85113
in-theory        85113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     43
proof            (modus-ponens tm-327 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-85113.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-327, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85114
in-theory        85114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-326 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-85114.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-326, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85115
in-theory        85115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-325 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-85115.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-325, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85116
in-theory        85116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     49
proof            (modus-ponens tm-324 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85116.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-324, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85117
in-theory        85117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-323 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-85117.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-323, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85118
in-theory        85118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85118.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85119
in-theory        85119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85119.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85120
in-theory        85120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-85120.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85121
in-theory        85121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-85121.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (A -> A)), M:tm-316, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85122
in-theory        85122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85122.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85123
in-theory        85123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((A -> (not ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85123.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((A -> (not ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))) -> (not A))), M:tm-313, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85124
in-theory        85124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((((((B or C) -> D) -> ((C or (B or C)) -> D)) and A) -> E) -> ((A or ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
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-312.          ((A -> B) -> ((A -> B) and ((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-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-85124.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((((((B or C) -> D) -> ((C or (B or C)) -> D)) and A) -> E) -> ((A or ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) -> E))), M:tm-312, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85125
in-theory        85125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E or (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-311 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-85125.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E or (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-311, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85126
in-theory        85126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-85126.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) or E)), M:tm-310, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85127
in-theory        85127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85127.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and E))), M:tm-309, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85128
in-theory        85128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-305 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-85128.        ((A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)) and (E -> (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)))), M:tm-305, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85129
in-theory        85129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-303 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85129.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-303, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85130
in-theory        85130
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> (C -> (B and C))) and A)))
theorem-size     35
proof            (modus-ponens tm-300 tm-930 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85130.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-930, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-85131
in-theory        85131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-270 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 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-270.          (A -> ((B -> (((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-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-85131.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-270, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85132
in-theory        85132
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((B and C) -> C) and A)))
theorem-size     31
proof            (modus-ponens tm-267 tm-930 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85132.        ((A or (((B and C) -> C) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((B and C) -> C) and A))), M:tm-267, m:tm-930, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-85133
in-theory        85133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-239 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 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-239.          (A -> ((B -> (((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-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-85133.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-239, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85134
in-theory        85134
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((B and C) -> B) and A)))
theorem-size     31
proof            (modus-ponens tm-236 tm-930 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85134.        ((A or (((B and C) -> B) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((B and C) -> B) and A))), M:tm-236, m:tm-930, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-85135
in-theory        85135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E)))
theorem-size     35
proof            (modus-ponens tm-210 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85135.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E))), M:tm-210, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85136
in-theory        85136
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     47
proof            (modus-ponens tm-207 tm-930 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85136.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-930, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-85137
in-theory        85137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-183 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 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-183.          (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-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-85137.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-183, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85138
in-theory        85138
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> (C -> B)) and A)))
theorem-size     31
proof            (modus-ponens tm-180 tm-930 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85138.        ((A or ((B -> (C -> B)) and A)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-930, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-85139
in-theory        85139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-157 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85139.        ((A -> ((B and C) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-157, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85140
in-theory        85140
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B and C) -> C)))
theorem-size     27
proof            (modus-ponens tm-154 tm-930 ((Am (-> (and A B) B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 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-4.            ((A 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-50.           (((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-85140.        ((A or ((B and C) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B and C) -> C))), M:tm-154, m:tm-930, u:((Am (-> (and A B) B)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (and A B) B))))
================================================================
tm-name          tm-85141
in-theory        85141
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-147 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85141.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-147, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85142
in-theory        85142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A and (B -> C)) -> C)))
theorem-size     37
proof            (modus-ponens tm-144 tm-930 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (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-50.           (((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-85142.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-930, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-85143
in-theory        85143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-134 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85143.        ((A -> ((B and C) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-134, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85144
in-theory        85144
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B and C) -> B)))
theorem-size     27
proof            (modus-ponens tm-131 tm-930 ((Am (-> (and A B) A)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 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-3.            ((A 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-50.           (((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-85144.        ((A or ((B and C) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B and C) -> B))), M:tm-131, m:tm-930, u:((Am (-> (and A B) A)) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (and A B) A))))
================================================================
tm-name          tm-85145
in-theory        85145
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-125 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85145.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-125, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85146
in-theory        85146
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((A -> B) and C) -> B)))
theorem-size     37
proof            (modus-ponens tm-122 tm-930 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) 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-50.           (((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-85146.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-930, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-85147
in-theory        85147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-113 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85147.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E))), M:tm-113, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85148
in-theory        85148
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     43
proof            (modus-ponens tm-110 tm-930 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85148.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-930, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-85149
in-theory        85149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     37
proof            (modus-ponens tm-105 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85149.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-105, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85150
in-theory        85150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-102 tm-930 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85150.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-930, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-85151
in-theory        85151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-95 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85151.        (((A -> B) -> (A -> A)) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C))), M:tm-95, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85152
in-theory        85152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> A)))
theorem-size     25
proof            (modus-ponens tm-92 tm-930 ((Am (-> A A)) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85152.        (((A -> B) or (A -> A)) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and (A -> A))), M:tm-92, m:tm-930, u:((Am (-> A A)) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A A))))
================================================================
tm-name          tm-85153
in-theory        85153
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and A)))
theorem-size     19
proof            (modus-ponens tm-84 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85153.        (A -> (B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and A))), M:tm-84, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85154
in-theory        85154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-83 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85154.        ((A -> (B -> (C -> B))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-83, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85155
in-theory        85155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (B -> (C -> B))))
theorem-size     27
proof            (modus-ponens tm-80 tm-930 ((Am (-> A (-> B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (-> B A))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-50.           (((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-85155.        ((A or (B -> (C -> B))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and (B -> (C -> B)))), M:tm-80, m:tm-930, u:((Am (-> A (-> B A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> A (-> B A)))))
================================================================
tm-name          tm-85156
in-theory        85156
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B)))
theorem-size     23
proof            (modus-ponens tm-76 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85156.        (((not (not A)) -> A) and (B -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and B))), M:tm-76, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85157
in-theory        85157
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-930 ((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85157.        (((not (not A)) or A) -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)), M:tm-73, m:tm-930, u:((A Am) (B (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-85158
in-theory        85158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C)))
theorem-size     29
proof            (modus-ponens tm-69 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85158.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and C))), M:tm-69, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85159
in-theory        85159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and ((A -> (not B)) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-66 tm-930 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85159.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C or D) -> E) -> ((D or (C or D)) -> E)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-930, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-85160
in-theory        85160
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-54 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
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-50.           (((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-85160.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and D))), M:tm-54, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-85161
in-theory        85161
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-51 tm-930 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85161.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-930, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-85162
in-theory        85162
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-931 tm-365 ((Am (-> (or A (-> Bm (-> Cm Bm))) C)) (B (-> Bm (-> Cm Bm))) (Dm (or A (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85162.        (((A or (B -> (C -> B))) -> D) -> D), M:tm-931, m:tm-365, u:((Am (-> (or A (-> Bm (-> Cm Bm))) C)) (B (-> Bm (-> Cm Bm))) (Dm (or A (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-85163
in-theory        85163
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> E)
theorem-size     19
proof            (modus-ponens tm-931 tm-374 ((Am (-> (or A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) C)) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (or A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85163.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> E), M:tm-931, m:tm-374, u:((Am (-> (or A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) C)) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (or A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-85164
in-theory        85164
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-931 tm-383 ((Am (-> (or A (-> (and Bm Cm) Bm)) C)) (B (-> (and Bm Cm) Bm)) (Dm (or A (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85164.        (((A or ((B and C) -> B)) -> D) -> D), M:tm-931, m:tm-383, u:((Am (-> (or A (-> (and Bm Cm) Bm)) C)) (B (-> (and Bm Cm) Bm)) (Dm (or A (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-85165
in-theory        85165
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-931 tm-392 ((Am (-> (or A (-> (and Bm Cm) Cm)) C)) (B (-> (and Bm Cm) Cm)) (Dm (or A (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85165.        (((A or ((B and C) -> C)) -> D) -> D), M:tm-931, m:tm-392, u:((Am (-> (or A (-> (and Bm Cm) Cm)) C)) (B (-> (and Bm Cm) Cm)) (Dm (or A (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-85166
in-theory        85166
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) -> D) -> D)
theorem-size     13
proof            (modus-ponens tm-931 tm-401 ((Am (-> (or A (-> Bm (-> Cm (and Bm Cm)))) C)) (B (-> Bm (-> Cm (and Bm Cm)))) (Dm (or A (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85166.        (((A or (B -> (C -> (B and C)))) -> D) -> D), M:tm-931, m:tm-401, u:((Am (-> (or A (-> Bm (-> Cm (and Bm Cm)))) C)) (B (-> Bm (-> Cm (and Bm Cm)))) (Dm (or A (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-85167
in-theory        85167
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-931 tm-410 ((Am (-> (or A (-> Bm (or Bm Cm))) C)) (B (-> Bm (or Bm Cm))) (Dm (or A (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85167.        (((A or (B -> (B or C))) -> D) -> D), M:tm-931, m:tm-410, u:((Am (-> (or A (-> Bm (or Bm Cm))) C)) (B (-> Bm (or Bm Cm))) (Dm (or A (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-85168
in-theory        85168
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-931 tm-551 ((Am (-> (or A (-> Bm (or Cm Bm))) C)) (B (-> Bm (or Cm Bm))) (Dm (or A (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-85168.        (((A or (B -> (C or B))) -> D) -> D), M:tm-931, m:tm-551, u:((Am (-> (or A (-> Bm (or Cm Bm))) C)) (B (-> Bm (or Cm Bm))) (Dm (or A (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-85169
in-theory        85169
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-930 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-85169.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-930, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85170
in-theory        85170
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-893 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-7)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85170.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-893, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85171
in-theory        85171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     37
proof            (modus-ponens tm-855 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85171.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-855, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85172
in-theory        85172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-808 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85172.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-808, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85173
in-theory        85173
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((D and (((A or B) -> C) -> (B or (A or B)))) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C)))
theorem-size     53
proof            (modus-ponens tm-798 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85173.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((D and (((A or B) -> C) -> (B or (A or B)))) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C))), M:tm-798, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85174
in-theory        85174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-757 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85174.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-757, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85175
in-theory        85175
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((((((A or B) -> C) -> (B or (A or B))) and D) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C)))
theorem-size     53
proof            (modus-ponens tm-747 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-85175.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((((((A or B) -> C) -> (B or (A or B))) and D) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C))), M:tm-747, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85176
in-theory        85176
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))) -> (((E or F) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-708 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85176.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G))), M:tm-708, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85177
in-theory        85177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-665 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85177.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-665, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85178
in-theory        85178
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((B or (A or B)) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C)))
theorem-size     45
proof            (modus-ponens tm-654 tm-931 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C (-> (-> (or Am Bm) Cm) Cm))))
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-50.           (((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-85178.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((B or (A or B)) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C))), M:tm-654, m:tm-931, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85179
in-theory        85179
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (B or (A or B))) -> (D or (((A or B) -> C) -> C)))
theorem-size     21
proof            (modus-ponens tm-623 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or 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-50.           (((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-85179.        ((((A or B) -> C) -> (B or (A or B))) -> (D or (((A or B) -> C) -> C))), M:tm-623, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85180
in-theory        85180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-622 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or 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-50.           (((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-85180.        ((A -> (B -> (C or B))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-622, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85181
in-theory        85181
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or 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-50.           (((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-85181.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E or D))), M:tm-609, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85182
in-theory        85182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-605 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-85182.        ((A -> ((B -> (C or B)) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-605, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85183
in-theory        85183
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E or D)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-595 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
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-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-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-85183.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E or D)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-595, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85184
in-theory        85184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-550 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-50.           (((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-85184.        (((A -> (B or A)) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-550, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85185
in-theory        85185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-540 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-50.           (((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-85185.        ((A or (B -> (C or B))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-540, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85186
in-theory        85186
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-530 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-50.           (((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-85186.        ((A or (B -> (B or C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-530, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85187
in-theory        85187
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-520 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-85187.        ((A or (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-520, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85188
in-theory        85188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-510 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-50.           (((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-85188.        ((A or ((B and C) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-510, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85189
in-theory        85189
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-500 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-50.           (((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-85189.        ((A or ((B and C) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-500, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85190
in-theory        85190
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-490 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-50.           (((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-85190.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G))), M:tm-490, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85191
in-theory        85191
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-480 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or 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-50.           (((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-85191.        ((A or (B -> (C -> B))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-480, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85192
in-theory        85192
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (B or (A or B))) -> ((((A or B) -> C) -> C) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85192.        ((((A or B) -> C) -> (B or (A or B))) -> ((((A or B) -> C) -> C) or D)), M:tm-470, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85193
in-theory        85193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-469 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85193.        ((A -> (B -> (B or C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-469, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85194
in-theory        85194
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85194.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (D or E))), M:tm-456, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85195
in-theory        85195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-453 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-453.          (A -> ((B -> ((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85195.        ((A -> ((B -> (B or C)) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-453, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85196
in-theory        85196
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (D or E)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-443 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-85196.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (D or E)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-443, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85197
in-theory        85197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-409 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85197.        (((A -> (A or B)) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-409, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85198
in-theory        85198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-400 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85198.        (((A -> (B -> (A and B))) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-400, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85199
in-theory        85199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-391 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85199.        ((((A and B) -> B) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-391, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85200
in-theory        85200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-382 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85200.        ((((A and B) -> A) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-382, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85201
in-theory        85201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-373 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85201.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G))), M:tm-373, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85202
in-theory        85202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-364 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85202.        (((A -> (B -> A)) or C) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-364, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85203
in-theory        85203
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (B or (A or B))) -> (D -> ((((A or B) -> C) -> C) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85203.        ((((A or B) -> C) -> (B or (A or B))) -> (D -> ((((A or B) -> C) -> C) and D))), M:tm-355, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85204
in-theory        85204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-354 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85204.        ((A -> (B -> (C -> (B and C)))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-354, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85205
in-theory        85205
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-85205.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85206
in-theory        85206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-338 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-85206.        (((A -> B) -> (A -> (A and B))) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E))), M:tm-338, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85207
in-theory        85207
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((((A or B) -> C) -> (B or (A or B))) -> ((((A or B) -> C) -> (B or (A or B))) and (((A or B) -> C) -> C))))
theorem-size     51
proof            (modus-ponens tm-328 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-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-85207.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((((A or B) -> C) -> (B or (A or B))) -> ((((A or B) -> C) -> (B or (A or B))) and (((A or B) -> C) -> C)))), M:tm-328, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85208
in-theory        85208
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> (D and E))) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     47
proof            (modus-ponens tm-327 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-85208.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> (D and E))) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-327, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85209
in-theory        85209
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((D and E) -> E) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-326 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-85209.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((D and E) -> E) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-326, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85210
in-theory        85210
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((D and E) -> D) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-325 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-85210.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((D and E) -> D) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-325, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85211
in-theory        85211
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     53
proof            (modus-ponens tm-324 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-85211.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-324, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85212
in-theory        85212
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> D)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-323 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-85212.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> D)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-323, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85213
in-theory        85213
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85213.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85214
in-theory        85214
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85214.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85215
in-theory        85215
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-85215.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85216
in-theory        85216
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> (B or (A or B)))))
theorem-size     43
proof            (modus-ponens tm-316 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-85216.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> (B or (A or B))))), M:tm-316, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85217
in-theory        85217
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85217.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85218
in-theory        85218
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (B or (A or B))) -> (not (((A or B) -> C) -> C))) -> (not (((A or B) -> C) -> (B or (A or B))))))
theorem-size     53
proof            (modus-ponens tm-313 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85218.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (B or (A or B))) -> (not (((A or B) -> C) -> C))) -> (not (((A or B) -> C) -> (B or (A or B)))))), M:tm-313, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85219
in-theory        85219
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> C) -> D) -> (((((A or B) -> C) -> (B or (A or B))) or (((A or B) -> C) -> C)) -> D)))
theorem-size     51
proof            (modus-ponens tm-312 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
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-50.           (((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-85219.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> C) -> D) -> (((((A or B) -> C) -> (B or (A or B))) or (((A or B) -> C) -> C)) -> D))), M:tm-312, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85220
in-theory        85220
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D or ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     41
proof            (modus-ponens tm-311 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-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-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-85220.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D or ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-311, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85221
in-theory        85221
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-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-85221.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) or D)), M:tm-310, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85222
in-theory        85222
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-85222.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and D))), M:tm-309, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85223
in-theory        85223
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (B or (A or B))) -> ((A or B) -> C)) -> ((((A or B) -> C) -> (B or (A or B))) -> C)))
theorem-size     51
proof            (modus-ponens tm-306 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (or Am Bm) Cm)) (C 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-85223.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (((((A or B) -> C) -> (B or (A or B))) -> ((A or B) -> C)) -> ((((A or B) -> C) -> (B or (A or B))) -> C))), M:tm-306, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (or Am Bm) Cm)) (C Cm))
================================================================
tm-name          tm-85224
in-theory        85224
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))))
theorem-size     41
proof            (modus-ponens tm-305 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-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-85224.        (((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)) and (D -> ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))), M:tm-305, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85225
in-theory        85225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-303 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85225.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-303, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85226
in-theory        85226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-270 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 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-270.          (A -> ((B -> (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85226.        ((A -> (((B and C) -> C) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-270, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85227
in-theory        85227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-239 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 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-239.          (A -> ((B -> (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85227.        ((A -> (((B and C) -> B) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-239, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85228
in-theory        85228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     37
proof            (modus-ponens tm-210 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85228.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G))), M:tm-210, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85229
in-theory        85229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-183 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85229.        ((A -> ((B -> (C -> B)) and A)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-183, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85230
in-theory        85230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-157 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85230.        ((A -> ((B and C) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-157, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85231
in-theory        85231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-147 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-85231.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-147, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85232
in-theory        85232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-134 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85232.        ((A -> ((B and C) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-134, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85233
in-theory        85233
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-125 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-85233.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-125, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85234
in-theory        85234
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> D)) -> (B or (A or B))) -> ((((A or B) -> (C -> D)) -> C) -> (((A or B) -> (C -> D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-114 tm-931 ((A (-> (-> (or Am Bm) (-> C D)) (or Bm (or Am Bm)))) (B (-> (or Am Bm) (-> C D))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85234.        ((((A or B) -> (C -> D)) -> (B or (A or B))) -> ((((A or B) -> (C -> D)) -> C) -> (((A or B) -> (C -> D)) -> D))), M:tm-114, m:tm-931, u:((A (-> (-> (or Am Bm) (-> C D)) (or Bm (or Am Bm)))) (B (-> (or Am Bm) (-> C D))) (Cm (-> C D)))
================================================================
tm-name          tm-85235
in-theory        85235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-113 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85235.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G))), M:tm-113, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85236
in-theory        85236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     39
proof            (modus-ponens tm-105 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-85236.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-105, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85237
in-theory        85237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-95 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-85237.        (((A -> B) -> (A -> A)) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E))), M:tm-95, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85238
in-theory        85238
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (B or (A or B))) -> (D -> (((A or B) -> C) -> C)))
theorem-size     21
proof            (modus-ponens tm-84 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85238.        ((((A or B) -> C) -> (B or (A or B))) -> (D -> (((A or B) -> C) -> C))), M:tm-84, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85239
in-theory        85239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-83 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85239.        ((A -> (B -> (C -> B))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-83, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85240
in-theory        85240
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or C) -> D) -> (C or (B or C))) -> (((B or C) -> D) -> D)))
theorem-size     25
proof            (modus-ponens tm-76 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85240.        (((not (not A)) -> A) and ((((B or C) -> D) -> (C or (B or C))) -> (((B or C) -> D) -> D))), M:tm-76, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85241
in-theory        85241
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A or B) -> C) -> (B or (A or B))))) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-73 tm-931 ((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85241.        (((not (not (((A or B) -> C) -> (B or (A or B))))) or (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C)), M:tm-73, m:tm-931, u:((A (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm)))) (B (-> (-> (or Am Bm) Cm) Cm)))
================================================================
tm-name          tm-85242
in-theory        85242
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (not (B or (A or B)))) -> (B or (A or B))) -> (not ((A or B) -> (not (B or (A or B))))))
theorem-size     28
proof            (modus-ponens tm-70 tm-931 ((B (or Bm (or Am Bm))) (A (-> (or Am Bm) (not (or Bm (or Am Bm))))) (Cm (not (or Bm (or Am Bm))))))
axioms-used      (tm-2 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85242.        ((((A or B) -> (not (B or (A or B)))) -> (B or (A or B))) -> (not ((A or B) -> (not (B or (A or B)))))), M:tm-70, m:tm-931, u:((B (or Bm (or Am Bm))) (A (-> (or Am Bm) (not (or Bm (or Am Bm))))) (Cm (not (or Bm (or Am Bm)))))
================================================================
tm-name          tm-85243
in-theory        85243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-69 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85243.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or D) -> E) -> (D or (C or D))) -> (((C or D) -> E) -> E))), M:tm-69, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85244
in-theory        85244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-54 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85244.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or E) -> F) -> (E or (D or E))) -> (((D or E) -> F) -> F))), M:tm-54, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-85245
in-theory        85245
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-930 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
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-85245.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-930, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85246
in-theory        85246
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-927 tm-932 ((Am (-> (or A (or B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       147
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-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-1.            (A -> (B -> A)), axiom
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-85246.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-927, m:tm-932, u:((Am (-> (or A (or B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85247
in-theory        85247
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((B or (A or B)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     37
proof            (modus-ponens tm-920 tm-932 ((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
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-85247.        (((A or B) -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((B or (A or B)) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-920, m:tm-932, u:((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85248
in-theory        85248
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-893 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85248.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-893, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85249
in-theory        85249
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-890 tm-932 ((Am (-> (or A (or A B)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85249.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-890, m:tm-932, u:((Am (-> (or A (or A B)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85250
in-theory        85250
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     17
proof            (modus-ponens tm-888 tm-932 ((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-7)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85250.        ((A or B) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-888, m:tm-932, u:((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85251
in-theory        85251
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((A or (A or B)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     37
proof            (modus-ponens tm-882 tm-932 ((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85251.        (((A or B) -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((A or (A or B)) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-882, m:tm-932, u:((Am (or A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85252
in-theory        85252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-855 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85252.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-855, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85253
in-theory        85253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-852 tm-932 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85253.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-852, m:tm-932, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85254
in-theory        85254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-850 tm-932 ((Am (-> A (and B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85254.        ((A -> (B and A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-850, m:tm-932, u:((Am (-> A (and B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85255
in-theory        85255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((B or (A -> (B and A))) -> (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     41
proof            (modus-ponens tm-844 tm-932 ((Am (-> A (and B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85255.        (((A -> (B and A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((B or (A -> (B and A))) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-844, m:tm-932, u:((Am (-> A (and B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85256
in-theory        85256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-808 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-7)
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85256.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-808, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85257
in-theory        85257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-805 tm-932 ((Am (-> (or (and A B) B) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
proof-size       141
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85257.        (((A -> B) or (((C and A) or A) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-805, m:tm-932, u:((Am (-> (or (and A B) B) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85258
in-theory        85258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and A) or A) -> (((B or C) -> D) -> ((C or (B or C)) -> D))))
theorem-size     35
proof            (modus-ponens tm-798 tm-932 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-85258.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and A) or A) -> (((B or C) -> D) -> ((C or (B or C)) -> D)))), M:tm-798, m:tm-932, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85259
in-theory        85259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-757 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85259.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-757, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85260
in-theory        85260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-754 tm-932 ((Am (-> (or (and A B) A) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85260.        (((A -> B) or (((A and C) or A) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-754, m:tm-932, u:((Am (-> (or (and A B) A) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85261
in-theory        85261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((A and E) or A) -> (((B or C) -> D) -> ((C or (B or C)) -> D))))
theorem-size     35
proof            (modus-ponens tm-747 tm-932 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-50.           (((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-85261.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((A and E) or A) -> (((B or C) -> D) -> ((C or (B or C)) -> D)))), M:tm-747, m:tm-932, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85262
in-theory        85262
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 or (F or G)) -> H))))
theorem-size     41
proof            (modus-ponens tm-708 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-50.           (((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-85262.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-708, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85263
in-theory        85263
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-705 tm-932 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85263.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-705, m:tm-932, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85264
in-theory        85264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-703 tm-932 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-50.           (((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-85264.        (((A -> B) -> (A -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-703, m:tm-932, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85265
in-theory        85265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     49
proof            (modus-ponens tm-697 tm-932 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-50.           (((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-85265.        ((((A -> B) -> (A -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-697, m:tm-932, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85266
in-theory        85266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-665 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85266.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-665, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85267
in-theory        85267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-662 tm-932 ((Am (-> (or A (-> B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85267.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-662, m:tm-932, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85268
in-theory        85268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     17
proof            (modus-ponens tm-660 tm-932 ((Am (-> A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85268.        ((A -> B) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-660, m:tm-932, u:((Am (-> A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85269
in-theory        85269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((B or (A -> B)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     37
proof            (modus-ponens tm-654 tm-932 ((Am (-> A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-85269.        (((A -> B) -> (((C or D) -> E) -> ((D or (C or D)) -> E))) and ((B or (A -> B)) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-654, m:tm-932, u:((Am (-> A B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85270
in-theory        85270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-622 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85270.        ((A -> (B -> (C or B))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-622, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85271
in-theory        85271
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-619 tm-932 ((Am (-> A (or B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85271.        ((A or (B -> (C or B))) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-619, m:tm-932, u:((Am (-> A (or B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85272
in-theory        85272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85272.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85273
in-theory        85273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-605 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85273.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-605, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85274
in-theory        85274
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-602 tm-932 ((Am (and (-> A (or B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85274.        ((A or ((B -> (C or B)) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-602, m:tm-932, u:((Am (and (-> A (or B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85275
in-theory        85275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F or E)) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85275.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F or E)) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-595, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85276
in-theory        85276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-550 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85276.        (((A -> (B or A)) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-550, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85277
in-theory        85277
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-540 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85277.        ((A or (B -> (C or B))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-540, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85278
in-theory        85278
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-530 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85278.        ((A or (B -> (B or C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-530, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85279
in-theory        85279
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-520 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85279.        ((A or (B -> (C -> (B and C)))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-520, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85280
in-theory        85280
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-510 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85280.        ((A or ((B and C) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-510, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85281
in-theory        85281
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-500 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85281.        ((A or ((B and C) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-500, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85282
in-theory        85282
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-490 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85282.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-490, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85283
in-theory        85283
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-480 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85283.        ((A or (B -> (C -> B))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-480, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85284
in-theory        85284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-469 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85284.        ((A -> (B -> (B or C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-469, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85285
in-theory        85285
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-466 tm-932 ((Am (-> A (or A B))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-6 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-6.            (A -> (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-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-85285.        ((A or (B -> (B or C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-466, m:tm-932, u:((Am (-> A (or A B))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85286
in-theory        85286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85286.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85287
in-theory        85287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-453 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85287.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-453, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85288
in-theory        85288
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-450 tm-932 ((Am (and (-> A (or A B)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85288.        ((A or ((B -> (B or C)) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-450, m:tm-932, u:((Am (and (-> A (or A B)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85289
in-theory        85289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (E or F)) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85289.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (E or F)) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-443, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85290
in-theory        85290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-409 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85290.        (((A -> (A or B)) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-409, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85291
in-theory        85291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-400 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85291.        (((A -> (B -> (A and B))) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-400, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85292
in-theory        85292
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-391 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85292.        ((((A and B) -> B) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-391, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85293
in-theory        85293
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-382 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85293.        ((((A and B) -> A) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-382, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85294
in-theory        85294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-373 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85294.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-373, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85295
in-theory        85295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-364 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85295.        (((A -> (B -> A)) or C) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-364, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85296
in-theory        85296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-354 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85296.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-354, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85297
in-theory        85297
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-351 tm-932 ((Am (-> A (-> B (and A B)))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
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-5.            (A -> (B -> (A and 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-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-85297.        ((A or (B -> (C -> (B and C)))) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-351, m:tm-932, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85298
in-theory        85298
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (A and (C or B))))
theorem-size     13
proof            (modus-ponens tm-349 tm-932 ((A Am) (B (or Bm Cm)) (Dm (and Am (or Bm Cm))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85298.        (A -> ((B or (C or B)) -> (A and (C or B)))), M:tm-349, m:tm-932, u:((A Am) (B (or Bm Cm)) (Dm (and Am (or Bm Cm))) (C (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))
================================================================
tm-name          tm-85299
in-theory        85299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-85299.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85300
in-theory        85300
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) -> ((((A or B) -> C) -> ((B or (A or B)) -> C)) and D))
theorem-size     31
proof            (modus-ponens tm-339 tm-932 ((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B)) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85300.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) -> ((((A or B) -> C) -> ((B or (A or B)) -> C)) and D)), M:tm-339, m:tm-932, u:((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B)) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85301
in-theory        85301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-338 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85301.        (((A -> B) -> (A -> (A and B))) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-338, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85302
in-theory        85302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-335 tm-932 ((Am (-> A (and A B))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 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-5.            (A -> (B -> (A and B))), axiom
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-50.           (((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-85302.        (((A -> B) or (A -> (A and B))) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-335, m:tm-932, u:((Am (-> A (and A B))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85303
in-theory        85303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (A -> (A and (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-328 tm-932 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-328.          ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85303.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (A -> (A and (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-328, m:tm-932, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85304
in-theory        85304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85304.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-327, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85305
in-theory        85305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and F) -> F) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85305.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and F) -> F) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-326, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85306
in-theory        85306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and F) -> E) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85306.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E and F) -> E) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-325, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85307
in-theory        85307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-85307.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-324, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85308
in-theory        85308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> E)) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-50.           (((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-85308.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> E)) and (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-323, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85309
in-theory        85309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85309.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85310
in-theory        85310
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E)) -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E)) -> E))
theorem-size     51
proof            (modus-ponens tm-321 tm-932 ((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) C))) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 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-17.           (((A and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85310.        (((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E)) -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E)) -> E)), M:tm-321, m:tm-932, u:((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) C))) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85311
in-theory        85311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85311.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85312
in-theory        85312
times-derived    1
----------------------------------------------------------------
theorem          (((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) and E) -> (((A or B) -> C) -> ((B or (A or B)) -> C))) and ((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) and E) -> D))
theorem-size     51
proof            (modus-ponens tm-319 tm-932 ((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B) C)) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85312.        (((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) and E) -> (((A or B) -> C) -> ((B or (A or B)) -> C))) and ((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) and E) -> D)), M:tm-319, m:tm-932, u:((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B) C)) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85313
in-theory        85313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-85313.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85314
in-theory        85314
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> (((B or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> ((B or (A or B)) -> C))) and ((((A or B) -> C) -> (((B or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> D)))
theorem-size     53
proof            (modus-ponens tm-317 tm-932 ((Am (-> (-> (or Bm Cm) Dm) (-> (-> (or Cm (or Bm Cm)) Dm) C))) (A (-> (or Bm Cm) Dm)) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-13.           (((A -> (B -> C)) -> (A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85314.        (((((A or B) -> C) -> (((B or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> ((B or (A or B)) -> C))) and ((((A or B) -> C) -> (((B or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> D))), M:tm-317, m:tm-932, u:((Am (-> (-> (or Bm Cm) Dm) (-> (-> (or Cm (or Bm Cm)) Dm) C))) (A (-> (or Bm Cm) Dm)) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-85315
in-theory        85315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (A -> A))
theorem-size     19
proof            (modus-ponens tm-316 tm-932 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85315.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (A -> A)), M:tm-316, m:tm-932, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85316
in-theory        85316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85316.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85317
in-theory        85317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A -> (not (((B or C) -> D) -> ((C or (B or C)) -> D)))) -> (not A)))
theorem-size     35
proof            (modus-ponens tm-313 tm-932 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85317.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A -> (not (((B or C) -> D) -> ((C or (B or C)) -> D)))) -> (not A))), M:tm-313, m:tm-932, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85318
in-theory        85318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E) -> ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-932 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85318.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E) -> ((A or (((B or C) -> D) -> ((C or (B or C)) -> D))) -> E))), M:tm-312, m:tm-932, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85319
in-theory        85319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E or (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-50.           (((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-85319.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E or (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-311, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85320
in-theory        85320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85320.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) or E)), M:tm-310, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85321
in-theory        85321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85321.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and E))), M:tm-309, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85322
in-theory        85322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A -> ((B or C) -> D)) -> (A -> ((C or (B or C)) -> D))))
theorem-size     33
proof            (modus-ponens tm-306 tm-932 ((A Am) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-306.          ((A -> (B -> C)) -> ((A -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85322.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and ((A -> ((B or C) -> D)) -> (A -> ((C or (B or C)) -> D)))), M:tm-306, m:tm-932, u:((A Am) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-85323
in-theory        85323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-50.           (((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-85323.        ((A -> (((B or C) -> D) -> ((C or (B or C)) -> D))) and (E -> (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))))), M:tm-305, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85324
in-theory        85324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-303 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85324.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-303, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85325
in-theory        85325
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-300 tm-932 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85325.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-300, m:tm-932, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85326
in-theory        85326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-270 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85326.        ((A -> (((B and C) -> C) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-270, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85327
in-theory        85327
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-267 tm-932 ((Am (and (-> (and A B) B) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85327.        ((A or (((B and C) -> C) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-267, m:tm-932, u:((Am (and (-> (and A B) B) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85328
in-theory        85328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-239 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85328.        ((A -> (((B and C) -> B) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-239, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85329
in-theory        85329
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-236 tm-932 ((Am (and (-> (and A B) A) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85329.        ((A or (((B and C) -> B) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-236, m:tm-932, u:((Am (and (-> (and A B) A) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85330
in-theory        85330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-210 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85330.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-210, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85331
in-theory        85331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-207 tm-932 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85331.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-207, m:tm-932, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85332
in-theory        85332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-183 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85332.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-183, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85333
in-theory        85333
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-180 tm-932 ((Am (and (-> A (-> B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85333.        ((A or ((B -> (C -> B)) and A)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-180, m:tm-932, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85334
in-theory        85334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-157 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85334.        ((A -> ((B and C) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-157, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85335
in-theory        85335
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-154 tm-932 ((Am (-> (and A B) B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-4 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-4.            ((A 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-50.           (((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-85335.        ((A or ((B and C) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-154, m:tm-932, u:((Am (-> (and A B) B)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85336
in-theory        85336
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or C) -> D)) -> ((C or (B or C)) -> D))
theorem-size     15
proof            (modus-ponens tm-152 tm-932 ((Am (and A (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85336.        ((A and ((B or C) -> D)) -> ((C or (B or C)) -> D)), M:tm-152, m:tm-932, u:((Am (and A (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-85337
in-theory        85337
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-147 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85337.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-147, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85338
in-theory        85338
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-144 tm-932 ((Am (-> (and A (-> B C)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85338.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-144, m:tm-932, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85339
in-theory        85339
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E)) -> (((B or C) -> D) -> ((C or (B or C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-142 tm-932 ((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) C))) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85339.        ((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> E)) -> (((B or C) -> D) -> ((C or (B or C)) -> D))), M:tm-142, m:tm-932, u:((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) C))) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85340
in-theory        85340
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> ((B or C) -> D))) -> ((C or (B or C)) -> D))
theorem-size     29
proof            (modus-ponens tm-141 tm-932 ((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or Bm Cm) Dm)))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-4 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85340.        ((A and ((((B or C) -> D) -> ((C or (B or C)) -> D)) -> ((B or C) -> D))) -> ((C or (B or C)) -> D)), M:tm-141, m:tm-932, u:((Am (and A (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or Bm Cm) Dm)))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-85341
in-theory        85341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-134 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85341.        ((A -> ((B and C) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-134, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85342
in-theory        85342
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-131 tm-932 ((Am (-> (and A B) A)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-3 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-3.            ((A 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-50.           (((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-85342.        ((A or ((B and C) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-131, m:tm-932, u:((Am (-> (and A B) A)) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85343
in-theory        85343
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) and D) -> ((B or (A or B)) -> C))
theorem-size     15
proof            (modus-ponens tm-129 tm-932 ((Am (and (-> (or Bm Cm) Dm) B)) (A (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85343.        ((((A or B) -> C) and D) -> ((B or (A or B)) -> C)), M:tm-129, m:tm-932, u:((Am (and (-> (or Bm Cm) Dm) B)) (A (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-85344
in-theory        85344
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-125 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85344.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-125, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85345
in-theory        85345
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-122 tm-932 ((Am (-> (and (-> A B) C) B)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85345.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-122, m:tm-932, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85346
in-theory        85346
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) and E) -> (((A or B) -> C) -> ((B or (A or B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-120 tm-932 ((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B) C)) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85346.        ((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) and E) -> (((A or B) -> C) -> ((B or (A or B)) -> C))), M:tm-120, m:tm-932, u:((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B) C)) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85347
in-theory        85347
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> ((A or B) -> C)) and D) -> ((B or (A or B)) -> C))
theorem-size     29
proof            (modus-ponens tm-119 tm-932 ((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or Bm Cm) Dm)) C)) (A (-> (or Bm Cm) Dm)) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85347.        ((((((A or B) -> C) -> ((B or (A or B)) -> C)) -> ((A or B) -> C)) and D) -> ((B or (A or B)) -> C)), M:tm-119, m:tm-932, u:((Am (and (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or Bm Cm) Dm)) C)) (A (-> (or Bm Cm) Dm)) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-85348
in-theory        85348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-113 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85348.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-113, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85349
in-theory        85349
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-110 tm-932 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85349.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-110, m:tm-932, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85350
in-theory        85350
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-106 tm-932 ((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> (or Bm Cm) Dm) (or Cm (or Bm Cm))))) (A (-> (or Bm Cm) Dm)) (B (or Cm (or Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85350.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> (((A or B) -> C) -> (B or (A or B)))) -> (((A or B) -> C) -> C)), M:tm-106, m:tm-932, u:((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> (or Bm Cm) Dm) (or Cm (or Bm Cm))))) (A (-> (or Bm Cm) Dm)) (B (or Cm (or Bm Cm))) (C Dm))
================================================================
tm-name          tm-85351
in-theory        85351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-105 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85351.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-105, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85352
in-theory        85352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-102 tm-932 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85352.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-102, m:tm-932, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85353
in-theory        85353
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (((B or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-100 tm-932 ((Am (-> (-> (or Bm Cm) Dm) (-> (-> (or Cm (or Bm Cm)) Dm) C))) (A (-> (or Bm Cm) Dm)) (B (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85353.        ((((A or B) -> C) -> (((B or (A or B)) -> C) -> D)) -> (((A or B) -> C) -> ((B or (A or B)) -> C))), M:tm-100, m:tm-932, u:((Am (-> (-> (or Bm Cm) Dm) (-> (-> (or Cm (or Bm Cm)) Dm) C))) (A (-> (or Bm Cm) Dm)) (B (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-85354
in-theory        85354
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> A))
theorem-size     9
proof            (modus-ponens tm-98 tm-932 ((Dm Am) (B (or Bm Cm)) (A Am) (C (-> (or Cm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85354.        (A -> ((B or (C or B)) -> A)), M:tm-98, m:tm-932, u:((Dm Am) (B (or Bm Cm)) (A Am) (C (-> (or Cm (or Bm Cm)) Am)))
================================================================
tm-name          tm-85355
in-theory        85355
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) -> (((A or B) -> C) -> ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-96 tm-932 ((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B)) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85355.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) -> (((A or B) -> C) -> ((B or (A or B)) -> C))), M:tm-96, m:tm-932, u:((Am (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B)) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85356
in-theory        85356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-95 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-85356.        (((A -> B) -> (A -> A)) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-95, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85357
in-theory        85357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-92 tm-932 ((Am (-> A A)) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 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-1.            (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-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-85357.        (((A -> B) or (A -> A)) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-92, m:tm-932, u:((Am (-> A A)) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85358
in-theory        85358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-83 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85358.        ((A -> (B -> (C -> B))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-83, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85359
in-theory        85359
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-80 tm-932 ((Am (-> A (-> B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((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-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-85359.        ((A or (B -> (C -> B))) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-80, m:tm-932, u:((Am (-> A (-> B A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85360
in-theory        85360
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D))) -> D)
theorem-size     19
proof            (modus-ponens tm-77 tm-932 ((Am (not (not (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B)))) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85360.        ((not (not ((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D))) -> D), M:tm-77, m:tm-932, u:((Am (not (not (-> (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) B)))) (A (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85361
in-theory        85361
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C or D) -> E) -> ((D or (C or D)) -> E))))
theorem-size     21
proof            (modus-ponens tm-76 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85361.        (((not (not A)) -> A) and (B -> (((C or D) -> E) -> ((D or (C or D)) -> E)))), M:tm-76, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85362
in-theory        85362
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B or C) -> D) -> ((C or (B or C)) -> D)))
theorem-size     19
proof            (modus-ponens tm-73 tm-932 ((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85362.        (((not (not A)) or A) -> (((B or C) -> D) -> ((C or (B or C)) -> D))), M:tm-73, m:tm-932, u:((A Am) (B (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85363
in-theory        85363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-69 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8 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-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-85363.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-69, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85364
in-theory        85364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-66 tm-932 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85364.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-66, m:tm-932, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85365
in-theory        85365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or C) -> D)) -> ((A or ((B or C) -> D)) -> ((C or (B or C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-55 tm-932 ((Am (-> A (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85365.        ((A -> ((B or C) -> D)) -> ((A or ((B or C) -> D)) -> ((C or (B or C)) -> D))), M:tm-55, m:tm-932, u:((Am (-> A (-> (or Bm Cm) Dm))) (B (-> (or Bm Cm) Dm)) (C (-> (or Cm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-85366
in-theory        85366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-54 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (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-54.           (A -> (((B -> C) -> ((C -> 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-50.           (((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-85366.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-54, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-85367
in-theory        85367
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-51 tm-932 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-85367.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-51, m:tm-932, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-85368
in-theory        85368
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D or B))) -> ((D or B) -> (C -> (D or B)))))
theorem-size     19
proof            (modus-ponens tm-933 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       133
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-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-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-85368.        (A -> ((B -> (C -> (D or B))) -> ((D or B) -> (C -> (D or B))))), M:tm-933, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-85369
in-theory        85369
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> ((D or B) and C))) -> ((D or B) -> (C -> ((D or B) and C)))))
theorem-size     23
proof            (modus-ponens tm-933 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       143
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-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-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-85369.        (A -> ((B -> (C -> ((D or B) and C))) -> ((D or B) -> (C -> ((D or B) and C))))), M:tm-933, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-85370
in-theory        85370
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or B) or D)) -> ((C or B) -> ((C or B) or D))))
theorem-size     19
proof            (modus-ponens tm-933 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       133
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-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-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-85370.        (A -> ((B -> ((C or B) or D)) -> ((C or B) -> ((C or B) or D)))), M:tm-933, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-85371
in-theory        85371
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or (D or B))) -> ((D or B) -> (C or (D or B)))))
theorem-size     19
proof            (modus-ponens tm-933 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       133
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-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-7.            (A -> (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-85371.        (A -> ((B -> (C or (D or B))) -> ((D or B) -> (C or (D or B))))), M:tm-933, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-85372
in-theory        85372
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-930 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85372.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85373
in-theory        85373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     61
proof            (modus-ponens tm-920 tm-933 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85373.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C))))), M:tm-920, m:tm-933, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85374
in-theory        85374
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-893 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85374.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85375
in-theory        85375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     55
proof            (modus-ponens tm-882 tm-933 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85375.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C))))), M:tm-882, m:tm-933, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85376
in-theory        85376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-855 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85376.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85377
in-theory        85377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-808 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85377.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85378
in-theory        85378
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     67
proof            (modus-ponens tm-798 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85378.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C))))), M:tm-798, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85379
in-theory        85379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-85379.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85380
in-theory        85380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     67
proof            (modus-ponens tm-747 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-85380.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C))))), M:tm-747, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85381
in-theory        85381
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85381.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85382
in-theory        85382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-85382.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85383
in-theory        85383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     27
proof            (modus-ponens tm-623 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85383.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> ((B -> C) -> ((A or B) -> C))))), M:tm-623, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85384
in-theory        85384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85384.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85385
in-theory        85385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85385.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (F or E))), M:tm-609, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85386
in-theory        85386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-85386.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85387
in-theory        85387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-85387.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-595, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85388
in-theory        85388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-85388.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85389
in-theory        85389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-85389.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85390
in-theory        85390
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-85390.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85391
in-theory        85391
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-85391.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85392
in-theory        85392
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-85392.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85393
in-theory        85393
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-85393.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85394
in-theory        85394
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85394.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85395
in-theory        85395
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85395.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85396
in-theory        85396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((B -> C) -> ((A or B) -> C))) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85396.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((B -> C) -> ((A or B) -> C))) or E)), M:tm-470, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85397
in-theory        85397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85397.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85398
in-theory        85398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85398.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (E or F))), M:tm-456, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85399
in-theory        85399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-85399.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85400
in-theory        85400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-85400.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-443, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85401
in-theory        85401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-85401.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85402
in-theory        85402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-85402.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85403
in-theory        85403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-85403.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85404
in-theory        85404
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-85404.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85405
in-theory        85405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85405.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85406
in-theory        85406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85406.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85407
in-theory        85407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85407.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85408
in-theory        85408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85408.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85409
in-theory        85409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85409.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85410
in-theory        85410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-85410.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85411
in-theory        85411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-328 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) 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-328.          ((A -> 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-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-85411.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85412
in-theory        85412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-85412.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-327, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85413
in-theory        85413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-85413.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-326, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85414
in-theory        85414
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-85414.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-325, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85415
in-theory        85415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-85415.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-324, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85416
in-theory        85416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85416.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-323, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85417
in-theory        85417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85417.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E and F) -> F)), M:tm-322, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85418
in-theory        85418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85418.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E and F) -> E)), M:tm-320, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85419
in-theory        85419
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85419.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85420
in-theory        85420
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-316 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85420.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85421
in-theory        85421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85421.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (F -> E))), M:tm-315, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85422
in-theory        85422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     67
proof            (modus-ponens tm-313 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85422.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85423
in-theory        85423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((D -> ((B -> C) -> ((A or B) -> C))) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> ((B -> C) -> ((A or B) -> C)))) -> E)))
theorem-size     67
proof            (modus-ponens tm-312 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85423.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (((D -> ((B -> C) -> ((A or B) -> C))) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> ((B -> C) -> ((A or B) -> C)))) -> E))), M:tm-312, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85424
in-theory        85424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-85424.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-311, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85425
in-theory        85425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-85425.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) or E)), M:tm-310, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85426
in-theory        85426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-85426.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and E))), M:tm-309, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85427
in-theory        85427
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-306 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85427.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((A or B) -> C))))), M:tm-306, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-85428
in-theory        85428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85428.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))))), M:tm-305, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85429
in-theory        85429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85429.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85430
in-theory        85430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85430.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85431
in-theory        85431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85431.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85432
in-theory        85432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85432.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85433
in-theory        85433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85433.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85434
in-theory        85434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85434.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85435
in-theory        85435
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85435.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85436
in-theory        85436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85436.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85437
in-theory        85437
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85437.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85438
in-theory        85438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (B -> C)) -> (D -> ((A or B) -> C))))
theorem-size     27
proof            (modus-ponens tm-114 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Bm Cm)) (D (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-1 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-14.           (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-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-85438.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (B -> C)) -> (D -> ((A or B) -> C)))), M:tm-114, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Bm Cm)) (D (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-85439
in-theory        85439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85439.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85440
in-theory        85440
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85440.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85441
in-theory        85441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85441.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85442
in-theory        85442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     27
proof            (modus-ponens tm-84 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85442.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> ((B -> C) -> ((A or B) -> C))))), M:tm-84, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85443
in-theory        85443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85443.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85444
in-theory        85444
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85444.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85445
in-theory        85445
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-73 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85445.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C)))), M:tm-73, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85446
in-theory        85446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85446.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85447
in-theory        85447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85447.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85448
in-theory        85448
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> ((A -> B) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-50 tm-933 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       149
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85448.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-933, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85449
in-theory        85449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-49 tm-933 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       143
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85449.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> ((B -> C) -> ((A or B) -> C)))), M:tm-49, m:tm-933, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85450
in-theory        85450
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> ((C -> D) -> ((B or C) -> D))))
theorem-size     41
proof            (modus-ponens tm-47 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85450.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85451
in-theory        85451
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-46 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85451.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85452
in-theory        85452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85452.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85453
in-theory        85453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85453.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85454
in-theory        85454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     39
proof            (modus-ponens tm-24 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85454.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85455
in-theory        85455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85455.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85456
in-theory        85456
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85456.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85457
in-theory        85457
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85457.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85458
in-theory        85458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85458.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85459
in-theory        85459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85459.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85460
in-theory        85460
times-derived    27
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))
theorem-size     27
proof            (modus-ponens tm-12 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85460.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))), M:tm-12, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85461
in-theory        85461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-9 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85461.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85462
in-theory        85462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> ((D or B) -> C))) -> E) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) or (A -> ((B -> C) -> ((D or B) -> C)))) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-1)
proof-size       137
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-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-85462.        (((A -> ((B -> C) -> ((D or B) -> C))) -> E) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) or (A -> ((B -> C) -> ((D or B) -> C)))) -> E)), M:tm-8, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85463
in-theory        85463
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85463.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85464
in-theory        85464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85464.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))) or E), M:tm-6, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85465
in-theory        85465
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85465.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85466
in-theory        85466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-2 tm-933 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85466.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((A or B) -> C)))), M:tm-2, m:tm-933, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-85467
in-theory        85467
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8)
proof-size       115
proof-steps      7
----------------------------------------------------------------
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-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-85467.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85468
in-theory        85468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or A))) -> (C or A)) -> ((A -> (B -> (C or A))) -> (B -> (C or A))))
theorem-size     25
proof            (modus-ponens tm-934 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-2 tm-7 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-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-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-85468.        (((A -> (B -> (C or A))) -> (C or A)) -> ((A -> (B -> (C or A))) -> (B -> (C or A)))), M:tm-934, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-85469
in-theory        85469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> ((C or A) and B))) -> (C or A)) -> ((A -> (B -> ((C or A) and B))) -> (B -> ((C or A) and B))))
theorem-size     31
proof            (modus-ponens tm-934 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 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-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-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-85469.        (((A -> (B -> ((C or A) and B))) -> (C or A)) -> ((A -> (B -> ((C or A) and B))) -> (B -> ((C or A) and B)))), M:tm-934, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-85470
in-theory        85470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) or C)) -> (B or A)) -> ((A -> ((B or A) or C)) -> ((B or A) or C)))
theorem-size     25
proof            (modus-ponens tm-934 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-2 tm-7 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-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-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-85470.        (((A -> ((B or A) or C)) -> (B or A)) -> ((A -> ((B or A) or C)) -> ((B or A) or C))), M:tm-934, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-85471
in-theory        85471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or (C or A))) -> (C or A)) -> ((A -> (B or (C or A))) -> (B or (C or A))))
theorem-size     25
proof            (modus-ponens tm-934 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-2 tm-7 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-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-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-85471.        (((A -> (B or (C or A))) -> (C or A)) -> ((A -> (B or (C or A))) -> (B or (C or A)))), M:tm-934, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-85472
in-theory        85472
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     41
proof            (modus-ponens tm-930 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85472.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-930, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85473
in-theory        85473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))
theorem-size     65
proof            (modus-ponens tm-920 tm-934 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85473.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))), M:tm-920, m:tm-934, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85474
in-theory        85474
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     41
proof            (modus-ponens tm-893 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85474.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-893, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85475
in-theory        85475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))
theorem-size     59
proof            (modus-ponens tm-882 tm-934 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85475.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))), M:tm-882, m:tm-934, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85476
in-theory        85476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     45
proof            (modus-ponens tm-855 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85476.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-855, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85477
in-theory        85477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     39
proof            (modus-ponens tm-808 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85477.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-808, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85478
in-theory        85478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))
theorem-size     71
proof            (modus-ponens tm-798 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85478.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))), M:tm-798, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85479
in-theory        85479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     39
proof            (modus-ponens tm-757 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-85479.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-757, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85480
in-theory        85480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))
theorem-size     71
proof            (modus-ponens tm-747 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85480.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))), M:tm-747, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85481
in-theory        85481
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G))))
theorem-size     53
proof            (modus-ponens tm-708 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-85481.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G)))), M:tm-708, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85482
in-theory        85482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     41
proof            (modus-ponens tm-665 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-85482.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-665, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85483
in-theory        85483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((B -> C) -> (A or B)) -> ((B -> C) -> C))))
theorem-size     29
proof            (modus-ponens tm-623 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85483.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((B -> C) -> (A or B)) -> ((B -> C) -> C)))), M:tm-623, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85484
in-theory        85484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-622 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85484.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-622, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85485
in-theory        85485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (E or D)))
theorem-size     33
proof            (modus-ponens tm-609 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85485.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (E or D))), M:tm-609, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85486
in-theory        85486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     37
proof            (modus-ponens tm-605 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-85486.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-605, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85487
in-theory        85487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-85487.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-595, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85488
in-theory        85488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-550 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-85488.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-550, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85489
in-theory        85489
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-540 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-85489.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-540, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85490
in-theory        85490
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-530 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-85490.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-530, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85491
in-theory        85491
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     37
proof            (modus-ponens tm-520 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-85491.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-520, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85492
in-theory        85492
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-510 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-85492.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-510, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85493
in-theory        85493
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-500 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-85493.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-500, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85494
in-theory        85494
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G))))
theorem-size     43
proof            (modus-ponens tm-490 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-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-85494.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G)))), M:tm-490, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85495
in-theory        85495
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-480 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-85495.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-480, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85496
in-theory        85496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) -> (A or B)) -> ((B -> C) -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-470 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85496.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) -> (A or B)) -> ((B -> C) -> C)) or D)), M:tm-470, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85497
in-theory        85497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-469 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85497.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-469, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85498
in-theory        85498
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (D or E)))
theorem-size     33
proof            (modus-ponens tm-456 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85498.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (D or E))), M:tm-456, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85499
in-theory        85499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     37
proof            (modus-ponens tm-453 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-85499.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-453, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85500
in-theory        85500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-85500.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-443, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85501
in-theory        85501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-409 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-85501.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-409, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85502
in-theory        85502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     37
proof            (modus-ponens tm-400 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-85502.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-400, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85503
in-theory        85503
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-391 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-85503.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-391, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85504
in-theory        85504
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-382 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-85504.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-382, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85505
in-theory        85505
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G))))
theorem-size     43
proof            (modus-ponens tm-373 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-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-85505.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G)))), M:tm-373, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85506
in-theory        85506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-364 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-85506.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-364, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85507
in-theory        85507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((B -> C) -> (A or B)) -> ((B -> C) -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       169
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85507.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((B -> C) -> (A or B)) -> ((B -> C) -> C)) and D))), M:tm-355, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85508
in-theory        85508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     37
proof            (modus-ponens tm-354 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-85508.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-354, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85509
in-theory        85509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (E -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-341 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-85509.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85510
in-theory        85510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E))))
theorem-size     37
proof            (modus-ponens tm-338 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-85510.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E)))), M:tm-338, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85511
in-theory        85511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     69
proof            (modus-ponens tm-328 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
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-328.          ((A -> 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-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-85511.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-328, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85512
in-theory        85512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-85512.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-327, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85513
in-theory        85513
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-85513.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-326, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85514
in-theory        85514
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-85514.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-325, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85515
in-theory        85515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-85515.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-324, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85516
in-theory        85516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-85516.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-323, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85517
in-theory        85517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D and E) -> E))
theorem-size     33
proof            (modus-ponens tm-322 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85517.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85518
in-theory        85518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D and E) -> D))
theorem-size     33
proof            (modus-ponens tm-320 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85518.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85519
in-theory        85519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-318 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-85519.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85520
in-theory        85520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85520.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85521
in-theory        85521
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (E -> D)))
theorem-size     33
proof            (modus-ponens tm-315 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85521.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85522
in-theory        85522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> (A or B)) -> ((B -> C) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-85522.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> (A or B)) -> ((B -> C) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85523
in-theory        85523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((((B -> C) -> (A or B)) -> ((B -> C) -> C)) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((B -> C) -> (A or B)) -> ((B -> C) -> C))) -> D)))
theorem-size     73
proof            (modus-ponens tm-312 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-85523.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (((((B -> C) -> (A or B)) -> ((B -> C) -> C)) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((B -> C) -> (A or B)) -> ((B -> C) -> C))) -> D))), M:tm-312, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85524
in-theory        85524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-85524.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-311, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85525
in-theory        85525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) or D))
theorem-size     57
proof            (modus-ponens tm-310 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-85525.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) or D)), M:tm-310, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85526
in-theory        85526
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and D)))
theorem-size     59
proof            (modus-ponens tm-309 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) 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-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-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-85526.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and D))), M:tm-309, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85527
in-theory        85527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (A or B))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> C))))
theorem-size     69
proof            (modus-ponens tm-306 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (or Am Bm))) (C (-> (-> Bm Cm) 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-85527.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (A or B))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> C)))), M:tm-306, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (or Am Bm))) (C (-> (-> Bm Cm) Cm)))
================================================================
tm-name          tm-85528
in-theory        85528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-85528.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))), M:tm-305, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85529
in-theory        85529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     39
proof            (modus-ponens tm-303 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-85529.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-303, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85530
in-theory        85530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     37
proof            (modus-ponens tm-270 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-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-85530.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-270, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85531
in-theory        85531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     37
proof            (modus-ponens tm-239 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-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-85531.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-239, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85532
in-theory        85532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G))))
theorem-size     45
proof            (modus-ponens tm-210 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-85532.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G)))), M:tm-210, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85533
in-theory        85533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     37
proof            (modus-ponens tm-183 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-85533.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-183, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85534
in-theory        85534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-157 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85534.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-157, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85535
in-theory        85535
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     43
proof            (modus-ponens tm-147 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-85535.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-147, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85536
in-theory        85536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-134 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85536.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-134, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85537
in-theory        85537
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     43
proof            (modus-ponens tm-125 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-85537.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-125, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85538
in-theory        85538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) -> (A or B)) -> (B -> C)) -> (((B -> C) -> (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-114 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (or Am Bm))) (C (-> Bm Cm)) (D Cm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85538.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) -> (A or B)) -> (B -> C)) -> (((B -> C) -> (A or B)) -> C))), M:tm-114, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (or Am Bm))) (C (-> Bm Cm)) (D Cm))
================================================================
tm-name          tm-85539
in-theory        85539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G))))
theorem-size     43
proof            (modus-ponens tm-113 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-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-85539.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G)))), M:tm-113, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85540
in-theory        85540
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     47
proof            (modus-ponens tm-105 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-85540.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-105, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85541
in-theory        85541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E))))
theorem-size     35
proof            (modus-ponens tm-95 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-85541.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E)))), M:tm-95, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85542
in-theory        85542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))))
theorem-size     29
proof            (modus-ponens tm-84 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85542.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))), M:tm-84, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85543
in-theory        85543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     35
proof            (modus-ponens tm-83 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85543.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-83, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85544
in-theory        85544
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D))))
theorem-size     33
proof            (modus-ponens tm-76 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-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-85544.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D)))), M:tm-76, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85545
in-theory        85545
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))
theorem-size     43
proof            (modus-ponens tm-73 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       165
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85545.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))), M:tm-73, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85546
in-theory        85546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E))))
theorem-size     39
proof            (modus-ponens tm-69 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-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-85546.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E)))), M:tm-69, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85547
in-theory        85547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     41
proof            (modus-ponens tm-54 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-85547.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-54, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85548
in-theory        85548
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B)))
theorem-size     37
proof            (modus-ponens tm-50 tm-934 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85548.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B))), M:tm-50, m:tm-934, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85549
in-theory        85549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))
theorem-size     31
proof            (modus-ponens tm-49 tm-934 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-8 tm-6 tm-2)
proof-size       155
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85549.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))), M:tm-49, m:tm-934, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85550
in-theory        85550
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D)))
theorem-size     43
proof            (modus-ponens tm-47 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       165
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85550.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D))), M:tm-47, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85551
in-theory        85551
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))
theorem-size     43
proof            (modus-ponens tm-46 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       165
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85551.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))), M:tm-46, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85552
in-theory        85552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E))))
theorem-size     33
proof            (modus-ponens tm-42 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-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-85552.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E)))), M:tm-42, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85553
in-theory        85553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E))))
theorem-size     33
proof            (modus-ponens tm-32 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-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-85553.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E)))), M:tm-32, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85554
in-theory        85554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> (A or B)) -> ((B -> C) -> C))))
theorem-size     41
proof            (modus-ponens tm-24 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-85554.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> (A or B)) -> ((B -> C) -> C)))), M:tm-24, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85555
in-theory        85555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E))))
theorem-size     35
proof            (modus-ponens tm-23 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85555.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E)))), M:tm-23, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85556
in-theory        85556
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E))))
theorem-size     33
proof            (modus-ponens tm-22 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-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-85556.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E)))), M:tm-22, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85557
in-theory        85557
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E))))
theorem-size     33
proof            (modus-ponens tm-21 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-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-85557.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E)))), M:tm-21, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85558
in-theory        85558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F))))
theorem-size     41
proof            (modus-ponens tm-20 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-85558.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (D or E)) -> ((E -> F) -> F)))), M:tm-20, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85559
in-theory        85559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E))))
theorem-size     33
proof            (modus-ponens tm-19 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-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-85559.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (C or D)) -> ((D -> E) -> E)))), M:tm-19, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85560
in-theory        85560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> (A or B)) -> ((B -> C) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85560.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> (A or B)) -> ((B -> C) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85561
in-theory        85561
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (C or A)) -> ((A -> B) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or (((A -> B) -> (C or A)) -> ((A -> B) -> B))) -> D))
theorem-size     45
proof            (modus-ponens tm-8 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) 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-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-85561.        (((((A -> B) -> (C or A)) -> ((A -> B) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or (((A -> B) -> (C or A)) -> ((A -> B) -> B))) -> D)), M:tm-8, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-85562
in-theory        85562
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D))))
theorem-size     29
proof            (modus-ponens tm-7 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       127
proof-steps      7
----------------------------------------------------------------
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-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-85562.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D)))), M:tm-7, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85563
in-theory        85563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) or D)
theorem-size     29
proof            (modus-ponens tm-6 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       127
proof-steps      7
----------------------------------------------------------------
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-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-85563.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))) or D), M:tm-6, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85564
in-theory        85564
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85564.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D))) and A)), M:tm-5, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85565
in-theory        85565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (A or B))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> C)))
theorem-size     41
proof            (modus-ponens tm-2 tm-934 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (or Am Bm))) (C (-> (-> Bm Cm) Cm))))
axioms-used      (tm-2 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85565.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (A or B))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> C))), M:tm-2, m:tm-934, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (or Am Bm))) (C (-> (-> Bm Cm) Cm)))
================================================================
tm-name          tm-85566
in-theory        85566
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D))))
theorem-size     29
proof            (modus-ponens tm-1 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       127
proof-steps      7
----------------------------------------------------------------
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-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-85566.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D)))), M:tm-1, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-85567
in-theory        85567
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (D or B))) -> ((D or B) -> (C -> (D or B)))) and A))
theorem-size     21
proof            (modus-ponens tm-935 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       139
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-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-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-85567.        (A -> (((B -> (C -> (D or B))) -> ((D or B) -> (C -> (D or B)))) and A)), M:tm-935, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-85568
in-theory        85568
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> ((D or B) and C))) -> ((D or B) -> (C -> ((D or B) and C)))) and A))
theorem-size     25
proof            (modus-ponens tm-935 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 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-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-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-85568.        (A -> (((B -> (C -> ((D or B) and C))) -> ((D or B) -> (C -> ((D or B) and C)))) and A)), M:tm-935, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-85569
in-theory        85569
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C or B) or D)) -> ((C or B) -> ((C or B) or D))) and A))
theorem-size     21
proof            (modus-ponens tm-935 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       139
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-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-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-85569.        (A -> (((B -> ((C or B) or D)) -> ((C or B) -> ((C or B) or D))) and A)), M:tm-935, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-85570
in-theory        85570
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or (D or B))) -> ((D or B) -> (C or (D or B)))) and A))
theorem-size     21
proof            (modus-ponens tm-935 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       139
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-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-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-85570.        (A -> (((B -> (C or (D or B))) -> ((D or B) -> (C or (D or B)))) and A)), M:tm-935, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-85571
in-theory        85571
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     41
proof            (modus-ponens tm-930 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85571.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-930, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85572
in-theory        85572
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))
theorem-size     65
proof            (modus-ponens tm-920 tm-935 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85572.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))), M:tm-920, m:tm-935, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85573
in-theory        85573
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     41
proof            (modus-ponens tm-893 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85573.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-893, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85574
in-theory        85574
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))
theorem-size     59
proof            (modus-ponens tm-882 tm-935 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85574.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))), M:tm-882, m:tm-935, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85575
in-theory        85575
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     45
proof            (modus-ponens tm-855 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85575.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-855, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85576
in-theory        85576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     39
proof            (modus-ponens tm-808 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85576.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-808, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85577
in-theory        85577
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))
theorem-size     71
proof            (modus-ponens tm-798 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85577.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))), M:tm-798, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85578
in-theory        85578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     39
proof            (modus-ponens tm-757 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-85578.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-757, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85579
in-theory        85579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))
theorem-size     71
proof            (modus-ponens tm-747 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-85579.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))), M:tm-747, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85580
in-theory        85580
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H))))
theorem-size     53
proof            (modus-ponens tm-708 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85580.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H)))), M:tm-708, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85581
in-theory        85581
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     41
proof            (modus-ponens tm-665 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85581.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-665, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85582
in-theory        85582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (((B -> C) -> ((A or B) -> C)) and E))))
theorem-size     29
proof            (modus-ponens tm-623 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85582.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (((B -> C) -> ((A or B) -> C)) and E)))), M:tm-623, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85583
in-theory        85583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-622 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85583.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-622, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85584
in-theory        85584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D or ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     39
proof            (modus-ponens tm-617 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85584.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D or ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-617, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
================================================================
tm-name          tm-85585
in-theory        85585
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-609 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85585.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (F or E))), M:tm-609, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85586
in-theory        85586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-605 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85586.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-605, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85587
in-theory        85587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-85587.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-595, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85588
in-theory        85588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-550 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85588.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-550, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85589
in-theory        85589
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-540 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85589.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-540, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85590
in-theory        85590
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-530 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85590.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-530, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85591
in-theory        85591
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-520 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85591.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-520, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85592
in-theory        85592
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-510 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85592.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-510, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85593
in-theory        85593
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-500 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85593.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-500, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85594
in-theory        85594
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H))))
theorem-size     43
proof            (modus-ponens tm-490 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85594.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H)))), M:tm-490, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85595
in-theory        85595
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-480 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85595.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-480, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85596
in-theory        85596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((B -> C) -> ((A or B) -> C)) and D)) or E))
theorem-size     29
proof            (modus-ponens tm-470 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85596.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((B -> C) -> ((A or B) -> C)) and D)) or E)), M:tm-470, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85597
in-theory        85597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-469 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85597.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-469, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85598
in-theory        85598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     39
proof            (modus-ponens tm-464 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85598.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) or D))), M:tm-464, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))))
================================================================
tm-name          tm-85599
in-theory        85599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-456 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85599.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (E or F))), M:tm-456, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85600
in-theory        85600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-453 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85600.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-453, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85601
in-theory        85601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-85601.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-443, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85602
in-theory        85602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-409 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85602.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-409, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85603
in-theory        85603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-400 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85603.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-400, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85604
in-theory        85604
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-391 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85604.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-391, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85605
in-theory        85605
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-382 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85605.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-382, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85606
in-theory        85606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H))))
theorem-size     43
proof            (modus-ponens tm-373 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85606.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H)))), M:tm-373, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85607
in-theory        85607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-364 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85607.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-364, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85608
in-theory        85608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (((B -> C) -> ((A or B) -> C)) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85608.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (((B -> C) -> ((A or B) -> C)) and E)) and D))), M:tm-355, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85609
in-theory        85609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-354 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85609.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-354, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85610
in-theory        85610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and D))))
theorem-size     41
proof            (modus-ponens tm-349 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85610.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and D)))), M:tm-349, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)))))
================================================================
tm-name          tm-85611
in-theory        85611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-341 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-85611.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85612
in-theory        85612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F))))
theorem-size     37
proof            (modus-ponens tm-338 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85612.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F)))), M:tm-338, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85613
in-theory        85613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     69
proof            (modus-ponens tm-328 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) 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-328.          ((A -> 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-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-85613.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-328, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85614
in-theory        85614
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-85614.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-327, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85615
in-theory        85615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-85615.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-326, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85616
in-theory        85616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-85616.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-325, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85617
in-theory        85617
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-85617.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-324, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85618
in-theory        85618
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-85618.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-323, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85619
in-theory        85619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-322 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85619.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E and F) -> F)), M:tm-322, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85620
in-theory        85620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-320 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85620.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E and F) -> E)), M:tm-320, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85621
in-theory        85621
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-318 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-85621.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85622
in-theory        85622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-85622.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85623
in-theory        85623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-315 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85623.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (F -> E))), M:tm-315, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85624
in-theory        85624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (((B -> C) -> ((A or B) -> C)) and D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-85624.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (((B -> C) -> ((A or B) -> C)) and D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85625
in-theory        85625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((D -> (((B -> C) -> ((A or B) -> C)) and D)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (((B -> C) -> ((A or B) -> C)) and D))) -> E)))
theorem-size     73
proof            (modus-ponens tm-312 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-85625.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (((D -> (((B -> C) -> ((A or B) -> C)) and D)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (((B -> C) -> ((A or B) -> C)) and D))) -> E))), M:tm-312, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85626
in-theory        85626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
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-7.            (A -> (B or 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-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-85626.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-311, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85627
in-theory        85627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) or E))
theorem-size     57
proof            (modus-ponens tm-310 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
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-6.            (A -> (A or 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-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-85627.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) or E)), M:tm-310, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85628
in-theory        85628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and E)))
theorem-size     59
proof            (modus-ponens tm-309 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or 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-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-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-85628.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and E))), M:tm-309, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85629
in-theory        85629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and D))))
theorem-size     69
proof            (modus-ponens tm-306 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-85629.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and D)))), M:tm-306, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85630
in-theory        85630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
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-1.            (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-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-85630.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))))), M:tm-305, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85631
in-theory        85631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     39
proof            (modus-ponens tm-303 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85631.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-303, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85632
in-theory        85632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-270 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85632.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-270, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85633
in-theory        85633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-239 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85633.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-239, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85634
in-theory        85634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H))))
theorem-size     45
proof            (modus-ponens tm-210 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85634.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H)))), M:tm-210, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85635
in-theory        85635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-183 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85635.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-183, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85636
in-theory        85636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-157 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85636.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-157, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85637
in-theory        85637
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     43
proof            (modus-ponens tm-147 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85637.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-147, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85638
in-theory        85638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-134 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85638.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-134, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85639
in-theory        85639
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     43
proof            (modus-ponens tm-125 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85639.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-125, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85640
in-theory        85640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H))))
theorem-size     43
proof            (modus-ponens tm-113 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85640.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H)))), M:tm-113, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85641
in-theory        85641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     47
proof            (modus-ponens tm-105 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85641.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-105, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85642
in-theory        85642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     37
proof            (modus-ponens tm-99 tm-935 ((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       203
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85642.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-99, m:tm-935, u:((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85643
in-theory        85643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     39
proof            (modus-ponens tm-98 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85643.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-98, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
================================================================
tm-name          tm-85644
in-theory        85644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F))))
theorem-size     35
proof            (modus-ponens tm-95 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-85644.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F)))), M:tm-95, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85645
in-theory        85645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (((B -> C) -> ((A or B) -> C)) and E))))
theorem-size     29
proof            (modus-ponens tm-84 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85645.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (((B -> C) -> ((A or B) -> C)) and E)))), M:tm-84, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85646
in-theory        85646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-83 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85646.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-83, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85647
in-theory        85647
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E))))
theorem-size     33
proof            (modus-ponens tm-76 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85647.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E)))), M:tm-76, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85648
in-theory        85648
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))
theorem-size     43
proof            (modus-ponens tm-73 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-10 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85648.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))), M:tm-73, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85649
in-theory        85649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F))))
theorem-size     39
proof            (modus-ponens tm-69 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85649.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F)))), M:tm-69, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85650
in-theory        85650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     41
proof            (modus-ponens tm-54 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85650.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-54, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85651
in-theory        85651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (((A -> B) -> ((C or A) -> B)) and D)))
theorem-size     37
proof            (modus-ponens tm-50 tm-935 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85651.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (((A -> B) -> ((C or A) -> B)) and D))), M:tm-50, m:tm-935, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85652
in-theory        85652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-49 tm-935 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       149
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85652.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))), M:tm-49, m:tm-935, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85653
in-theory        85653
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E)))
theorem-size     43
proof            (modus-ponens tm-47 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85653.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E))), M:tm-47, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85654
in-theory        85654
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (((B -> C) -> ((A or B) -> C)) and E)))
theorem-size     43
proof            (modus-ponens tm-46 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85654.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (((B -> C) -> ((A or B) -> C)) and E))), M:tm-46, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85655
in-theory        85655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F))))
theorem-size     33
proof            (modus-ponens tm-42 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85655.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F)))), M:tm-42, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85656
in-theory        85656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F))))
theorem-size     33
proof            (modus-ponens tm-32 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85656.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F)))), M:tm-32, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85657
in-theory        85657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (((B -> C) -> ((A or B) -> C)) and D))))
theorem-size     41
proof            (modus-ponens tm-24 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) 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-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-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-85657.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (((B -> C) -> ((A or B) -> C)) and D)))), M:tm-24, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85658
in-theory        85658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F))))
theorem-size     35
proof            (modus-ponens tm-23 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85658.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F)))), M:tm-23, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85659
in-theory        85659
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F))))
theorem-size     33
proof            (modus-ponens tm-22 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85659.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F)))), M:tm-22, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85660
in-theory        85660
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F))))
theorem-size     33
proof            (modus-ponens tm-21 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85660.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F)))), M:tm-21, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85661
in-theory        85661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G))))
theorem-size     41
proof            (modus-ponens tm-20 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85661.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (((E -> F) -> ((D or E) -> F)) and G)))), M:tm-20, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85662
in-theory        85662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F))))
theorem-size     33
proof            (modus-ponens tm-19 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85662.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (((D -> E) -> ((C or D) -> E)) and F)))), M:tm-19, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85663
in-theory        85663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (((B -> C) -> ((A or B) -> C)) and D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-9 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85663.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (((B -> C) -> ((A or B) -> C)) and D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85664
in-theory        85664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> C) -> ((D or B) -> C)) and A)) -> E) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) or (A -> (((B -> C) -> ((D or B) -> C)) and A))) -> E))
theorem-size     45
proof            (modus-ponens tm-8 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-5)
proof-size       145
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-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-85664.        (((A -> (((B -> C) -> ((D or B) -> C)) and A)) -> E) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) or (A -> (((B -> C) -> ((D or B) -> C)) and A))) -> E)), M:tm-8, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85665
in-theory        85665
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E))))
theorem-size     29
proof            (modus-ponens tm-7 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-7 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85665.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E)))), M:tm-7, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85666
in-theory        85666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) or E)
theorem-size     29
proof            (modus-ponens tm-6 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-6 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85666.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))) or E), M:tm-6, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85667
in-theory        85667
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85667.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E))) and A)), M:tm-5, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85668
in-theory        85668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and D)))
theorem-size     41
proof            (modus-ponens tm-2 tm-935 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85668.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and D))), M:tm-2, m:tm-935, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85669
in-theory        85669
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E))))
theorem-size     29
proof            (modus-ponens tm-1 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       121
proof-steps      7
----------------------------------------------------------------
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-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-85669.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (((C -> D) -> ((B or C) -> D)) and E)))), M:tm-1, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85670
in-theory        85670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or A))) -> ((C or A) -> (B -> (C or A)))) or D)
theorem-size     19
proof            (modus-ponens tm-936 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-6 tm-7 tm-1)
proof-size       133
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-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-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-85670.        (((A -> (B -> (C or A))) -> ((C or A) -> (B -> (C or A)))) or D), M:tm-936, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-85671
in-theory        85671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> ((C or A) and B))) -> ((C or A) -> (B -> ((C or A) and B)))) or D)
theorem-size     23
proof            (modus-ponens tm-936 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-6 tm-7 tm-1 tm-5)
proof-size       143
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-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-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-85671.        (((A -> (B -> ((C or A) and B))) -> ((C or A) -> (B -> ((C or A) and B)))) or D), M:tm-936, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-85672
in-theory        85672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) or C)) -> ((B or A) -> ((B or A) or C))) or D)
theorem-size     19
proof            (modus-ponens tm-936 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-6 tm-7 tm-1)
proof-size       133
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-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-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-85672.        (((A -> ((B or A) or C)) -> ((B or A) -> ((B or A) or C))) or D), M:tm-936, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-85673
in-theory        85673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or (C or A))) -> ((C or A) -> (B or (C or A)))) or D)
theorem-size     19
proof            (modus-ponens tm-936 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-6 tm-7 tm-1)
proof-size       133
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-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-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-85673.        (((A -> (B or (C or A))) -> ((C or A) -> (B or (C or A)))) or D), M:tm-936, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-85674
in-theory        85674
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     39
proof            (modus-ponens tm-930 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85674.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-930, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85675
in-theory        85675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D)))
theorem-size     61
proof            (modus-ponens tm-920 tm-936 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85675.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D))), M:tm-920, m:tm-936, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85676
in-theory        85676
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     39
proof            (modus-ponens tm-893 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85676.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-893, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85677
in-theory        85677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D)))
theorem-size     55
proof            (modus-ponens tm-882 tm-936 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85677.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D))), M:tm-882, m:tm-936, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85678
in-theory        85678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     43
proof            (modus-ponens tm-855 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85678.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-855, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85679
in-theory        85679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     37
proof            (modus-ponens tm-808 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85679.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-808, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85680
in-theory        85680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D)))
theorem-size     67
proof            (modus-ponens tm-798 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85680.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D))), M:tm-798, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85681
in-theory        85681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     37
proof            (modus-ponens tm-757 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-85681.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-757, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85682
in-theory        85682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D)))
theorem-size     67
proof            (modus-ponens tm-747 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-85682.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D))), M:tm-747, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85683
in-theory        85683
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H)))
theorem-size     51
proof            (modus-ponens tm-708 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85683.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H))), M:tm-708, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85684
in-theory        85684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     39
proof            (modus-ponens tm-665 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-85684.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-665, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85685
in-theory        85685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((B -> C) -> ((A or B) -> C)) or E)))
theorem-size     27
proof            (modus-ponens tm-623 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85685.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((B -> C) -> ((A or B) -> C)) or E))), M:tm-623, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85686
in-theory        85686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-622 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85686.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-622, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85687
in-theory        85687
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85687.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (F or E))), M:tm-609, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85688
in-theory        85688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-605 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85688.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-605, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85689
in-theory        85689
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     57
proof            (modus-ponens tm-595 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-85689.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-595, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85690
in-theory        85690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-550 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85690.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-550, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85691
in-theory        85691
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-540 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-85691.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-540, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85692
in-theory        85692
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-530 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85692.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-530, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85693
in-theory        85693
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-520 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85693.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-520, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85694
in-theory        85694
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-510 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-85694.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-510, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85695
in-theory        85695
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-500 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-85695.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-500, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85696
in-theory        85696
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H)))
theorem-size     41
proof            (modus-ponens tm-490 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85696.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H))), M:tm-490, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85697
in-theory        85697
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-480 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-85697.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-480, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85698
in-theory        85698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) -> ((A or B) -> C)) or D) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85698.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) -> ((A or B) -> C)) or D) or E)), M:tm-470, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85699
in-theory        85699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-469 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85699.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-469, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85700
in-theory        85700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85700.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (E or F))), M:tm-456, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85701
in-theory        85701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-453 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85701.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-453, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85702
in-theory        85702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     57
proof            (modus-ponens tm-443 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85702.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-443, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85703
in-theory        85703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-409 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85703.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-409, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85704
in-theory        85704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-400 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85704.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-400, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85705
in-theory        85705
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-391 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85705.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-391, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85706
in-theory        85706
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-382 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85706.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-382, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85707
in-theory        85707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H)))
theorem-size     41
proof            (modus-ponens tm-373 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85707.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H))), M:tm-373, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85708
in-theory        85708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-364 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85708.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-364, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85709
in-theory        85709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((B -> C) -> ((A or B) -> C)) or E) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-85709.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((B -> C) -> ((A or B) -> C)) or E) and D))), M:tm-355, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85710
in-theory        85710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-354 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85710.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-354, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85711
in-theory        85711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-85711.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85712
in-theory        85712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F)))
theorem-size     35
proof            (modus-ponens tm-338 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-85712.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F))), M:tm-338, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85713
in-theory        85713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     65
proof            (modus-ponens tm-328 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85713.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-328, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85714
in-theory        85714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     59
proof            (modus-ponens tm-327 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85714.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-327, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85715
in-theory        85715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     57
proof            (modus-ponens tm-326 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-85715.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-326, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85716
in-theory        85716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     57
proof            (modus-ponens tm-325 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-85716.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-325, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85717
in-theory        85717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     65
proof            (modus-ponens tm-324 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85717.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-324, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85718
in-theory        85718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     57
proof            (modus-ponens tm-323 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-85718.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-323, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85719
in-theory        85719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85719.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E and F) -> F)), M:tm-322, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85720
in-theory        85720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85720.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E and F) -> E)), M:tm-320, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85721
in-theory        85721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-85721.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85722
in-theory        85722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-316 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-85722.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85723
in-theory        85723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85723.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (F -> E))), M:tm-315, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85724
in-theory        85724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> ((A or B) -> C)) or D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     67
proof            (modus-ponens tm-313 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85724.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> ((A or B) -> C)) or D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85725
in-theory        85725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((((B -> C) -> ((A or B) -> C)) or D) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((B -> C) -> ((A or B) -> C)) or D)) -> E)))
theorem-size     67
proof            (modus-ponens tm-312 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85725.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (((((B -> C) -> ((A or B) -> C)) or D) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((B -> C) -> ((A or B) -> C)) or D)) -> E))), M:tm-312, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85726
in-theory        85726
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     53
proof            (modus-ponens tm-311 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85726.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-311, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85727
in-theory        85727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85727.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) or E)), M:tm-310, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85728
in-theory        85728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85728.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and E))), M:tm-309, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85729
in-theory        85729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))))
theorem-size     53
proof            (modus-ponens tm-305 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85729.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)))), M:tm-305, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85730
in-theory        85730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     37
proof            (modus-ponens tm-303 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85730.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-303, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85731
in-theory        85731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-270 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85731.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-270, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85732
in-theory        85732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-239 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85732.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-239, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85733
in-theory        85733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H)))
theorem-size     43
proof            (modus-ponens tm-210 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85733.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H))), M:tm-210, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85734
in-theory        85734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-183 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85734.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-183, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85735
in-theory        85735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-157 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85735.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-157, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85736
in-theory        85736
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     41
proof            (modus-ponens tm-147 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85736.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-147, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85737
in-theory        85737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-134 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85737.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-134, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85738
in-theory        85738
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     41
proof            (modus-ponens tm-125 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85738.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-125, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85739
in-theory        85739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H)))
theorem-size     41
proof            (modus-ponens tm-113 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85739.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H))), M:tm-113, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85740
in-theory        85740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     45
proof            (modus-ponens tm-105 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85740.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-105, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85741
in-theory        85741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F)))
theorem-size     33
proof            (modus-ponens tm-95 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-85741.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F))), M:tm-95, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85742
in-theory        85742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) or E)))
theorem-size     27
proof            (modus-ponens tm-84 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85742.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) or E))), M:tm-84, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85743
in-theory        85743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-83 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85743.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-83, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85744
in-theory        85744
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> ((B or C) -> D)) or E)))
theorem-size     31
proof            (modus-ponens tm-76 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85744.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> ((B or C) -> D)) or E))), M:tm-76, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85745
in-theory        85745
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D))
theorem-size     41
proof            (modus-ponens tm-73 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85745.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D)), M:tm-73, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85746
in-theory        85746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F)))
theorem-size     37
proof            (modus-ponens tm-69 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85746.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F))), M:tm-69, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85747
in-theory        85747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     39
proof            (modus-ponens tm-54 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85747.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-54, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85748
in-theory        85748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) or D))
theorem-size     35
proof            (modus-ponens tm-50 tm-936 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-7 tm-6)
proof-size       149
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85748.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) or D)), M:tm-50, m:tm-936, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85749
in-theory        85749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-49 tm-936 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-6)
proof-size       143
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85749.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or D)), M:tm-49, m:tm-936, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85750
in-theory        85750
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((C -> D) -> ((B or C) -> D)) or E))
theorem-size     41
proof            (modus-ponens tm-47 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85750.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((C -> D) -> ((B or C) -> D)) or E)), M:tm-47, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85751
in-theory        85751
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or E))
theorem-size     41
proof            (modus-ponens tm-46 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85751.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> ((A or B) -> C)) or E)), M:tm-46, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85752
in-theory        85752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F)))
theorem-size     31
proof            (modus-ponens tm-42 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85752.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F))), M:tm-42, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85753
in-theory        85753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F)))
theorem-size     31
proof            (modus-ponens tm-32 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85753.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F))), M:tm-32, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85754
in-theory        85754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> ((A or B) -> C)) or D)))
theorem-size     39
proof            (modus-ponens tm-24 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85754.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> ((A or B) -> C)) or D))), M:tm-24, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85755
in-theory        85755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F)))
theorem-size     33
proof            (modus-ponens tm-23 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85755.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F))), M:tm-23, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85756
in-theory        85756
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F)))
theorem-size     31
proof            (modus-ponens tm-22 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85756.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F))), M:tm-22, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85757
in-theory        85757
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F)))
theorem-size     31
proof            (modus-ponens tm-21 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85757.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F))), M:tm-21, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85758
in-theory        85758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G)))
theorem-size     39
proof            (modus-ponens tm-20 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85758.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> ((D or E) -> F)) or G))), M:tm-20, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85759
in-theory        85759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F)))
theorem-size     31
proof            (modus-ponens tm-19 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85759.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> ((C or D) -> E)) or F))), M:tm-19, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85760
in-theory        85760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> ((A or B) -> C)) or D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-9 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85760.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> ((A or B) -> C)) or D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85761
in-theory        85761
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) or D) -> E) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or (((A -> B) -> ((C or A) -> B)) or D)) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-936 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-6)
proof-size       137
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-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-85761.        (((((A -> B) -> ((C or A) -> B)) or D) -> E) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or (((A -> B) -> ((C or A) -> B)) or D)) -> E)), M:tm-8, m:tm-936, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85762
in-theory        85762
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> ((B or C) -> D)) or E)))
theorem-size     27
proof            (modus-ponens tm-7 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85762.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> ((B or C) -> D)) or E))), M:tm-7, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85763
in-theory        85763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85763.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)) or E), M:tm-6, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85764
in-theory        85764
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> ((B or C) -> D)) or E)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85764.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> ((B or C) -> D)) or E)) and A)), M:tm-5, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85765
in-theory        85765
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> ((B or C) -> D)) or E)))
theorem-size     27
proof            (modus-ponens tm-1 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-6)
proof-size       115
proof-steps      7
----------------------------------------------------------------
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-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-85765.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> ((B or C) -> D)) or E))), M:tm-1, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85766
in-theory        85766
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (D or B))) -> ((D or B) -> (C -> (D or B)))))
theorem-size     19
proof            (modus-ponens tm-937 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       133
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-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-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-85766.        (A or ((B -> (C -> (D or B))) -> ((D or B) -> (C -> (D or B))))), M:tm-937, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-85767
in-theory        85767
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> ((D or B) and C))) -> ((D or B) -> (C -> ((D or B) and C)))))
theorem-size     23
proof            (modus-ponens tm-937 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       143
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-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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-85767.        (A or ((B -> (C -> ((D or B) and C))) -> ((D or B) -> (C -> ((D or B) and C))))), M:tm-937, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-85768
in-theory        85768
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> ((C or B) or D)) -> ((C or B) -> ((C or B) or D))))
theorem-size     19
proof            (modus-ponens tm-937 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       133
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-85768.        (A or ((B -> ((C or B) or D)) -> ((C or B) -> ((C or B) or D)))), M:tm-937, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-85769
in-theory        85769
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or (D or B))) -> ((D or B) -> (C or (D or B)))))
theorem-size     19
proof            (modus-ponens tm-937 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       133
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-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-1.            (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-85769.        (A or ((B -> (C or (D or B))) -> ((D or B) -> (C or (D or B))))), M:tm-937, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-85770
in-theory        85770
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-930 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85770.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85771
in-theory        85771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C)))))
theorem-size     61
proof            (modus-ponens tm-920 tm-937 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85771.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C))))), M:tm-920, m:tm-937, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85772
in-theory        85772
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-893 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85772.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85773
in-theory        85773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C)))))
theorem-size     55
proof            (modus-ponens tm-882 tm-937 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85773.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C))))), M:tm-882, m:tm-937, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85774
in-theory        85774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-855 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85774.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85775
in-theory        85775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-808 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85775.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85776
in-theory        85776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C)))))
theorem-size     67
proof            (modus-ponens tm-798 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85776.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C))))), M:tm-798, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85777
in-theory        85777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-85777.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85778
in-theory        85778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C)))))
theorem-size     67
proof            (modus-ponens tm-747 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-85778.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C))))), M:tm-747, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85779
in-theory        85779
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85779.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85780
in-theory        85780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-85780.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85781
in-theory        85781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E or ((B -> C) -> ((A or B) -> C)))))
theorem-size     27
proof            (modus-ponens tm-623 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85781.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E or ((B -> C) -> ((A or B) -> C))))), M:tm-623, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85782
in-theory        85782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85782.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85783
in-theory        85783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85783.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (F or E))), M:tm-609, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85784
in-theory        85784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85784.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85785
in-theory        85785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85785.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-595, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85786
in-theory        85786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85786.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85787
in-theory        85787
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85787.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85788
in-theory        85788
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85788.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85789
in-theory        85789
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85789.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85790
in-theory        85790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85790.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85791
in-theory        85791
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85791.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85792
in-theory        85792
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85792.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85793
in-theory        85793
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85793.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85794
in-theory        85794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((B -> C) -> ((A or B) -> C))) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85794.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((B -> C) -> ((A or B) -> C))) or E)), M:tm-470, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85795
in-theory        85795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85795.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85796
in-theory        85796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85796.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (E or F))), M:tm-456, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85797
in-theory        85797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85797.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85798
in-theory        85798
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-85798.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-443, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85799
in-theory        85799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-85799.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85800
in-theory        85800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85800.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85801
in-theory        85801
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-85801.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85802
in-theory        85802
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-85802.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85803
in-theory        85803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85803.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85804
in-theory        85804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-85804.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85805
in-theory        85805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E or ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-85805.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E or ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85806
in-theory        85806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85806.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85807
in-theory        85807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-85807.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85808
in-theory        85808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-85808.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85809
in-theory        85809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-328 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85809.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85810
in-theory        85810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85810.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-327, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85811
in-theory        85811
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-85811.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-326, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85812
in-theory        85812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-85812.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-325, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85813
in-theory        85813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85813.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-324, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85814
in-theory        85814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-85814.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-323, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85815
in-theory        85815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85815.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E and F) -> F)), M:tm-322, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85816
in-theory        85816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85816.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E and F) -> E)), M:tm-320, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85817
in-theory        85817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-85817.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85818
in-theory        85818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-316 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-85818.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85819
in-theory        85819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85819.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (F -> E))), M:tm-315, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85820
in-theory        85820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D or ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     67
proof            (modus-ponens tm-313 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85820.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D or ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85821
in-theory        85821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((D or ((B -> C) -> ((A or B) -> C))) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D or ((B -> C) -> ((A or B) -> C)))) -> E)))
theorem-size     67
proof            (modus-ponens tm-312 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85821.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (((D or ((B -> C) -> ((A or B) -> C))) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D or ((B -> C) -> ((A or B) -> C)))) -> E))), M:tm-312, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85822
in-theory        85822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85822.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-311, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85823
in-theory        85823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85823.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) or E)), M:tm-310, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85824
in-theory        85824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85824.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and E))), M:tm-309, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85825
in-theory        85825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85825.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))))), M:tm-305, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85826
in-theory        85826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85826.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85827
in-theory        85827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85827.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85828
in-theory        85828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85828.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85829
in-theory        85829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85829.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85830
in-theory        85830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85830.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85831
in-theory        85831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85831.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85832
in-theory        85832
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85832.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85833
in-theory        85833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85833.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85834
in-theory        85834
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85834.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85835
in-theory        85835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85835.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85836
in-theory        85836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85836.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85837
in-theory        85837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-85837.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85838
in-theory        85838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or ((B -> C) -> ((A or B) -> C)))))
theorem-size     27
proof            (modus-ponens tm-84 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85838.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or ((B -> C) -> ((A or B) -> C))))), M:tm-84, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85839
in-theory        85839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85839.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85840
in-theory        85840
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E or ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85840.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E or ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85841
in-theory        85841
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-73 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85841.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C)))), M:tm-73, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85842
in-theory        85842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85842.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85843
in-theory        85843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85843.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85844
in-theory        85844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D or ((A -> B) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-50 tm-937 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7)
proof-size       149
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85844.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D or ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-937, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85845
in-theory        85845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-49 tm-937 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 tm-7)
proof-size       143
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85845.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D or ((B -> C) -> ((A or B) -> C)))), M:tm-49, m:tm-937, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85846
in-theory        85846
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E or ((C -> D) -> ((B or C) -> D))))
theorem-size     41
proof            (modus-ponens tm-47 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85846.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E or ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85847
in-theory        85847
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E or ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-46 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85847.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E or ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85848
in-theory        85848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85848.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85849
in-theory        85849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85849.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85850
in-theory        85850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D or ((B -> C) -> ((A or B) -> C)))))
theorem-size     39
proof            (modus-ponens tm-24 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85850.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D or ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85851
in-theory        85851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85851.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85852
in-theory        85852
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85852.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85853
in-theory        85853
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85853.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85854
in-theory        85854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85854.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G or ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85855
in-theory        85855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85855.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F or ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85856
in-theory        85856
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D or ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-9 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85856.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D or ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85857
in-theory        85857
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((D or B) -> C))) -> E) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) or (A or ((B -> C) -> ((D or B) -> C)))) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-937 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7)
proof-size       137
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-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-85857.        (((A or ((B -> C) -> ((D or B) -> C))) -> E) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) or (A or ((B -> C) -> ((D or B) -> C)))) -> E)), M:tm-8, m:tm-937, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85858
in-theory        85858
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E or ((C -> D) -> ((B or C) -> D)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-85858.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E or ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85859
in-theory        85859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85859.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))) or E), M:tm-6, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85860
in-theory        85860
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E or ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85860.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E or ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85861
in-theory        85861
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E or ((C -> D) -> ((B or C) -> D)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-7)
proof-size       115
proof-steps      7
----------------------------------------------------------------
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-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-85861.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E or ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85862
in-theory        85862
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> (A or B))) -> D) -> (((B -> (C -> (A or B))) or ((A or B) -> (C -> (A or B)))) -> D))
theorem-size     31
proof            (modus-ponens tm-938 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-7 tm-1)
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-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-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-85862.        ((((A or B) -> (C -> (A or B))) -> D) -> (((B -> (C -> (A or B))) or ((A or B) -> (C -> (A or B)))) -> D)), M:tm-938, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-85863
in-theory        85863
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C -> ((A or B) and C))) -> D) -> (((B -> (C -> ((A or B) and C))) or ((A or B) -> (C -> ((A or B) and C)))) -> D))
theorem-size     37
proof            (modus-ponens tm-938 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       173
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-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-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-85863.        ((((A or B) -> (C -> ((A or B) and C))) -> D) -> (((B -> (C -> ((A or B) and C))) or ((A or B) -> (C -> ((A or B) and C)))) -> D)), M:tm-938, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-85864
in-theory        85864
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> ((A or B) or C)) -> D) -> (((B -> ((A or B) or C)) or ((A or B) -> ((A or B) or C))) -> D))
theorem-size     31
proof            (modus-ponens tm-938 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-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-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-85864.        ((((A or B) -> ((A or B) or C)) -> D) -> (((B -> ((A or B) or C)) or ((A or B) -> ((A or B) or C))) -> D)), M:tm-938, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-85865
in-theory        85865
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> (C or (A or B))) -> D) -> (((B -> (C or (A or B))) or ((A or B) -> (C or (A or B)))) -> D))
theorem-size     31
proof            (modus-ponens tm-938 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-7 tm-1)
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-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-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-85865.        ((((A or B) -> (C or (A or B))) -> D) -> (((B -> (C or (A or B))) or ((A or B) -> (C or (A or B)))) -> D)), M:tm-938, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-85866
in-theory        85866
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-930 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85866.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-930, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85867
in-theory        85867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))
theorem-size     77
proof            (modus-ponens tm-920 tm-938 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85867.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))), M:tm-920, m:tm-938, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85868
in-theory        85868
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-893 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85868.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-893, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85869
in-theory        85869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))
theorem-size     71
proof            (modus-ponens tm-882 tm-938 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85869.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))), M:tm-882, m:tm-938, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85870
in-theory        85870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     51
proof            (modus-ponens tm-855 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85870.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-855, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85871
in-theory        85871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-808 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85871.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-808, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85872
in-theory        85872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))
theorem-size     83
proof            (modus-ponens tm-798 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85872.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))), M:tm-798, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85873
in-theory        85873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-757 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-85873.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-757, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85874
in-theory        85874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))
theorem-size     83
proof            (modus-ponens tm-747 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85874.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))), M:tm-747, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85875
in-theory        85875
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H))))
theorem-size     59
proof            (modus-ponens tm-708 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       245
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-85875.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H)))), M:tm-708, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85876
in-theory        85876
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-665 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-85876.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-665, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85877
in-theory        85877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((((A or B) -> C) -> E) -> (((B -> C) or ((A or B) -> C)) -> E))))
theorem-size     35
proof            (modus-ponens tm-623 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85877.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((((A or B) -> C) -> E) -> (((B -> C) or ((A or B) -> C)) -> E)))), M:tm-623, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85878
in-theory        85878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-622 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85878.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-622, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85879
in-theory        85879
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (F or E)))
theorem-size     39
proof            (modus-ponens tm-609 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85879.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85880
in-theory        85880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-605 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-85880.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-605, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85881
in-theory        85881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     73
proof            (modus-ponens tm-595 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-85881.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-595, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85882
in-theory        85882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-550 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-85882.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-550, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85883
in-theory        85883
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-540 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-85883.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-540, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85884
in-theory        85884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-530 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-85884.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-530, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85885
in-theory        85885
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-520 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-85885.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-520, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85886
in-theory        85886
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-510 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-85886.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-510, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85887
in-theory        85887
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-500 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-85887.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-500, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85888
in-theory        85888
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H))))
theorem-size     49
proof            (modus-ponens tm-490 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-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-85888.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H)))), M:tm-490, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85889
in-theory        85889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-480 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-85889.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-480, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85890
in-theory        85890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)) or E))
theorem-size     35
proof            (modus-ponens tm-470 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85890.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)) or E)), M:tm-470, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85891
in-theory        85891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-469 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85891.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-469, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85892
in-theory        85892
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (E or F)))
theorem-size     39
proof            (modus-ponens tm-456 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85892.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85893
in-theory        85893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-453 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-85893.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-453, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85894
in-theory        85894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     73
proof            (modus-ponens tm-443 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-85894.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-443, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85895
in-theory        85895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-409 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-85895.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-409, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85896
in-theory        85896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-400 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-85896.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-400, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85897
in-theory        85897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-391 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-85897.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-391, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85898
in-theory        85898
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-382 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-85898.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-382, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85899
in-theory        85899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H))))
theorem-size     49
proof            (modus-ponens tm-373 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-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-85899.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H)))), M:tm-373, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85900
in-theory        85900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-364 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-85900.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-364, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85901
in-theory        85901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((((A or B) -> C) -> E) -> (((B -> C) or ((A or B) -> C)) -> E)) and D)))
theorem-size     37
proof            (modus-ponens tm-355 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85901.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((((A or B) -> C) -> E) -> (((B -> C) or ((A or B) -> C)) -> E)) and D))), M:tm-355, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85902
in-theory        85902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-354 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-85902.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-354, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85903
in-theory        85903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) or ((A or B) -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-349 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Am Bm) Cm)) (Dm (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Am Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       221
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85903.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) or ((A or B) -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((A or B) -> C)))), M:tm-349, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Am Bm) Cm)) (Dm (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Am Bm) Cm))) (C (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-85904
in-theory        85904
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (F -> (E and F))))
theorem-size     41
proof            (modus-ponens tm-341 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-85904.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85905
in-theory        85905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F))))
theorem-size     43
proof            (modus-ponens tm-338 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-85905.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F)))), M:tm-338, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85906
in-theory        85906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     81
proof            (modus-ponens tm-328 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) 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-328.          ((A -> 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-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-85906.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-328, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85907
in-theory        85907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     75
proof            (modus-ponens tm-327 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-85907.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-327, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85908
in-theory        85908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     73
proof            (modus-ponens tm-326 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-85908.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-326, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85909
in-theory        85909
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     73
proof            (modus-ponens tm-325 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-85909.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-325, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85910
in-theory        85910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     81
proof            (modus-ponens tm-324 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-85910.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-324, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85911
in-theory        85911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     73
proof            (modus-ponens tm-323 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-85911.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-323, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85912
in-theory        85912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E and F) -> F))
theorem-size     39
proof            (modus-ponens tm-322 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85912.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85913
in-theory        85913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E and F) -> E))
theorem-size     39
proof            (modus-ponens tm-320 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85913.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85914
in-theory        85914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-318 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-85914.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85915
in-theory        85915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     61
proof            (modus-ponens tm-316 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-85915.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85916
in-theory        85916
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (F -> E)))
theorem-size     39
proof            (modus-ponens tm-315 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85916.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85917
in-theory        85917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     83
proof            (modus-ponens tm-313 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85917.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85918
in-theory        85918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) -> E)))
theorem-size     91
proof            (modus-ponens tm-312 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-85918.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) -> E))), M:tm-312, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85919
in-theory        85919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     69
proof            (modus-ponens tm-311 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-85919.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-311, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85920
in-theory        85920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) or E))
theorem-size     69
proof            (modus-ponens tm-310 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-85920.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) or E)), M:tm-310, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85921
in-theory        85921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and E)))
theorem-size     71
proof            (modus-ponens tm-309 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
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-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-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-85921.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and E))), M:tm-309, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85922
in-theory        85922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A or B) -> C) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) or ((A or B) -> C)) -> D))))
theorem-size     81
proof            (modus-ponens tm-306 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Am Bm) Cm) Dm)) (C (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-85922.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A or B) -> C) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) or ((A or B) -> C)) -> D)))), M:tm-306, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Am Bm) Cm) Dm)) (C (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85923
in-theory        85923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))))
theorem-size     69
proof            (modus-ponens tm-305 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-85923.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))), M:tm-305, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85924
in-theory        85924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-303 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
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-303.          (A -> ((B -> ((C -> (D -> (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-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-85924.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-303, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85925
in-theory        85925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-270 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-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-85925.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-270, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85926
in-theory        85926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-239 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-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-85926.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-239, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85927
in-theory        85927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H))))
theorem-size     51
proof            (modus-ponens tm-210 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-85927.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H)))), M:tm-210, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85928
in-theory        85928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-183 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-85928.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-183, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85929
in-theory        85929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-157 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-85929.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-157, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85930
in-theory        85930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     49
proof            (modus-ponens tm-147 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-85930.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-147, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85931
in-theory        85931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-134 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-85931.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-134, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85932
in-theory        85932
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     49
proof            (modus-ponens tm-125 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-85932.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-125, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85933
in-theory        85933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((A or B) -> C) -> D) -> ((B -> C) or ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> D)))
theorem-size     41
proof            (modus-ponens tm-114 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Am Bm) Cm) Dm)) (C (or (-> Bm Cm) (-> (or Am Bm) Cm))) (D Dm)))
axioms-used      (tm-2 tm-1 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-14.           (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-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-85933.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((A or B) -> C) -> D) -> ((B -> C) or ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> D))), M:tm-114, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Am Bm) Cm) Dm)) (C (or (-> Bm Cm) (-> (or Am Bm) Cm))) (D Dm))
================================================================
tm-name          tm-85934
in-theory        85934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H))))
theorem-size     49
proof            (modus-ponens tm-113 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-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-85934.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H)))), M:tm-113, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85935
in-theory        85935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     53
proof            (modus-ponens tm-105 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-85935.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-105, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85936
in-theory        85936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) or ((A or B) -> C)) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     37
proof            (modus-ponens tm-98 tm-938 ((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Am Bm) Cm)) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (C (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85936.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) or ((A or B) -> C)) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-98, m:tm-938, u:((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Am Bm) Cm)) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (C (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-85937
in-theory        85937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F))))
theorem-size     41
proof            (modus-ponens tm-95 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-85937.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F)))), M:tm-95, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85938
in-theory        85938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((A or B) -> C) -> E) -> (((B -> C) or ((A or B) -> C)) -> E))))
theorem-size     35
proof            (modus-ponens tm-84 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85938.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((A or B) -> C) -> E) -> (((B -> C) or ((A or B) -> C)) -> E)))), M:tm-84, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85939
in-theory        85939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-83 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-85939.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-83, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85940
in-theory        85940
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E))))
theorem-size     39
proof            (modus-ponens tm-76 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-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-85940.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E)))), M:tm-76, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85941
in-theory        85941
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))
theorem-size     49
proof            (modus-ponens tm-73 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-10)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85941.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))), M:tm-73, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85942
in-theory        85942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F))))
theorem-size     45
proof            (modus-ponens tm-69 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-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-85942.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F)))), M:tm-69, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85943
in-theory        85943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-54 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-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-85943.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-54, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85944
in-theory        85944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D)))
theorem-size     43
proof            (modus-ponens tm-50 tm-938 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-7)
proof-size       173
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85944.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D))), M:tm-50, m:tm-938, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85945
in-theory        85945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))
theorem-size     37
proof            (modus-ponens tm-49 tm-938 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-6)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85945.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))), M:tm-49, m:tm-938, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85946
in-theory        85946
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E)))
theorem-size     49
proof            (modus-ponens tm-47 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-4)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85946.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E))), M:tm-47, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85947
in-theory        85947
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> E) -> (((B -> C) or ((A or B) -> C)) -> E)))
theorem-size     49
proof            (modus-ponens tm-46 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8 tm-3)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85947.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((A or B) -> C) -> E) -> (((B -> C) or ((A or B) -> C)) -> E))), M:tm-46, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85948
in-theory        85948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-42 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-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-85948.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F)))), M:tm-42, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85949
in-theory        85949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-32 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-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-85949.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F)))), M:tm-32, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85950
in-theory        85950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))
theorem-size     47
proof            (modus-ponens tm-24 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85950.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))), M:tm-24, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85951
in-theory        85951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F))))
theorem-size     41
proof            (modus-ponens tm-23 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-85951.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F)))), M:tm-23, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85952
in-theory        85952
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-22 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-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-85952.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F)))), M:tm-22, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85953
in-theory        85953
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-21 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-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-85953.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F)))), M:tm-21, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85954
in-theory        85954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-20 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       183
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-85954.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((D or E) -> F) -> G) -> (((E -> F) or ((D or E) -> F)) -> G)))), M:tm-20, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85955
in-theory        85955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-19 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-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-85955.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((C or D) -> E) -> F) -> (((D -> E) or ((C or D) -> E)) -> F)))), M:tm-19, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85956
in-theory        85956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-9 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-9 tm-8)
proof-size       159
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85956.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85957
in-theory        85957
times-derived    1
----------------------------------------------------------------
theorem          ((((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) -> E))
theorem-size     57
proof            (modus-ponens tm-8 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-8)
proof-size       169
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-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-85957.        ((((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) -> E)), M:tm-8, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-85958
in-theory        85958
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E))))
theorem-size     35
proof            (modus-ponens tm-7 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-7 tm-8)
proof-size       139
proof-steps      7
----------------------------------------------------------------
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-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-85958.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E)))), M:tm-7, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85959
in-theory        85959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) or E)
theorem-size     35
proof            (modus-ponens tm-6 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-6 tm-8)
proof-size       139
proof-steps      7
----------------------------------------------------------------
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-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-85959.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))) or E), M:tm-6, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85960
in-theory        85960
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
proof-size       143
proof-steps      7
----------------------------------------------------------------
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-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-85960.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E))) and A)), M:tm-5, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85961
in-theory        85961
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A or B) -> C) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) or ((A or B) -> C)) -> D)))
theorem-size     47
proof            (modus-ponens tm-2 tm-938 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Am Bm) Cm) Dm)) (C (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-8)
proof-size       159
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85961.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A or B) -> C) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) or ((A or B) -> C)) -> D))), M:tm-2, m:tm-938, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Am Bm) Cm) Dm)) (C (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))
================================================================
tm-name          tm-85962
in-theory        85962
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E))))
theorem-size     35
proof            (modus-ponens tm-1 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-1 tm-8)
proof-size       139
proof-steps      7
----------------------------------------------------------------
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-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-85962.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((B or C) -> D) -> E) -> (((C -> D) or ((B or C) -> D)) -> E)))), M:tm-1, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-85963
in-theory        85963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or A))) -> (not ((C or A) -> (B -> (C or A))))) -> (not (A -> (B -> (C or A)))))
theorem-size     27
proof            (modus-ponens tm-939 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-9 tm-7 tm-1)
proof-size       151
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-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-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-85963.        (((A -> (B -> (C or A))) -> (not ((C or A) -> (B -> (C or A))))) -> (not (A -> (B -> (C or A))))), M:tm-939, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-85964
in-theory        85964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> ((C or A) and B))) -> (not ((C or A) -> (B -> ((C or A) and B))))) -> (not (A -> (B -> ((C or A) and B)))))
theorem-size     33
proof            (modus-ponens tm-939 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-9 tm-7 tm-1 tm-5)
proof-size       163
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-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-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-85964.        (((A -> (B -> ((C or A) and B))) -> (not ((C or A) -> (B -> ((C or A) and B))))) -> (not (A -> (B -> ((C or A) and B))))), M:tm-939, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-85965
in-theory        85965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) or C)) -> (not ((B or A) -> ((B or A) or C)))) -> (not (A -> ((B or A) or C))))
theorem-size     27
proof            (modus-ponens tm-939 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-9 tm-7 tm-1 tm-6)
proof-size       151
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-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-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-85965.        (((A -> ((B or A) or C)) -> (not ((B or A) -> ((B or A) or C)))) -> (not (A -> ((B or A) or C)))), M:tm-939, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-85966
in-theory        85966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or (C or A))) -> (not ((C or A) -> (B or (C or A))))) -> (not (A -> (B or (C or A)))))
theorem-size     27
proof            (modus-ponens tm-939 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-9 tm-7 tm-1)
proof-size       151
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-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-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-85966.        (((A -> (B or (C or A))) -> (not ((C or A) -> (B or (C or A))))) -> (not (A -> (B or (C or A))))), M:tm-939, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-85967
in-theory        85967
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     43
proof            (modus-ponens tm-930 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85967.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-930, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85968
in-theory        85968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))
theorem-size     69
proof            (modus-ponens tm-920 tm-939 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-9)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85968.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))), M:tm-920, m:tm-939, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-85969
in-theory        85969
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     43
proof            (modus-ponens tm-893 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-9)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85969.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-893, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85970
in-theory        85970
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))
theorem-size     63
proof            (modus-ponens tm-882 tm-939 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85970.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))), M:tm-882, m:tm-939, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-85971
in-theory        85971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     47
proof            (modus-ponens tm-855 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-9)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85971.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-855, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85972
in-theory        85972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     41
proof            (modus-ponens tm-808 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85972.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-808, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85973
in-theory        85973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))
theorem-size     75
proof            (modus-ponens tm-798 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85973.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))), M:tm-798, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-85974
in-theory        85974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     41
proof            (modus-ponens tm-757 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-85974.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-757, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85975
in-theory        85975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))
theorem-size     75
proof            (modus-ponens tm-747 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85975.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))), M:tm-747, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-85976
in-theory        85976
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G)))))
theorem-size     55
proof            (modus-ponens tm-708 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85976.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G))))), M:tm-708, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85977
in-theory        85977
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     43
proof            (modus-ponens tm-665 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85977.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-665, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85978
in-theory        85978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))
theorem-size     31
proof            (modus-ponens tm-623 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85978.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))), M:tm-623, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-85979
in-theory        85979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-622 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85979.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-622, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85980
in-theory        85980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (E or D)))
theorem-size     35
proof            (modus-ponens tm-609 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-85980.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (E or D))), M:tm-609, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85981
in-theory        85981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-605 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85981.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-605, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85982
in-theory        85982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-85982.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-595, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85983
in-theory        85983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-550 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85983.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-550, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85984
in-theory        85984
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-540 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85984.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-540, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85985
in-theory        85985
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-530 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85985.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-530, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85986
in-theory        85986
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-520 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85986.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-520, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85987
in-theory        85987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-510 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85987.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-510, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85988
in-theory        85988
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-500 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85988.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-500, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85989
in-theory        85989
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G)))))
theorem-size     45
proof            (modus-ponens tm-490 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85989.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G))))), M:tm-490, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85990
in-theory        85990
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-480 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85990.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-480, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85991
in-theory        85991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))) or D))
theorem-size     31
proof            (modus-ponens tm-470 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85991.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))) or D)), M:tm-470, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-85992
in-theory        85992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-469 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85992.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-469, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85993
in-theory        85993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (D or E)))
theorem-size     35
proof            (modus-ponens tm-456 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-85993.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (D or E))), M:tm-456, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85994
in-theory        85994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-453 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85994.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-453, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85995
in-theory        85995
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-85995.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-443, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85996
in-theory        85996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-409 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85996.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-409, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85997
in-theory        85997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-400 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85997.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-400, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85998
in-theory        85998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-391 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85998.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-391, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-85999
in-theory        85999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-382 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-85999.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-382, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86000
in-theory        86000
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G)))))
theorem-size     45
proof            (modus-ponens tm-373 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86000.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G))))), M:tm-373, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86001
in-theory        86001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-364 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86001.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-364, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86002
in-theory        86002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86002.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))) and D))), M:tm-355, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86003
in-theory        86003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-354 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86003.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-354, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86004
in-theory        86004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (E -> (D and E))))
theorem-size     37
proof            (modus-ponens tm-341 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-86004.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86005
in-theory        86005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-338 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-86005.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E))))), M:tm-338, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86006
in-theory        86006
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     73
proof            (modus-ponens tm-328 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86006.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-328, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86007
in-theory        86007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86007.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-327, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86008
in-theory        86008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-86008.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-326, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86009
in-theory        86009
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-86009.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-325, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86010
in-theory        86010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86010.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-324, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86011
in-theory        86011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-86011.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-323, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86012
in-theory        86012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D and E) -> E))
theorem-size     35
proof            (modus-ponens tm-322 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-86012.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D and E) -> E)), M:tm-322, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86013
in-theory        86013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D and E) -> D))
theorem-size     35
proof            (modus-ponens tm-320 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-86013.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D and E) -> D)), M:tm-320, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86014
in-theory        86014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-318 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86014.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86015
in-theory        86015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86015.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86016
in-theory        86016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (E -> D)))
theorem-size     35
proof            (modus-ponens tm-315 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-86016.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (E -> D))), M:tm-315, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86017
in-theory        86017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86017.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86018
in-theory        86018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) -> D)))
theorem-size     79
proof            (modus-ponens tm-312 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86018.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (((((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) -> D))), M:tm-312, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86019
in-theory        86019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86019.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-311, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86020
in-theory        86020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) or D))
theorem-size     61
proof            (modus-ponens tm-310 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86020.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) or D)), M:tm-310, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86021
in-theory        86021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and D)))
theorem-size     63
proof            (modus-ponens tm-309 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86021.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and D))), M:tm-309, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86022
in-theory        86022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (not ((A or B) -> C)))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (B -> C)))))
theorem-size     73
proof            (modus-ponens tm-306 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (not (-> (or Am Bm) Cm)))) (C (not (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86022.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (not ((A or B) -> C)))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (B -> C))))), M:tm-306, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (not (-> (or Am Bm) Cm)))) (C (not (-> Bm Cm))))
================================================================
tm-name          tm-86023
in-theory        86023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86023.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))), M:tm-305, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86024
in-theory        86024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     41
proof            (modus-ponens tm-303 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86024.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-303, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86025
in-theory        86025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-270 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86025.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-270, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86026
in-theory        86026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-239 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86026.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-239, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86027
in-theory        86027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G)))))
theorem-size     47
proof            (modus-ponens tm-210 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86027.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G))))), M:tm-210, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86028
in-theory        86028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     39
proof            (modus-ponens tm-183 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86028.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-183, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86029
in-theory        86029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-157 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86029.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-157, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86030
in-theory        86030
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     45
proof            (modus-ponens tm-147 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86030.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-147, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86031
in-theory        86031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-134 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86031.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-134, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86032
in-theory        86032
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     45
proof            (modus-ponens tm-125 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86032.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-125, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86033
in-theory        86033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G)))))
theorem-size     45
proof            (modus-ponens tm-113 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86033.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G))))), M:tm-113, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86034
in-theory        86034
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     49
proof            (modus-ponens tm-105 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86034.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-105, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86035
in-theory        86035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-95 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-86035.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E))))), M:tm-95, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86036
in-theory        86036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))
theorem-size     31
proof            (modus-ponens tm-84 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86036.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))), M:tm-84, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86037
in-theory        86037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-83 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86037.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-83, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86038
in-theory        86038
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D)))))
theorem-size     35
proof            (modus-ponens tm-76 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86038.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D))))), M:tm-76, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86039
in-theory        86039
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))
theorem-size     45
proof            (modus-ponens tm-73 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-8 tm-10 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86039.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))), M:tm-73, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86040
in-theory        86040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-69 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86040.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E))))), M:tm-69, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86041
in-theory        86041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     43
proof            (modus-ponens tm-54 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86041.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-54, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86042
in-theory        86042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B))))
theorem-size     39
proof            (modus-ponens tm-50 tm-939 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-9)
proof-size       163
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86042.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B)))), M:tm-50, m:tm-939, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86043
in-theory        86043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-939 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-9)
proof-size       157
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86043.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))), M:tm-49, m:tm-939, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86044
in-theory        86044
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D))))
theorem-size     45
proof            (modus-ponens tm-47 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86044.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D)))), M:tm-47, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86045
in-theory        86045
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))
theorem-size     45
proof            (modus-ponens tm-46 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86045.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))), M:tm-46, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86046
in-theory        86046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-42 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86046.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E))))), M:tm-42, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86047
in-theory        86047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-32 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86047.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E))))), M:tm-32, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86048
in-theory        86048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))
theorem-size     43
proof            (modus-ponens tm-24 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm 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-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-86048.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))), M:tm-24, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86049
in-theory        86049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-23 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86049.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E))))), M:tm-23, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86050
in-theory        86050
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-22 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86050.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E))))), M:tm-22, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86051
in-theory        86051
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-21 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86051.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E))))), M:tm-21, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86052
in-theory        86052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F)))))
theorem-size     43
proof            (modus-ponens tm-20 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86052.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((E -> F) -> (not ((D or E) -> F))) -> (not (E -> F))))), M:tm-20, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86053
in-theory        86053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-19 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86053.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((D -> E) -> (not ((C or D) -> E))) -> (not (D -> E))))), M:tm-19, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86054
in-theory        86054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-9 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86054.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86055
in-theory        86055
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B))) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B)))) -> D))
theorem-size     49
proof            (modus-ponens tm-8 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
axioms-used      (tm-8 tm-9)
proof-size       155
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-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-86055.        (((((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B))) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B)))) -> D)), M:tm-8, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))
================================================================
tm-name          tm-86056
in-theory        86056
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D)))))
theorem-size     31
proof            (modus-ponens tm-7 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-7 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86056.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D))))), M:tm-7, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86057
in-theory        86057
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) or D)
theorem-size     31
proof            (modus-ponens tm-6 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-6 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86057.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))) or D), M:tm-6, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86058
in-theory        86058
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D)))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86058.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D)))) and A)), M:tm-5, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86059
in-theory        86059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (not ((A or B) -> C)))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (B -> C))))
theorem-size     43
proof            (modus-ponens tm-2 tm-939 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (not (-> (or Am Bm) Cm)))) (C (not (-> Bm Cm)))))
axioms-used      (tm-2 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86059.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (not ((A or B) -> C)))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (B -> C)))), M:tm-2, m:tm-939, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (not (-> (or Am Bm) Cm)))) (C (not (-> Bm Cm))))
================================================================
tm-name          tm-86060
in-theory        86060
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D)))))
theorem-size     31
proof            (modus-ponens tm-1 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-1 tm-8 tm-9)
proof-size       129
proof-steps      7
----------------------------------------------------------------
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-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-86060.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((C -> D) -> (not ((B or C) -> D))) -> (not (C -> D))))), M:tm-1, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-86061
in-theory        86061
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86061.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-930, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86062
in-theory        86062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D))))
theorem-size     49
proof            (modus-ponens tm-920 tm-940 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86062.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D)))), M:tm-920, m:tm-940, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86063
in-theory        86063
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86063.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-893, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86064
in-theory        86064
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D))))
theorem-size     43
proof            (modus-ponens tm-882 tm-940 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86064.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D)))), M:tm-882, m:tm-940, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86065
in-theory        86065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-855 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86065.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-855, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86066
in-theory        86066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86066.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-808, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86067
in-theory        86067
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D))))
theorem-size     55
proof            (modus-ponens tm-798 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86067.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D)))), M:tm-798, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86068
in-theory        86068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86068.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-757, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86069
in-theory        86069
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D))))
theorem-size     55
proof            (modus-ponens tm-747 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86069.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D)))), M:tm-747, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86070
in-theory        86070
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86070.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H)))), M:tm-708, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86071
in-theory        86071
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-86071.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-665, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86072
in-theory        86072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86072.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-622, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86073
in-theory        86073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     31
proof            (modus-ponens tm-617 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> Em (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86073.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-617, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> Em (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
================================================================
tm-name          tm-86074
in-theory        86074
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-86074.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (G or F))), M:tm-609, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86075
in-theory        86075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-86075.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-605, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86076
in-theory        86076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-86076.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))))), M:tm-595, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86077
in-theory        86077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-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-86077.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-550, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86078
in-theory        86078
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-86078.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-540, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86079
in-theory        86079
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-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-86079.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-530, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86080
in-theory        86080
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-86080.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-520, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86081
in-theory        86081
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-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-86081.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-510, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86082
in-theory        86082
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-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-86082.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-500, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86083
in-theory        86083
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-86083.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H)))), M:tm-490, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86084
in-theory        86084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86084.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-480, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86085
in-theory        86085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86085.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-469, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86086
in-theory        86086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) or E)))
theorem-size     31
proof            (modus-ponens tm-464 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (-> Em (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86086.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) or E))), M:tm-464, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (-> Em (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))))
================================================================
tm-name          tm-86087
in-theory        86087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-86087.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (F or G))), M:tm-456, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86088
in-theory        86088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-86088.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-453, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86089
in-theory        86089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-86089.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))))), M:tm-443, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86090
in-theory        86090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-86090.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-409, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86091
in-theory        86091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-86091.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-400, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86092
in-theory        86092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-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-86092.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-391, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86093
in-theory        86093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-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-86093.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-382, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86094
in-theory        86094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-86094.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H)))), M:tm-373, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86095
in-theory        86095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86095.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-364, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86096
in-theory        86096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86096.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-354, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86097
in-theory        86097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and E))))
theorem-size     33
proof            (modus-ponens tm-349 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (-> Em (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86097.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and E)))), M:tm-349, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (-> Em (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)))))
================================================================
tm-name          tm-86098
in-theory        86098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-86098.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86099
in-theory        86099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-86099.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F)))), M:tm-338, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86100
in-theory        86100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
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-328.          ((A -> 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-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-86100.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-328, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86101
in-theory        86101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-86101.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))))), M:tm-327, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86102
in-theory        86102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-86102.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))))), M:tm-326, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86103
in-theory        86103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-86103.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))))), M:tm-325, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86104
in-theory        86104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-86104.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))))), M:tm-324, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86105
in-theory        86105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-86105.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))))), M:tm-323, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86106
in-theory        86106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86106.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F and G) -> G)), M:tm-322, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86107
in-theory        86107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-86107.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F and G) -> F)), M:tm-320, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86108
in-theory        86108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-86108.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86109
in-theory        86109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-86109.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86110
in-theory        86110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-86110.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (G -> F))), M:tm-315, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86111
in-theory        86111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E -> D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-86111.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E -> D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86112
in-theory        86112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((D -> (E -> D)) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (E -> D))) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-86112.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (((D -> (E -> D)) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (E -> D))) -> F))), M:tm-312, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86113
in-theory        86113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-86113.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))))), M:tm-311, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86114
in-theory        86114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-86114.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) or F)), M:tm-310, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86115
in-theory        86115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-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-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-86115.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and F))), M:tm-309, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86116
in-theory        86116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E -> D))))
theorem-size     53
proof            (modus-ponens tm-306 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Em Dm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-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-86116.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E -> D)))), M:tm-306, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Em Dm)))
================================================================
tm-name          tm-86117
in-theory        86117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-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-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-86117.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))))), M:tm-305, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86118
in-theory        86118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-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-86118.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-303, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86119
in-theory        86119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-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-86119.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-270, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86120
in-theory        86120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-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-86120.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-239, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86121
in-theory        86121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-86121.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H)))), M:tm-210, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86122
in-theory        86122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86122.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-183, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86123
in-theory        86123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86123.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-157, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86124
in-theory        86124
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-86124.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-147, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86125
in-theory        86125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86125.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-134, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86126
in-theory        86126
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-86126.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-125, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86127
in-theory        86127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86127.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H)))), M:tm-113, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86128
in-theory        86128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-86128.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-105, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86129
in-theory        86129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-99 tm-940 ((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Em (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       197
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86129.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-99, m:tm-940, u:((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Em (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86130
in-theory        86130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     31
proof            (modus-ponens tm-98 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> Em (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86130.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-98, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> Em (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
================================================================
tm-name          tm-86131
in-theory        86131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-86131.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F)))), M:tm-95, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86132
in-theory        86132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86132.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-83, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86133
in-theory        86133
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-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-86133.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> E)))), M:tm-76, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86134
in-theory        86134
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D)))
theorem-size     35
proof            (modus-ponens tm-73 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-10 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86134.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D))), M:tm-73, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86135
in-theory        86135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-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-86135.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F)))), M:tm-69, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86136
in-theory        86136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86136.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-54, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86137
in-theory        86137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-50 tm-940 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-7 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86137.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (E -> D))), M:tm-50, m:tm-940, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86138
in-theory        86138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-49 tm-940 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86138.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> D))), M:tm-49, m:tm-940, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86139
in-theory        86139
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (F -> E)))
theorem-size     35
proof            (modus-ponens tm-47 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86139.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (F -> E))), M:tm-47, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86140
in-theory        86140
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (F -> E)))
theorem-size     35
proof            (modus-ponens tm-46 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86140.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (F -> E))), M:tm-46, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86141
in-theory        86141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 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-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-86141.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F)))), M:tm-42, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86142
in-theory        86142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 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-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-86142.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F)))), M:tm-32, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86143
in-theory        86143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))
theorem-size     33
proof            (modus-ponens tm-24 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
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-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-86143.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))), M:tm-24, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86144
in-theory        86144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 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-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-86144.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F)))), M:tm-23, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86145
in-theory        86145
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-4 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-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-86145.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F)))), M:tm-22, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86146
in-theory        86146
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-3 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-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-86146.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F)))), M:tm-21, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86147
in-theory        86147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-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-86147.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> G)))), M:tm-20, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86148
in-theory        86148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 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-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-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-86148.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> F)))), M:tm-19, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86149
in-theory        86149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E -> D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86149.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E -> D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86150
in-theory        86150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or (A -> (B -> A))) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em 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-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-86150.        (((A -> (B -> A)) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or (A -> (B -> A))) -> C)), M:tm-8, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-86151
in-theory        86151
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-7 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86151.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> E)))), M:tm-7, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86152
in-theory        86152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-6 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86152.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))) or F), M:tm-6, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86153
in-theory        86153
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86153.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> E))) and A)), M:tm-5, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86154
in-theory        86154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E -> D)))
theorem-size     33
proof            (modus-ponens tm-2 tm-940 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Em Dm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86154.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E -> D))), M:tm-2, m:tm-940, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Em Dm)))
================================================================
tm-name          tm-86155
in-theory        86155
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-1 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
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-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-86155.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> E)))), M:tm-1, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-86156
in-theory        86156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or A))) -> (A -> (B -> (C or A))))
theorem-size     15
proof            (modus-ponens tm-941 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
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-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-86156.        ((A -> (B -> (C or A))) -> (A -> (B -> (C or A)))), M:tm-941, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-86157
in-theory        86157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C or A) and B))) -> (A -> (B -> ((C or A) and B))))
theorem-size     19
proof            (modus-ponens tm-941 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86157.        ((A -> (B -> ((C or A) and B))) -> (A -> (B -> ((C or A) and B)))), M:tm-941, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-86158
in-theory        86158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) or C)) -> (A -> ((B or A) or C)))
theorem-size     15
proof            (modus-ponens tm-941 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
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-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-86158.        ((A -> ((B or A) or C)) -> (A -> ((B or A) or C))), M:tm-941, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-86159
in-theory        86159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C or A))) -> (A -> (B or (C or A))))
theorem-size     15
proof            (modus-ponens tm-941 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (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-86159.        ((A -> (B or (C or A))) -> (A -> (B or (C or A)))), M:tm-941, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-86160
in-theory        86160
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-930 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86160.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-930, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86161
in-theory        86161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C))))
theorem-size     53
proof            (modus-ponens tm-920 tm-941 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86161.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C)))), M:tm-920, m:tm-941, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86162
in-theory        86162
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-893 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86162.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-893, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86163
in-theory        86163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C))))
theorem-size     47
proof            (modus-ponens tm-882 tm-941 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86163.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C)))), M:tm-882, m:tm-941, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86164
in-theory        86164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     39
proof            (modus-ponens tm-855 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86164.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-855, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86165
in-theory        86165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     33
proof            (modus-ponens tm-808 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86165.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-808, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86166
in-theory        86166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C))))
theorem-size     59
proof            (modus-ponens tm-798 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86166.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C)))), M:tm-798, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86167
in-theory        86167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     33
proof            (modus-ponens tm-757 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86167.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-757, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86168
in-theory        86168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C))))
theorem-size     59
proof            (modus-ponens tm-747 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (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-86168.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C)))), M:tm-747, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86169
in-theory        86169
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G))))
theorem-size     47
proof            (modus-ponens tm-708 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86169.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G)))), M:tm-708, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86170
in-theory        86170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-665 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-86170.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-665, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86171
in-theory        86171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> (B -> C))))
theorem-size     23
proof            (modus-ponens tm-623 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-86171.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> (B -> C)))), M:tm-623, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86172
in-theory        86172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-622 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
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-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-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-86172.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-622, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86173
in-theory        86173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-609 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
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-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-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-86173.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (E or D))), M:tm-609, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86174
in-theory        86174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     31
proof            (modus-ponens tm-605 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86174.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-605, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86175
in-theory        86175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (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-86175.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))))), M:tm-595, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86176
in-theory        86176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-550 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86176.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-550, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86177
in-theory        86177
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-540 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86177.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-540, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86178
in-theory        86178
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-530 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86178.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-530, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86179
in-theory        86179
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     31
proof            (modus-ponens tm-520 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86179.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-520, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86180
in-theory        86180
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-510 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86180.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-510, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86181
in-theory        86181
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-500 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86181.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-500, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86182
in-theory        86182
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G))))
theorem-size     37
proof            (modus-ponens tm-490 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
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-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-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-86182.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G)))), M:tm-490, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86183
in-theory        86183
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-480 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
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-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-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-86183.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-480, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86184
in-theory        86184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (B -> C)) or D))
theorem-size     23
proof            (modus-ponens tm-470 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-86184.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (B -> C)) or D)), M:tm-470, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86185
in-theory        86185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-469 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
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-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-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-86185.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-469, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86186
in-theory        86186
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-456 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
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-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-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-86186.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (D or E))), M:tm-456, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86187
in-theory        86187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     31
proof            (modus-ponens tm-453 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86187.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-453, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86188
in-theory        86188
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (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-86188.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))))), M:tm-443, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86189
in-theory        86189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-409 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86189.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-409, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86190
in-theory        86190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     31
proof            (modus-ponens tm-400 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86190.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-400, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86191
in-theory        86191
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-391 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86191.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-391, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86192
in-theory        86192
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-382 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86192.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-382, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86193
in-theory        86193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G))))
theorem-size     37
proof            (modus-ponens tm-373 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
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-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-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-86193.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G)))), M:tm-373, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86194
in-theory        86194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-364 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
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-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-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-86194.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-364, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86195
in-theory        86195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> (B -> C)) and D)))
theorem-size     25
proof            (modus-ponens tm-355 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-86195.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> (B -> C)) and D))), M:tm-355, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86196
in-theory        86196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     31
proof            (modus-ponens tm-354 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-86196.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-354, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86197
in-theory        86197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-341 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-86197.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86198
in-theory        86198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-338 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (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-86198.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E)))), M:tm-338, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86199
in-theory        86199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((B -> C) -> (B -> C)))))
theorem-size     57
proof            (modus-ponens tm-328 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm 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-328.          ((A -> 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-1.            (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-86199.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((B -> C) -> (B -> C))))), M:tm-328, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86200
in-theory        86200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (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-86200.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))))), M:tm-327, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86201
in-theory        86201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (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-86201.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))))), M:tm-326, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86202
in-theory        86202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (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-86202.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))))), M:tm-325, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86203
in-theory        86203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (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-86203.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))))), M:tm-324, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86204
in-theory        86204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-86204.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))))), M:tm-323, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86205
in-theory        86205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-322 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
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-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-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-86205.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D and E) -> E)), M:tm-322, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86206
in-theory        86206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-320 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
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-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-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-86206.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D and E) -> D)), M:tm-320, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86207
in-theory        86207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-318 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-86207.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86208
in-theory        86208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-316 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-86208.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86209
in-theory        86209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-315 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
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-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-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-86209.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (E -> D))), M:tm-315, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86210
in-theory        86210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((B -> C) -> (B -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     59
proof            (modus-ponens tm-313 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (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-86210.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((B -> C) -> (B -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86211
in-theory        86211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((B -> C) -> (B -> C)) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((B -> C) -> (B -> C))) -> D)))
theorem-size     55
proof            (modus-ponens tm-312 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
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-312.          ((A -> B) -> ((A -> B) and ((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-1.            (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-86211.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((B -> C) -> (B -> C)) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((B -> C) -> (B -> C))) -> D))), M:tm-312, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86212
in-theory        86212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (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-86212.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))))), M:tm-311, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86213
in-theory        86213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) or D))
theorem-size     45
proof            (modus-ponens tm-310 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (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-86213.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) or D)), M:tm-310, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86214
in-theory        86214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and D)))
theorem-size     47
proof            (modus-ponens tm-309 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-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-1.            (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-86214.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and D))), M:tm-309, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86215
in-theory        86215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C))))
theorem-size     57
proof            (modus-ponens tm-306 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C (-> Bm Cm))))
axioms-used      (tm-2 tm-5 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (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-86215.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)))), M:tm-306, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C (-> Bm Cm)))
================================================================
tm-name          tm-86216
in-theory        86216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-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-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-86216.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))))), M:tm-305, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86217
in-theory        86217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     33
proof            (modus-ponens tm-303 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-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-86217.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-303, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86218
in-theory        86218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     31
proof            (modus-ponens tm-270 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
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-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-86218.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-270, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86219
in-theory        86219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     31
proof            (modus-ponens tm-239 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
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-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-86219.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-239, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86220
in-theory        86220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G))))
theorem-size     39
proof            (modus-ponens tm-210 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (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-86220.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G)))), M:tm-210, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86221
in-theory        86221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     31
proof            (modus-ponens tm-183 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-86221.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-183, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86222
in-theory        86222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-157 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-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-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-86222.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-157, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86223
in-theory        86223
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     37
proof            (modus-ponens tm-147 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-1.            (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-86223.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-147, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86224
in-theory        86224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-134 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-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-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-86224.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-134, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86225
in-theory        86225
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     37
proof            (modus-ponens tm-125 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-1.            (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-86225.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-125, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86226
in-theory        86226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> B) -> ((B -> C) -> C)))
theorem-size     25
proof            (modus-ponens tm-114 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C Bm) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86226.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> B) -> ((B -> C) -> C))), M:tm-114, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C Bm) (D Cm))
================================================================
tm-name          tm-86227
in-theory        86227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G))))
theorem-size     37
proof            (modus-ponens tm-113 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-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-86227.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G)))), M:tm-113, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86228
in-theory        86228
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     41
proof            (modus-ponens tm-105 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-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-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-86228.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-105, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86229
in-theory        86229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-95 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-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-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-86229.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E)))), M:tm-95, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86230
in-theory        86230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> (B -> C))))
theorem-size     23
proof            (modus-ponens tm-84 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-86230.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> (B -> C)))), M:tm-84, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86231
in-theory        86231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     29
proof            (modus-ponens tm-83 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
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-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-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-86231.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-83, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86232
in-theory        86232
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-76 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1)
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-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-86232.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> (C -> D)))), M:tm-76, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86233
in-theory        86233
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C)))
theorem-size     37
proof            (modus-ponens tm-73 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       165
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86233.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C))), M:tm-73, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86234
in-theory        86234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E))))
theorem-size     33
proof            (modus-ponens tm-69 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1)
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-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-86234.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E)))), M:tm-69, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86235
in-theory        86235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-54 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86235.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-54, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86236
in-theory        86236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((A -> B) -> (A -> B)))
theorem-size     31
proof            (modus-ponens tm-50 tm-941 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       161
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86236.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((A -> B) -> (A -> B))), M:tm-50, m:tm-941, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86237
in-theory        86237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C)))
theorem-size     25
proof            (modus-ponens tm-49 tm-941 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (-> Bm Cm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86237.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C))), M:tm-49, m:tm-941, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86238
in-theory        86238
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((C -> D) -> (C -> D)))
theorem-size     37
proof            (modus-ponens tm-47 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       165
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86238.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((C -> D) -> (C -> D))), M:tm-47, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86239
in-theory        86239
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C)))
theorem-size     37
proof            (modus-ponens tm-46 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       165
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86239.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> (B -> C))), M:tm-46, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86240
in-theory        86240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-42 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-42.           (A -> ((B -> (C or B)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86240.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E)))), M:tm-42, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86241
in-theory        86241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-32 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-32.           (A -> ((B -> (B or C)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86241.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E)))), M:tm-32, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86242
in-theory        86242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((B -> C) -> (B -> C))))
theorem-size     35
proof            (modus-ponens tm-24 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86242.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((B -> C) -> (B -> C)))), M:tm-24, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86243
in-theory        86243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-23 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86243.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E)))), M:tm-23, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86244
in-theory        86244
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-22 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
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-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-86244.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E)))), M:tm-22, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86245
in-theory        86245
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-21 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
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-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-86245.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E)))), M:tm-21, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86246
in-theory        86246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-20 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (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-86246.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> (E -> F)))), M:tm-20, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86247
in-theory        86247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-19 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
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-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-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-86247.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> (D -> E)))), M:tm-19, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86248
in-theory        86248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((B -> C) -> (B -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     37
proof            (modus-ponens tm-9 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-9 tm-8 tm-2 tm-1)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86248.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((B -> C) -> (B -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86249
in-theory        86249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> B)) -> C) -> ((((D -> A) or ((A -> B) -> ((D or A) -> B))) or ((A -> B) -> (A -> B))) -> C))
theorem-size     33
proof            (modus-ponens tm-8 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-8 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86249.        ((((A -> B) -> (A -> B)) -> C) -> ((((D -> A) or ((A -> B) -> ((D or A) -> B))) or ((A -> B) -> (A -> B))) -> C)), M:tm-8, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-86250
in-theory        86250
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> (C -> D))))
theorem-size     23
proof            (modus-ponens tm-7 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-7 tm-8 tm-2 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86250.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> (C -> D)))), M:tm-7, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86251
in-theory        86251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) or D)
theorem-size     23
proof            (modus-ponens tm-6 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-6 tm-8 tm-2 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-86251.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))) or D), M:tm-6, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86252
in-theory        86252
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> (C -> D))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86252.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> (C -> D))) and A)), M:tm-5, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86253
in-theory        86253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)))
theorem-size     35
proof            (modus-ponens tm-2 tm-941 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C (-> Bm Cm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86253.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C))), M:tm-2, m:tm-941, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C (-> Bm Cm)))
================================================================
tm-name          tm-86254
in-theory        86254
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> (C -> D))))
theorem-size     23
proof            (modus-ponens tm-1 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-86254.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> (C -> D)))), M:tm-1, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-86255
in-theory        86255
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-930 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-2)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86255.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-930, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86256
in-theory        86256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     65
proof            (modus-ponens tm-920 tm-942 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-14.           (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-86256.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-920, m:tm-942, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86257
in-theory        86257
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-893 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (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       209
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86257.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-893, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86258
in-theory        86258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     59
proof            (modus-ponens tm-882 tm-942 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-14.           (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-86258.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-882, m:tm-942, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86259
in-theory        86259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-855 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86259.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-855, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86260
in-theory        86260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-808 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86260.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-808, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86261
in-theory        86261
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     71
proof            (modus-ponens tm-798 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-14.           (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-86261.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-798, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86262
in-theory        86262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86262.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-757, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86263
in-theory        86263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and G) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86263.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and G) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-747, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86264
in-theory        86264
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86264.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-708, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86265
in-theory        86265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86265.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-665, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86266
in-theory        86266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86266.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-622, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86267
in-theory        86267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-14.           (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-86267.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H or G))), M:tm-609, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86268
in-theory        86268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86268.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-605, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86269
in-theory        86269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86269.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-595, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86270
in-theory        86270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86270.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-550, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86271
in-theory        86271
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86271.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-540, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86272
in-theory        86272
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86272.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-530, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86273
in-theory        86273
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86273.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-520, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86274
in-theory        86274
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86274.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-510, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86275
in-theory        86275
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86275.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-500, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86276
in-theory        86276
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86276.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-490, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86277
in-theory        86277
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86277.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-480, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86278
in-theory        86278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86278.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-469, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86279
in-theory        86279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-14.           (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-86279.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (G or H))), M:tm-456, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86280
in-theory        86280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86280.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-453, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86281
in-theory        86281
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (G or H)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86281.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (G or H)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-443, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86282
in-theory        86282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86282.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-409, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86283
in-theory        86283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86283.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-400, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86284
in-theory        86284
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86284.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-391, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86285
in-theory        86285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86285.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-382, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86286
in-theory        86286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86286.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-373, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86287
in-theory        86287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86287.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-364, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86288
in-theory        86288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86288.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-354, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86289
in-theory        86289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> (G and H))))
theorem-size     35
proof            (modus-ponens tm-341 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-14.           (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-86289.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86290
in-theory        86290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86290.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-338, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86291
in-theory        86291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
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-328.          ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86291.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-328, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86292
in-theory        86292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86292.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-327, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86293
in-theory        86293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> H) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86293.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> H) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-326, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86294
in-theory        86294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86294.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-325, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86295
in-theory        86295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86295.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-324, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86296
in-theory        86296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-14.           (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-86296.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-323, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86297
in-theory        86297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-14.           (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-86297.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> H)), M:tm-322, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86298
in-theory        86298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-14.           (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-86298.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> G)), M:tm-320, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86299
in-theory        86299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> 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-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-86299.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86300
in-theory        86300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-14.           (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-86300.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86301
in-theory        86301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-14.           (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-86301.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> G))), M:tm-315, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86302
in-theory        86302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86302.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86303
in-theory        86303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     73
proof            (modus-ponens tm-312 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86303.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-312, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86304
in-theory        86304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86304.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-311, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86305
in-theory        86305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86305.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-310, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86306
in-theory        86306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 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-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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86306.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and G))), M:tm-309, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86307
in-theory        86307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> F))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (D -> F)))))
theorem-size     69
proof            (modus-ponens tm-306 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Fm))) (C (-> (-> 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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86307.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> F))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (D -> F))))), M:tm-306, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Fm))) (C (-> (-> Dm Em) (-> Dm Fm))))
================================================================
tm-name          tm-86308
in-theory        86308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-1.            (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-14.           (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-86308.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-305, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86309
in-theory        86309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86309.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-303, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86310
in-theory        86310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86310.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-270, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86311
in-theory        86311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86311.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-239, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86312
in-theory        86312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86312.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-210, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86313
in-theory        86313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86313.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-183, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86314
in-theory        86314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86314.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-157, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86315
in-theory        86315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86315.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-147, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86316
in-theory        86316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86316.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-134, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86317
in-theory        86317
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86317.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-125, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86318
in-theory        86318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-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-86318.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-113, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86319
in-theory        86319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-86319.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-105, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86320
in-theory        86320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-14.           (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-86320.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-95, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86321
in-theory        86321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86321.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-83, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86322
in-theory        86322
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86322.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-76, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86323
in-theory        86323
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-73 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86323.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-73, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86324
in-theory        86324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86324.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-69, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86325
in-theory        86325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86325.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-54, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86326
in-theory        86326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-50 tm-942 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86326.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-50, m:tm-942, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86327
in-theory        86327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-49 tm-942 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86327.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-49, m:tm-942, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86328
in-theory        86328
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-47 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86328.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-47, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86329
in-theory        86329
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-46 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86329.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-46, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86330
in-theory        86330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-86330.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-42, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86331
in-theory        86331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-86331.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-32, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86332
in-theory        86332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-24 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-14.           (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-86332.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-24, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86333
in-theory        86333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or 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      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86333.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-23, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86334
in-theory        86334
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-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-86334.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-22, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86335
in-theory        86335
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-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-86335.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-21, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86336
in-theory        86336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-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-14.           (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-86336.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-20, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86337
in-theory        86337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86337.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-19, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86338
in-theory        86338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-9 tm-8 tm-1 tm-2)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86338.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86339
in-theory        86339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((E -> F) or ((F -> G) -> ((E or F) -> G))) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     45
proof            (modus-ponens tm-8 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86339.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((E -> F) or ((F -> G) -> ((E or F) -> G))) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-86340
in-theory        86340
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-7 tm-8 tm-1 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86340.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-7, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86341
in-theory        86341
times-derived    1
----------------------------------------------------------------
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-6 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-6 tm-8 tm-1 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86341.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G), M:tm-6, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86342
in-theory        86342
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86342.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and A)), M:tm-5, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86343
in-theory        86343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> F))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-2 tm-942 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Fm))) (C (-> (-> Dm Em) (-> Dm Fm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-14.           (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-86343.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> F))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (D -> F)))), M:tm-2, m:tm-942, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Fm))) (C (-> (-> Dm Em) (-> Dm Fm))))
================================================================
tm-name          tm-86344
in-theory        86344
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-86344.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-1, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-86345
in-theory        86345
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-930 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86345.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-930, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86346
in-theory        86346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D)))
theorem-size     49
proof            (modus-ponens tm-920 tm-943 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86346.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D))), M:tm-920, m:tm-943, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86347
in-theory        86347
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-893 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86347.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-893, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86348
in-theory        86348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D)))
theorem-size     43
proof            (modus-ponens tm-882 tm-943 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86348.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D))), M:tm-882, m:tm-943, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86349
in-theory        86349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-855 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86349.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-855, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86350
in-theory        86350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-808 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86350.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-808, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86351
in-theory        86351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D)))
theorem-size     55
proof            (modus-ponens tm-798 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86351.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D))), M:tm-798, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86352
in-theory        86352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-757 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86352.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-757, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86353
in-theory        86353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D)))
theorem-size     55
proof            (modus-ponens tm-747 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86353.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D))), M:tm-747, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86354
in-theory        86354
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H)))
theorem-size     45
proof            (modus-ponens tm-708 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86354.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H))), M:tm-708, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86355
in-theory        86355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-665 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-3.            ((A 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-86355.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-665, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86356
in-theory        86356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-622 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A 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-86356.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-622, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86357
in-theory        86357
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A 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-86357.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (G or F))), M:tm-609, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86358
in-theory        86358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-605 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-86358.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-605, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86359
in-theory        86359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-595 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86359.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)))), M:tm-595, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86360
in-theory        86360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-550 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 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-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-86360.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-550, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86361
in-theory        86361
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-540 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-86361.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-540, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86362
in-theory        86362
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-530 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 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-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-86362.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-530, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86363
in-theory        86363
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-520 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-86363.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-520, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86364
in-theory        86364
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-510 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 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-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-86364.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-510, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86365
in-theory        86365
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-500 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-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-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-86365.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-500, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86366
in-theory        86366
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-490 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86366.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H))), M:tm-490, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86367
in-theory        86367
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-480 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A 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-86367.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-480, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86368
in-theory        86368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-469 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A 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-86368.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-469, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86369
in-theory        86369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A 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-86369.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (F or G))), M:tm-456, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86370
in-theory        86370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-453 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-86370.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-453, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86371
in-theory        86371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-443 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86371.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)))), M:tm-443, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86372
in-theory        86372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-409 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-86372.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-409, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86373
in-theory        86373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-400 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-86373.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-400, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86374
in-theory        86374
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-391 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 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-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-86374.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-391, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86375
in-theory        86375
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-382 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-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-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-86375.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-382, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86376
in-theory        86376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-373 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86376.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H))), M:tm-373, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86377
in-theory        86377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-364 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A 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-86377.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-364, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86378
in-theory        86378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-354 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-3.            ((A 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-86378.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-354, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86379
in-theory        86379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A 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-86379.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86380
in-theory        86380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-338 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86380.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F))), M:tm-338, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86381
in-theory        86381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     53
proof            (modus-ponens tm-328 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
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-328.          ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86381.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-328, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86382
in-theory        86382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))))
theorem-size     47
proof            (modus-ponens tm-327 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86382.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)))), M:tm-327, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86383
in-theory        86383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-326 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86383.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)))), M:tm-326, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86384
in-theory        86384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-325 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (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-86384.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)))), M:tm-325, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86385
in-theory        86385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))))
theorem-size     53
proof            (modus-ponens tm-324 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-86385.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)))), M:tm-324, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86386
in-theory        86386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-323 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A 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-86386.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)))), M:tm-323, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86387
in-theory        86387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A 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-86387.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F and G) -> G)), M:tm-322, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86388
in-theory        86388
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-86388.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F and G) -> F)), M:tm-320, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86389
in-theory        86389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-3.            ((A 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-86389.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86390
in-theory        86390
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-3.            ((A 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-86390.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86391
in-theory        86391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A 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-86391.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (G -> F))), M:tm-315, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86392
in-theory        86392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D and E) -> D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86392.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D and E) -> D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86393
in-theory        86393
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((D and E) -> D) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D and E) -> D)) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86393.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((D and E) -> D) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D and E) -> D)) -> F))), M:tm-312, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86394
in-theory        86394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-311 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86394.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)))), M:tm-311, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86395
in-theory        86395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86395.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) or F)), M:tm-310, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86396
in-theory        86396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86396.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and F))), M:tm-309, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86397
in-theory        86397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-306 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and Dm Em)) (C Dm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86397.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))), M:tm-306, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and Dm Em)) (C Dm))
================================================================
tm-name          tm-86398
in-theory        86398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-305 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-3.            ((A 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-86398.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)))), M:tm-305, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86399
in-theory        86399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-303 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-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-86399.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-303, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86400
in-theory        86400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-270 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-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-86400.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-270, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86401
in-theory        86401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-239 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 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-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-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-86401.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-239, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86402
in-theory        86402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H)))
theorem-size     37
proof            (modus-ponens tm-210 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86402.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H))), M:tm-210, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86403
in-theory        86403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-183 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-3.            ((A 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-86403.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-183, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86404
in-theory        86404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-157 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A 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-86404.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-157, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86405
in-theory        86405
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     35
proof            (modus-ponens tm-147 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86405.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-147, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86406
in-theory        86406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-134 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86406.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-134, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86407
in-theory        86407
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     35
proof            (modus-ponens tm-125 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-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-86407.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-125, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86408
in-theory        86408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-113 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86408.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H))), M:tm-113, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86409
in-theory        86409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-105 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86409.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-105, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86410
in-theory        86410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-95 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86410.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F))), M:tm-95, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86411
in-theory        86411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-83 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A 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-86411.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-83, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86412
in-theory        86412
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-76 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 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-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-86412.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> E))), M:tm-76, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86413
in-theory        86413
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D))
theorem-size     35
proof            (modus-ponens tm-73 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-10 tm-1 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86413.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D)), M:tm-73, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86414
in-theory        86414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-69 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 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-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-86414.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F))), M:tm-69, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86415
in-theory        86415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-54 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86415.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-54, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86416
in-theory        86416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-50 tm-943 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86416.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D and E) -> D)), M:tm-50, m:tm-943, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86417
in-theory        86417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-49 tm-943 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86417.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> D)), M:tm-49, m:tm-943, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86418
in-theory        86418
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E and F) -> E))
theorem-size     35
proof            (modus-ponens tm-47 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86418.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E and F) -> E)), M:tm-47, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86419
in-theory        86419
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E and F) -> E))
theorem-size     35
proof            (modus-ponens tm-46 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86419.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E and F) -> E)), M:tm-46, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86420
in-theory        86420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-42 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-86420.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F))), M:tm-42, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86421
in-theory        86421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-32 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-86421.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F))), M:tm-32, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86422
in-theory        86422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))
theorem-size     33
proof            (modus-ponens tm-24 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
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-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-86422.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))), M:tm-24, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86423
in-theory        86423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-23 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86423.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F))), M:tm-23, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86424
in-theory        86424
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-22 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-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-86424.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F))), M:tm-22, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86425
in-theory        86425
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-21 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-3 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-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-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-86425.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F))), M:tm-21, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86426
in-theory        86426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-20 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-86426.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> G))), M:tm-20, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86427
in-theory        86427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-19 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and 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-3.            ((A 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-86427.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> F))), M:tm-19, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86428
in-theory        86428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D and E) -> D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-9 tm-8 tm-1 tm-3)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86428.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D and E) -> D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86429
in-theory        86429
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or ((A and B) -> A)) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-1 tm-3)
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-3.            ((A 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-86429.        ((((A and B) -> A) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or ((A and B) -> A)) -> C)), M:tm-8, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-86430
in-theory        86430
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-7 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86430.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> E))), M:tm-7, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86431
in-theory        86431
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86431.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)) or F), M:tm-6, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86432
in-theory        86432
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> E)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86432.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> E)) and A)), M:tm-5, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86433
in-theory        86433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))
theorem-size     33
proof            (modus-ponens tm-2 tm-943 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and Dm Em)) (C Dm)))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86433.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)), M:tm-2, m:tm-943, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and Dm Em)) (C Dm))
================================================================
tm-name          tm-86434
in-theory        86434
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-1 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
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-3.            ((A 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-86434.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> E))), M:tm-1, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-86435
in-theory        86435
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-930 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86435.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-930, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86436
in-theory        86436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E)))
theorem-size     49
proof            (modus-ponens tm-920 tm-944 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86436.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E))), M:tm-920, m:tm-944, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86437
in-theory        86437
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-893 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86437.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-893, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86438
in-theory        86438
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E)))
theorem-size     43
proof            (modus-ponens tm-882 tm-944 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86438.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E))), M:tm-882, m:tm-944, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86439
in-theory        86439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-855 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86439.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-855, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86440
in-theory        86440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-808 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86440.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-808, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86441
in-theory        86441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E)))
theorem-size     55
proof            (modus-ponens tm-798 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86441.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E))), M:tm-798, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86442
in-theory        86442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-757 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86442.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-757, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86443
in-theory        86443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E)))
theorem-size     55
proof            (modus-ponens tm-747 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86443.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E))), M:tm-747, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86444
in-theory        86444
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I)))
theorem-size     45
proof            (modus-ponens tm-708 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86444.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I))), M:tm-708, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86445
in-theory        86445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-665 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-4.            ((A 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-86445.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-665, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86446
in-theory        86446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-622 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A 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-86446.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-622, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86447
in-theory        86447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86447.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (G or F))), M:tm-609, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86448
in-theory        86448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-605 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-86448.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-605, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86449
in-theory        86449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-595 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86449.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)))), M:tm-595, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86450
in-theory        86450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-550 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 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-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-86450.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-550, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86451
in-theory        86451
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-540 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-86451.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-540, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86452
in-theory        86452
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-530 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 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-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-86452.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-530, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86453
in-theory        86453
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-520 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-86453.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-520, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86454
in-theory        86454
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-510 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-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-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-86454.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-510, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86455
in-theory        86455
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-500 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 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-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-86455.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-500, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86456
in-theory        86456
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-490 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86456.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I))), M:tm-490, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86457
in-theory        86457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-480 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A 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-86457.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-480, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86458
in-theory        86458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-469 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A 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-86458.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-469, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86459
in-theory        86459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86459.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (F or G))), M:tm-456, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86460
in-theory        86460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-453 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-86460.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-453, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86461
in-theory        86461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-443 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86461.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)))), M:tm-443, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86462
in-theory        86462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-409 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-86462.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-409, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86463
in-theory        86463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-400 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-86463.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-400, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86464
in-theory        86464
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-391 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-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-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-86464.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-391, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86465
in-theory        86465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-382 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 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-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-86465.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-382, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86466
in-theory        86466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-373 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86466.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I))), M:tm-373, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86467
in-theory        86467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-364 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A 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-86467.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-364, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86468
in-theory        86468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-354 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-4.            ((A 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-86468.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-354, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86469
in-theory        86469
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A 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-86469.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86470
in-theory        86470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-338 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86470.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G))), M:tm-338, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86471
in-theory        86471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     53
proof            (modus-ponens tm-328 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
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-328.          ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86471.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-328, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86472
in-theory        86472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))))
theorem-size     47
proof            (modus-ponens tm-327 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86472.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)))), M:tm-327, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86473
in-theory        86473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-326 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), 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-86473.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)))), M:tm-326, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86474
in-theory        86474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-325 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86474.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)))), M:tm-325, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86475
in-theory        86475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))))
theorem-size     53
proof            (modus-ponens tm-324 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-86475.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)))), M:tm-324, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86476
in-theory        86476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-323 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A 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-86476.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)))), M:tm-323, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86477
in-theory        86477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86477.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F and G) -> G)), M:tm-322, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86478
in-theory        86478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86478.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F and G) -> F)), M:tm-320, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86479
in-theory        86479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86479.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86480
in-theory        86480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-4.            ((A 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-86480.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86481
in-theory        86481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A 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-86481.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (G -> F))), M:tm-315, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86482
in-theory        86482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D and E) -> E))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86482.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D and E) -> E))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86483
in-theory        86483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((D and E) -> E) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D and E) -> E)) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86483.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((D and E) -> E) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D and E) -> E)) -> F))), M:tm-312, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86484
in-theory        86484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))))
theorem-size     41
proof            (modus-ponens tm-311 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86484.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)))), M:tm-311, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86485
in-theory        86485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86485.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) or F)), M:tm-310, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86486
in-theory        86486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86486.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and F))), M:tm-309, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86487
in-theory        86487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)))
theorem-size     53
proof            (modus-ponens tm-306 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and Dm Em)) (C Em)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86487.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))), M:tm-306, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and Dm Em)) (C Em))
================================================================
tm-name          tm-86488
in-theory        86488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))))
theorem-size     41
proof            (modus-ponens tm-305 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-4.            ((A 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-86488.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)))), M:tm-305, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86489
in-theory        86489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-303 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-1 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-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-86489.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-303, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86490
in-theory        86490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-270 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-4 tm-8 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-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-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-86490.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-270, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86491
in-theory        86491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-239 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-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-86491.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-239, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86492
in-theory        86492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I)))
theorem-size     37
proof            (modus-ponens tm-210 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86492.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I))), M:tm-210, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86493
in-theory        86493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-183 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-4.            ((A 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-86493.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-183, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86494
in-theory        86494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-157 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86494.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-157, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86495
in-theory        86495
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     35
proof            (modus-ponens tm-147 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-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-86495.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-147, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86496
in-theory        86496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-134 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A 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-86496.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-134, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86497
in-theory        86497
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     35
proof            (modus-ponens tm-125 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86497.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-125, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86498
in-theory        86498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-113 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86498.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I))), M:tm-113, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86499
in-theory        86499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-105 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86499.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-105, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86500
in-theory        86500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-95 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86500.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G))), M:tm-95, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86501
in-theory        86501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-83 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A 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-86501.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-83, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86502
in-theory        86502
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-76 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 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-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-86502.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> F))), M:tm-76, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86503
in-theory        86503
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E))
theorem-size     35
proof            (modus-ponens tm-73 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-10 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86503.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E)), M:tm-73, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86504
in-theory        86504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-69 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 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-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-86504.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G))), M:tm-69, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86505
in-theory        86505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-54 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86505.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-54, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86506
in-theory        86506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-50 tm-944 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86506.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D and E) -> E)), M:tm-50, m:tm-944, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86507
in-theory        86507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-49 tm-944 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86507.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D and E) -> E)), M:tm-49, m:tm-944, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86508
in-theory        86508
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E and F) -> F))
theorem-size     35
proof            (modus-ponens tm-47 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86508.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E and F) -> F)), M:tm-47, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86509
in-theory        86509
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E and F) -> F))
theorem-size     35
proof            (modus-ponens tm-46 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-3 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86509.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E and F) -> F)), M:tm-46, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86510
in-theory        86510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-42 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-86510.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G))), M:tm-42, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86511
in-theory        86511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-32 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-86511.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G))), M:tm-32, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86512
in-theory        86512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))
theorem-size     33
proof            (modus-ponens tm-24 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
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-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-86512.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))), M:tm-24, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86513
in-theory        86513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-23 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86513.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G))), M:tm-23, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86514
in-theory        86514
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-22 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-4 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-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-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-86514.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G))), M:tm-22, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86515
in-theory        86515
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-21 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-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-86515.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G))), M:tm-21, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86516
in-theory        86516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-20 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-86516.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G and H) -> H))), M:tm-20, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86517
in-theory        86517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-19 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-8 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-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-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-86517.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F and G) -> G))), M:tm-19, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86518
in-theory        86518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D and E) -> E))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-9 tm-8 tm-1 tm-4)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86518.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D and E) -> E))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86519
in-theory        86519
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or ((A and B) -> B)) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-1 tm-4)
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-4.            ((A 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-86519.        ((((A and B) -> B) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or ((A and B) -> B)) -> C)), M:tm-8, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-86520
in-theory        86520
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-7 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-7 tm-8 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86520.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> F))), M:tm-7, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86521
in-theory        86521
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-6 tm-8 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86521.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)) or F), M:tm-6, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86522
in-theory        86522
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> F)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86522.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> F)) and A)), M:tm-5, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86523
in-theory        86523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))
theorem-size     33
proof            (modus-ponens tm-2 tm-944 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and Dm Em)) (C Em)))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86523.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)), M:tm-2, m:tm-944, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and Dm Em)) (C Em))
================================================================
tm-name          tm-86524
in-theory        86524
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-1 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
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-4.            ((A 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-86524.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E and F) -> F))), M:tm-1, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-86525
in-theory        86525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C)))))
theorem-size     23
proof            (modus-ponens tm-945 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-86525.        ((A -> (B -> A)) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C))))), M:tm-945, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-86526
in-theory        86526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D)))))
theorem-size     27
proof            (modus-ponens tm-945 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-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-86526.        ((A -> (B -> A)) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D))))), M:tm-945, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-86527
in-theory        86527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E))))
theorem-size     23
proof            (modus-ponens tm-945 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-86527.        ((A -> (B -> A)) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E)))), M:tm-945, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-86528
in-theory        86528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C)))))
theorem-size     23
proof            (modus-ponens tm-945 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (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-86528.        ((A -> (B -> A)) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C))))), M:tm-945, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-86529
in-theory        86529
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-930 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86529.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86530
in-theory        86530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     69
proof            (modus-ponens tm-920 tm-945 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86530.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-920, m:tm-945, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86531
in-theory        86531
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-893 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86531.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86532
in-theory        86532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     63
proof            (modus-ponens tm-882 tm-945 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86532.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-882, m:tm-945, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86533
in-theory        86533
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-855 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86533.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86534
in-theory        86534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-808 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86534.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86535
in-theory        86535
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-798 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86535.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-798, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86536
in-theory        86536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-757 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-1.            (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-86536.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86537
in-theory        86537
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-747 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86537.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-747, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86538
in-theory        86538
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     55
proof            (modus-ponens tm-708 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86538.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86539
in-theory        86539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-665 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-86539.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86540
in-theory        86540
times-derived    1
----------------------------------------------------------------
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-623 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-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-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-86540.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E -> (F -> E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-623, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86541
in-theory        86541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-622 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-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-86541.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86542
in-theory        86542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-86542.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F))), M:tm-609, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86543
in-theory        86543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-605 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
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-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-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-86543.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86544
in-theory        86544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (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-86544.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-595, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86545
in-theory        86545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-550 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
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-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-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-86545.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86546
in-theory        86546
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-540 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
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-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-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-86546.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86547
in-theory        86547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-530 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
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-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-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-86547.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86548
in-theory        86548
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-520 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
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-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-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-86548.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86549
in-theory        86549
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-510 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
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-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-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-86549.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86550
in-theory        86550
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-500 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
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-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-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-86550.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86551
in-theory        86551
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-490 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
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-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-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-86551.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86552
in-theory        86552
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-480 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-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-86552.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86553
in-theory        86553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))) or F))
theorem-size     31
proof            (modus-ponens tm-470 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-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-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-86553.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))) or F)), M:tm-470, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86554
in-theory        86554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-469 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-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-86554.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86555
in-theory        86555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-86555.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G))), M:tm-456, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86556
in-theory        86556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-453 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
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-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-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-86556.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86557
in-theory        86557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (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-86557.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-443, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86558
in-theory        86558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-409 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
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-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-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-86558.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86559
in-theory        86559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-400 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
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-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-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-86559.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86560
in-theory        86560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-391 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
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-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-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-86560.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86561
in-theory        86561
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-382 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
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-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-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-86561.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86562
in-theory        86562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-373 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
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-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-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-86562.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86563
in-theory        86563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-364 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-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-86563.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86564
in-theory        86564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (F -> E)) and ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
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-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-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-86564.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (F -> E)) and ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86565
in-theory        86565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-354 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-86565.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86566
in-theory        86566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-86566.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86567
in-theory        86567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     39
proof            (modus-ponens tm-338 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (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-86567.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86568
in-theory        86568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-328 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86568.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86569
in-theory        86569
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (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-86569.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-327, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86570
in-theory        86570
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (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-86570.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-326, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86571
in-theory        86571
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (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-86571.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-325, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86572
in-theory        86572
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86572.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-324, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86573
in-theory        86573
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-86573.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-323, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86574
in-theory        86574
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-86574.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86575
in-theory        86575
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-86575.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86576
in-theory        86576
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-86576.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86577
in-theory        86577
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86577.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86578
in-theory        86578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-86578.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86579
in-theory        86579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86579.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86580
in-theory        86580
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) -> F)))
theorem-size     79
proof            (modus-ponens tm-312 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (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-86580.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) -> F))), M:tm-312, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86581
in-theory        86581
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (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-86581.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-311, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86582
in-theory        86582
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (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-86582.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) or F)), M:tm-310, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86583
in-theory        86583
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-1.            (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-86583.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and F))), M:tm-309, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86584
in-theory        86584
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-86584.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-305, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86585
in-theory        86585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-303 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-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-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-86585.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86586
in-theory        86586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-270 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-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-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-86586.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86587
in-theory        86587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-239 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-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-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-86587.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86588
in-theory        86588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-210 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-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-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-86588.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86589
in-theory        86589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-183 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-86589.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86590
in-theory        86590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-157 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-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-86590.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86591
in-theory        86591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-147 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-1.            (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-86591.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86592
in-theory        86592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-134 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-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-86592.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86593
in-theory        86593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-125 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-1.            (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-86593.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86594
in-theory        86594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-113 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-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-86594.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86595
in-theory        86595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-105 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-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-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-86595.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86596
in-theory        86596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-95 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-86596.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86597
in-theory        86597
times-derived    1
----------------------------------------------------------------
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-84 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-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-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-86597.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F -> E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-84, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86598
in-theory        86598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-83 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-86598.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86599
in-theory        86599
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     35
proof            (modus-ponens tm-76 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
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-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-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-86599.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86600
in-theory        86600
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-73 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86600.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-73, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86601
in-theory        86601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     41
proof            (modus-ponens tm-69 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
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-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-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-86601.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86602
in-theory        86602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-54 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86602.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86603
in-theory        86603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     39
proof            (modus-ponens tm-50 tm-945 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86603.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-945, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86604
in-theory        86604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-945 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86604.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-49, m:tm-945, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86605
in-theory        86605
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D))))
theorem-size     45
proof            (modus-ponens tm-47 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86605.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86606
in-theory        86606
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (F -> E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-46 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86606.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (F -> E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86607
in-theory        86607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-42 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-1.            (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-86607.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86608
in-theory        86608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-32 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-1.            (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-86608.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86609
in-theory        86609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-24 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-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-86609.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86610
in-theory        86610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-23 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-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-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-86610.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86611
in-theory        86611
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-22 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-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-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-86611.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86612
in-theory        86612
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-21 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-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-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-86612.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86613
in-theory        86613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-20 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-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-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-86613.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86614
in-theory        86614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-19 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-86614.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86615
in-theory        86615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-1)
proof-size       159
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86615.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86616
in-theory        86616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or ((A -> (B -> A)) and ((C -> D) -> ((E or C) -> D)))) -> F))
theorem-size     49
proof            (modus-ponens tm-8 tm-945 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (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-86616.        ((((A -> (B -> A)) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or ((A -> (B -> A)) and ((C -> D) -> ((E or C) -> D)))) -> F)), M:tm-8, m:tm-945, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86617
in-theory        86617
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-7 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-1)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (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-86617.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86618
in-theory        86618
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) or F)
theorem-size     31
proof            (modus-ponens tm-6 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-1)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (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-86618.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))) or F), M:tm-6, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86619
in-theory        86619
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86619.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86620
in-theory        86620
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-1 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-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-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-86620.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> E)) and ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86621
in-theory        86621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F or D))) -> ((F or D) -> (E -> (F or D)))))
theorem-size     31
proof            (modus-ponens tm-946 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-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-86621.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F or D))) -> ((F or D) -> (E -> (F or D))))), M:tm-946, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-86622
in-theory        86622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> ((F or D) and E))) -> ((F or D) -> (E -> ((F or D) and E)))))
theorem-size     35
proof            (modus-ponens tm-946 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
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-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-86622.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> ((F or D) and E))) -> ((F or D) -> (E -> ((F or D) and E))))), M:tm-946, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-86623
in-theory        86623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E or D) or F)) -> ((E or D) -> ((E or D) or F))))
theorem-size     31
proof            (modus-ponens tm-946 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-5 tm-2 tm-7 tm-1 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-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-86623.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E or D) or F)) -> ((E or D) -> ((E or D) or F)))), M:tm-946, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-86624
in-theory        86624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or (F or D))) -> ((F or D) -> (E or (F or D)))))
theorem-size     31
proof            (modus-ponens tm-946 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-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-86624.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or (F or D))) -> ((F or D) -> (E or (F or D))))), M:tm-946, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-86625
in-theory        86625
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-930 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-20.           (A -> (((B -> (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-86625.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86626
in-theory        86626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((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     85
proof            (modus-ponens tm-920 tm-946 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86626.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((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-920, m:tm-946, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86627
in-theory        86627
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-893 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-20.           (A -> (((B -> (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-86627.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86628
in-theory        86628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((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     79
proof            (modus-ponens tm-882 tm-946 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86628.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((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-882, m:tm-946, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86629
in-theory        86629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     55
proof            (modus-ponens tm-855 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-20.           (A -> (((B -> (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-86629.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86630
in-theory        86630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-808 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-20.           (A -> (((B -> (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-86630.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86631
in-theory        86631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((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     91
proof            (modus-ponens tm-798 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86631.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((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-798, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86632
in-theory        86632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-757 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86632.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86633
in-theory        86633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and G) or ((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     91
proof            (modus-ponens tm-747 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-20.           (A -> (((B -> (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-86633.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and G) or ((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-747, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86634
in-theory        86634
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     63
proof            (modus-ponens tm-708 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       277
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-20.           (A -> (((B -> (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-86634.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86635
in-theory        86635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-665 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86635.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86636
in-theory        86636
times-derived    1
----------------------------------------------------------------
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-623 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-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-86636.        (((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-623, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86637
in-theory        86637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-622 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86637.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86638
in-theory        86638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (H or G)))
theorem-size     43
proof            (modus-ponens tm-609 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-20.           (A -> (((B -> (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-86638.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (H or G))), M:tm-609, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86639
in-theory        86639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-605 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86639.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86640
in-theory        86640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H or G)) and (((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     81
proof            (modus-ponens tm-595 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-20.           (A -> (((B -> (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-86640.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H or G)) and (((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-595, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86641
in-theory        86641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-550 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86641.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86642
in-theory        86642
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-540 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86642.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86643
in-theory        86643
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-530 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86643.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86644
in-theory        86644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-520 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86644.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86645
in-theory        86645
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-510 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86645.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86646
in-theory        86646
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-500 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86646.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86647
in-theory        86647
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-490 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-20.           (A -> (((B -> (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-86647.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86648
in-theory        86648
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-480 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86648.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86649
in-theory        86649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))) or G))
theorem-size     39
proof            (modus-ponens tm-470 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-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-86649.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))) or G)), M:tm-470, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86650
in-theory        86650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-469 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86650.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86651
in-theory        86651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (G or H)))
theorem-size     43
proof            (modus-ponens tm-456 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-20.           (A -> (((B -> (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-86651.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (G or H))), M:tm-456, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86652
in-theory        86652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-453 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86652.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86653
in-theory        86653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (G or H)) and (((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     81
proof            (modus-ponens tm-443 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-20.           (A -> (((B -> (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-86653.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (G or H)) and (((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-443, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86654
in-theory        86654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-409 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86654.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86655
in-theory        86655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-400 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86655.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86656
in-theory        86656
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-391 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86656.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86657
in-theory        86657
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-382 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86657.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86658
in-theory        86658
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-373 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-20.           (A -> (((B -> (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-86658.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86659
in-theory        86659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-364 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86659.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86660
in-theory        86660
times-derived    1
----------------------------------------------------------------
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))) and D)))
theorem-size     41
proof            (modus-ponens tm-355 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       213
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86660.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86661
in-theory        86661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-354 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86661.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86662
in-theory        86662
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (H -> (G and H))))
theorem-size     45
proof            (modus-ponens tm-341 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-20.           (A -> (((B -> (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-86662.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86663
in-theory        86663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     47
proof            (modus-ponens tm-338 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-20.           (A -> (((B -> (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-86663.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86664
in-theory        86664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     89
proof            (modus-ponens tm-328 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       287
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-20.           (A -> (((B -> (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-86664.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86665
in-theory        86665
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H -> (G and H))) and (((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     83
proof            (modus-ponens tm-327 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-20.           (A -> (((B -> (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-86665.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H -> (G and H))) and (((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-327, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86666
in-theory        86666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G and H) -> H) and (((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     81
proof            (modus-ponens tm-326 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-20.           (A -> (((B -> (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-86666.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G and H) -> H) and (((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-326, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86667
in-theory        86667
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G and H) -> G) and (((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     81
proof            (modus-ponens tm-325 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-20.           (A -> (((B -> (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-86667.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G and H) -> G) and (((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-325, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86668
in-theory        86668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((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     89
proof            (modus-ponens tm-324 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-86668.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((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-324, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86669
in-theory        86669
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H -> G)) and (((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     81
proof            (modus-ponens tm-323 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-20.           (A -> (((B -> (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-86669.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H -> G)) and (((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-323, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86670
in-theory        86670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G and H) -> H))
theorem-size     43
proof            (modus-ponens tm-322 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-20.           (A -> (((B -> (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-86670.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G and H) -> H)), M:tm-322, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86671
in-theory        86671
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G and H) -> G))
theorem-size     43
proof            (modus-ponens tm-320 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-20.           (A -> (((B -> (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-86671.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G and H) -> G)), M:tm-320, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86672
in-theory        86672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     51
proof            (modus-ponens tm-318 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-20.           (A -> (((B -> (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-86672.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86673
in-theory        86673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-316 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-20.           (A -> (((B -> (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-86673.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86674
in-theory        86674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (H -> G)))
theorem-size     43
proof            (modus-ponens tm-315 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-20.           (A -> (((B -> (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-86674.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (H -> G))), M:tm-315, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86675
in-theory        86675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     91
proof            (modus-ponens tm-313 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-20.           (A -> (((B -> (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-86675.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86676
in-theory        86676
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))) -> G) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) -> G)))
theorem-size     103
proof            (modus-ponens tm-312 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-20.           (A -> (((B -> (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-86676.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))) -> G) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) -> G))), M:tm-312, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86677
in-theory        86677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G or (((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     77
proof            (modus-ponens tm-311 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-20.           (A -> (((B -> (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-86677.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G or (((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-311, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86678
in-theory        86678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) or G))
theorem-size     77
proof            (modus-ponens tm-310 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-20.           (A -> (((B -> (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-86678.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) or G)), M:tm-310, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86679
in-theory        86679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and G)))
theorem-size     79
proof            (modus-ponens tm-309 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-20.           (A -> (((B -> (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-86679.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and G))), M:tm-309, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86680
in-theory        86680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (((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     77
proof            (modus-ponens tm-305 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-20.           (A -> (((B -> (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-86680.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (((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-305, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86681
in-theory        86681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-303 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86681.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86682
in-theory        86682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-270 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86682.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86683
in-theory        86683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-239 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86683.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86684
in-theory        86684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     55
proof            (modus-ponens tm-210 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-86684.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86685
in-theory        86685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-183 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86685.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86686
in-theory        86686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-157 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86686.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86687
in-theory        86687
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     53
proof            (modus-ponens tm-147 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-20.           (A -> (((B -> (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-86687.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86688
in-theory        86688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-134 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86688.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86689
in-theory        86689
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     53
proof            (modus-ponens tm-125 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-20.           (A -> (((B -> (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-86689.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86690
in-theory        86690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-113 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-20.           (A -> (((B -> (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-86690.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86691
in-theory        86691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     57
proof            (modus-ponens tm-105 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       259
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-20.           (A -> (((B -> (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-86691.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86692
in-theory        86692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     45
proof            (modus-ponens tm-95 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-20.           (A -> (((B -> (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-86692.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86693
in-theory        86693
times-derived    1
----------------------------------------------------------------
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-84 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-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-86693.        (((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-84, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86694
in-theory        86694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-83 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86694.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86695
in-theory        86695
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-76 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86695.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86696
in-theory        86696
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((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     53
proof            (modus-ponens tm-73 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-2)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86696.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((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-73, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86697
in-theory        86697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     49
proof            (modus-ponens tm-69 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86697.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86698
in-theory        86698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-54 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86698.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86699
in-theory        86699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     47
proof            (modus-ponens tm-50 tm-946 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86699.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-946, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86700
in-theory        86700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((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     41
proof            (modus-ponens tm-49 tm-946 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       199
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86700.        (((A -> B) or ((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-49, m:tm-946, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86701
in-theory        86701
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D))))
theorem-size     53
proof            (modus-ponens tm-47 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86701.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86702
in-theory        86702
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     53
proof            (modus-ponens tm-46 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86702.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86703
in-theory        86703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-42 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86703.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86704
in-theory        86704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-32 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86704.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86705
in-theory        86705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     51
proof            (modus-ponens tm-24 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86705.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86706
in-theory        86706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     45
proof            (modus-ponens tm-23 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86706.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86707
in-theory        86707
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-22 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86707.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86708
in-theory        86708
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-21 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86708.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86709
in-theory        86709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-20 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-86709.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86710
in-theory        86710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-19 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86710.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86711
in-theory        86711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-9 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-2)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86711.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86712
in-theory        86712
times-derived    1
----------------------------------------------------------------
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))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((F or D) -> E)))) -> G))
theorem-size     65
proof            (modus-ponens tm-8 tm-946 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86712.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((F or D) -> E))) -> G) -> ((((F -> D) or ((D -> E) -> ((F or D) -> E))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((F or D) -> E)))) -> G)), M:tm-8, m:tm-946, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86713
in-theory        86713
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     39
proof            (modus-ponens tm-7 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-2)
proof-size       171
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86713.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86714
in-theory        86714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) or G)
theorem-size     39
proof            (modus-ponens tm-6 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-2)
proof-size       171
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86714.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))) or G), M:tm-6, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86715
in-theory        86715
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     41
proof            (modus-ponens tm-5 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-20.           (A -> (((B -> (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-86715.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86716
in-theory        86716
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     39
proof            (modus-ponens tm-1 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-2)
proof-size       171
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-86716.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86717
in-theory        86717
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C)))))
theorem-size     23
proof            (modus-ponens tm-947 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-86717.        (((A and B) -> A) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C))))), M:tm-947, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-86718
in-theory        86718
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D)))))
theorem-size     27
proof            (modus-ponens tm-947 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-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-86718.        (((A and B) -> A) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D))))), M:tm-947, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-86719
in-theory        86719
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E))))
theorem-size     23
proof            (modus-ponens tm-947 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-5 tm-3 tm-7 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-86719.        (((A and B) -> A) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E)))), M:tm-947, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-86720
in-theory        86720
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C)))))
theorem-size     23
proof            (modus-ponens tm-947 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-86720.        (((A and B) -> A) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C))))), M:tm-947, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-86721
in-theory        86721
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-930 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86721.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86722
in-theory        86722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     69
proof            (modus-ponens tm-920 tm-947 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86722.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))), M:tm-920, m:tm-947, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86723
in-theory        86723
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-893 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86723.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86724
in-theory        86724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     63
proof            (modus-ponens tm-882 tm-947 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86724.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))), M:tm-882, m:tm-947, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86725
in-theory        86725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-855 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86725.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86726
in-theory        86726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-808 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86726.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86727
in-theory        86727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-798 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86727.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))), M:tm-798, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86728
in-theory        86728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-757 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-86728.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86729
in-theory        86729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-747 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86729.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))), M:tm-747, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86730
in-theory        86730
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     55
proof            (modus-ponens tm-708 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86730.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86731
in-theory        86731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-665 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-3.            ((A and B) -> 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-86731.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86732
in-theory        86732
times-derived    1
----------------------------------------------------------------
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-623 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-86732.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((E and F) -> E) and ((B -> C) -> ((A or B) -> C))))), M:tm-623, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86733
in-theory        86733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-622 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> 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-86733.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86734
in-theory        86734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> 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-86734.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F))), M:tm-609, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86735
in-theory        86735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-605 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-3.            ((A and B) -> 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-86735.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86736
in-theory        86736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86736.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-595, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86737
in-theory        86737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-550 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
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-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-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-86737.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86738
in-theory        86738
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-540 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
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-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-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-86738.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86739
in-theory        86739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-530 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
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-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-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-86739.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86740
in-theory        86740
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-520 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-3.            ((A and B) -> 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-86740.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86741
in-theory        86741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-510 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
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-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-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-86741.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86742
in-theory        86742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-500 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-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-86742.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86743
in-theory        86743
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-490 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
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-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-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-86743.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86744
in-theory        86744
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-480 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
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-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-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-86744.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86745
in-theory        86745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and E) -> D) and ((B -> C) -> ((A or B) -> C))) or F))
theorem-size     31
proof            (modus-ponens tm-470 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-86745.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and E) -> D) and ((B -> C) -> ((A or B) -> C))) or F)), M:tm-470, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86746
in-theory        86746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-469 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> 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-86746.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86747
in-theory        86747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> 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-86747.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G))), M:tm-456, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86748
in-theory        86748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-453 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-3.            ((A and B) -> 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-86748.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86749
in-theory        86749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86749.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-443, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86750
in-theory        86750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-409 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
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-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-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-86750.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86751
in-theory        86751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-400 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-3.            ((A and B) -> 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-86751.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86752
in-theory        86752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-391 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
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-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-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-86752.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86753
in-theory        86753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-382 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-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-86753.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86754
in-theory        86754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-373 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
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-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-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-86754.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86755
in-theory        86755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-364 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
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-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-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-86755.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86756
in-theory        86756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((E and F) -> E) and ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
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-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-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-86756.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((E and F) -> E) and ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86757
in-theory        86757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-354 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-3.            ((A and B) -> 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-86757.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86758
in-theory        86758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A and B) -> 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-86758.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86759
in-theory        86759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     39
proof            (modus-ponens tm-338 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-3.            ((A and B) -> 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-86759.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86760
in-theory        86760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-328 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86760.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86761
in-theory        86761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86761.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-327, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86762
in-theory        86762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86762.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-326, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86763
in-theory        86763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86763.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-325, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86764
in-theory        86764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86764.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-324, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86765
in-theory        86765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86765.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-323, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86766
in-theory        86766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> 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-86766.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86767
in-theory        86767
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-86767.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86768
in-theory        86768
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-3.            ((A and B) -> 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-86768.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86769
in-theory        86769
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-3.            ((A and B) -> 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-86769.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86770
in-theory        86770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> 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-86770.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86771
in-theory        86771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86771.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86772
in-theory        86772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((((D and E) -> D) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) -> F)))
theorem-size     79
proof            (modus-ponens tm-312 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86772.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (((((D and E) -> D) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) -> F))), M:tm-312, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86773
in-theory        86773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86773.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-311, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86774
in-theory        86774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86774.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) or F)), M:tm-310, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86775
in-theory        86775
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86775.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and F))), M:tm-309, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86776
in-theory        86776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86776.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))), M:tm-305, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86777
in-theory        86777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-303 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3)
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-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-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-86777.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86778
in-theory        86778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-270 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
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-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-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-86778.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86779
in-theory        86779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-239 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-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-86779.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86780
in-theory        86780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-210 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-3.            ((A and B) -> 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-86780.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86781
in-theory        86781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-183 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-3.            ((A and B) -> 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-86781.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86782
in-theory        86782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-157 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> 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-86782.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86783
in-theory        86783
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-147 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-3.            ((A and B) -> 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-86783.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86784
in-theory        86784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-134 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-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-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-86784.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86785
in-theory        86785
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-125 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-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-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-86785.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86786
in-theory        86786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-113 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
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-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-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-86786.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86787
in-theory        86787
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-105 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
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-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-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-86787.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86788
in-theory        86788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-95 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-3.            ((A and B) -> 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-86788.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86789
in-theory        86789
times-derived    1
----------------------------------------------------------------
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-84 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-86789.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E and F) -> E) and ((B -> C) -> ((A or B) -> C))))), M:tm-84, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86790
in-theory        86790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-83 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> 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-86790.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86791
in-theory        86791
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     35
proof            (modus-ponens tm-76 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
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-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-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-86791.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86792
in-theory        86792
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-73 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-3)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86792.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))), M:tm-73, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86793
in-theory        86793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     41
proof            (modus-ponens tm-69 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
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-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-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-86793.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86794
in-theory        86794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-54 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86794.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86795
in-theory        86795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D and E) -> D) and ((A -> B) -> ((C or A) -> B))))
theorem-size     39
proof            (modus-ponens tm-50 tm-947 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86795.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D and E) -> D) and ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-947, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86796
in-theory        86796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-947 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86796.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))), M:tm-49, m:tm-947, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86797
in-theory        86797
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D))))
theorem-size     45
proof            (modus-ponens tm-47 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-3)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86797.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86798
in-theory        86798
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E and F) -> E) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-46 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86798.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E and F) -> E) and ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86799
in-theory        86799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-42 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-3.            ((A and B) -> 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-86799.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86800
in-theory        86800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-32 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-3.            ((A and B) -> 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-86800.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86801
in-theory        86801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-24 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86801.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86802
in-theory        86802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-23 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3)
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-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-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-86802.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86803
in-theory        86803
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-22 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
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-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-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-86803.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86804
in-theory        86804
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-21 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-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-86804.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86805
in-theory        86805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-20 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-86805.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> G) and ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86806
in-theory        86806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-19 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and 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-3.            ((A and B) -> 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-86806.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> F) and ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86807
in-theory        86807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-3)
proof-size       159
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86807.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86808
in-theory        86808
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or (((A and B) -> A) and ((C -> D) -> ((E or C) -> D)))) -> F))
theorem-size     49
proof            (modus-ponens tm-8 tm-947 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-86808.        (((((A and B) -> A) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or (((A and B) -> A) and ((C -> D) -> ((E or C) -> D)))) -> F)), M:tm-8, m:tm-947, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86809
in-theory        86809
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-7 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-86809.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86810
in-theory        86810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) or F)
theorem-size     31
proof            (modus-ponens tm-6 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-86810.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))) or F), M:tm-6, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86811
in-theory        86811
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86811.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86812
in-theory        86812
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-1 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-86812.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> E) and ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86813
in-theory        86813
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C)))))
theorem-size     23
proof            (modus-ponens tm-948 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-86813.        (((A and B) -> B) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C))))), M:tm-948, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-86814
in-theory        86814
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D)))))
theorem-size     27
proof            (modus-ponens tm-948 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-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-86814.        (((A and B) -> B) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D))))), M:tm-948, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-86815
in-theory        86815
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E))))
theorem-size     23
proof            (modus-ponens tm-948 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-5 tm-4 tm-7 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-86815.        (((A and B) -> B) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E)))), M:tm-948, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-86816
in-theory        86816
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C)))))
theorem-size     23
proof            (modus-ponens tm-948 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-86816.        (((A and B) -> B) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C))))), M:tm-948, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-86817
in-theory        86817
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-930 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86817.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86818
in-theory        86818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     69
proof            (modus-ponens tm-920 tm-948 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86818.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))), M:tm-920, m:tm-948, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86819
in-theory        86819
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-893 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86819.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86820
in-theory        86820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     63
proof            (modus-ponens tm-882 tm-948 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86820.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))), M:tm-882, m:tm-948, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86821
in-theory        86821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-855 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86821.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86822
in-theory        86822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-808 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86822.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86823
in-theory        86823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-798 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-86823.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))), M:tm-798, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86824
in-theory        86824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-757 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-4.            ((A and B) -> 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-86824.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86825
in-theory        86825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-747 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86825.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))), M:tm-747, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86826
in-theory        86826
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     55
proof            (modus-ponens tm-708 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86826.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86827
in-theory        86827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-665 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-4.            ((A and B) -> 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-86827.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86828
in-theory        86828
times-derived    1
----------------------------------------------------------------
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-623 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-86828.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((E and F) -> F) and ((B -> C) -> ((A or B) -> C))))), M:tm-623, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86829
in-theory        86829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-622 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> 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-86829.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86830
in-theory        86830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> 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-86830.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F))), M:tm-609, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86831
in-theory        86831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-605 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-4.            ((A and B) -> 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-86831.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86832
in-theory        86832
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> 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-86832.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-595, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86833
in-theory        86833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-550 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
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-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-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-86833.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86834
in-theory        86834
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-540 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-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-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-86834.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86835
in-theory        86835
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-530 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
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-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-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-86835.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86836
in-theory        86836
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-520 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-4.            ((A and B) -> 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-86836.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86837
in-theory        86837
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-510 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-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-86837.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86838
in-theory        86838
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-500 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
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-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-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-86838.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86839
in-theory        86839
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-490 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
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-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-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-86839.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86840
in-theory        86840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-480 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
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-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-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-86840.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86841
in-theory        86841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and E) -> E) and ((B -> C) -> ((A or B) -> C))) or F))
theorem-size     31
proof            (modus-ponens tm-470 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-86841.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and E) -> E) and ((B -> C) -> ((A or B) -> C))) or F)), M:tm-470, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86842
in-theory        86842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-469 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> 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-86842.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86843
in-theory        86843
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> 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-86843.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G))), M:tm-456, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86844
in-theory        86844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-453 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-4.            ((A and B) -> 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-86844.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86845
in-theory        86845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> 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-86845.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-443, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86846
in-theory        86846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-409 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-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-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-86846.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86847
in-theory        86847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-400 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-4.            ((A and B) -> 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-86847.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86848
in-theory        86848
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-391 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-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-86848.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86849
in-theory        86849
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-382 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
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-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-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-86849.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86850
in-theory        86850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-373 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
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-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-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-86850.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86851
in-theory        86851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-364 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
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-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-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-86851.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86852
in-theory        86852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((E and F) -> F) and ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
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-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-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-86852.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((E and F) -> F) and ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86853
in-theory        86853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-354 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-4.            ((A and B) -> 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-86853.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86854
in-theory        86854
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> 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-86854.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86855
in-theory        86855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     39
proof            (modus-ponens tm-338 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> 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-86855.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86856
in-theory        86856
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-328 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86856.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86857
in-theory        86857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> 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-86857.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-327, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86858
in-theory        86858
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-86858.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-326, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86859
in-theory        86859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> 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-86859.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-325, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86860
in-theory        86860
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> 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-86860.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-324, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86861
in-theory        86861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> 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-86861.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-323, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86862
in-theory        86862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-86862.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86863
in-theory        86863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> 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-86863.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86864
in-theory        86864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A and B) -> 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-86864.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86865
in-theory        86865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-4.            ((A and B) -> 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-86865.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86866
in-theory        86866
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> 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-86866.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86867
in-theory        86867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86867.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86868
in-theory        86868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((((D and E) -> E) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) -> F)))
theorem-size     79
proof            (modus-ponens tm-312 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86868.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (((((D and E) -> E) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) -> F))), M:tm-312, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86869
in-theory        86869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> 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-86869.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-311, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86870
in-theory        86870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> 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-86870.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) or F)), M:tm-310, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86871
in-theory        86871
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-4.            ((A and B) -> 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-86871.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and F))), M:tm-309, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86872
in-theory        86872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-4.            ((A and B) -> 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-86872.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))), M:tm-305, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86873
in-theory        86873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-303 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-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-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-86873.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86874
in-theory        86874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-270 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-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-86874.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86875
in-theory        86875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-239 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-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-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-86875.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86876
in-theory        86876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-210 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> 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-86876.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86877
in-theory        86877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-183 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-4.            ((A and B) -> 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-86877.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86878
in-theory        86878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-157 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-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-86878.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86879
in-theory        86879
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-147 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-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-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-86879.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86880
in-theory        86880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-134 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> 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-86880.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86881
in-theory        86881
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-125 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> 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-86881.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86882
in-theory        86882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-113 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
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-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-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-86882.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86883
in-theory        86883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-105 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-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-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-86883.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86884
in-theory        86884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-95 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> 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-86884.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86885
in-theory        86885
times-derived    1
----------------------------------------------------------------
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-84 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-86885.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E and F) -> F) and ((B -> C) -> ((A or B) -> C))))), M:tm-84, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86886
in-theory        86886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-83 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> 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-86886.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86887
in-theory        86887
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     35
proof            (modus-ponens tm-76 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
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-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-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-86887.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86888
in-theory        86888
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-73 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-4)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86888.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))), M:tm-73, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86889
in-theory        86889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     41
proof            (modus-ponens tm-69 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
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-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-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-86889.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86890
in-theory        86890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-54 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86890.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86891
in-theory        86891
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D and E) -> E) and ((A -> B) -> ((C or A) -> B))))
theorem-size     39
proof            (modus-ponens tm-50 tm-948 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86891.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D and E) -> E) and ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-948, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86892
in-theory        86892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-948 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86892.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))), M:tm-49, m:tm-948, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86893
in-theory        86893
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D))))
theorem-size     45
proof            (modus-ponens tm-47 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86893.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86894
in-theory        86894
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E and F) -> F) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-46 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-5 tm-4)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86894.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E and F) -> F) and ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86895
in-theory        86895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-42 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-4.            ((A and B) -> 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-86895.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86896
in-theory        86896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-32 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-4.            ((A and B) -> 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-86896.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86897
in-theory        86897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-24 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86897.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86898
in-theory        86898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-23 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-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-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-86898.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86899
in-theory        86899
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-22 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-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-86899.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86900
in-theory        86900
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-21 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-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-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-86900.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86901
in-theory        86901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-20 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-86901.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and H) -> H) and ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86902
in-theory        86902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-19 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and 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-4.            ((A and B) -> 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-86902.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and G) -> G) and ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86903
in-theory        86903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-4)
proof-size       159
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86903.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86904
in-theory        86904
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or (((A and B) -> B) and ((C -> D) -> ((E or C) -> D)))) -> F))
theorem-size     49
proof            (modus-ponens tm-8 tm-948 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-5 tm-4)
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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-86904.        (((((A and B) -> B) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or (((A and B) -> B) and ((C -> D) -> ((E or C) -> D)))) -> F)), M:tm-8, m:tm-948, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86905
in-theory        86905
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-7 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-4)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-86905.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86906
in-theory        86906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) or F)
theorem-size     31
proof            (modus-ponens tm-6 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-4)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-86906.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))) or F), M:tm-6, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86907
in-theory        86907
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-86907.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86908
in-theory        86908
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-1 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-4)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-86908.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and F) -> F) and ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86909
in-theory        86909
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C)))))
theorem-size     25
proof            (modus-ponens tm-949 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-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-86909.        ((A -> (B -> (A and B))) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C))))), M:tm-949, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-86910
in-theory        86910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D)))))
theorem-size     29
proof            (modus-ponens tm-949 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
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-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-86910.        ((A -> (B -> (A and B))) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D))))), M:tm-949, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-86911
in-theory        86911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E))))
theorem-size     25
proof            (modus-ponens tm-949 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-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-86911.        ((A -> (B -> (A and B))) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E)))), M:tm-949, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-86912
in-theory        86912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C)))))
theorem-size     25
proof            (modus-ponens tm-949 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-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-86912.        ((A -> (B -> (A and B))) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C))))), M:tm-949, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-86913
in-theory        86913
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-930 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86913.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86914
in-theory        86914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     73
proof            (modus-ponens tm-920 tm-949 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86914.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))), M:tm-920, m:tm-949, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86915
in-theory        86915
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-893 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86915.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86916
in-theory        86916
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     67
proof            (modus-ponens tm-882 tm-949 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86916.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))), M:tm-882, m:tm-949, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86917
in-theory        86917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-855 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86917.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86918
in-theory        86918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-808 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86918.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86919
in-theory        86919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     79
proof            (modus-ponens tm-798 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-86919.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))), M:tm-798, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86920
in-theory        86920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-757 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-86920.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86921
in-theory        86921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     79
proof            (modus-ponens tm-747 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-86921.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))), M:tm-747, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86922
in-theory        86922
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     57
proof            (modus-ponens tm-708 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-86922.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86923
in-theory        86923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-665 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-86923.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86924
in-theory        86924
times-derived    1
----------------------------------------------------------------
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-623 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-5.            (A -> (B -> (A and B))), axiom
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-86924.        (((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-623, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86925
in-theory        86925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-622 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-86925.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86926
in-theory        86926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F)))
theorem-size     37
proof            (modus-ponens tm-609 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-86926.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F))), M:tm-609, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86927
in-theory        86927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-605 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-86927.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86928
in-theory        86928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     69
proof            (modus-ponens tm-595 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-86928.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-595, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86929
in-theory        86929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-550 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-86929.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86930
in-theory        86930
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-540 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-86930.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86931
in-theory        86931
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-530 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-86931.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86932
in-theory        86932
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-520 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-86932.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86933
in-theory        86933
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-510 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-86933.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86934
in-theory        86934
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-500 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-86934.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86935
in-theory        86935
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-490 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-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-86935.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86936
in-theory        86936
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-480 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-86936.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86937
in-theory        86937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))) or F))
theorem-size     33
proof            (modus-ponens tm-470 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-5.            (A -> (B -> (A and B))), axiom
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-86937.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))) or F)), M:tm-470, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86938
in-theory        86938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-469 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-86938.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86939
in-theory        86939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G)))
theorem-size     37
proof            (modus-ponens tm-456 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-86939.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G))), M:tm-456, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86940
in-theory        86940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-453 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-86940.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86941
in-theory        86941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     69
proof            (modus-ponens tm-443 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-86941.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-443, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86942
in-theory        86942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-409 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-86942.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86943
in-theory        86943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-400 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-86943.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86944
in-theory        86944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-391 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-86944.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86945
in-theory        86945
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-382 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-86945.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86946
in-theory        86946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-373 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-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-86946.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86947
in-theory        86947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-364 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-86947.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86948
in-theory        86948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (F -> (E and F))) and ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     35
proof            (modus-ponens tm-355 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-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-86948.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (F -> (E and F))) and ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86949
in-theory        86949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-354 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-86949.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86950
in-theory        86950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G))))
theorem-size     39
proof            (modus-ponens tm-341 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-86950.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86951
in-theory        86951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     41
proof            (modus-ponens tm-338 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-86951.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86952
in-theory        86952
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     77
proof            (modus-ponens tm-328 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-86952.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86953
in-theory        86953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     71
proof            (modus-ponens tm-327 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-86953.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-327, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86954
in-theory        86954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     69
proof            (modus-ponens tm-326 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-86954.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-326, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86955
in-theory        86955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     69
proof            (modus-ponens tm-325 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-86955.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-325, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86956
in-theory        86956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     77
proof            (modus-ponens tm-324 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-86956.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-324, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86957
in-theory        86957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     69
proof            (modus-ponens tm-323 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-86957.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-323, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86958
in-theory        86958
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G))
theorem-size     37
proof            (modus-ponens tm-322 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-86958.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86959
in-theory        86959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F))
theorem-size     37
proof            (modus-ponens tm-320 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-86959.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86960
in-theory        86960
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     45
proof            (modus-ponens tm-318 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-86960.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86961
in-theory        86961
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     59
proof            (modus-ponens tm-316 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-86961.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86962
in-theory        86962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F)))
theorem-size     37
proof            (modus-ponens tm-315 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-86962.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86963
in-theory        86963
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     79
proof            (modus-ponens tm-313 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-86963.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86964
in-theory        86964
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) -> F)))
theorem-size     85
proof            (modus-ponens tm-312 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-312.          ((A -> B) -> ((A -> B) and ((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-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-86964.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) -> F))), M:tm-312, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86965
in-theory        86965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-311 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-7.            (A -> (B or 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-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-86965.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-311, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86966
in-theory        86966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) or F))
theorem-size     65
proof            (modus-ponens tm-310 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-6.            (A -> (A or 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-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-86966.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) or F)), M:tm-310, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86967
in-theory        86967
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and F)))
theorem-size     67
proof            (modus-ponens tm-309 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-86967.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and F))), M:tm-309, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86968
in-theory        86968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-305 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-86968.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-305, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86969
in-theory        86969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-303 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-86969.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86970
in-theory        86970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-270 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-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-86970.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86971
in-theory        86971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-239 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-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-86971.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86972
in-theory        86972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     49
proof            (modus-ponens tm-210 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-86972.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86973
in-theory        86973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-183 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-86973.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86974
in-theory        86974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-157 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-86974.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86975
in-theory        86975
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-147 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-86975.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86976
in-theory        86976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-134 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-86976.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86977
in-theory        86977
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-125 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-86977.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86978
in-theory        86978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-113 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-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-86978.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86979
in-theory        86979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-105 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-86979.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86980
in-theory        86980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     39
proof            (modus-ponens tm-95 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-86980.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86981
in-theory        86981
times-derived    1
----------------------------------------------------------------
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-84 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-5.            (A -> (B -> (A and B))), axiom
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-86981.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F -> (E and F))) and ((B -> C) -> ((A or B) -> C))))), M:tm-84, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86982
in-theory        86982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-83 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-86982.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86983
in-theory        86983
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-76 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-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-86983.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86984
in-theory        86984
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     47
proof            (modus-ponens tm-73 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86984.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))), M:tm-73, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86985
in-theory        86985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-69 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-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-86985.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86986
in-theory        86986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-54 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-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-86986.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86987
in-theory        86987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-50 tm-949 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86987.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-949, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86988
in-theory        86988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-49 tm-949 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86988.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))), M:tm-49, m:tm-949, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86989
in-theory        86989
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D))))
theorem-size     47
proof            (modus-ponens tm-47 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86989.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86990
in-theory        86990
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (F -> (E and F))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     47
proof            (modus-ponens tm-46 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86990.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (F -> (E and F))) and ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86991
in-theory        86991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-42 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-86991.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86992
in-theory        86992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-32 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-86992.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86993
in-theory        86993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-24 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-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-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-86993.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-86994
in-theory        86994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     39
proof            (modus-ponens tm-23 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
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-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-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-86994.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86995
in-theory        86995
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-22 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-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-86995.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86996
in-theory        86996
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-21 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-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-86996.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86997
in-theory        86997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-20 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-86997.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H -> (G and H))) and ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86998
in-theory        86998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-19 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-86998.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G -> (F and G))) and ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-86999
in-theory        86999
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     47
proof            (modus-ponens tm-9 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-5)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86999.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87000
in-theory        87000
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or ((A -> (B -> (A and B))) and ((C -> D) -> ((E or C) -> D)))) -> F))
theorem-size     53
proof            (modus-ponens tm-8 tm-949 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-5)
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-5.            (A -> (B -> (A and B))), axiom
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-87000.        ((((A -> (B -> (A and B))) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or ((A -> (B -> (A and B))) and ((C -> D) -> ((E or C) -> D)))) -> F)), M:tm-8, m:tm-949, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87001
in-theory        87001
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     33
proof            (modus-ponens tm-7 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
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-87001.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87002
in-theory        87002
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) or F)
theorem-size     33
proof            (modus-ponens tm-6 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
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-87002.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))) or F), M:tm-6, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87003
in-theory        87003
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87003.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87004
in-theory        87004
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     33
proof            (modus-ponens tm-1 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
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-87004.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F -> (E and F))) and ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87005
in-theory        87005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or A))) -> ((A -> (B -> (C or A))) and ((C or A) -> (B -> (C or A)))))
theorem-size     25
proof            (modus-ponens tm-950 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-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-87005.        ((A -> (B -> (C or A))) -> ((A -> (B -> (C or A))) and ((C or A) -> (B -> (C or A))))), M:tm-950, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-87006
in-theory        87006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C or A) and B))) -> ((A -> (B -> ((C or A) and B))) and ((C or A) -> (B -> ((C or A) and B)))))
theorem-size     31
proof            (modus-ponens tm-950 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87006.        ((A -> (B -> ((C or A) and B))) -> ((A -> (B -> ((C or A) and B))) and ((C or A) -> (B -> ((C or A) and B))))), M:tm-950, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-87007
in-theory        87007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) or C)) -> ((A -> ((B or A) or C)) and ((B or A) -> ((B or A) or C))))
theorem-size     25
proof            (modus-ponens tm-950 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-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-87007.        ((A -> ((B or A) or C)) -> ((A -> ((B or A) or C)) and ((B or A) -> ((B or A) or C)))), M:tm-950, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-87008
in-theory        87008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C or A))) -> ((A -> (B or (C or A))) and ((C or A) -> (B or (C or A)))))
theorem-size     25
proof            (modus-ponens tm-950 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-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-87008.        ((A -> (B or (C or A))) -> ((A -> (B or (C or A))) and ((C or A) -> (B or (C or A))))), M:tm-950, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-87009
in-theory        87009
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-930 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87009.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-930, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87010
in-theory        87010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-920 tm-950 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87010.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))), M:tm-920, m:tm-950, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87011
in-theory        87011
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-893 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87011.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-893, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87012
in-theory        87012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))
theorem-size     59
proof            (modus-ponens tm-882 tm-950 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87012.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))), M:tm-882, m:tm-950, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87013
in-theory        87013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-855 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87013.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-855, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87014
in-theory        87014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-808 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87014.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-808, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87015
in-theory        87015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))
theorem-size     71
proof            (modus-ponens tm-798 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87015.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))), M:tm-798, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87016
in-theory        87016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87016.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-757, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87017
in-theory        87017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87017.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))), M:tm-747, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87018
in-theory        87018
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87018.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G))))), M:tm-708, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87019
in-theory        87019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87019.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-665, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87020
in-theory        87020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((B -> C) and ((A or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-623 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87020.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((B -> C) and ((A or B) -> C))))), M:tm-623, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87021
in-theory        87021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87021.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-622, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87022
in-theory        87022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (E or D)))
theorem-size     33
proof            (modus-ponens tm-609 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87022.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (E or D))), M:tm-609, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87023
in-theory        87023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87023.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-605, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87024
in-theory        87024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87024.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-595, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87025
in-theory        87025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-87025.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-550, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87026
in-theory        87026
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-87026.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-540, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87027
in-theory        87027
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-87027.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-530, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87028
in-theory        87028
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87028.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-520, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87029
in-theory        87029
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87029.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-510, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87030
in-theory        87030
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87030.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-500, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87031
in-theory        87031
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87031.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G))))), M:tm-490, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87032
in-theory        87032
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87032.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-480, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87033
in-theory        87033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((B -> C) and ((A or B) -> C))) or D))
theorem-size     29
proof            (modus-ponens tm-470 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87033.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((B -> C) and ((A or B) -> C))) or D)), M:tm-470, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87034
in-theory        87034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87034.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-469, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87035
in-theory        87035
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (D or E)))
theorem-size     33
proof            (modus-ponens tm-456 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87035.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (D or E))), M:tm-456, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87036
in-theory        87036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87036.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-453, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87037
in-theory        87037
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87037.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-443, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87038
in-theory        87038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-87038.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-409, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87039
in-theory        87039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87039.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-400, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87040
in-theory        87040
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87040.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-391, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87041
in-theory        87041
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87041.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-382, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87042
in-theory        87042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87042.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G))))), M:tm-373, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87043
in-theory        87043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87043.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-364, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87044
in-theory        87044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((B -> C) and ((A or B) -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87044.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((B -> C) and ((A or B) -> C))) and D))), M:tm-355, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87045
in-theory        87045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87045.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-354, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87046
in-theory        87046
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (E -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-341 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87046.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87047
in-theory        87047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87047.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E))))), M:tm-338, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87048
in-theory        87048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87048.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-328, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87049
in-theory        87049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87049.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-327, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87050
in-theory        87050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87050.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-326, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87051
in-theory        87051
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87051.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-325, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87052
in-theory        87052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87052.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-324, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87053
in-theory        87053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87053.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-323, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87054
in-theory        87054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D and E) -> E))
theorem-size     33
proof            (modus-ponens tm-322 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87054.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D and E) -> E)), M:tm-322, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87055
in-theory        87055
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D and E) -> D))
theorem-size     33
proof            (modus-ponens tm-320 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87055.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D and E) -> D)), M:tm-320, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87056
in-theory        87056
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-318 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87056.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87057
in-theory        87057
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-87057.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87058
in-theory        87058
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (E -> D)))
theorem-size     33
proof            (modus-ponens tm-315 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-87058.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (E -> D))), M:tm-315, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87059
in-theory        87059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((B -> C) -> ((B -> C) and ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87059.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((B -> C) -> ((B -> C) and ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87060
in-theory        87060
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((B -> C) -> ((B -> C) and ((A or B) -> C))) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((B -> C) -> ((B -> C) and ((A or B) -> C)))) -> D)))
theorem-size     73
proof            (modus-ponens tm-312 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-87060.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((B -> C) -> ((B -> C) and ((A or B) -> C))) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((B -> C) -> ((B -> C) and ((A or B) -> C)))) -> D))), M:tm-312, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87061
in-theory        87061
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or 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-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-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-87061.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-311, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87062
in-theory        87062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) or D))
theorem-size     57
proof            (modus-ponens tm-310 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or 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-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-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-87062.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) or D)), M:tm-310, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87063
in-theory        87063
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and D)))
theorem-size     59
proof            (modus-ponens tm-309 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87063.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and D))), M:tm-309, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87064
in-theory        87064
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) and ((A or B) -> C)))))
theorem-size     69
proof            (modus-ponens tm-306 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C (and (-> Bm Cm) (-> (or 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-306.          ((A -> (B -> C)) -> ((A -> (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-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-87064.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) and ((A or B) -> C))))), M:tm-306, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C (and (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87065
in-theory        87065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or 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-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-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-87065.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))), M:tm-305, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87066
in-theory        87066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87066.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-303, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87067
in-theory        87067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87067.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-270, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87068
in-theory        87068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87068.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-239, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87069
in-theory        87069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87069.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G))))), M:tm-210, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87070
in-theory        87070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87070.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-183, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87071
in-theory        87071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87071.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-157, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87072
in-theory        87072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87072.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-147, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87073
in-theory        87073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87073.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-134, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87074
in-theory        87074
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87074.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-125, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87075
in-theory        87075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87075.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G))))), M:tm-113, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87076
in-theory        87076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87076.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-105, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87077
in-theory        87077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87077.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E))))), M:tm-95, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87078
in-theory        87078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-84 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87078.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))), M:tm-84, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87079
in-theory        87079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-87079.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-83, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87080
in-theory        87080
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87080.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D))))), M:tm-76, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87081
in-theory        87081
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-73 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87081.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))), M:tm-73, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87082
in-theory        87082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87082.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E))))), M:tm-69, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87083
in-theory        87083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87083.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-54, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87084
in-theory        87084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((A -> B) -> ((A -> B) and ((C or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-50 tm-950 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87084.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((A -> B) -> ((A -> B) and ((C or A) -> B)))), M:tm-50, m:tm-950, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87085
in-theory        87085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-49 tm-950 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87085.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))), M:tm-49, m:tm-950, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87086
in-theory        87086
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D))))
theorem-size     43
proof            (modus-ponens tm-47 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87086.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D)))), M:tm-47, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87087
in-theory        87087
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-46 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87087.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))), M:tm-46, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87088
in-theory        87088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87088.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E))))), M:tm-42, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87089
in-theory        87089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87089.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E))))), M:tm-32, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87090
in-theory        87090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((B -> C) -> ((B -> C) and ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-24 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87090.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((B -> C) -> ((B -> C) and ((A or B) -> C))))), M:tm-24, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87091
in-theory        87091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 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-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-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-87091.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E))))), M:tm-23, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87092
in-theory        87092
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87092.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E))))), M:tm-22, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87093
in-theory        87093
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87093.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E))))), M:tm-21, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87094
in-theory        87094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-87094.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((E -> F) -> ((E -> F) and ((D or E) -> F))))), M:tm-20, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87095
in-theory        87095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87095.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((D -> E) -> ((D -> E) and ((C or D) -> E))))), M:tm-19, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87096
in-theory        87096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((B -> C) -> ((B -> C) and ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-5)
proof-size       163
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87096.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((B -> C) -> ((B -> C) and ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87097
in-theory        87097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> B) and ((C or A) -> B))) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or ((A -> B) -> ((A -> B) and ((C or A) -> B)))) -> D))
theorem-size     45
proof            (modus-ponens tm-8 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87097.        ((((A -> B) -> ((A -> B) and ((C or A) -> B))) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or ((A -> B) -> ((A -> B) and ((C or A) -> B)))) -> D)), M:tm-8, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87098
in-theory        87098
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87098.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D))))), M:tm-7, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87099
in-theory        87099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) or D)
theorem-size     29
proof            (modus-ponens tm-6 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87099.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))) or D), M:tm-6, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87100
in-theory        87100
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or 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-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-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-87100.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D)))) and A)), M:tm-5, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87101
in-theory        87101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) and ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-2 tm-950 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C (and (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       163
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87101.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (B -> C)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) and ((A or B) -> C)))), M:tm-2, m:tm-950, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Bm Cm)) (C (and (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87102
in-theory        87102
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-87102.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((C -> D) -> ((C -> D) and ((B or C) -> D))))), M:tm-1, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87103
in-theory        87103
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87103.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-930, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87104
in-theory        87104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E)))))
theorem-size     53
proof            (modus-ponens tm-920 tm-951 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87104.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E))))), M:tm-920, m:tm-951, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87105
in-theory        87105
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87105.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-893, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87106
in-theory        87106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E)))))
theorem-size     47
proof            (modus-ponens tm-882 tm-951 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87106.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E))))), M:tm-882, m:tm-951, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87107
in-theory        87107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87107.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-855, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87108
in-theory        87108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87108.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-808, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87109
in-theory        87109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E)))))
theorem-size     59
proof            (modus-ponens tm-798 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87109.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E))))), M:tm-798, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87110
in-theory        87110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87110.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-757, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87111
in-theory        87111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E)))))
theorem-size     59
proof            (modus-ponens tm-747 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), 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-87111.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E))))), M:tm-747, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87112
in-theory        87112
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87112.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I))))), M:tm-708, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87113
in-theory        87113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-87113.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-665, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87114
in-theory        87114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-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-87114.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-622, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87115
in-theory        87115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) and D)))
theorem-size     33
proof            (modus-ponens tm-617 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> Em (and (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Em)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87115.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) and D))), M:tm-617, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> Em (and (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Em))))
================================================================
tm-name          tm-87116
in-theory        87116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-87116.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (G or F))), M:tm-609, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87117
in-theory        87117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-1.            (A -> (B -> A)), 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-87117.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-605, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87118
in-theory        87118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87118.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))))), M:tm-595, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87119
in-theory        87119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
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-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-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-87119.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-550, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87120
in-theory        87120
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
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-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-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-87120.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-540, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87121
in-theory        87121
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
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-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-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-87121.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-530, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87122
in-theory        87122
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-1.            (A -> (B -> A)), 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-87122.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-520, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87123
in-theory        87123
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
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-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-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-87123.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-510, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87124
in-theory        87124
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
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-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-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-87124.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-500, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87125
in-theory        87125
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-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-87125.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I))))), M:tm-490, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87126
in-theory        87126
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-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-87126.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-480, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87127
in-theory        87127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-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-87127.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-469, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87128
in-theory        87128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or E) and D)))
theorem-size     33
proof            (modus-ponens tm-464 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (-> Em (and (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B) Em)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87128.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or E) and D))), M:tm-464, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (-> Em (and (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B) Em))))
================================================================
tm-name          tm-87129
in-theory        87129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-87129.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (F or G))), M:tm-456, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87130
in-theory        87130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-1.            (A -> (B -> A)), 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-87130.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-453, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87131
in-theory        87131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87131.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))))), M:tm-443, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87132
in-theory        87132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
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-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-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-87132.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-409, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87133
in-theory        87133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-1.            (A -> (B -> A)), 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-87133.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-400, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87134
in-theory        87134
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
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-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-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-87134.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-391, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87135
in-theory        87135
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
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-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-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-87135.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-382, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87136
in-theory        87136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-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-87136.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I))))), M:tm-373, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87137
in-theory        87137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-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-87137.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-364, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87138
in-theory        87138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-87138.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-354, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87139
in-theory        87139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and E)) and D)))
theorem-size     35
proof            (modus-ponens tm-349 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (-> Em (and (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) Em)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87139.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and E)) and D))), M:tm-349, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (-> Em (and (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) Em))))
================================================================
tm-name          tm-87140
in-theory        87140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-87140.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87141
in-theory        87141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), 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-87141.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G))))), M:tm-338, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87142
in-theory        87142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     57
proof            (modus-ponens tm-328 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-1.            (A -> (B -> A)), 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-87142.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-328, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87143
in-theory        87143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87143.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))))), M:tm-327, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87144
in-theory        87144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87144.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))))), M:tm-326, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87145
in-theory        87145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87145.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))))), M:tm-325, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87146
in-theory        87146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87146.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))))), M:tm-324, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87147
in-theory        87147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or 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-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-87147.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))))), M:tm-323, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87148
in-theory        87148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-87148.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F and G) -> G)), M:tm-322, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87149
in-theory        87149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and 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-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-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-87149.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F and G) -> F)), M:tm-320, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87150
in-theory        87150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-87150.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87151
in-theory        87151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-316 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-87151.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87152
in-theory        87152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-87152.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (G -> F))), M:tm-315, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87153
in-theory        87153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E -> (D and E))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     59
proof            (modus-ponens tm-313 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), 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-87153.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E -> (D and E))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87154
in-theory        87154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((D -> (E -> (D and E))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (E -> (D and E)))) -> F)))
theorem-size     55
proof            (modus-ponens tm-312 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), 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-87154.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (((D -> (E -> (D and E))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (E -> (D and E)))) -> F))), M:tm-312, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87155
in-theory        87155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87155.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))))), M:tm-311, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87156
in-theory        87156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87156.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) or F)), M:tm-310, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87157
in-theory        87157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87157.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and F))), M:tm-309, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87158
in-theory        87158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E -> (D and E)))))
theorem-size     57
proof            (modus-ponens tm-306 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Em (and Dm Em)))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), 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-87158.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E -> (D and E))))), M:tm-306, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Em (and Dm Em))))
================================================================
tm-name          tm-87159
in-theory        87159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or 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-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-87159.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))))), M:tm-305, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87160
in-theory        87160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-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-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-87160.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-303, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87161
in-theory        87161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-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-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-87161.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-270, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87162
in-theory        87162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-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-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-87162.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-239, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87163
in-theory        87163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-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-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-87163.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I))))), M:tm-210, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87164
in-theory        87164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-87164.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-183, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87165
in-theory        87165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-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-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-87165.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-157, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87166
in-theory        87166
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-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-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-87166.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-147, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87167
in-theory        87167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-87167.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-134, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87168
in-theory        87168
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-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-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-87168.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-125, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87169
in-theory        87169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-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-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-87169.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I))))), M:tm-113, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87170
in-theory        87170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-1.            (A -> (B -> A)), 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-87170.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-105, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87171
in-theory        87171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-99 tm-951 ((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Em (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87171.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and D))), M:tm-99, m:tm-951, u:((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Em (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Em))))
================================================================
tm-name          tm-87172
in-theory        87172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))) and D)))
theorem-size     33
proof            (modus-ponens tm-98 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> Em (and (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Em)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87172.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))) and D))), M:tm-98, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> Em (and (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Em))))
================================================================
tm-name          tm-87173
in-theory        87173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-87173.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G))))), M:tm-95, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87174
in-theory        87174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-87174.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-83, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87175
in-theory        87175
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
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-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-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-87175.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> (E and F))))), M:tm-76, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87176
in-theory        87176
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E))))
theorem-size     37
proof            (modus-ponens tm-73 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87176.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E)))), M:tm-73, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87177
in-theory        87177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
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-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-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-87177.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G))))), M:tm-69, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87178
in-theory        87178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-1.            (A -> (B -> A)), 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-87178.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-54, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87179
in-theory        87179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-50 tm-951 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87179.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (E -> (D and E)))), M:tm-50, m:tm-951, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87180
in-theory        87180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-49 tm-951 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87180.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E -> (D and E)))), M:tm-49, m:tm-951, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87181
in-theory        87181
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (F -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-47 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87181.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (F -> (E and F)))), M:tm-47, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87182
in-theory        87182
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (F -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-46 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87182.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (F -> (E and F)))), M:tm-46, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87183
in-theory        87183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-1.            (A -> (B -> A)), 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-87183.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G))))), M:tm-42, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87184
in-theory        87184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-1.            (A -> (B -> A)), 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-87184.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G))))), M:tm-32, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87185
in-theory        87185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-24 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87185.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))), M:tm-24, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87186
in-theory        87186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (A -> (B -> A)), 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-87186.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G))))), M:tm-23, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87187
in-theory        87187
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-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-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-87187.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G))))), M:tm-22, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87188
in-theory        87188
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-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-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-87188.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G))))), M:tm-21, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87189
in-theory        87189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (A -> (B -> A)), 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-87189.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H -> (G and H))))), M:tm-20, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87190
in-theory        87190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-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-87190.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G -> (F and G))))), M:tm-19, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87191
in-theory        87191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E -> (D and E))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     37
proof            (modus-ponens tm-9 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-9 tm-8 tm-1 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87191.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E -> (D and E))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87192
in-theory        87192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or (A -> (B -> (A and B)))) -> C))
theorem-size     33
proof            (modus-ponens tm-8 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87192.        (((A -> (B -> (A and B))) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-87193
in-theory        87193
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-87193.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> (E and F))))), M:tm-7, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87194
in-theory        87194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-87194.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))) or F), M:tm-6, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87195
in-theory        87195
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> (E and F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87195.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> (E and F)))) and A)), M:tm-5, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87196
in-theory        87196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-2 tm-951 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Em (and Dm Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87196.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E -> (D and E)))), M:tm-2, m:tm-951, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (-> Em (and Dm Em))))
================================================================
tm-name          tm-87197
in-theory        87197
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and 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-87197.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F -> (E and F))))), M:tm-1, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-87198
in-theory        87198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C)))))
theorem-size     23
proof            (modus-ponens tm-952 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-87198.        ((A -> (A or B)) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C))))), M:tm-952, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-87199
in-theory        87199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D)))))
theorem-size     27
proof            (modus-ponens tm-952 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-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-87199.        ((A -> (A or B)) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D))))), M:tm-952, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-87200
in-theory        87200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E))))
theorem-size     23
proof            (modus-ponens tm-952 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-5 tm-6 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-87200.        ((A -> (A or B)) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E)))), M:tm-952, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-87201
in-theory        87201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C)))))
theorem-size     23
proof            (modus-ponens tm-952 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-87201.        ((A -> (A or B)) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C))))), M:tm-952, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-87202
in-theory        87202
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-930 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87202.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87203
in-theory        87203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     69
proof            (modus-ponens tm-920 tm-952 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-6)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87203.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-920, m:tm-952, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87204
in-theory        87204
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-893 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (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-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-87204.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87205
in-theory        87205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     63
proof            (modus-ponens tm-882 tm-952 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (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-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-87205.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-882, m:tm-952, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87206
in-theory        87206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-855 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87206.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87207
in-theory        87207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-808 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87207.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87208
in-theory        87208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-798 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87208.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-798, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87209
in-theory        87209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-757 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-6.            (A -> (A or 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-87209.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87210
in-theory        87210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-747 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87210.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-747, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87211
in-theory        87211
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     55
proof            (modus-ponens tm-708 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87211.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87212
in-theory        87212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-665 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87212.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87213
in-theory        87213
times-derived    1
----------------------------------------------------------------
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-623 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-87213.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E -> (E or F)) and ((B -> C) -> ((A or B) -> C))))), M:tm-623, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87214
in-theory        87214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-622 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-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-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-87214.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87215
in-theory        87215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or 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-87215.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F))), M:tm-609, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87216
in-theory        87216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-605 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-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-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-87216.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87217
in-theory        87217
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or 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-87217.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-595, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87218
in-theory        87218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-550 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-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-87218.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87219
in-theory        87219
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-540 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-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-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-87219.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87220
in-theory        87220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-530 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-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-87220.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87221
in-theory        87221
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-520 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-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-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-87221.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87222
in-theory        87222
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-510 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-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-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-87222.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87223
in-theory        87223
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-500 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-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-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-87223.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87224
in-theory        87224
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-490 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-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-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-87224.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87225
in-theory        87225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-480 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-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-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-87225.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87226
in-theory        87226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))) or F))
theorem-size     31
proof            (modus-ponens tm-470 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 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-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-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-87226.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))) or F)), M:tm-470, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87227
in-theory        87227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-469 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-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-87227.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87228
in-theory        87228
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-87228.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G))), M:tm-456, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87229
in-theory        87229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-453 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-87229.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87230
in-theory        87230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-87230.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-443, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87231
in-theory        87231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-409 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-87231.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87232
in-theory        87232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-400 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-87232.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87233
in-theory        87233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-391 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-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-87233.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87234
in-theory        87234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-382 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-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-87234.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87235
in-theory        87235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-373 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-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-87235.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87236
in-theory        87236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-364 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-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-87236.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87237
in-theory        87237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (E or F)) and ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
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-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-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-87237.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (E or F)) and ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87238
in-theory        87238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-354 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-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-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-87238.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87239
in-theory        87239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or 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-87239.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87240
in-theory        87240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     39
proof            (modus-ponens tm-338 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-6.            (A -> (A or 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-87240.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87241
in-theory        87241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-328 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87241.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87242
in-theory        87242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87242.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-327, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87243
in-theory        87243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or 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-87243.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-326, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87244
in-theory        87244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or 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-87244.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-325, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87245
in-theory        87245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87245.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-324, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87246
in-theory        87246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or 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-87246.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-323, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87247
in-theory        87247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or 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-87247.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87248
in-theory        87248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or 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-87248.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87249
in-theory        87249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or 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-87249.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87250
in-theory        87250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-6.            (A -> (A or 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-87250.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87251
in-theory        87251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or 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-87251.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87252
in-theory        87252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87252.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87253
in-theory        87253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) -> F)))
theorem-size     79
proof            (modus-ponens tm-312 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87253.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) -> F))), M:tm-312, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87254
in-theory        87254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or 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-6.            (A -> (A or 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-87254.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-311, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87255
in-theory        87255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-87255.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) or F)), M:tm-310, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87256
in-theory        87256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-6.            (A -> (A or 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-87256.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and F))), M:tm-309, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87257
in-theory        87257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-6.            (A -> (A or 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-87257.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-305, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87258
in-theory        87258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-303 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-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-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-87258.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87259
in-theory        87259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-270 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-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-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-87259.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87260
in-theory        87260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-239 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-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-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-87260.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87261
in-theory        87261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-210 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-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-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-87261.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87262
in-theory        87262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-183 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-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-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-87262.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87263
in-theory        87263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-157 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
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-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-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-87263.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87264
in-theory        87264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-147 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
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-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-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-87264.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87265
in-theory        87265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-134 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
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-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-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-87265.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87266
in-theory        87266
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-125 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
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-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-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-87266.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87267
in-theory        87267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-113 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-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-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-87267.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87268
in-theory        87268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-105 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-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-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-87268.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87269
in-theory        87269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-95 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-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-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-87269.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87270
in-theory        87270
times-derived    1
----------------------------------------------------------------
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-84 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-87270.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (E or F)) and ((B -> C) -> ((A or B) -> C))))), M:tm-84, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87271
in-theory        87271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-83 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-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-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-87271.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87272
in-theory        87272
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     35
proof            (modus-ponens tm-76 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-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-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-87272.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87273
in-theory        87273
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-73 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87273.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-73, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87274
in-theory        87274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     41
proof            (modus-ponens tm-69 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-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-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-87274.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87275
in-theory        87275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-54 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87275.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87276
in-theory        87276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     39
proof            (modus-ponens tm-50 tm-952 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87276.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-952, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87277
in-theory        87277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-952 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87277.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-49, m:tm-952, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87278
in-theory        87278
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D))))
theorem-size     45
proof            (modus-ponens tm-47 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87278.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87279
in-theory        87279
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (E or F)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-46 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87279.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (E or F)) and ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87280
in-theory        87280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-42 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-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-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-87280.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87281
in-theory        87281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-32 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-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-87281.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87282
in-theory        87282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-24 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-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-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-87282.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87283
in-theory        87283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-23 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-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-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-87283.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87284
in-theory        87284
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-22 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-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-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-87284.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87285
in-theory        87285
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-21 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-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-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-87285.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87286
in-theory        87286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-20 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-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-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-87286.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (G or H)) and ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87287
in-theory        87287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-19 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-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-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-87287.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (F or G)) and ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87288
in-theory        87288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-6)
proof-size       159
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87288.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87289
in-theory        87289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or ((A -> (A or B)) and ((C -> D) -> ((E or C) -> D)))) -> F))
theorem-size     49
proof            (modus-ponens tm-8 tm-952 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-5 tm-6)
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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-87289.        ((((A -> (A or B)) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or ((A -> (A or B)) and ((C -> D) -> ((E or C) -> D)))) -> F)), M:tm-8, m:tm-952, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87290
in-theory        87290
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-7 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-5 tm-6)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-87290.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87291
in-theory        87291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) or F)
theorem-size     31
proof            (modus-ponens tm-6 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-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-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-87291.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))) or F), M:tm-6, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87292
in-theory        87292
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87292.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87293
in-theory        87293
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-1 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-6)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-87293.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (E or F)) and ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87294
in-theory        87294
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87294.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-930, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87295
in-theory        87295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E))))
theorem-size     49
proof            (modus-ponens tm-920 tm-953 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87295.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E)))), M:tm-920, m:tm-953, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87296
in-theory        87296
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87296.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-893, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87297
in-theory        87297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E))))
theorem-size     43
proof            (modus-ponens tm-882 tm-953 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87297.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E)))), M:tm-882, m:tm-953, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87298
in-theory        87298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87298.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-855, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87299
in-theory        87299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-6)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87299.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-808, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87300
in-theory        87300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E))))
theorem-size     55
proof            (modus-ponens tm-798 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87300.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E)))), M:tm-798, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87301
in-theory        87301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87301.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-757, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87302
in-theory        87302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E))))
theorem-size     55
proof            (modus-ponens tm-747 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87302.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E)))), M:tm-747, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87303
in-theory        87303
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87303.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I)))), M:tm-708, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87304
in-theory        87304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-6.            (A -> (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-87304.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-665, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87305
in-theory        87305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87305.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-622, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87306
in-theory        87306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or E))
theorem-size     31
proof            (modus-ponens tm-617 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (or (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Em))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87306.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or E)), M:tm-617, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (or (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Em)))
================================================================
tm-name          tm-87307
in-theory        87307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (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-87307.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (G or F))), M:tm-609, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87308
in-theory        87308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87308.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-605, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87309
in-theory        87309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87309.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))))), M:tm-595, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87310
in-theory        87310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-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-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-87310.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-550, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87311
in-theory        87311
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87311.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-540, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87312
in-theory        87312
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-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-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-87312.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-530, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87313
in-theory        87313
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87313.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-520, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87314
in-theory        87314
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87314.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-510, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87315
in-theory        87315
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87315.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-500, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87316
in-theory        87316
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87316.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I)))), M:tm-490, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87317
in-theory        87317
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87317.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-480, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87318
in-theory        87318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87318.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-469, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87319
in-theory        87319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or D) or E))
theorem-size     31
proof            (modus-ponens tm-464 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (or (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B) Em))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87319.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or D) or E)), M:tm-464, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (or (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B) Em)))
================================================================
tm-name          tm-87320
in-theory        87320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-87320.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (F or G))), M:tm-456, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87321
in-theory        87321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-87321.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-453, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87322
in-theory        87322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), 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-87322.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))))), M:tm-443, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87323
in-theory        87323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-87323.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-409, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87324
in-theory        87324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-87324.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-400, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87325
in-theory        87325
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-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-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-87325.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-391, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87326
in-theory        87326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-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-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-87326.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-382, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87327
in-theory        87327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-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-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-87327.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I)))), M:tm-373, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87328
in-theory        87328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87328.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-364, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87329
in-theory        87329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87329.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-354, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87330
in-theory        87330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and D)) or E))
theorem-size     33
proof            (modus-ponens tm-349 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (or (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) Em))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87330.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and D)) or E)), M:tm-349, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (or (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) Em)))
================================================================
tm-name          tm-87331
in-theory        87331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (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-87331.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87332
in-theory        87332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87332.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G)))), M:tm-338, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87333
in-theory        87333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
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-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-87333.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-328, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87334
in-theory        87334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-87334.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))))), M:tm-327, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87335
in-theory        87335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87335.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))))), M:tm-326, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87336
in-theory        87336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87336.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))))), M:tm-325, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87337
in-theory        87337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-87337.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))))), M:tm-324, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87338
in-theory        87338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (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-87338.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))))), M:tm-323, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87339
in-theory        87339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (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-87339.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F and G) -> G)), M:tm-322, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87340
in-theory        87340
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (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-87340.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F and G) -> F)), M:tm-320, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87341
in-theory        87341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (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-87341.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87342
in-theory        87342
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-6.            (A -> (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-87342.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87343
in-theory        87343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (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-87343.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (G -> F))), M:tm-315, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87344
in-theory        87344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (D or E)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87344.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (D or E)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87345
in-theory        87345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((D -> (D or E)) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (D or E))) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87345.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (((D -> (D or E)) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (D or E))) -> F))), M:tm-312, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87346
in-theory        87346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87346.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))))), M:tm-311, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87347
in-theory        87347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), 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-87347.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) or F)), M:tm-310, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87348
in-theory        87348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87348.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and F))), M:tm-309, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87349
in-theory        87349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or E))))
theorem-size     53
proof            (modus-ponens tm-306 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (or Dm Em))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87349.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or E)))), M:tm-306, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (or Dm Em)))
================================================================
tm-name          tm-87350
in-theory        87350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
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-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-6.            (A -> (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-87350.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))))), M:tm-305, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87351
in-theory        87351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87351.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-303, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87352
in-theory        87352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87352.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-270, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87353
in-theory        87353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87353.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-239, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87354
in-theory        87354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87354.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I)))), M:tm-210, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87355
in-theory        87355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87355.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-183, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87356
in-theory        87356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87356.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-157, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87357
in-theory        87357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87357.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-147, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87358
in-theory        87358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87358.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-134, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87359
in-theory        87359
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87359.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-125, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87360
in-theory        87360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87360.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I)))), M:tm-113, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87361
in-theory        87361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87361.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-105, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87362
in-theory        87362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) or D))
theorem-size     29
proof            (modus-ponens tm-99 tm-953 ((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       197
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87362.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) or D)), M:tm-99, m:tm-953, u:((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Em)))
================================================================
tm-name          tm-87363
in-theory        87363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or E))
theorem-size     31
proof            (modus-ponens tm-98 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (or (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87363.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or E)), M:tm-98, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (or (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Em)))
================================================================
tm-name          tm-87364
in-theory        87364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-6.            (A -> (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-87364.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G)))), M:tm-95, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87365
in-theory        87365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87365.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-83, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87366
in-theory        87366
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87366.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (E or F)))), M:tm-76, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87367
in-theory        87367
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E)))
theorem-size     35
proof            (modus-ponens tm-73 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87367.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E))), M:tm-73, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87368
in-theory        87368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87368.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G)))), M:tm-69, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87369
in-theory        87369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87369.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-54, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87370
in-theory        87370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-50 tm-953 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87370.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (D or E))), M:tm-50, m:tm-953, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87371
in-theory        87371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-49 tm-953 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87371.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (D or E))), M:tm-49, m:tm-953, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87372
in-theory        87372
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (E or F)))
theorem-size     35
proof            (modus-ponens tm-47 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87372.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (E or F))), M:tm-47, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87373
in-theory        87373
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (E or F)))
theorem-size     35
proof            (modus-ponens tm-46 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87373.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (E or F))), M:tm-46, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87374
in-theory        87374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87374.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G)))), M:tm-42, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87375
in-theory        87375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 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-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-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-87375.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G)))), M:tm-32, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87376
in-theory        87376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))
theorem-size     33
proof            (modus-ponens tm-24 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
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-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-87376.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))), M:tm-24, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87377
in-theory        87377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87377.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G)))), M:tm-23, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87378
in-theory        87378
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87378.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G)))), M:tm-22, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87379
in-theory        87379
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87379.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G)))), M:tm-21, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87380
in-theory        87380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87380.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (G or H)))), M:tm-20, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87381
in-theory        87381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87381.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (F or G)))), M:tm-19, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87382
in-theory        87382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (D or E)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-9 tm-8 tm-1 tm-6)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87382.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (D or E)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87383
in-theory        87383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or (A -> (A or B))) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-1 tm-6)
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-6.            (A -> (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-87383.        (((A -> (A or B)) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or (A -> (A or B))) -> C)), M:tm-8, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-87384
in-theory        87384
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-7 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-7 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87384.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (E or F)))), M:tm-7, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87385
in-theory        87385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-6 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87385.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))) or F), M:tm-6, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87386
in-theory        87386
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (E or F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87386.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (E or F))) and A)), M:tm-5, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87387
in-theory        87387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or E)))
theorem-size     33
proof            (modus-ponens tm-2 tm-953 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (or Dm Em))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87387.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or E))), M:tm-2, m:tm-953, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (or Dm Em)))
================================================================
tm-name          tm-87388
in-theory        87388
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-1 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-1 tm-8 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (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-87388.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (E or F)))), M:tm-1, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-87389
in-theory        87389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C)))))
theorem-size     23
proof            (modus-ponens tm-954 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-87389.        ((A -> (B or A)) and ((C -> (D -> (E or C))) -> ((E or C) -> (D -> (E or C))))), M:tm-954, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-87390
in-theory        87390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D)))))
theorem-size     27
proof            (modus-ponens tm-954 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> 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-87390.        ((A -> (B or A)) and ((C -> (D -> ((E or C) and D))) -> ((E or C) -> (D -> ((E or C) and D))))), M:tm-954, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-87391
in-theory        87391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E))))
theorem-size     23
proof            (modus-ponens tm-954 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-87391.        ((A -> (B or A)) and ((C -> ((D or C) or E)) -> ((D or C) -> ((D or C) or E)))), M:tm-954, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-87392
in-theory        87392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C)))))
theorem-size     23
proof            (modus-ponens tm-954 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-1.            (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-87392.        ((A -> (B or A)) and ((C -> (D or (E or C))) -> ((E or C) -> (D or (E or C))))), M:tm-954, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-87393
in-theory        87393
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-930 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87393.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87394
in-theory        87394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     69
proof            (modus-ponens tm-920 tm-954 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87394.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-920, m:tm-954, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87395
in-theory        87395
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-893 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87395.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87396
in-theory        87396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     63
proof            (modus-ponens tm-882 tm-954 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87396.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-882, m:tm-954, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87397
in-theory        87397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-855 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87397.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87398
in-theory        87398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-808 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87398.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87399
in-theory        87399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-798 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87399.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-798, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87400
in-theory        87400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-757 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-7.            (A -> (B or 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-87400.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87401
in-theory        87401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-747 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87401.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-747, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87402
in-theory        87402
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     55
proof            (modus-ponens tm-708 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87402.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87403
in-theory        87403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-665 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87403.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87404
in-theory        87404
times-derived    1
----------------------------------------------------------------
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-623 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 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-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-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-87404.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E -> (F or E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-623, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87405
in-theory        87405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-622 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-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-87405.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87406
in-theory        87406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-87406.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G or F))), M:tm-609, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87407
in-theory        87407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-605 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-87407.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87408
in-theory        87408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-87408.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-595, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87409
in-theory        87409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-550 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-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-87409.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87410
in-theory        87410
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-540 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-87410.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87411
in-theory        87411
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-530 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-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-87411.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87412
in-theory        87412
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-520 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-87412.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87413
in-theory        87413
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-510 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-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-87413.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87414
in-theory        87414
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-500 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-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-87414.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87415
in-theory        87415
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-490 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-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-87415.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87416
in-theory        87416
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-480 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-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-87416.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87417
in-theory        87417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))) or F))
theorem-size     31
proof            (modus-ponens tm-470 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-87417.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))) or F)), M:tm-470, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87418
in-theory        87418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-469 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-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-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-87418.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87419
in-theory        87419
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or 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-87419.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (F or G))), M:tm-456, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87420
in-theory        87420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-453 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-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-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-87420.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87421
in-theory        87421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or 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-87421.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-443, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87422
in-theory        87422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-409 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-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-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-87422.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87423
in-theory        87423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-400 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-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-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-87423.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87424
in-theory        87424
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-391 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-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-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-87424.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87425
in-theory        87425
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-382 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-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-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-87425.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87426
in-theory        87426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-373 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-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-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-87426.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87427
in-theory        87427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-364 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-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-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-87427.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87428
in-theory        87428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (F or E)) and ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
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-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-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-87428.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (F or E)) and ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87429
in-theory        87429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-354 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-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-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-87429.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87430
in-theory        87430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or 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-87430.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87431
in-theory        87431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     39
proof            (modus-ponens tm-338 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-7.            (A -> (B or 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-87431.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87432
in-theory        87432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-328 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87432.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87433
in-theory        87433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87433.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-327, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87434
in-theory        87434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or 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-87434.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-326, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87435
in-theory        87435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or 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-87435.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-325, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87436
in-theory        87436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87436.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-324, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87437
in-theory        87437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or 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-87437.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-323, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87438
in-theory        87438
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or 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-87438.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87439
in-theory        87439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or 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-87439.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87440
in-theory        87440
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or 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-87440.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87441
in-theory        87441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-7.            (A -> (B or 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-87441.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87442
in-theory        87442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or 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-87442.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87443
in-theory        87443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87443.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87444
in-theory        87444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) -> F)))
theorem-size     79
proof            (modus-ponens tm-312 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87444.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) -> F))), M:tm-312, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87445
in-theory        87445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-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-87445.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-311, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87446
in-theory        87446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or 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-7.            (A -> (B or 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-87446.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) or F)), M:tm-310, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87447
in-theory        87447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-7.            (A -> (B or 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-87447.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and F))), M:tm-309, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87448
in-theory        87448
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (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-7.            (A -> (B or 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-87448.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))), M:tm-305, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87449
in-theory        87449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     41
proof            (modus-ponens tm-303 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-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-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-87449.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87450
in-theory        87450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-270 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-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-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-87450.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87451
in-theory        87451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-239 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-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-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-87451.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87452
in-theory        87452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-210 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-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-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-87452.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87453
in-theory        87453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-183 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-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-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-87453.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87454
in-theory        87454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-157 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
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-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-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-87454.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87455
in-theory        87455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-147 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
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-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-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-87455.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87456
in-theory        87456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-134 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
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-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-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-87456.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87457
in-theory        87457
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-125 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
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-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-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-87457.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87458
in-theory        87458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-113 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-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-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-87458.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87459
in-theory        87459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-105 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-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-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-87459.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87460
in-theory        87460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-95 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
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-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-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-87460.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87461
in-theory        87461
times-derived    1
----------------------------------------------------------------
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-84 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-87461.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F or E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-84, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87462
in-theory        87462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-83 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-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-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-87462.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87463
in-theory        87463
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     35
proof            (modus-ponens tm-76 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-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-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-87463.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87464
in-theory        87464
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-73 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87464.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-73, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87465
in-theory        87465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     41
proof            (modus-ponens tm-69 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-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-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-87465.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87466
in-theory        87466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-54 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87466.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87467
in-theory        87467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     39
proof            (modus-ponens tm-50 tm-954 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87467.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-954, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87468
in-theory        87468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-954 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87468.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-49, m:tm-954, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87469
in-theory        87469
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D))))
theorem-size     45
proof            (modus-ponens tm-47 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87469.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87470
in-theory        87470
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (F or E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-46 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       177
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87470.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((E -> (F or E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87471
in-theory        87471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-42 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-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-87471.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87472
in-theory        87472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-32 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-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-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-87472.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87473
in-theory        87473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-24 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-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-87473.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87474
in-theory        87474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-23 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-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-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-87474.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87475
in-theory        87475
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-22 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-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-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-87475.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87476
in-theory        87476
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-21 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-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-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-87476.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87477
in-theory        87477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     43
proof            (modus-ponens tm-20 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-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-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-87477.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((G -> (H or G)) and ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87478
in-theory        87478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-19 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-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-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-87478.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((F -> (G or F)) and ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87479
in-theory        87479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-5 tm-7)
proof-size       159
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87479.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87480
in-theory        87480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or ((A -> (B or A)) and ((C -> D) -> ((E or C) -> D)))) -> F))
theorem-size     49
proof            (modus-ponens tm-8 tm-954 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-5 tm-7)
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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-87480.        ((((A -> (B or A)) and ((C -> D) -> ((E or C) -> D))) -> F) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) or ((A -> (B or A)) and ((C -> D) -> ((E or C) -> D)))) -> F)), M:tm-8, m:tm-954, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87481
in-theory        87481
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-7 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-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-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-87481.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87482
in-theory        87482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) or F)
theorem-size     31
proof            (modus-ponens tm-6 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-5 tm-7)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-87482.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))) or F), M:tm-6, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87483
in-theory        87483
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87483.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87484
in-theory        87484
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     31
proof            (modus-ponens tm-1 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-5 tm-7)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-87484.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((E -> (F or E)) and ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87485
in-theory        87485
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87485.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-930, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87486
in-theory        87486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D))))
theorem-size     49
proof            (modus-ponens tm-920 tm-955 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87486.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D)))), M:tm-920, m:tm-955, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87487
in-theory        87487
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87487.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-893, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87488
in-theory        87488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D))))
theorem-size     43
proof            (modus-ponens tm-882 tm-955 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87488.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D)))), M:tm-882, m:tm-955, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87489
in-theory        87489
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-855 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87489.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-855, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87490
in-theory        87490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-7)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87490.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-808, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87491
in-theory        87491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D))))
theorem-size     55
proof            (modus-ponens tm-798 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87491.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((F and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D)))), M:tm-798, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87492
in-theory        87492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87492.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-757, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87493
in-theory        87493
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D))))
theorem-size     55
proof            (modus-ponens tm-747 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87493.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and F) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D)))), M:tm-747, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87494
in-theory        87494
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87494.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H)))), M:tm-708, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87495
in-theory        87495
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-7.            (A -> (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-87495.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-665, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87496
in-theory        87496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87496.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-622, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87497
in-theory        87497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E or ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     31
proof            (modus-ponens tm-617 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (or Em (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87497.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-617, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (or Em (or B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
================================================================
tm-name          tm-87498
in-theory        87498
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-87498.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (G or F))), M:tm-609, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87499
in-theory        87499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-87499.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-605, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87500
in-theory        87500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> 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-87500.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (G or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))))), M:tm-595, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87501
in-theory        87501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-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-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-87501.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-550, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87502
in-theory        87502
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-87502.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-540, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87503
in-theory        87503
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-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-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-87503.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-530, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87504
in-theory        87504
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-87504.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-520, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87505
in-theory        87505
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-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-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-87505.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-510, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87506
in-theory        87506
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-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-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-87506.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-500, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87507
in-theory        87507
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-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-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-87507.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H)))), M:tm-490, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87508
in-theory        87508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87508.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-480, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87509
in-theory        87509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87509.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-469, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87510
in-theory        87510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) or E)))
theorem-size     31
proof            (modus-ponens tm-464 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (or Em (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87510.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) or E))), M:tm-464, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)) (C (or Em (or (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))))
================================================================
tm-name          tm-87511
in-theory        87511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (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-87511.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (F or G))), M:tm-456, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87512
in-theory        87512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87512.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-453, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87513
in-theory        87513
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87513.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (F or G)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))))), M:tm-443, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87514
in-theory        87514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87514.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-409, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87515
in-theory        87515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87515.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-400, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87516
in-theory        87516
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87516.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-391, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87517
in-theory        87517
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87517.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-382, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87518
in-theory        87518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87518.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H)))), M:tm-373, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87519
in-theory        87519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87519.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-364, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87520
in-theory        87520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87520.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-354, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87521
in-theory        87521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and E))))
theorem-size     33
proof            (modus-ponens tm-349 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (or Em (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87521.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and E)))), M:tm-349, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B))) (C (or Em (-> B (and (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B)))))
================================================================
tm-name          tm-87522
in-theory        87522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (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-87522.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87523
in-theory        87523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87523.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F)))), M:tm-338, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87524
in-theory        87524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
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-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-87524.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-328, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87525
in-theory        87525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-87525.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (G -> (F and G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))))), M:tm-327, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87526
in-theory        87526
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87526.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((F and G) -> G) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))))), M:tm-326, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87527
in-theory        87527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87527.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((F and G) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))))), M:tm-325, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87528
in-theory        87528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-87528.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))))), M:tm-324, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87529
in-theory        87529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (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-87529.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (G -> F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))))), M:tm-323, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87530
in-theory        87530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (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-87530.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F and G) -> G)), M:tm-322, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87531
in-theory        87531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (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-87531.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F and G) -> F)), M:tm-320, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87532
in-theory        87532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (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-87532.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87533
in-theory        87533
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-7.            (A -> (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-87533.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87534
in-theory        87534
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (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-87534.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (G -> F))), M:tm-315, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87535
in-theory        87535
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E or D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87535.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E or D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87536
in-theory        87536
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((D -> (E or D)) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (E or D))) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87536.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (((D -> (E or D)) -> F) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (D -> (E or D))) -> F))), M:tm-312, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87537
in-theory        87537
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> 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-87537.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))))), M:tm-311, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87538
in-theory        87538
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87538.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) or F)), M:tm-310, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87539
in-theory        87539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87539.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and F))), M:tm-309, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87540
in-theory        87540
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E or D))))
theorem-size     53
proof            (modus-ponens tm-306 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (or Em Dm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87540.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E or D)))), M:tm-306, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (or Em Dm)))
================================================================
tm-name          tm-87541
in-theory        87541
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-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-7.            (A -> (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-87541.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) and (F -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))))), M:tm-305, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87542
in-theory        87542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87542.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-303, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87543
in-theory        87543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87543.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-270, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87544
in-theory        87544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87544.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-239, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87545
in-theory        87545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87545.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H)))), M:tm-210, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87546
in-theory        87546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87546.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-183, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87547
in-theory        87547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87547.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-157, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87548
in-theory        87548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87548.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-147, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87549
in-theory        87549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87549.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-134, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87550
in-theory        87550
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87550.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-125, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87551
in-theory        87551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87551.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H)))), M:tm-113, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87552
in-theory        87552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87552.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-105, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87553
in-theory        87553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-99 tm-955 ((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Em (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       197
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87553.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-99, m:tm-955, u:((Dm (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Em (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-87554
in-theory        87554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     31
proof            (modus-ponens tm-98 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (or Em (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87554.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-98, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (or Em (-> B (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
================================================================
tm-name          tm-87555
in-theory        87555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-7.            (A -> (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-87555.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F)))), M:tm-95, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87556
in-theory        87556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87556.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-83, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87557
in-theory        87557
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87557.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F or E)))), M:tm-76, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87558
in-theory        87558
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D)))
theorem-size     35
proof            (modus-ponens tm-73 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87558.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D))), M:tm-73, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87559
in-theory        87559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87559.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F)))), M:tm-69, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87560
in-theory        87560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87560.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-54, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87561
in-theory        87561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-50 tm-955 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-7 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87561.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (D -> (E or D))), M:tm-50, m:tm-955, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87562
in-theory        87562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-49 tm-955 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87562.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (D -> (E or D))), M:tm-49, m:tm-955, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87563
in-theory        87563
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (F or E)))
theorem-size     35
proof            (modus-ponens tm-47 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87563.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (E -> (F or E))), M:tm-47, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87564
in-theory        87564
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (F or E)))
theorem-size     35
proof            (modus-ponens tm-46 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87564.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (E -> (F or E))), M:tm-46, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87565
in-theory        87565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 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-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-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-87565.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F)))), M:tm-42, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87566
in-theory        87566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87566.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F)))), M:tm-32, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87567
in-theory        87567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))
theorem-size     33
proof            (modus-ponens tm-24 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
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-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-87567.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))), M:tm-24, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87568
in-theory        87568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87568.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F)))), M:tm-23, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87569
in-theory        87569
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87569.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F)))), M:tm-22, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87570
in-theory        87570
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87570.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F)))), M:tm-21, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87571
in-theory        87571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-87571.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (G -> (H or G)))), M:tm-20, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87572
in-theory        87572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87572.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (F -> (G or F)))), M:tm-19, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87573
in-theory        87573
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E or D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-9 tm-8 tm-1 tm-7)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87573.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (D -> (E or D)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87574
in-theory        87574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or (A -> (B or A))) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-1 tm-7)
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-7.            (A -> (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-87574.        (((A -> (B or A)) -> C) -> ((((D -> E) or ((E -> F) -> ((D or E) -> F))) or (A -> (B or A))) -> C)), M:tm-8, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-87575
in-theory        87575
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-7 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-87575.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F or E)))), M:tm-7, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87576
in-theory        87576
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-6 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87576.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))) or F), M:tm-6, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87577
in-theory        87577
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F or E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87577.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F or E))) and A)), M:tm-5, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87578
in-theory        87578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E or D)))
theorem-size     33
proof            (modus-ponens tm-2 tm-955 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (or Em Dm))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       135
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87578.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (E or D))), M:tm-2, m:tm-955, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (C (or Em Dm)))
================================================================
tm-name          tm-87579
in-theory        87579
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-1 tm-8 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (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-87579.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> (F or E)))), M:tm-1, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-87580
in-theory        87580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or C)) or (C -> (A -> (B or C)))) -> ((B or C) -> (A -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-956 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
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-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-87580.        (((A -> (B or C)) or (C -> (A -> (B or C)))) -> ((B or C) -> (A -> (B or C)))), M:tm-956, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-87581
in-theory        87581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or C) and A)) or (C -> (A -> ((B or C) and A)))) -> ((B or C) -> (A -> ((B or C) and A))))
theorem-size     29
proof            (modus-ponens tm-956 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
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-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-87581.        (((A -> ((B or C) and A)) or (C -> (A -> ((B or C) and A)))) -> ((B or C) -> (A -> ((B or C) and A)))), M:tm-956, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-87582
in-theory        87582
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) or C) or (B -> ((A or B) or C))) -> ((A or B) -> ((A or B) or C)))
theorem-size     23
proof            (modus-ponens tm-956 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
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-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-87582.        ((((A or B) or C) or (B -> ((A or B) or C))) -> ((A or B) -> ((A or B) or C))), M:tm-956, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-87583
in-theory        87583
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or C)) or (C -> (A or (B or C)))) -> ((B or C) -> (A or (B or C))))
theorem-size     23
proof            (modus-ponens tm-956 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (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-87583.        (((A or (B or C)) or (C -> (A or (B or C)))) -> ((B or C) -> (A or (B or C)))), M:tm-956, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-87584
in-theory        87584
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-930 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87584.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-930, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87585
in-theory        87585
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C))))
theorem-size     61
proof            (modus-ponens tm-920 tm-956 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87585.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C)))), M:tm-920, m:tm-956, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87586
in-theory        87586
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-893 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87586.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-893, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87587
in-theory        87587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C))))
theorem-size     55
proof            (modus-ponens tm-882 tm-956 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87587.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C)))), M:tm-882, m:tm-956, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87588
in-theory        87588
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-855 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87588.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-855, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87589
in-theory        87589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-808 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87589.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-808, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87590
in-theory        87590
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C))))
theorem-size     67
proof            (modus-ponens tm-798 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87590.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((D and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C)))), M:tm-798, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87591
in-theory        87591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-757 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-1.            (A -> (B -> A)), 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-87591.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-757, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87592
in-theory        87592
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C))))
theorem-size     67
proof            (modus-ponens tm-747 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-1.            (A -> (B -> A)), 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-87592.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C)))), M:tm-747, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87593
in-theory        87593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G))))
theorem-size     51
proof            (modus-ponens tm-708 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87593.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G)))), M:tm-708, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87594
in-theory        87594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-665 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-87594.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-665, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87595
in-theory        87595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((C or (B -> C)) -> ((A or B) -> C))))
theorem-size     27
proof            (modus-ponens tm-623 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-87595.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((C or (B -> C)) -> ((A or B) -> C)))), M:tm-623, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87596
in-theory        87596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-622 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87596.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-622, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87597
in-theory        87597
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (E or D)))
theorem-size     31
proof            (modus-ponens tm-609 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87597.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (E or D))), M:tm-609, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87598
in-theory        87598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-605 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87598.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-605, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87599
in-theory        87599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), 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-87599.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (E or D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-595, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87600
in-theory        87600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-550 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-1.            (A -> (B -> A)), 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-87600.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-550, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87601
in-theory        87601
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-540 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-1.            (A -> (B -> A)), 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-87601.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-540, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87602
in-theory        87602
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-530 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-1.            (A -> (B -> A)), 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-87602.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-530, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87603
in-theory        87603
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-520 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87603.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-520, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87604
in-theory        87604
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-510 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-1.            (A -> (B -> A)), 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-87604.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-510, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87605
in-theory        87605
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-500 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-1.            (A -> (B -> A)), 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-87605.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-500, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87606
in-theory        87606
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-490 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87606.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G)))), M:tm-490, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87607
in-theory        87607
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-480 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87607.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-480, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87608
in-theory        87608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((C or (B -> C)) -> ((A or B) -> C)) or D))
theorem-size     27
proof            (modus-ponens tm-470 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-87608.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((C or (B -> C)) -> ((A or B) -> C)) or D)), M:tm-470, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87609
in-theory        87609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-469 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87609.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-469, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87610
in-theory        87610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (D or E)))
theorem-size     31
proof            (modus-ponens tm-456 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87610.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (D or E))), M:tm-456, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87611
in-theory        87611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-453 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87611.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-453, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87612
in-theory        87612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), 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-87612.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (D or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-443, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87613
in-theory        87613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-409 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-1.            (A -> (B -> A)), 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-87613.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-409, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87614
in-theory        87614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-400 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87614.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-400, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87615
in-theory        87615
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-391 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-1.            (A -> (B -> A)), 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-87615.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-391, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87616
in-theory        87616
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-382 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-1.            (A -> (B -> A)), 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-87616.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-382, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87617
in-theory        87617
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-373 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87617.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G)))), M:tm-373, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87618
in-theory        87618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-364 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87618.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-364, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87619
in-theory        87619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((C or (B -> C)) -> ((A or B) -> C)) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87619.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((C or (B -> C)) -> ((A or B) -> C)) and D))), M:tm-355, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87620
in-theory        87620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-354 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87620.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-354, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87621
in-theory        87621
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (E -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-341 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87621.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87622
in-theory        87622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-338 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-1.            (A -> (B -> A)), 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-87622.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E)))), M:tm-338, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87623
in-theory        87623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-328 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-328.          ((A -> 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-1.            (A -> (B -> A)), 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-87623.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-328, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87624
in-theory        87624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), 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-87624.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-327, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87625
in-theory        87625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), 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-87625.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((D and E) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-326, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87626
in-theory        87626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), 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-87626.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((D and E) -> D) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-325, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87627
in-theory        87627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> A)), 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-87627.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-324, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87628
in-theory        87628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-87628.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-323, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87629
in-theory        87629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D and E) -> E))
theorem-size     31
proof            (modus-ponens tm-322 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87629.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87630
in-theory        87630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D and E) -> D))
theorem-size     31
proof            (modus-ponens tm-320 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87630.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87631
in-theory        87631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-318 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87631.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87632
in-theory        87632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-316 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87632.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87633
in-theory        87633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (E -> D)))
theorem-size     31
proof            (modus-ponens tm-315 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87633.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87634
in-theory        87634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((C or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     67
proof            (modus-ponens tm-313 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-1.            (A -> (B -> A)), 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-87634.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((C or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87635
in-theory        87635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((C or (B -> C)) -> ((A or B) -> C)) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((C or (B -> C)) -> ((A or B) -> C))) -> D)))
theorem-size     67
proof            (modus-ponens tm-312 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
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-312.          ((A -> B) -> ((A -> B) and ((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-1.            (A -> (B -> A)), 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-87635.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((C or (B -> C)) -> ((A or B) -> C)) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((C or (B -> C)) -> ((A or B) -> C))) -> D))), M:tm-312, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87636
in-theory        87636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), 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-87636.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-311, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87637
in-theory        87637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) or D))
theorem-size     53
proof            (modus-ponens tm-310 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), 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-87637.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) or D)), M:tm-310, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87638
in-theory        87638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and D)))
theorem-size     55
proof            (modus-ponens tm-309 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-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-1.            (A -> (B -> A)), 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-87638.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and D))), M:tm-309, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87639
in-theory        87639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (C or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C))))
theorem-size     65
proof            (modus-ponens tm-306 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Cm (-> Bm Cm))) (C (-> (or Am Bm) Cm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-1.            (A -> (B -> A)), 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-87639.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (C or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C)))), M:tm-306, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Cm (-> Bm Cm))) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-87640
in-theory        87640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
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-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-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-87640.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) and (D -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))))), M:tm-305, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87641
in-theory        87641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-303 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87641.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-303, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87642
in-theory        87642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-270 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87642.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-270, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87643
in-theory        87643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-239 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87643.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-239, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87644
in-theory        87644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G))))
theorem-size     43
proof            (modus-ponens tm-210 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> A)), 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-87644.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G)))), M:tm-210, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87645
in-theory        87645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     35
proof            (modus-ponens tm-183 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87645.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-183, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87646
in-theory        87646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-157 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87646.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-157, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87647
in-theory        87647
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-147 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-1.            (A -> (B -> A)), 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-87647.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-147, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87648
in-theory        87648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-134 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87648.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-134, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87649
in-theory        87649
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-125 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-1.            (A -> (B -> A)), 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-87649.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-125, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87650
in-theory        87650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((C or (B -> C)) -> (A or B)) -> ((C or (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-114 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Cm (-> Bm Cm))) (C (or Am Bm)) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       203
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87650.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((C or (B -> C)) -> (A or B)) -> ((C or (B -> C)) -> C))), M:tm-114, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Cm (-> Bm Cm))) (C (or Am Bm)) (D Cm))
================================================================
tm-name          tm-87651
in-theory        87651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-113 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87651.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G)))), M:tm-113, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87652
in-theory        87652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     45
proof            (modus-ponens tm-105 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87652.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-105, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87653
in-theory        87653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-95 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87653.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E)))), M:tm-95, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87654
in-theory        87654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((C or (B -> C)) -> ((A or B) -> C))))
theorem-size     27
proof            (modus-ponens tm-84 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-87654.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((C or (B -> C)) -> ((A or B) -> C)))), M:tm-84, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87655
in-theory        87655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-83 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87655.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-83, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87656
in-theory        87656
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((D or (C -> D)) -> ((B or C) -> D))))
theorem-size     31
proof            (modus-ponens tm-76 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87656.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((D or (C -> D)) -> ((B or C) -> D)))), M:tm-76, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87657
in-theory        87657
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C)))
theorem-size     41
proof            (modus-ponens tm-73 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87657.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C))), M:tm-73, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87658
in-theory        87658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E))))
theorem-size     37
proof            (modus-ponens tm-69 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87658.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E)))), M:tm-69, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87659
in-theory        87659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-54 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-1.            (A -> (B -> A)), 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-87659.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-54, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87660
in-theory        87660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((B or (A -> B)) -> ((C or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-50 tm-956 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       175
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87660.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((B or (A -> B)) -> ((C or A) -> B))), M:tm-50, m:tm-956, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87661
in-theory        87661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C)))
theorem-size     29
proof            (modus-ponens tm-49 tm-956 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87661.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C))), M:tm-49, m:tm-956, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87662
in-theory        87662
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((D or (C -> D)) -> ((B or C) -> D)))
theorem-size     41
proof            (modus-ponens tm-47 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87662.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((D or (C -> D)) -> ((B or C) -> D))), M:tm-47, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87663
in-theory        87663
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C)))
theorem-size     41
proof            (modus-ponens tm-46 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87663.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((C or (B -> C)) -> ((A or B) -> C))), M:tm-46, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87664
in-theory        87664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-42 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87664.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E)))), M:tm-42, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87665
in-theory        87665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-32 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87665.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E)))), M:tm-32, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87666
in-theory        87666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((C or (B -> C)) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-24 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87666.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((C or (B -> C)) -> ((A or B) -> C)))), M:tm-24, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87667
in-theory        87667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-23 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87667.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E)))), M:tm-23, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87668
in-theory        87668
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-22 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87668.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E)))), M:tm-22, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87669
in-theory        87669
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-21 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87669.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E)))), M:tm-21, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87670
in-theory        87670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-20 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) 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-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-87670.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((F or (E -> F)) -> ((D or E) -> F)))), M:tm-20, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87671
in-theory        87671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-19 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am 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-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-87671.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((E or (D -> E)) -> ((C or D) -> E)))), M:tm-19, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87672
in-theory        87672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((C or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-9 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-9 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87672.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((C or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87673
in-theory        87673
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> ((C or B) -> A)) -> D) -> ((((C -> B) or ((B -> A) -> ((C or B) -> A))) or ((A or (B -> A)) -> ((C or B) -> A))) -> D))
theorem-size     41
proof            (modus-ponens tm-8 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-1)
proof-size       163
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-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-87673.        ((((A or (B -> A)) -> ((C or B) -> A)) -> D) -> ((((C -> B) or ((B -> A) -> ((C or B) -> A))) or ((A or (B -> A)) -> ((C or B) -> A))) -> D)), M:tm-8, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87674
in-theory        87674
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((D or (C -> D)) -> ((B or C) -> D))))
theorem-size     27
proof            (modus-ponens tm-7 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-7 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87674.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((D or (C -> D)) -> ((B or C) -> D)))), M:tm-7, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87675
in-theory        87675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) or D)
theorem-size     27
proof            (modus-ponens tm-6 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-6 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87675.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))) or D), M:tm-6, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87676
in-theory        87676
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((D or (C -> D)) -> ((B or C) -> D))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87676.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((D or (C -> D)) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87677
in-theory        87677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (C or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C)))
theorem-size     39
proof            (modus-ponens tm-2 tm-956 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Cm (-> Bm Cm))) (C (-> (or Am Bm) Cm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87677.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (C or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C))), M:tm-2, m:tm-956, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Cm (-> Bm Cm))) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-87678
in-theory        87678
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((D or (C -> D)) -> ((B or C) -> D))))
theorem-size     27
proof            (modus-ponens tm-1 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-1 tm-8)
proof-size       141
proof-steps      9
----------------------------------------------------------------
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-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-87678.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((D or (C -> D)) -> ((B or C) -> D)))), M:tm-1, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87679
in-theory        87679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or (A -> B)))) or ((A -> B) -> (A -> (C or (A -> B))))) -> ((C or (A -> B)) -> (A -> (C or (A -> B)))))
theorem-size     35
proof            (modus-ponens tm-957 tm-81 ((Am (-> A (-> Dm C))) (Bm (-> (-> Dm C) (-> Dm (or A (-> Dm C))))) (Cm (or A (-> Dm C))) (B Dm) (D (or A (-> Dm C)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-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-87679.        (((A -> (B -> (C or (A -> B)))) or ((A -> B) -> (A -> (C or (A -> B))))) -> ((C or (A -> B)) -> (A -> (C or (A -> B))))), M:tm-957, m:tm-81, u:((Am (-> A (-> Dm C))) (Bm (-> (-> Dm C) (-> Dm (or A (-> Dm C))))) (Cm (or A (-> Dm C))) (B Dm) (D (or A (-> Dm C))))
================================================================
tm-name          tm-87680
in-theory        87680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> ((C or (A -> B)) and A))) or ((A -> B) -> (A -> ((C or (A -> B)) and A)))) -> ((C or (A -> B)) -> (A -> ((C or (A -> B)) and A))))
theorem-size     41
proof            (modus-ponens tm-957 tm-352 ((Am (-> A (-> Dm C))) (Bm (-> (-> Dm C) (-> Dm (and (or A (-> Dm C)) Dm)))) (Cm (or A (-> Dm C))) (B Dm) (D (and (or A (-> Dm C)) Dm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-5)
proof-size       229
proof-steps      13
----------------------------------------------------------------
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-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-87680.        (((A -> (B -> ((C or (A -> B)) and A))) or ((A -> B) -> (A -> ((C or (A -> B)) and A)))) -> ((C or (A -> B)) -> (A -> ((C or (A -> B)) and A)))), M:tm-957, m:tm-352, u:((Am (-> A (-> Dm C))) (Bm (-> (-> Dm C) (-> Dm (and (or A (-> Dm C)) Dm)))) (Cm (or A (-> Dm C))) (B Dm) (D (and (or A (-> Dm C)) Dm)))
================================================================
tm-name          tm-87681
in-theory        87681
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     61
proof            (modus-ponens tm-930 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87681.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-930, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87682
in-theory        87682
times-derived    1
----------------------------------------------------------------
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)))) and (((((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))) or ((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     113
proof            (modus-ponens tm-920 tm-957 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       343
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87682.        ((((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)))) and (((((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))) or ((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-920, m:tm-957, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87683
in-theory        87683
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     61
proof            (modus-ponens tm-893 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87683.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-893, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87684
in-theory        87684
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> (B -> C)) or ((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     101
proof            (modus-ponens tm-882 tm-957 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87684.        ((((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)))) and (((A -> (B -> C)) or ((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-882, m:tm-957, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87685
in-theory        87685
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     65
proof            (modus-ponens tm-855 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       281
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87685.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-855, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87686
in-theory        87686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     59
proof            (modus-ponens tm-808 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87686.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-808, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87687
in-theory        87687
times-derived    1
----------------------------------------------------------------
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)))) and (((E and ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))))) or ((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     121
proof            (modus-ponens tm-798 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       345
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87687.        ((((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)))) and (((E and ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))))) or ((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-798, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87688
in-theory        87688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     59
proof            (modus-ponens tm-757 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87688.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-757, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87689
in-theory        87689
times-derived    1
----------------------------------------------------------------
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)))) and (((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) and E) or ((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     121
proof            (modus-ponens tm-747 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       345
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87689.        ((((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)))) and (((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) and E) or ((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-747, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87690
in-theory        87690
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H)))))
theorem-size     73
proof            (modus-ponens tm-708 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       311
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-87690.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H))))), M:tm-708, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87691
in-theory        87691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     61
proof            (modus-ponens tm-665 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87691.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-665, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87692
in-theory        87692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (E or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-623 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87692.        (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (E or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))))), M:tm-623, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87693
in-theory        87693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-622 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87693.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-622, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87694
in-theory        87694
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (F or E)))
theorem-size     53
proof            (modus-ponens tm-609 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87694.        ((((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)))) and (E -> (F or E))), M:tm-609, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87695
in-theory        87695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-605 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87695.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-605, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87696
in-theory        87696
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (F or E)) and (((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     101
proof            (modus-ponens tm-595 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87696.        ((((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)))) and ((E -> (F or E)) and (((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-595, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87697
in-theory        87697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-550 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87697.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-550, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87698
in-theory        87698
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-540 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87698.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-540, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87699
in-theory        87699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-530 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87699.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-530, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87700
in-theory        87700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-520 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87700.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-520, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87701
in-theory        87701
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-510 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87701.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-510, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87702
in-theory        87702
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-500 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87702.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-500, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87703
in-theory        87703
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H)))))
theorem-size     63
proof            (modus-ponens tm-490 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87703.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H))))), M:tm-490, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87704
in-theory        87704
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-480 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87704.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-480, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87705
in-theory        87705
times-derived    1
----------------------------------------------------------------
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))) or E))
theorem-size     49
proof            (modus-ponens tm-470 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87705.        (((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))) or E)), M:tm-470, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87706
in-theory        87706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-469 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87706.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-469, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87707
in-theory        87707
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (E or F)))
theorem-size     53
proof            (modus-ponens tm-456 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87707.        ((((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)))) and (E -> (E or F))), M:tm-456, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87708
in-theory        87708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-453 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87708.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-453, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87709
in-theory        87709
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (E or F)) and (((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     101
proof            (modus-ponens tm-443 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87709.        ((((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)))) and ((E -> (E or F)) and (((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-443, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87710
in-theory        87710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-409 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87710.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-409, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87711
in-theory        87711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-400 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87711.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-400, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87712
in-theory        87712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-391 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87712.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-391, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87713
in-theory        87713
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-382 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87713.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-382, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87714
in-theory        87714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H)))))
theorem-size     63
proof            (modus-ponens tm-373 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87714.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H))))), M:tm-373, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87715
in-theory        87715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-364 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87715.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-364, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87716
in-theory        87716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (E -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))) and E)))
theorem-size     51
proof            (modus-ponens tm-355 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       247
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87716.        (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (E -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))) and E))), M:tm-355, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87717
in-theory        87717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-354 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87717.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-354, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87718
in-theory        87718
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (F -> (E and F))))
theorem-size     55
proof            (modus-ponens tm-341 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87718.        ((((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)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87719
in-theory        87719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F)))))
theorem-size     57
proof            (modus-ponens tm-338 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       257
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87719.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F))))), M:tm-338, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87720
in-theory        87720
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (((A -> (B -> C)) or (((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     119
proof            (modus-ponens tm-328 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       341
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87720.        ((((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)))) and (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (((A -> (B -> C)) or (((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-328, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87721
in-theory        87721
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (F -> (E and F))) and (((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     103
proof            (modus-ponens tm-327 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       321
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87721.        ((((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)))) and ((E -> (F -> (E and F))) and (((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-327, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87722
in-theory        87722
times-derived    1
----------------------------------------------------------------
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)))) and (((E and F) -> F) and (((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     101
proof            (modus-ponens tm-326 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87722.        ((((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)))) and (((E and F) -> F) and (((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-326, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87723
in-theory        87723
times-derived    1
----------------------------------------------------------------
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)))) and (((E and F) -> E) and (((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     101
proof            (modus-ponens tm-325 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87723.        ((((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)))) and (((E and F) -> E) and (((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-325, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87724
in-theory        87724
times-derived    1
----------------------------------------------------------------
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)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((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     109
proof            (modus-ponens tm-324 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       345
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87724.        ((((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)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((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-324, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87725
in-theory        87725
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (F -> E)) and (((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     101
proof            (modus-ponens tm-323 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87725.        ((((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)))) and ((E -> (F -> E)) and (((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-323, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87726
in-theory        87726
times-derived    1
----------------------------------------------------------------
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)))) and ((E and F) -> F))
theorem-size     53
proof            (modus-ponens tm-322 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87726.        ((((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)))) and ((E and F) -> F)), M:tm-322, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87727
in-theory        87727
times-derived    1
----------------------------------------------------------------
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)))) and ((E and F) -> E))
theorem-size     53
proof            (modus-ponens tm-320 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87727.        ((((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)))) and ((E and F) -> E)), M:tm-320, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87728
in-theory        87728
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     61
proof            (modus-ponens tm-318 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87728.        ((((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)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87729
in-theory        87729
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))))))
theorem-size     95
proof            (modus-ponens tm-316 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       311
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87729.        ((((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)))) and (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))))), M:tm-316, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87730
in-theory        87730
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (F -> E)))
theorem-size     53
proof            (modus-ponens tm-315 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87730.        ((((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)))) and (E -> (F -> E))), M:tm-315, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87731
in-theory        87731
times-derived    1
----------------------------------------------------------------
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)))) and ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))))) -> (not ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))))))
theorem-size     121
proof            (modus-ponens tm-313 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       327
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87731.        ((((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)))) and ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))))) -> (not ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))))))), M:tm-313, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87732
in-theory        87732
times-derived    1
----------------------------------------------------------------
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)))) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))) -> E) -> ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D)))) -> E)))
theorem-size     123
proof            (modus-ponens tm-312 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       333
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87732.        ((((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)))) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))) -> E) -> ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D)))) -> E))), M:tm-312, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87733
in-theory        87733
times-derived    1
----------------------------------------------------------------
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)))) and (E or (((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     97
proof            (modus-ponens tm-311 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87733.        ((((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)))) and (E or (((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-311, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87734
in-theory        87734
times-derived    1
----------------------------------------------------------------
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)))) and ((((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)))) or E))
theorem-size     97
proof            (modus-ponens tm-310 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87734.        ((((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)))) and ((((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)))) or E)), M:tm-310, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87735
in-theory        87735
times-derived    1
----------------------------------------------------------------
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)))) and (E -> ((((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)))) and E)))
theorem-size     99
proof            (modus-ponens tm-309 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       295
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87735.        ((((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)))) and (E -> ((((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)))) and E))), M:tm-309, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87736
in-theory        87736
times-derived    1
----------------------------------------------------------------
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)))) and ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((A or (B -> C)) -> (B -> D)))))
theorem-size     119
proof            (modus-ponens tm-306 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       331
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87736.        ((((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)))) and ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((A or (B -> C)) -> (B -> D))))), M:tm-306, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (or Am (-> Bm Cm)) (-> Bm Dm))))
================================================================
tm-name          tm-87737
in-theory        87737
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (((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     97
proof            (modus-ponens tm-305 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87737.        ((((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)))) and (E -> (((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-305, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87738
in-theory        87738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     59
proof            (modus-ponens tm-303 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       257
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87738.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-303, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87739
in-theory        87739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-270 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87739.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-270, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87740
in-theory        87740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-239 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87740.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-239, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87741
in-theory        87741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H)))))
theorem-size     65
proof            (modus-ponens tm-210 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       281
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87741.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H))))), M:tm-210, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87742
in-theory        87742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-183 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87742.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-183, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87743
in-theory        87743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-157 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87743.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-157, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87744
in-theory        87744
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     63
proof            (modus-ponens tm-147 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87744.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-147, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87745
in-theory        87745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-134 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87745.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-134, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87746
in-theory        87746
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     63
proof            (modus-ponens tm-125 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87746.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-125, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87747
in-theory        87747
times-derived    1
----------------------------------------------------------------
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 -> (C -> D)) or ((B -> C) -> (B -> D))) -> (B -> D))))
theorem-size     61
proof            (modus-ponens tm-114 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (or Am (-> Bm Cm))) (D (-> Bm Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       275
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87747.        (((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 -> (C -> D)) or ((B -> C) -> (B -> D))) -> (B -> D)))), M:tm-114, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (or Am (-> Bm Cm))) (D (-> Bm Dm)))
================================================================
tm-name          tm-87748
in-theory        87748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H)))))
theorem-size     63
proof            (modus-ponens tm-113 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87748.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H))))), M:tm-113, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87749
in-theory        87749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     67
proof            (modus-ponens tm-105 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       293
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87749.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-105, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87750
in-theory        87750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F)))))
theorem-size     55
proof            (modus-ponens tm-95 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87750.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F))))), M:tm-95, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87751
in-theory        87751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (E -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-84 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87751.        (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (E -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))))), M:tm-84, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87752
in-theory        87752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-83 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87752.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-83, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87753
in-theory        87753
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E)))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E)))))
theorem-size     53
proof            (modus-ponens tm-76 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87753.        (((not (not A)) -> A) and (((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E)))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E))))), M:tm-76, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87754
in-theory        87754
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))))) or ((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     73
proof            (modus-ponens tm-73 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87754.        (((not (not ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))))) or ((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-73, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87755
in-theory        87755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F)))))
theorem-size     59
proof            (modus-ponens tm-69 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87755.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F))))), M:tm-69, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87756
in-theory        87756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     61
proof            (modus-ponens tm-54 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87756.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-54, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87757
in-theory        87757
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) or ((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C))))
theorem-size     65
proof            (modus-ponens tm-50 tm-957 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-7 tm-2)
proof-size       247
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87757.        (((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) or ((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C)))), M:tm-50, m:tm-957, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87758
in-theory        87758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((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     53
proof            (modus-ponens tm-49 tm-957 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-6 tm-2)
proof-size       235
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87758.        (((A -> (B -> C)) or ((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-49, m:tm-957, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87759
in-theory        87759
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E))))) or ((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E))))
theorem-size     73
proof            (modus-ponens tm-47 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87759.        (((A and ((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E))))) or ((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E))))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E)))), M:tm-47, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87760
in-theory        87760
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) and E) or ((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     73
proof            (modus-ponens tm-46 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87760.        (((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) and E) or ((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-46, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87761
in-theory        87761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F)))))
theorem-size     53
proof            (modus-ponens tm-42 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87761.        ((A -> (B or A)) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F))))), M:tm-42, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87762
in-theory        87762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F)))))
theorem-size     53
proof            (modus-ponens tm-32 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87762.        ((A -> (A or B)) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F))))), M:tm-32, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87763
in-theory        87763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (((A -> (B -> C)) or (((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     71
proof            (modus-ponens tm-24 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87763.        (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (((A -> (B -> C)) or (((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-24, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87764
in-theory        87764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F)))))
theorem-size     55
proof            (modus-ponens tm-23 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87764.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F))))), M:tm-23, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87765
in-theory        87765
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F)))))
theorem-size     53
proof            (modus-ponens tm-22 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87765.        (((A and B) -> B) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F))))), M:tm-22, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87766
in-theory        87766
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F)))))
theorem-size     53
proof            (modus-ponens tm-21 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87766.        (((A and B) -> A) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F))))), M:tm-21, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87767
in-theory        87767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G)))))
theorem-size     61
proof            (modus-ponens tm-20 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87767.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or (((E -> F) -> (E -> G)) -> ((D or (E -> F)) -> (E -> G)))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((D or (E -> F)) -> (E -> G))))), M:tm-20, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87768
in-theory        87768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F)))))
theorem-size     53
proof            (modus-ponens tm-19 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87768.        ((A -> (B -> A)) and (((C -> (D -> E)) or (((D -> E) -> (D -> F)) -> ((C or (D -> E)) -> (D -> F)))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((C or (D -> E)) -> (D -> F))))), M:tm-19, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87769
in-theory        87769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))))
theorem-size     47
proof            (modus-ponens tm-12 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       223
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87769.        (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))))), M:tm-12, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87770
in-theory        87770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))))) -> (not ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))))))
theorem-size     73
proof            (modus-ponens tm-9 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       235
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87770.        ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))))) -> (not ((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))))), M:tm-9, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87771
in-theory        87771
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C))) -> E) -> ((((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C)))) -> E))
theorem-size     75
proof            (modus-ponens tm-8 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2)
proof-size       239
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-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-87771.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C))) -> E) -> ((((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C)))) -> E)), M:tm-8, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
================================================================
tm-name          tm-87772
in-theory        87772
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E)))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E)))))
theorem-size     49
proof            (modus-ponens tm-7 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       205
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87772.        (A or (((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E)))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E))))), M:tm-7, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87773
in-theory        87773
times-derived    1
----------------------------------------------------------------
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)))) or E)
theorem-size     49
proof            (modus-ponens tm-6 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       205
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87773.        ((((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)))) or E), M:tm-6, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87774
in-theory        87774
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E)))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E)))) and A))
theorem-size     51
proof            (modus-ponens tm-5 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       209
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87774.        (A -> ((((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E)))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E)))) and A)), M:tm-5, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87775
in-theory        87775
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((A or (B -> C)) -> (B -> D))))
theorem-size     71
proof            (modus-ponens tm-2 tm-957 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-8)
proof-size       235
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87775.        ((((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((A or (B -> C)) -> (B -> D)))), M:tm-2, m:tm-957, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (or Am (-> Bm Cm)) (-> Bm Dm))))
================================================================
tm-name          tm-87776
in-theory        87776
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E)))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E)))))
theorem-size     49
proof            (modus-ponens tm-1 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       205
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-87776.        (A -> (((B -> (C -> D)) or (((C -> D) -> (C -> E)) -> ((B or (C -> D)) -> (C -> E)))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((B or (C -> D)) -> (C -> E))))), M:tm-1, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-87777
in-theory        87777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (C or A))) and D) or (A -> (B -> (C or A)))) -> ((C or A) -> (B -> (C or A))))
theorem-size     27
proof            (modus-ponens tm-958 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-3 tm-7 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
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-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-87777.        ((((A -> (B -> (C or A))) and D) or (A -> (B -> (C or A)))) -> ((C or A) -> (B -> (C or A)))), M:tm-958, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-87778
in-theory        87778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> ((C or A) and B))) and D) or (A -> (B -> ((C or A) and B)))) -> ((C or A) -> (B -> ((C or A) and B))))
theorem-size     33
proof            (modus-ponens tm-958 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-3 tm-7 tm-1 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
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-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-87778.        ((((A -> (B -> ((C or A) and B))) and D) or (A -> (B -> ((C or A) and B)))) -> ((C or A) -> (B -> ((C or A) and B)))), M:tm-958, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-87779
in-theory        87779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B or A) or C)) and D) or (A -> ((B or A) or C))) -> ((B or A) -> ((B or A) or C)))
theorem-size     27
proof            (modus-ponens tm-958 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-3 tm-7 tm-1 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
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-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-87779.        ((((A -> ((B or A) or C)) and D) or (A -> ((B or A) or C))) -> ((B or A) -> ((B or A) or C))), M:tm-958, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-87780
in-theory        87780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or (C or A))) and D) or (A -> (B or (C or A)))) -> ((C or A) -> (B or (C or A))))
theorem-size     27
proof            (modus-ponens tm-958 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-3 tm-7 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
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-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-87780.        ((((A -> (B or (C or A))) and D) or (A -> (B or (C or A)))) -> ((C or A) -> (B or (C or A)))), M:tm-958, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-87781
in-theory        87781
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-930 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87781.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-930, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87782
in-theory        87782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))
theorem-size     69
proof            (modus-ponens tm-920 tm-958 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87782.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))), M:tm-920, m:tm-958, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87783
in-theory        87783
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-893 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87783.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-893, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87784
in-theory        87784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))
theorem-size     63
proof            (modus-ponens tm-882 tm-958 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87784.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))), M:tm-882, m:tm-958, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87785
in-theory        87785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     47
proof            (modus-ponens tm-855 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87785.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-855, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87786
in-theory        87786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-808 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87786.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-808, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87787
in-theory        87787
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))
theorem-size     75
proof            (modus-ponens tm-798 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87787.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))), M:tm-798, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87788
in-theory        87788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-757 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-87788.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-757, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87789
in-theory        87789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))
theorem-size     75
proof            (modus-ponens tm-747 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-87789.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))), M:tm-747, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87790
in-theory        87790
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G))))
theorem-size     55
proof            (modus-ponens tm-708 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-3.            ((A and B) -> A), axiom
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-87790.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G)))), M:tm-708, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87791
in-theory        87791
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-665 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-3.            ((A and B) -> A), axiom
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-87791.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-665, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87792
in-theory        87792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((((B -> C) and E) or (B -> C)) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-623 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87792.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((((B -> C) and E) or (B -> C)) -> ((A or B) -> C)))), M:tm-623, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87793
in-theory        87793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-622 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> A), axiom
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-87793.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-622, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87794
in-theory        87794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (F or E)))
theorem-size     35
proof            (modus-ponens tm-609 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> A), axiom
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-87794.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (F or E))), M:tm-609, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87795
in-theory        87795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-605 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-3.            ((A and B) -> A), axiom
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-87795.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-605, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87796
in-theory        87796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-3.            ((A and B) -> A), axiom
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-87796.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-595, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87797
in-theory        87797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-550 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-3.            ((A and B) -> A), axiom
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-87797.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-550, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87798
in-theory        87798
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-540 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-3.            ((A and B) -> A), axiom
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-87798.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-540, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87799
in-theory        87799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-530 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-3.            ((A and B) -> A), axiom
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-87799.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-530, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87800
in-theory        87800
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-520 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-3.            ((A and B) -> A), axiom
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-87800.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-520, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87801
in-theory        87801
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-510 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-3.            ((A and B) -> A), axiom
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-87801.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-510, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87802
in-theory        87802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-500 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-87802.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-500, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87803
in-theory        87803
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-490 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-3.            ((A and B) -> A), axiom
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-87803.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G)))), M:tm-490, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87804
in-theory        87804
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-480 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and B) -> A), axiom
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-87804.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-480, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87805
in-theory        87805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)) or E))
theorem-size     31
proof            (modus-ponens tm-470 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87805.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)) or E)), M:tm-470, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87806
in-theory        87806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-469 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> A), axiom
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-87806.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-469, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87807
in-theory        87807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (E or F)))
theorem-size     35
proof            (modus-ponens tm-456 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> A), axiom
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-87807.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (E or F))), M:tm-456, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87808
in-theory        87808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-453 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-3.            ((A and B) -> A), axiom
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-87808.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-453, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87809
in-theory        87809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-3.            ((A and B) -> A), axiom
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-87809.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-443, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87810
in-theory        87810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-409 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-3.            ((A and B) -> A), axiom
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-87810.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-409, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87811
in-theory        87811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-400 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-3.            ((A and B) -> A), axiom
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-87811.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-400, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87812
in-theory        87812
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-391 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-3.            ((A and B) -> A), axiom
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-87812.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-391, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87813
in-theory        87813
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-382 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-87813.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-382, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87814
in-theory        87814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-373 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-3.            ((A and B) -> A), axiom
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-87814.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G)))), M:tm-373, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87815
in-theory        87815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-364 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and B) -> A), axiom
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-87815.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-364, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87816
in-theory        87816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((((B -> C) and E) or (B -> C)) -> ((A or B) -> C)) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       189
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87816.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((((B -> C) and E) or (B -> C)) -> ((A or B) -> C)) and D))), M:tm-355, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87817
in-theory        87817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-354 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-3.            ((A and B) -> A), axiom
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-87817.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-354, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87818
in-theory        87818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (F -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-341 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A and B) -> A), axiom
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-87818.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87819
in-theory        87819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E))))
theorem-size     39
proof            (modus-ponens tm-338 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-3.            ((A and B) -> A), axiom
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-87819.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E)))), M:tm-338, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87820
in-theory        87820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     73
proof            (modus-ponens tm-328 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
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-328.          ((A -> 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-3.            ((A and B) -> A), axiom
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-87820.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-328, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87821
in-theory        87821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-3.            ((A and B) -> A), axiom
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-87821.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-327, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87822
in-theory        87822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-3.            ((A and B) -> A), axiom
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-87822.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-326, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87823
in-theory        87823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-87823.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-325, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87824
in-theory        87824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-3.            ((A and B) -> A), axiom
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-87824.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-324, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87825
in-theory        87825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A and B) -> A), axiom
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-87825.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-323, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87826
in-theory        87826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E and F) -> F))
theorem-size     35
proof            (modus-ponens tm-322 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> A), axiom
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-87826.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87827
in-theory        87827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E and F) -> E))
theorem-size     35
proof            (modus-ponens tm-320 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-87827.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87828
in-theory        87828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-318 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-3.            ((A and B) -> A), axiom
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-87828.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87829
in-theory        87829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-3.            ((A and B) -> A), axiom
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-87829.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87830
in-theory        87830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (F -> E)))
theorem-size     35
proof            (modus-ponens tm-315 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> A), axiom
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-87830.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87831
in-theory        87831
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-3.            ((A and B) -> A), axiom
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-87831.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87832
in-theory        87832
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) -> E)))
theorem-size     79
proof            (modus-ponens tm-312 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-3.            ((A and B) -> A), axiom
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-87832.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) -> E))), M:tm-312, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87833
in-theory        87833
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-3.            ((A and B) -> A), axiom
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-87833.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-311, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87834
in-theory        87834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) or E))
theorem-size     61
proof            (modus-ponens tm-310 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-3.            ((A and B) -> A), axiom
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-87834.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) or E)), M:tm-310, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87835
in-theory        87835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and E)))
theorem-size     63
proof            (modus-ponens tm-309 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-3.            ((A and B) -> A), axiom
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-87835.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and E))), M:tm-309, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87836
in-theory        87836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) and D) or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C))))
theorem-size     73
proof            (modus-ponens tm-306 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and (-> Bm Cm) Dm) (-> Bm Cm))) (C (-> (or Am Bm) Cm))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-3.            ((A and B) -> A), axiom
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-87836.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) and D) or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C)))), M:tm-306, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and (-> Bm Cm) Dm) (-> Bm Cm))) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-87837
in-theory        87837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-3.            ((A and B) -> A), axiom
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-87837.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))), M:tm-305, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87838
in-theory        87838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-303 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-3.            ((A and B) -> A), axiom
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-87838.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-303, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87839
in-theory        87839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-270 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-3.            ((A and B) -> A), axiom
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-87839.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-270, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87840
in-theory        87840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-239 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-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-87840.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-239, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87841
in-theory        87841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G))))
theorem-size     47
proof            (modus-ponens tm-210 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-3.            ((A and B) -> A), axiom
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-87841.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G)))), M:tm-210, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87842
in-theory        87842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-183 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-3.            ((A and B) -> A), axiom
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-87842.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-183, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87843
in-theory        87843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-157 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> A), axiom
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-87843.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-157, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87844
in-theory        87844
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     45
proof            (modus-ponens tm-147 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-3.            ((A and B) -> A), axiom
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-87844.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-147, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87845
in-theory        87845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-134 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-87845.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-134, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87846
in-theory        87846
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     45
proof            (modus-ponens tm-125 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-87846.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-125, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87847
in-theory        87847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((B -> C) and D) or (B -> C)) -> (A or B)) -> ((((B -> C) and D) or (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-114 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and (-> Bm Cm) Dm) (-> Bm Cm))) (C (or Am Bm)) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       213
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87847.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((B -> C) and D) or (B -> C)) -> (A or B)) -> ((((B -> C) and D) or (B -> C)) -> C))), M:tm-114, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and (-> Bm Cm) Dm) (-> Bm Cm))) (C (or Am Bm)) (D Cm))
================================================================
tm-name          tm-87848
in-theory        87848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-113 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-3.            ((A and B) -> A), axiom
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-87848.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G)))), M:tm-113, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87849
in-theory        87849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     49
proof            (modus-ponens tm-105 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-3.            ((A and B) -> A), axiom
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-87849.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-105, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87850
in-theory        87850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E))))
theorem-size     37
proof            (modus-ponens tm-95 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-3.            ((A and B) -> A), axiom
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-87850.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E)))), M:tm-95, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87851
in-theory        87851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((B -> C) and E) or (B -> C)) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-84 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87851.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((B -> C) and E) or (B -> C)) -> ((A or B) -> C)))), M:tm-84, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87852
in-theory        87852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-83 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> A), axiom
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-87852.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-83, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87853
in-theory        87853
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D))))
theorem-size     35
proof            (modus-ponens tm-76 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-3.            ((A and B) -> A), axiom
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-87853.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D)))), M:tm-76, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87854
in-theory        87854
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))
theorem-size     45
proof            (modus-ponens tm-73 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-3)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87854.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))), M:tm-73, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87855
in-theory        87855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E))))
theorem-size     41
proof            (modus-ponens tm-69 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-3.            ((A and B) -> A), axiom
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-87855.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E)))), M:tm-69, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87856
in-theory        87856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-54 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-3.            ((A and B) -> A), axiom
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-87856.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-54, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87857
in-theory        87857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B)))
theorem-size     39
proof            (modus-ponens tm-50 tm-958 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-7 tm-3)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87857.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B))), M:tm-50, m:tm-958, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87858
in-theory        87858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))
theorem-size     33
proof            (modus-ponens tm-49 tm-958 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-6 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87858.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))), M:tm-49, m:tm-958, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87859
in-theory        87859
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D)))
theorem-size     45
proof            (modus-ponens tm-47 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87859.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D))), M:tm-47, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87860
in-theory        87860
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and E) or (B -> C)) -> ((A or B) -> C)))
theorem-size     45
proof            (modus-ponens tm-46 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87860.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> ((((B -> C) and E) or (B -> C)) -> ((A or B) -> C))), M:tm-46, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87861
in-theory        87861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-42 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
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-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-87861.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E)))), M:tm-42, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87862
in-theory        87862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-32 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
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-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-87862.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E)))), M:tm-32, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87863
in-theory        87863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-24 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
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-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-87863.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))), M:tm-24, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87864
in-theory        87864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E))))
theorem-size     37
proof            (modus-ponens tm-23 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
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-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-87864.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E)))), M:tm-23, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87865
in-theory        87865
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-22 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
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-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-87865.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E)))), M:tm-22, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87866
in-theory        87866
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-21 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-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-87866.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E)))), M:tm-21, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87867
in-theory        87867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-20 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-3.            ((A and B) -> A), axiom
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-87867.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> ((((E -> F) and G) or (E -> F)) -> ((D or E) -> F)))), M:tm-20, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87868
in-theory        87868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-19 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
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-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-87868.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> ((((D -> E) and F) or (D -> E)) -> ((C or D) -> E)))), M:tm-19, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87869
in-theory        87869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-9 tm-8 tm-3)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87869.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87870
in-theory        87870
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) or (A -> B)) -> ((D or A) -> B)) -> E) -> ((((D -> A) or ((A -> B) -> ((D or A) -> B))) or ((((A -> B) and C) or (A -> B)) -> ((D or A) -> B))) -> E))
theorem-size     49
proof            (modus-ponens tm-8 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-3)
proof-size       173
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-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-87870.        ((((((A -> B) and C) or (A -> B)) -> ((D or A) -> B)) -> E) -> ((((D -> A) or ((A -> B) -> ((D or A) -> B))) or ((((A -> B) and C) or (A -> B)) -> ((D or A) -> B))) -> E)), M:tm-8, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87871
in-theory        87871
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D))))
theorem-size     31
proof            (modus-ponens tm-7 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-7 tm-8 tm-3)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-87871.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D)))), M:tm-7, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87872
in-theory        87872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) or E)
theorem-size     31
proof            (modus-ponens tm-6 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-6 tm-8 tm-3)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-87872.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))) or E), M:tm-6, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87873
in-theory        87873
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87873.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87874
in-theory        87874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) and D) or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C)))
theorem-size     43
proof            (modus-ponens tm-2 tm-958 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and (-> Bm Cm) Dm) (-> Bm Cm))) (C (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87874.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) and D) or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C))), M:tm-2, m:tm-958, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and (-> Bm Cm) Dm) (-> Bm Cm))) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-87875
in-theory        87875
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D))))
theorem-size     31
proof            (modus-ponens tm-1 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-87875.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> ((((C -> D) and E) or (C -> D)) -> ((B or C) -> D)))), M:tm-1, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87876
in-theory        87876
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> (D or B)))) or (B -> (C -> (D or B)))) -> ((D or B) -> (C -> (D or B))))
theorem-size     27
proof            (modus-ponens tm-959 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-4 tm-7 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
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-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-87876.        (((A and (B -> (C -> (D or B)))) or (B -> (C -> (D or B)))) -> ((D or B) -> (C -> (D or B)))), M:tm-959, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-87877
in-theory        87877
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> ((D or B) and C)))) or (B -> (C -> ((D or B) and C)))) -> ((D or B) -> (C -> ((D or B) and C))))
theorem-size     33
proof            (modus-ponens tm-959 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-4 tm-7 tm-1 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
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-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-87877.        (((A and (B -> (C -> ((D or B) and C)))) or (B -> (C -> ((D or B) and C)))) -> ((D or B) -> (C -> ((D or B) and C)))), M:tm-959, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-87878
in-theory        87878
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> ((C or B) or D))) or (B -> ((C or B) or D))) -> ((C or B) -> ((C or B) or D)))
theorem-size     27
proof            (modus-ponens tm-959 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-4 tm-7 tm-1 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
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-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-87878.        (((A and (B -> ((C or B) or D))) or (B -> ((C or B) or D))) -> ((C or B) -> ((C or B) or D))), M:tm-959, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-87879
in-theory        87879
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C or (D or B)))) or (B -> (C or (D or B)))) -> ((D or B) -> (C or (D or B))))
theorem-size     27
proof            (modus-ponens tm-959 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-4 tm-7 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
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-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-87879.        (((A and (B -> (C or (D or B)))) or (B -> (C or (D or B)))) -> ((D or B) -> (C or (D or B)))), M:tm-959, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-87880
in-theory        87880
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-930 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87880.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-930, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87881
in-theory        87881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))
theorem-size     69
proof            (modus-ponens tm-920 tm-959 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87881.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((((B -> C) -> ((A or B) -> C)) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))), M:tm-920, m:tm-959, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87882
in-theory        87882
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-893 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87882.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-893, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87883
in-theory        87883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))
theorem-size     63
proof            (modus-ponens tm-882 tm-959 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87883.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))), M:tm-882, m:tm-959, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87884
in-theory        87884
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     47
proof            (modus-ponens tm-855 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87884.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-855, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87885
in-theory        87885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-808 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87885.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-808, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87886
in-theory        87886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))
theorem-size     75
proof            (modus-ponens tm-798 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87886.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((E and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))), M:tm-798, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87887
in-theory        87887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-757 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-4.            ((A and B) -> B), axiom
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-87887.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-757, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87888
in-theory        87888
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))
theorem-size     75
proof            (modus-ponens tm-747 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-4.            ((A and B) -> B), axiom
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-87888.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and E) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))), M:tm-747, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87889
in-theory        87889
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G))))
theorem-size     55
proof            (modus-ponens tm-708 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-4.            ((A and B) -> B), axiom
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-87889.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G)))), M:tm-708, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87890
in-theory        87890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-665 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-4.            ((A and B) -> B), axiom
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-87890.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-665, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87891
in-theory        87891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((E and (B -> C)) or (B -> C)) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-623 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87891.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((E and (B -> C)) or (B -> C)) -> ((A or B) -> C)))), M:tm-623, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87892
in-theory        87892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-622 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-87892.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-622, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87893
in-theory        87893
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (F or E)))
theorem-size     35
proof            (modus-ponens tm-609 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-87893.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (F or E))), M:tm-609, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87894
in-theory        87894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-605 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-87894.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-605, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87895
in-theory        87895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-87895.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F or E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-595, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87896
in-theory        87896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-550 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-4.            ((A and B) -> B), axiom
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-87896.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-550, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87897
in-theory        87897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-540 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> B), axiom
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-87897.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-540, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87898
in-theory        87898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-530 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-4.            ((A and B) -> B), axiom
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-87898.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-530, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87899
in-theory        87899
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-520 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-4.            ((A and B) -> B), axiom
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-87899.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-520, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87900
in-theory        87900
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-510 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-87900.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-510, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87901
in-theory        87901
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-500 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-4.            ((A and B) -> B), axiom
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-87901.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-500, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87902
in-theory        87902
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-490 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-4.            ((A and B) -> B), axiom
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-87902.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G)))), M:tm-490, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87903
in-theory        87903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-480 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-87903.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-480, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87904
in-theory        87904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)) or E))
theorem-size     31
proof            (modus-ponens tm-470 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87904.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)) or E)), M:tm-470, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87905
in-theory        87905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-469 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-87905.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-469, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87906
in-theory        87906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (E or F)))
theorem-size     35
proof            (modus-ponens tm-456 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-87906.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (E or F))), M:tm-456, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87907
in-theory        87907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-453 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-4.            ((A and B) -> B), axiom
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-87907.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-453, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87908
in-theory        87908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-87908.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (E or F)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-443, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87909
in-theory        87909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-409 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> B), axiom
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-87909.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-409, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87910
in-theory        87910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-400 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-4.            ((A and B) -> B), axiom
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-87910.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-400, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87911
in-theory        87911
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-391 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-87911.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-391, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87912
in-theory        87912
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-382 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-4.            ((A and B) -> B), axiom
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-87912.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-382, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87913
in-theory        87913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-373 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-87913.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G)))), M:tm-373, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87914
in-theory        87914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-364 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-87914.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-364, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87915
in-theory        87915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((E and (B -> C)) or (B -> C)) -> ((A or B) -> C)) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       189
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87915.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((E and (B -> C)) or (B -> C)) -> ((A or B) -> C)) and D))), M:tm-355, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87916
in-theory        87916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-354 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-4.            ((A and B) -> B), axiom
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-87916.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-354, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87917
in-theory        87917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (F -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-341 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> B), axiom
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-87917.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87918
in-theory        87918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E))))
theorem-size     39
proof            (modus-ponens tm-338 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> B), axiom
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-87918.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E)))), M:tm-338, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87919
in-theory        87919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     73
proof            (modus-ponens tm-328 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-328.          ((A -> 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-4.            ((A and B) -> B), axiom
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-87919.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-328, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87920
in-theory        87920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-87920.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> (E and F))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-327, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87921
in-theory        87921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-87921.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((E and F) -> F) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-326, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87922
in-theory        87922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> B), axiom
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-87922.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((E and F) -> E) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-325, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87923
in-theory        87923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-87923.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-324, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87924
in-theory        87924
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> B), axiom
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-87924.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> E)) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-323, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87925
in-theory        87925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E and F) -> F))
theorem-size     35
proof            (modus-ponens tm-322 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-87925.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87926
in-theory        87926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E and F) -> E))
theorem-size     35
proof            (modus-ponens tm-320 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-87926.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87927
in-theory        87927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-318 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
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-87927.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87928
in-theory        87928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-4.            ((A and B) -> B), axiom
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-87928.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87929
in-theory        87929
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (F -> E)))
theorem-size     35
proof            (modus-ponens tm-315 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-87929.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87930
in-theory        87930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-4.            ((A and B) -> B), axiom
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-87930.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87931
in-theory        87931
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) -> E)))
theorem-size     79
proof            (modus-ponens tm-312 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-4.            ((A and B) -> B), axiom
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-87931.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (((((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) -> E))), M:tm-312, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87932
in-theory        87932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-87932.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-311, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87933
in-theory        87933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) or E))
theorem-size     61
proof            (modus-ponens tm-310 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-87933.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) or E)), M:tm-310, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87934
in-theory        87934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and E)))
theorem-size     63
proof            (modus-ponens tm-309 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-4.            ((A and B) -> B), axiom
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-87934.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and E))), M:tm-309, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87935
in-theory        87935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and (B -> C)) or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C))))
theorem-size     73
proof            (modus-ponens tm-306 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and Dm (-> Bm Cm)) (-> Bm Cm))) (C (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-306.          ((A -> (B -> C)) -> ((A -> (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-4.            ((A and B) -> B), axiom
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-87935.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and (B -> C)) or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C)))), M:tm-306, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and Dm (-> Bm Cm)) (-> Bm Cm))) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-87936
in-theory        87936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-4.            ((A and B) -> B), axiom
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-87936.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) and (E -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))), M:tm-305, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87937
in-theory        87937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-303 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-4.            ((A and B) -> B), axiom
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-87937.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-303, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87938
in-theory        87938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-270 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-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-87938.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-270, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87939
in-theory        87939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-239 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-4.            ((A and B) -> B), axiom
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-87939.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-239, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87940
in-theory        87940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G))))
theorem-size     47
proof            (modus-ponens tm-210 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> B), axiom
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-87940.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G)))), M:tm-210, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87941
in-theory        87941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     39
proof            (modus-ponens tm-183 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-4.            ((A and B) -> B), axiom
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-87941.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-183, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87942
in-theory        87942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-157 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-87942.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-157, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87943
in-theory        87943
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     45
proof            (modus-ponens tm-147 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-87943.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-147, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87944
in-theory        87944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-134 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-87944.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-134, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87945
in-theory        87945
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     45
proof            (modus-ponens tm-125 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-87945.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-125, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87946
in-theory        87946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and (B -> C)) or (B -> C)) -> (A or B)) -> (((D and (B -> C)) or (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-114 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and Dm (-> Bm Cm)) (-> Bm Cm))) (C (or Am Bm)) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       213
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87946.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and (B -> C)) or (B -> C)) -> (A or B)) -> (((D and (B -> C)) or (B -> C)) -> C))), M:tm-114, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and Dm (-> Bm Cm)) (-> Bm Cm))) (C (or Am Bm)) (D Cm))
================================================================
tm-name          tm-87947
in-theory        87947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-113 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-4.            ((A and B) -> B), axiom
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-87947.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G)))), M:tm-113, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87948
in-theory        87948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     49
proof            (modus-ponens tm-105 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> B), axiom
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-87948.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-105, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87949
in-theory        87949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E))))
theorem-size     37
proof            (modus-ponens tm-95 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> B), axiom
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-87949.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E)))), M:tm-95, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87950
in-theory        87950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E and (B -> C)) or (B -> C)) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-84 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87950.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E and (B -> C)) or (B -> C)) -> ((A or B) -> C)))), M:tm-84, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87951
in-theory        87951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-83 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-87951.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-83, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87952
in-theory        87952
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D))))
theorem-size     35
proof            (modus-ponens tm-76 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-4.            ((A and B) -> B), axiom
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-87952.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D)))), M:tm-76, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87953
in-theory        87953
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))
theorem-size     45
proof            (modus-ponens tm-73 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-4)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87953.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))), M:tm-73, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87954
in-theory        87954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E))))
theorem-size     41
proof            (modus-ponens tm-69 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-4.            ((A and B) -> B), axiom
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-87954.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E)))), M:tm-69, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87955
in-theory        87955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-54 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-4.            ((A and B) -> B), axiom
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-87955.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-54, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87956
in-theory        87956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B)))
theorem-size     39
proof            (modus-ponens tm-50 tm-959 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-7 tm-4)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87956.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B))), M:tm-50, m:tm-959, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87957
in-theory        87957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))
theorem-size     33
proof            (modus-ponens tm-49 tm-959 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-6 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87957.        (((A -> B) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))), M:tm-49, m:tm-959, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87958
in-theory        87958
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D)))
theorem-size     45
proof            (modus-ponens tm-47 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-4)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87958.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D))), M:tm-47, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87959
in-theory        87959
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E and (B -> C)) or (B -> C)) -> ((A or B) -> C)))
theorem-size     45
proof            (modus-ponens tm-46 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87959.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E and (B -> C)) or (B -> C)) -> ((A or B) -> C))), M:tm-46, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87960
in-theory        87960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-42 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-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-87960.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E)))), M:tm-42, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87961
in-theory        87961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-32 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-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-87961.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E)))), M:tm-32, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87962
in-theory        87962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-24 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87962.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))), M:tm-24, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87963
in-theory        87963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E))))
theorem-size     37
proof            (modus-ponens tm-23 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-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-87963.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E)))), M:tm-23, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87964
in-theory        87964
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-22 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-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-87964.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E)))), M:tm-22, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87965
in-theory        87965
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-21 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-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-87965.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E)))), M:tm-21, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87966
in-theory        87966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-20 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-4.            ((A and B) -> B), axiom
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-87966.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G and (E -> F)) or (E -> F)) -> ((D or E) -> F)))), M:tm-20, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87967
in-theory        87967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-19 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-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-87967.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F and (D -> E)) or (D -> E)) -> ((C or D) -> E)))), M:tm-19, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87968
in-theory        87968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-9 tm-8 tm-4)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87968.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87969
in-theory        87969
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) or (B -> C)) -> ((D or B) -> C)) -> E) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) or (((A and (B -> C)) or (B -> C)) -> ((D or B) -> C))) -> E))
theorem-size     49
proof            (modus-ponens tm-8 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-4)
proof-size       173
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-4.            ((A and B) -> B), axiom
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-87969.        (((((A and (B -> C)) or (B -> C)) -> ((D or B) -> C)) -> E) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) or (((A and (B -> C)) or (B -> C)) -> ((D or B) -> C))) -> E)), M:tm-8, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-87970
in-theory        87970
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D))))
theorem-size     31
proof            (modus-ponens tm-7 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-7 tm-8 tm-4)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-87970.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D)))), M:tm-7, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87971
in-theory        87971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) or E)
theorem-size     31
proof            (modus-ponens tm-6 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-6 tm-8 tm-4)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-87971.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))) or E), M:tm-6, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87972
in-theory        87972
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87972.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87973
in-theory        87973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and (B -> C)) or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C)))
theorem-size     43
proof            (modus-ponens tm-2 tm-959 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and Dm (-> Bm Cm)) (-> Bm Cm))) (C (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87973.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and (B -> C)) or (B -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A or B) -> C))), M:tm-2, m:tm-959, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (and Dm (-> Bm Cm)) (-> Bm Cm))) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-87974
in-theory        87974
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D))))
theorem-size     31
proof            (modus-ponens tm-1 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       147
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-87974.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E and (C -> D)) or (C -> D)) -> ((B or C) -> D)))), M:tm-1, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-87975
in-theory        87975
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     47
proof            (modus-ponens tm-930 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87975.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-930, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87976
in-theory        87976
times-derived    1
----------------------------------------------------------------
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)))) and ((((B -> (C and B)) -> ((A or B) -> (C and B))) or ((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     81
proof            (modus-ponens tm-920 tm-960 ((A (-> Am Bm)) (B (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87976.        ((((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)))) and ((((B -> (C and B)) -> ((A or B) -> (C and B))) or ((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-920, m:tm-960, u:((A (-> Am Bm)) (B (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-87977
in-theory        87977
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     47
proof            (modus-ponens tm-893 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87977.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-893, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87978
in-theory        87978
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> B) or ((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     71
proof            (modus-ponens tm-882 tm-960 ((A (-> Am Bm)) (B (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87978.        ((((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)))) and (((A -> B) or ((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-882, m:tm-960, u:((A (-> Am Bm)) (B (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-87979
in-theory        87979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     51
proof            (modus-ponens tm-855 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-87979.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-855, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87980
in-theory        87980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     45
proof            (modus-ponens tm-808 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87980.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-808, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87981
in-theory        87981
times-derived    1
----------------------------------------------------------------
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)))) and (((D and ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B))))) or ((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     87
proof            (modus-ponens tm-798 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87981.        ((((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)))) and (((D and ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B))))) or ((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-798, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-87982
in-theory        87982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     45
proof            (modus-ponens tm-757 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-48.           (((A -> (B and 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-87982.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-757, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87983
in-theory        87983
times-derived    1
----------------------------------------------------------------
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)))) and (((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) and D) or ((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     87
proof            (modus-ponens tm-747 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-87983.        ((((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)))) and (((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) and D) or ((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-747, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-87984
in-theory        87984
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F)))))
theorem-size     59
proof            (modus-ponens tm-708 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       269
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-48.           (((A -> (B and 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-87984.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F))))), M:tm-708, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87985
in-theory        87985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     47
proof            (modus-ponens tm-665 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-48.           (((A -> (B and 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-87985.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-665, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87986
in-theory        87986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (D or ((C or (B -> (C and B))) -> ((A or B) -> (C and B)))))
theorem-size     35
proof            (modus-ponens tm-623 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       197
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87986.        (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (D or ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))), M:tm-623, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-87987
in-theory        87987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-622 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-87987.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-622, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87988
in-theory        87988
times-derived    1
----------------------------------------------------------------
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)))) and (D -> (E or D)))
theorem-size     39
proof            (modus-ponens tm-609 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-48.           (((A -> (B and 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-87988.        ((((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)))) and (D -> (E or D))), M:tm-609, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87989
in-theory        87989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     43
proof            (modus-ponens tm-605 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-48.           (((A -> (B and 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-87989.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-605, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87990
in-theory        87990
times-derived    1
----------------------------------------------------------------
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)))) and ((D -> (E or D)) and (((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     73
proof            (modus-ponens tm-595 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-87990.        ((((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)))) and ((D -> (E or D)) and (((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-595, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87991
in-theory        87991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-550 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-48.           (((A -> (B and 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-87991.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-550, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87992
in-theory        87992
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-540 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-48.           (((A -> (B and 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-87992.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-540, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87993
in-theory        87993
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-530 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-48.           (((A -> (B and 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-87993.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-530, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87994
in-theory        87994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     43
proof            (modus-ponens tm-520 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-48.           (((A -> (B and 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-87994.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-520, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87995
in-theory        87995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-510 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-48.           (((A -> (B and 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-87995.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-510, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87996
in-theory        87996
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-500 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-48.           (((A -> (B and 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-87996.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-500, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87997
in-theory        87997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F)))))
theorem-size     49
proof            (modus-ponens tm-490 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-48.           (((A -> (B and 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-87997.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F))))), M:tm-490, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87998
in-theory        87998
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-480 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-87998.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-480, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-87999
in-theory        87999
times-derived    1
----------------------------------------------------------------
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))) or D))
theorem-size     35
proof            (modus-ponens tm-470 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       197
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-87999.        (((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))) or D)), M:tm-470, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88000
in-theory        88000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-469 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-88000.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-469, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88001
in-theory        88001
times-derived    1
----------------------------------------------------------------
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)))) and (D -> (D or E)))
theorem-size     39
proof            (modus-ponens tm-456 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-48.           (((A -> (B and 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-88001.        ((((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)))) and (D -> (D or E))), M:tm-456, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88002
in-theory        88002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     43
proof            (modus-ponens tm-453 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-48.           (((A -> (B and 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-88002.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-453, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88003
in-theory        88003
times-derived    1
----------------------------------------------------------------
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)))) and ((D -> (D or E)) and (((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     73
proof            (modus-ponens tm-443 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-88003.        ((((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)))) and ((D -> (D or E)) and (((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-443, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88004
in-theory        88004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-409 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-48.           (((A -> (B and 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-88004.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-409, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88005
in-theory        88005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     43
proof            (modus-ponens tm-400 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-48.           (((A -> (B and 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-88005.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-400, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88006
in-theory        88006
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-391 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-48.           (((A -> (B and 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-88006.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-391, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88007
in-theory        88007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-382 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-48.           (((A -> (B and 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-88007.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-382, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88008
in-theory        88008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F)))))
theorem-size     49
proof            (modus-ponens tm-373 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-88008.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F))))), M:tm-373, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88009
in-theory        88009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-364 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-48.           (((A -> (B and 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-88009.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-364, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88010
in-theory        88010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (D -> (((C or (B -> (C and B))) -> ((A or B) -> (C and B))) and D)))
theorem-size     37
proof            (modus-ponens tm-355 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-88010.        (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (D -> (((C or (B -> (C and B))) -> ((A or B) -> (C and B))) and D))), M:tm-355, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88011
in-theory        88011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     43
proof            (modus-ponens tm-354 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-48.           (((A -> (B and 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-88011.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-354, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88012
in-theory        88012
times-derived    1
----------------------------------------------------------------
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)))) and (D -> (E -> (D and E))))
theorem-size     41
proof            (modus-ponens tm-341 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-48.           (((A -> (B and 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-88012.        ((((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)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88013
in-theory        88013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D)))))
theorem-size     43
proof            (modus-ponens tm-338 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-48.           (((A -> (B and 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-88013.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D))))), M:tm-338, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88014
in-theory        88014
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) and ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))))
theorem-size     85
proof            (modus-ponens tm-328 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-88014.        ((((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)))) and (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) and ((C or (B -> (C and B))) -> ((A or B) -> (C and B)))))), M:tm-328, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88015
in-theory        88015
times-derived    1
----------------------------------------------------------------
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)))) and ((D -> (E -> (D and E))) and (((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     75
proof            (modus-ponens tm-327 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-88015.        ((((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)))) and ((D -> (E -> (D and E))) and (((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-327, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88016
in-theory        88016
times-derived    1
----------------------------------------------------------------
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)))) and (((D and E) -> E) and (((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     73
proof            (modus-ponens tm-326 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-48.           (((A -> (B and 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-88016.        ((((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)))) and (((D and E) -> E) and (((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-326, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88017
in-theory        88017
times-derived    1
----------------------------------------------------------------
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)))) and (((D and E) -> D) and (((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     73
proof            (modus-ponens tm-325 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-48.           (((A -> (B and 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-88017.        ((((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)))) and (((D and E) -> D) and (((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-325, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88018
in-theory        88018
times-derived    1
----------------------------------------------------------------
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)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((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     81
proof            (modus-ponens tm-324 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-8)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-88018.        ((((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)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((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-324, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88019
in-theory        88019
times-derived    1
----------------------------------------------------------------
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)))) and ((D -> (E -> D)) and (((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     73
proof            (modus-ponens tm-323 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-88019.        ((((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)))) and ((D -> (E -> D)) and (((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-323, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88020
in-theory        88020
times-derived    1
----------------------------------------------------------------
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)))) and ((D and E) -> E))
theorem-size     39
proof            (modus-ponens tm-322 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-88020.        ((((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)))) and ((D and E) -> E)), M:tm-322, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88021
in-theory        88021
times-derived    1
----------------------------------------------------------------
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)))) and ((D and E) -> D))
theorem-size     39
proof            (modus-ponens tm-320 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-88021.        ((((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)))) and ((D and E) -> D)), M:tm-320, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88022
in-theory        88022
times-derived    1
----------------------------------------------------------------
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)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     47
proof            (modus-ponens tm-318 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-88022.        ((((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)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88023
in-theory        88023
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B))))))
theorem-size     69
proof            (modus-ponens tm-316 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-48.           (((A -> (B and 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-88023.        ((((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)))) and (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))))), M:tm-316, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88024
in-theory        88024
times-derived    1
----------------------------------------------------------------
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)))) and (D -> (E -> D)))
theorem-size     39
proof            (modus-ponens tm-315 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-88024.        ((((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)))) and (D -> (E -> D))), M:tm-315, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88025
in-theory        88025
times-derived    1
----------------------------------------------------------------
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)))) and ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (not ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))) -> (not ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))))))
theorem-size     87
proof            (modus-ponens tm-313 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-88025.        ((((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)))) and ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (not ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))) -> (not ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B))))))), M:tm-313, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88026
in-theory        88026
times-derived    1
----------------------------------------------------------------
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)))) and ((((C or (B -> (C and B))) -> ((A or B) -> (C and B))) -> D) -> ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) or ((C or (B -> (C and B))) -> ((A or B) -> (C and B)))) -> D)))
theorem-size     87
proof            (modus-ponens tm-312 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-48.           (((A -> (B and 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-88026.        ((((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)))) and ((((C or (B -> (C and B))) -> ((A or B) -> (C and B))) -> D) -> ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) or ((C or (B -> (C and B))) -> ((A or B) -> (C and B)))) -> D))), M:tm-312, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88027
in-theory        88027
times-derived    1
----------------------------------------------------------------
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)))) and (D or (((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     69
proof            (modus-ponens tm-311 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-88027.        ((((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)))) and (D or (((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-311, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88028
in-theory        88028
times-derived    1
----------------------------------------------------------------
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)))) and ((((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)))) or D))
theorem-size     69
proof            (modus-ponens tm-310 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-88028.        ((((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)))) and ((((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)))) or D)), M:tm-310, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88029
in-theory        88029
times-derived    1
----------------------------------------------------------------
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)))) and (D -> ((((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)))) and D)))
theorem-size     71
proof            (modus-ponens tm-309 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
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-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-48.           (((A -> (B and 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-88029.        ((((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)))) and (D -> ((((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)))) and D))), M:tm-309, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88030
in-theory        88030
times-derived    1
----------------------------------------------------------------
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)))) and ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (C or (B -> (C and B)))) -> (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((A or B) -> (C and B)))))
theorem-size     85
proof            (modus-ponens tm-306 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (-> (or Am Bm) (and Cm Bm)))))
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-306.          ((A -> (B -> C)) -> ((A -> (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-48.           (((A -> (B and 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-88030.        ((((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)))) and ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (C or (B -> (C and B)))) -> (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((A or B) -> (C and B))))), M:tm-306, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (-> (or Am Bm) (and Cm Bm))))
================================================================
tm-name          tm-88031
in-theory        88031
times-derived    1
----------------------------------------------------------------
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)))) and (D -> (((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     69
proof            (modus-ponens tm-305 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-48.           (((A -> (B and 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-88031.        ((((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)))) and (D -> (((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-305, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88032
in-theory        88032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     45
proof            (modus-ponens tm-303 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-48.           (((A -> (B and 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-88032.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-303, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88033
in-theory        88033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     43
proof            (modus-ponens tm-270 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-48.           (((A -> (B and 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-88033.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-270, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88034
in-theory        88034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     43
proof            (modus-ponens tm-239 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-48.           (((A -> (B and 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-88034.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-239, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88035
in-theory        88035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F)))))
theorem-size     51
proof            (modus-ponens tm-210 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-48.           (((A -> (B and 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-88035.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F))))), M:tm-210, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88036
in-theory        88036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     43
proof            (modus-ponens tm-183 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-48.           (((A -> (B and 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-88036.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-183, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88037
in-theory        88037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-157 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-48.           (((A -> (B and 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-88037.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-157, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88038
in-theory        88038
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     49
proof            (modus-ponens tm-147 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-48.           (((A -> (B and 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-88038.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-147, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88039
in-theory        88039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-134 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-48.           (((A -> (B and 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-88039.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-134, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88040
in-theory        88040
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     49
proof            (modus-ponens tm-125 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-48.           (((A -> (B and 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-88040.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-125, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88041
in-theory        88041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (((C or (B -> (C and B))) -> (A or B)) -> ((C or (B -> (C and B))) -> (C and B))))
theorem-size     41
proof            (modus-ponens tm-114 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (or Am Bm)) (D (and Cm Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       227
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88041.        (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (((C or (B -> (C and B))) -> (A or B)) -> ((C or (B -> (C and B))) -> (C and B)))), M:tm-114, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (or Am Bm)) (D (and Cm Bm)))
================================================================
tm-name          tm-88042
in-theory        88042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F)))))
theorem-size     49
proof            (modus-ponens tm-113 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-48.           (((A -> (B and 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-88042.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F))))), M:tm-113, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88043
in-theory        88043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     53
proof            (modus-ponens tm-105 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       251
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-48.           (((A -> (B and 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-88043.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-105, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88044
in-theory        88044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D)))))
theorem-size     41
proof            (modus-ponens tm-95 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-48.           (((A -> (B and 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-88044.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D))))), M:tm-95, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88045
in-theory        88045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (D -> ((C or (B -> (C and B))) -> ((A or B) -> (C and B)))))
theorem-size     35
proof            (modus-ponens tm-84 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-88045.        (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (D -> ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))), M:tm-84, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88046
in-theory        88046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     41
proof            (modus-ponens tm-83 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-48.           (((A -> (B and 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-88046.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-83, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88047
in-theory        88047
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C)))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C)))))
theorem-size     39
proof            (modus-ponens tm-76 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-48.           (((A -> (B and 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-88047.        (((not (not A)) -> A) and (((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C)))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C))))), M:tm-76, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88048
in-theory        88048
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))))) or ((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     53
proof            (modus-ponens tm-73 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88048.        (((not (not ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))))) or ((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-73, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88049
in-theory        88049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D)))))
theorem-size     45
proof            (modus-ponens tm-69 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-48.           (((A -> (B and 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-88049.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D))))), M:tm-69, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88050
in-theory        88050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     47
proof            (modus-ponens tm-54 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-48.           (((A -> (B and 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-88050.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-54, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88051
in-theory        88051
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> ((C or A) -> (B and A))) or ((C -> A) or ((A -> (B and A)) -> ((C or A) -> (B and A))))) -> ((B or (A -> (B and A))) -> ((C or A) -> (B and A))))
theorem-size     47
proof            (modus-ponens tm-50 tm-960 ((A (-> Am Bm)) (B (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88051.        ((((A -> (B and A)) -> ((C or A) -> (B and A))) or ((C -> A) or ((A -> (B and A)) -> ((C or A) -> (B and A))))) -> ((B or (A -> (B and A))) -> ((C or A) -> (B and A)))), M:tm-50, m:tm-960, u:((A (-> Am Bm)) (B (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88052
in-theory        88052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((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     37
proof            (modus-ponens tm-49 tm-960 ((A (-> Am Bm)) (B (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88052.        (((A -> B) or ((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-49, m:tm-960, u:((A (-> Am Bm)) (B (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (C (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88053
in-theory        88053
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C))))) or ((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C))))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C))))
theorem-size     53
proof            (modus-ponens tm-47 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88053.        (((A and ((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C))))) or ((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C))))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C)))), M:tm-47, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88054
in-theory        88054
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) and D) or ((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     53
proof            (modus-ponens tm-46 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88054.        (((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) and D) or ((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-46, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88055
in-theory        88055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D)))))
theorem-size     39
proof            (modus-ponens tm-42 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-48.           (((A -> (B and 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-88055.        ((A -> (B or A)) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D))))), M:tm-42, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88056
in-theory        88056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D)))))
theorem-size     39
proof            (modus-ponens tm-32 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-48.           (((A -> (B and 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-88056.        ((A -> (A or B)) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D))))), M:tm-32, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88057
in-theory        88057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) and ((C or (B -> (C and B))) -> ((A or B) -> (C and B)))))
theorem-size     51
proof            (modus-ponens tm-24 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-88057.        (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) and ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))), M:tm-24, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88058
in-theory        88058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D)))))
theorem-size     41
proof            (modus-ponens tm-23 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-48.           (((A -> (B and 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-88058.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D))))), M:tm-23, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88059
in-theory        88059
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D)))))
theorem-size     39
proof            (modus-ponens tm-22 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-48.           (((A -> (B and 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-88059.        (((A and B) -> B) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D))))), M:tm-22, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88060
in-theory        88060
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D)))))
theorem-size     39
proof            (modus-ponens tm-21 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-48.           (((A -> (B and 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-88060.        (((A and B) -> A) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D))))), M:tm-21, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88061
in-theory        88061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E)))))
theorem-size     47
proof            (modus-ponens tm-20 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
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-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-48.           (((A -> (B and 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-88061.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> (F and E)) -> ((D or E) -> (F and E)))) -> ((F or (E -> (F and E))) -> ((D or E) -> (F and E))))), M:tm-20, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88062
in-theory        88062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D)))))
theorem-size     39
proof            (modus-ponens tm-19 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-48.           (((A -> (B and 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-88062.        ((A -> (B -> A)) and (((C -> D) or ((D -> (E and D)) -> ((C or D) -> (E and D)))) -> ((E or (D -> (E and D))) -> ((C or D) -> (E and D))))), M:tm-19, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88063
in-theory        88063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))))
theorem-size     35
proof            (modus-ponens tm-12 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88063.        (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B))))), M:tm-12, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88064
in-theory        88064
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (not ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))) -> (not ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B))))))
theorem-size     53
proof            (modus-ponens tm-9 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-9 tm-8 tm-5)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88064.        ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (not ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))) -> (not ((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))))), M:tm-9, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88065
in-theory        88065
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> ((C or B) -> (A and B))) -> D) -> ((((C -> B) or ((B -> (A and B)) -> ((C or B) -> (A and B)))) or ((A or (B -> (A and B))) -> ((C or B) -> (A and B)))) -> D))
theorem-size     53
proof            (modus-ponens tm-8 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
axioms-used      (tm-8 tm-5)
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-48.           (((A -> (B and 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-88065.        ((((A or (B -> (A and B))) -> ((C or B) -> (A and B))) -> D) -> ((((C -> B) or ((B -> (A and B)) -> ((C or B) -> (A and B)))) or ((A or (B -> (A and B))) -> ((C or B) -> (A and B)))) -> D)), M:tm-8, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))
================================================================
tm-name          tm-88066
in-theory        88066
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C)))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C)))))
theorem-size     35
proof            (modus-ponens tm-7 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       163
proof-steps      9
----------------------------------------------------------------
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-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-88066.        (A or (((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C)))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C))))), M:tm-7, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88067
in-theory        88067
times-derived    1
----------------------------------------------------------------
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)))) or D)
theorem-size     35
proof            (modus-ponens tm-6 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       163
proof-steps      9
----------------------------------------------------------------
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-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-88067.        ((((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)))) or D), M:tm-6, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88068
in-theory        88068
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C)))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C)))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-88068.        (A -> ((((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C)))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C)))) and A)), M:tm-5, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88069
in-theory        88069
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (C or (B -> (C and B)))) -> (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((A or B) -> (C and B))))
theorem-size     51
proof            (modus-ponens tm-2 tm-960 ((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (-> (or Am Bm) (and Cm Bm)))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88069.        ((((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> (C or (B -> (C and B)))) -> (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((A or B) -> (C and B)))), M:tm-2, m:tm-960, u:((A (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm))))) (B (or Cm (-> Bm (and Cm Bm)))) (C (-> (or Am Bm) (and Cm Bm))))
================================================================
tm-name          tm-88070
in-theory        88070
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C)))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C)))))
theorem-size     35
proof            (modus-ponens tm-1 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       163
proof-steps      9
----------------------------------------------------------------
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-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-88070.        (A -> (((B -> C) or ((C -> (D and C)) -> ((B or C) -> (D and C)))) -> ((D or (C -> (D and C))) -> ((B or C) -> (D and C))))), M:tm-1, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-88071
in-theory        88071
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     67
proof            (modus-ponens tm-930 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       281
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88071.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-930, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88072
in-theory        88072
times-derived    1
----------------------------------------------------------------
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)))) and (((((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))) or ((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     129
proof            (modus-ponens tm-920 tm-961 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       367
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88072.        ((((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)))) and (((((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))) or ((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-920, m:tm-961, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88073
in-theory        88073
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     67
proof            (modus-ponens tm-893 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       281
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88073.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-893, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88074
in-theory        88074
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> (B -> C)) or ((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     113
proof            (modus-ponens tm-882 tm-961 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       351
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88074.        ((((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)))) and (((A -> (B -> C)) or ((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-882, m:tm-961, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88075
in-theory        88075
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     71
proof            (modus-ponens tm-855 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       295
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88075.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-855, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88076
in-theory        88076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     65
proof            (modus-ponens tm-808 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       275
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88076.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-808, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88077
in-theory        88077
times-derived    1
----------------------------------------------------------------
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)))) and (((E and ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))))) or ((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     137
proof            (modus-ponens tm-798 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       369
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88077.        ((((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)))) and (((E and ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))))) or ((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-798, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88078
in-theory        88078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     65
proof            (modus-ponens tm-757 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       275
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-88078.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-757, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88079
in-theory        88079
times-derived    1
----------------------------------------------------------------
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)))) and (((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) and E) or ((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     137
proof            (modus-ponens tm-747 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       369
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-88079.        ((((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)))) and (((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) and E) or ((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-747, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88080
in-theory        88080
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G)))))
theorem-size     79
proof            (modus-ponens tm-708 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       325
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-88080.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G))))), M:tm-708, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88081
in-theory        88081
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     67
proof            (modus-ponens tm-665 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       281
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-88081.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-665, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88082
in-theory        88082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (E or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C)))))
theorem-size     55
proof            (modus-ponens tm-623 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88082.        (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (E or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))), M:tm-623, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88083
in-theory        88083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-622 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-88083.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-622, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88084
in-theory        88084
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (F or E)))
theorem-size     59
proof            (modus-ponens tm-609 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-88084.        ((((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)))) and (E -> (F or E))), M:tm-609, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88085
in-theory        88085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     63
proof            (modus-ponens tm-605 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-88085.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-605, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88086
in-theory        88086
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (F or E)) and (((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     113
proof            (modus-ponens tm-595 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       333
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-88086.        ((((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)))) and ((E -> (F or E)) and (((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-595, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88087
in-theory        88087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-550 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-88087.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-550, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88088
in-theory        88088
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-540 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-88088.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-540, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88089
in-theory        88089
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-530 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-88089.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-530, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88090
in-theory        88090
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     63
proof            (modus-ponens tm-520 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-88090.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-520, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88091
in-theory        88091
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-510 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-88091.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-510, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88092
in-theory        88092
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-500 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-88092.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-500, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88093
in-theory        88093
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G)))))
theorem-size     69
proof            (modus-ponens tm-490 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-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-88093.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G))))), M:tm-490, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88094
in-theory        88094
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-480 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-88094.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-480, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88095
in-theory        88095
times-derived    1
----------------------------------------------------------------
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))) or E))
theorem-size     55
proof            (modus-ponens tm-470 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88095.        (((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))) or E)), M:tm-470, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88096
in-theory        88096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-469 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-88096.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-469, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88097
in-theory        88097
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (E or F)))
theorem-size     59
proof            (modus-ponens tm-456 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-88097.        ((((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)))) and (E -> (E or F))), M:tm-456, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88098
in-theory        88098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     63
proof            (modus-ponens tm-453 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-88098.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-453, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88099
in-theory        88099
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (E or F)) and (((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     113
proof            (modus-ponens tm-443 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       333
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-88099.        ((((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)))) and ((E -> (E or F)) and (((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-443, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88100
in-theory        88100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-409 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-88100.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-409, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88101
in-theory        88101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     63
proof            (modus-ponens tm-400 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-88101.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-400, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88102
in-theory        88102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-391 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-88102.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-391, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88103
in-theory        88103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-382 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-88103.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-382, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88104
in-theory        88104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G)))))
theorem-size     69
proof            (modus-ponens tm-373 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-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-88104.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G))))), M:tm-373, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88105
in-theory        88105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-364 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-88105.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-364, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88106
in-theory        88106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (E -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))) and E)))
theorem-size     57
proof            (modus-ponens tm-355 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       261
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88106.        (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (E -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))) and E))), M:tm-355, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88107
in-theory        88107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     63
proof            (modus-ponens tm-354 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-88107.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-354, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88108
in-theory        88108
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (F -> (E and F))))
theorem-size     61
proof            (modus-ponens tm-341 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-88108.        ((((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)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88109
in-theory        88109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E)))))
theorem-size     63
proof            (modus-ponens tm-338 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-88109.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E))))), M:tm-338, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88110
in-theory        88110
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))))
theorem-size     135
proof            (modus-ponens tm-328 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       365
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-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-88110.        ((((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)))) and (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C)))))), M:tm-328, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88111
in-theory        88111
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (F -> (E and F))) and (((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     115
proof            (modus-ponens tm-327 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       341
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-88111.        ((((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)))) and ((E -> (F -> (E and F))) and (((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-327, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88112
in-theory        88112
times-derived    1
----------------------------------------------------------------
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)))) and (((E and F) -> F) and (((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     113
proof            (modus-ponens tm-326 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       333
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-88112.        ((((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)))) and (((E and F) -> F) and (((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-326, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88113
in-theory        88113
times-derived    1
----------------------------------------------------------------
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)))) and (((E and F) -> E) and (((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     113
proof            (modus-ponens tm-325 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       333
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-88113.        ((((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)))) and (((E and F) -> E) and (((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-325, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88114
in-theory        88114
times-derived    1
----------------------------------------------------------------
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)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((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     121
proof            (modus-ponens tm-324 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       365
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-88114.        ((((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)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((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-324, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88115
in-theory        88115
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (F -> E)) and (((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     113
proof            (modus-ponens tm-323 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       333
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-88115.        ((((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)))) and ((E -> (F -> E)) and (((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-323, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88116
in-theory        88116
times-derived    1
----------------------------------------------------------------
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)))) and ((E and F) -> F))
theorem-size     59
proof            (modus-ponens tm-322 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-88116.        ((((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)))) and ((E and F) -> F)), M:tm-322, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88117
in-theory        88117
times-derived    1
----------------------------------------------------------------
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)))) and ((E and F) -> E))
theorem-size     59
proof            (modus-ponens tm-320 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-88117.        ((((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)))) and ((E and F) -> E)), M:tm-320, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88118
in-theory        88118
times-derived    1
----------------------------------------------------------------
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)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     67
proof            (modus-ponens tm-318 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-88118.        ((((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)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88119
in-theory        88119
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))))))
theorem-size     109
proof            (modus-ponens tm-316 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       333
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-88119.        ((((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)))) and (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))))), M:tm-316, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88120
in-theory        88120
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (F -> E)))
theorem-size     59
proof            (modus-ponens tm-315 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-88120.        ((((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)))) and (E -> (F -> E))), M:tm-315, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88121
in-theory        88121
times-derived    1
----------------------------------------------------------------
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)))) and ((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))) -> (not ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))))))
theorem-size     137
proof            (modus-ponens tm-313 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       351
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-88121.        ((((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)))) and ((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))) -> (not ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))))))), M:tm-313, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88122
in-theory        88122
times-derived    1
----------------------------------------------------------------
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)))) and (((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))) -> E) -> ((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> E)))
theorem-size     137
proof            (modus-ponens tm-312 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       355
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-88122.        ((((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)))) and (((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))) -> E) -> ((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> E))), M:tm-312, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88123
in-theory        88123
times-derived    1
----------------------------------------------------------------
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)))) and (E or (((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     109
proof            (modus-ponens tm-311 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-88123.        ((((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)))) and (E or (((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-311, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88124
in-theory        88124
times-derived    1
----------------------------------------------------------------
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)))) and ((((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)))) or E))
theorem-size     109
proof            (modus-ponens tm-310 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-88124.        ((((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)))) and ((((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)))) or E)), M:tm-310, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88125
in-theory        88125
times-derived    1
----------------------------------------------------------------
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)))) and (E -> ((((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)))) and E)))
theorem-size     111
proof            (modus-ponens tm-309 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
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-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-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-88125.        ((((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)))) and (E -> ((((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)))) and E))), M:tm-309, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88126
in-theory        88126
times-derived    1
----------------------------------------------------------------
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)))) and ((((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 -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((A or (B -> C)) -> ((D or B) -> C)))))
theorem-size     135
proof            (modus-ponens tm-306 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       355
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (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-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-88126.        ((((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)))) and ((((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 -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((A or (B -> C)) -> ((D or B) -> C))))), M:tm-306, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))
================================================================
tm-name          tm-88127
in-theory        88127
times-derived    1
----------------------------------------------------------------
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)))) and (E -> (((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     109
proof            (modus-ponens tm-305 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-88127.        ((((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)))) and (E -> (((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-305, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88128
in-theory        88128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     65
proof            (modus-ponens tm-303 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       271
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-88128.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-303, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88129
in-theory        88129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     63
proof            (modus-ponens tm-270 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-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-88129.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-270, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88130
in-theory        88130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     63
proof            (modus-ponens tm-239 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-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-88130.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-239, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88131
in-theory        88131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G)))))
theorem-size     71
proof            (modus-ponens tm-210 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       295
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-88131.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G))))), M:tm-210, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88132
in-theory        88132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     63
proof            (modus-ponens tm-183 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-88132.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-183, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88133
in-theory        88133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-157 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-88133.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-157, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88134
in-theory        88134
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     69
proof            (modus-ponens tm-147 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-88134.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-147, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88135
in-theory        88135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-134 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-88135.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-134, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88136
in-theory        88136
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     69
proof            (modus-ponens tm-125 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-88136.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-125, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88137
in-theory        88137
times-derived    1
----------------------------------------------------------------
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 -> B) or ((B -> C) -> ((D or B) -> C))) -> ((D or B) -> C))))
theorem-size     67
proof            (modus-ponens tm-114 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (or Am (-> Bm Cm))) (D (-> (or Dm Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       289
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88137.        (((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 -> B) or ((B -> C) -> ((D or B) -> C))) -> ((D or B) -> C)))), M:tm-114, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (or Am (-> Bm Cm))) (D (-> (or Dm Bm) Cm)))
================================================================
tm-name          tm-88138
in-theory        88138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G)))))
theorem-size     69
proof            (modus-ponens tm-113 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-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-88138.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G))))), M:tm-113, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88139
in-theory        88139
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     73
proof            (modus-ponens tm-105 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       307
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-88139.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-105, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88140
in-theory        88140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E)))))
theorem-size     61
proof            (modus-ponens tm-95 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-88140.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E))))), M:tm-95, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88141
in-theory        88141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (E -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C)))))
theorem-size     55
proof            (modus-ponens tm-84 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88141.        (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (E -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))), M:tm-84, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88142
in-theory        88142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     61
proof            (modus-ponens tm-83 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-88142.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-83, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88143
in-theory        88143
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D)))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D)))))
theorem-size     59
proof            (modus-ponens tm-76 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-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-88143.        (((not (not A)) -> A) and (((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D)))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D))))), M:tm-76, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88144
in-theory        88144
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))))) or ((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     83
proof            (modus-ponens tm-73 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-8 tm-10)
proof-size       271
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88144.        (((not (not ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))))) or ((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-73, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88145
in-theory        88145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E)))))
theorem-size     65
proof            (modus-ponens tm-69 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       257
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-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-88145.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E))))), M:tm-69, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88146
in-theory        88146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     67
proof            (modus-ponens tm-54 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       263
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-88146.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-54, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88147
in-theory        88147
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) or ((D -> (A -> B)) or (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B))))
theorem-size     75
proof            (modus-ponens tm-50 tm-961 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-8 tm-7)
proof-size       265
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88147.        (((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) or ((D -> (A -> B)) or (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B)))), M:tm-50, m:tm-961, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88148
in-theory        88148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((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     59
proof            (modus-ponens tm-49 tm-961 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-8 tm-6)
proof-size       249
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88148.        (((A -> (B -> C)) or ((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-49, m:tm-961, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88149
in-theory        88149
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D))))) or ((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D))))
theorem-size     83
proof            (modus-ponens tm-47 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-8 tm-4)
proof-size       271
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88149.        (((A and ((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D))))) or ((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D)))), M:tm-47, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88150
in-theory        88150
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) and E) or ((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     83
proof            (modus-ponens tm-46 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-8 tm-3)
proof-size       271
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88150.        (((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) and E) or ((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-46, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88151
in-theory        88151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E)))))
theorem-size     59
proof            (modus-ponens tm-42 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-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-88151.        ((A -> (B or A)) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E))))), M:tm-42, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88152
in-theory        88152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E)))))
theorem-size     59
proof            (modus-ponens tm-32 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-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-88152.        ((A -> (A or B)) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E))))), M:tm-32, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88153
in-theory        88153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C)))))
theorem-size     81
proof            (modus-ponens tm-24 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       269
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-88153.        (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))), M:tm-24, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88154
in-theory        88154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E)))))
theorem-size     61
proof            (modus-ponens tm-23 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       245
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-88154.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E))))), M:tm-23, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88155
in-theory        88155
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E)))))
theorem-size     59
proof            (modus-ponens tm-22 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-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-88155.        (((A and B) -> B) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E))))), M:tm-22, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88156
in-theory        88156
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E)))))
theorem-size     59
proof            (modus-ponens tm-21 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-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-88156.        (((A and B) -> A) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E))))), M:tm-21, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88157
in-theory        88157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F)))))
theorem-size     67
proof            (modus-ponens tm-20 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       263
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-88157.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or (((E -> F) -> ((G or E) -> F)) -> ((D or (E -> F)) -> ((G or E) -> F)))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((D or (E -> F)) -> ((G or E) -> F))))), M:tm-20, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88158
in-theory        88158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E)))))
theorem-size     59
proof            (modus-ponens tm-19 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-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-88158.        ((A -> (B -> A)) and (((C -> (D -> E)) or (((D -> E) -> ((F or D) -> E)) -> ((C or (D -> E)) -> ((F or D) -> E)))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((C or (D -> E)) -> ((F or D) -> E))))), M:tm-19, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88159
in-theory        88159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))))
theorem-size     55
proof            (modus-ponens tm-12 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88159.        (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))))), M:tm-12, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88160
in-theory        88160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))) -> (not ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))))))
theorem-size     83
proof            (modus-ponens tm-9 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-9 tm-8)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88160.        ((((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))) -> (not ((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))))), M:tm-9, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88161
in-theory        88161
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (B -> C)) -> ((A or B) -> C))) -> E) -> ((((D -> (B -> C)) or (((B -> C) -> ((A or B) -> C)) -> ((D or (B -> C)) -> ((A or B) -> C)))) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (B -> C)) -> ((A or B) -> C)))) -> E))
theorem-size     83
proof            (modus-ponens tm-8 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-8)
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-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-88161.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (B -> C)) -> ((A or B) -> C))) -> E) -> ((((D -> (B -> C)) or (((B -> C) -> ((A or B) -> C)) -> ((D or (B -> C)) -> ((A or B) -> C)))) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (B -> C)) -> ((A or B) -> C)))) -> E)), M:tm-8, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88162
in-theory        88162
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D)))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D)))))
theorem-size     55
proof            (modus-ponens tm-7 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-7 tm-8)
proof-size       219
proof-steps      9
----------------------------------------------------------------
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-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-88162.        (A or (((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D)))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D))))), M:tm-7, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88163
in-theory        88163
times-derived    1
----------------------------------------------------------------
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)))) or E)
theorem-size     55
proof            (modus-ponens tm-6 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-6 tm-8)
proof-size       219
proof-steps      9
----------------------------------------------------------------
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-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-88163.        ((((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)))) or E), M:tm-6, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88164
in-theory        88164
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D)))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D)))) and A))
theorem-size     57
proof            (modus-ponens tm-5 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       223
proof-steps      9
----------------------------------------------------------------
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-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-88164.        (A -> ((((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D)))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D)))) and A)), M:tm-5, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88165
in-theory        88165
times-derived    1
----------------------------------------------------------------
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 -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((A or (B -> C)) -> ((D or B) -> C))))
theorem-size     81
proof            (modus-ponens tm-2 tm-961 ((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))
axioms-used      (tm-2 tm-8)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88165.        ((((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 -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((A or (B -> C)) -> ((D or B) -> C)))), M:tm-2, m:tm-961, u:((A (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))
================================================================
tm-name          tm-88166
in-theory        88166
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D)))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D)))))
theorem-size     55
proof            (modus-ponens tm-1 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-1 tm-8)
proof-size       219
proof-steps      9
----------------------------------------------------------------
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-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-88166.        (A -> (((B -> (C -> D)) or (((C -> D) -> ((E or C) -> D)) -> ((B or (C -> D)) -> ((E or C) -> D)))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((B or (C -> D)) -> ((E or C) -> D))))), M:tm-1, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88167
in-theory        88167
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     63
proof            (modus-ponens tm-930 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-88167.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-930, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88168
in-theory        88168
times-derived    1
----------------------------------------------------------------
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))))) and (((((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))) or (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     121
proof            (modus-ponens tm-920 tm-962 ((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       339
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-48.           (((A -> (B and 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-88168.        (((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))))) and (((((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))) or (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-920, m:tm-962, u:((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88169
in-theory        88169
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     63
proof            (modus-ponens tm-893 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-88169.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-893, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88170
in-theory        88170
times-derived    1
----------------------------------------------------------------
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))))) and ((A or (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     101
proof            (modus-ponens tm-882 tm-962 ((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       319
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-48.           (((A -> (B and 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-88170.        (((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))))) and ((A or (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-882, m:tm-962, u:((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88171
in-theory        88171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     67
proof            (modus-ponens tm-855 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88171.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-855, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88172
in-theory        88172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-808 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-88172.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-808, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88173
in-theory        88173
times-derived    1
----------------------------------------------------------------
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))))) and (((E and (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))))) or (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     125
proof            (modus-ponens tm-798 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       337
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-48.           (((A -> (B and 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-88173.        (((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))))) and (((E and (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))))) or (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-798, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88174
in-theory        88174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-757 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-88174.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-757, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88175
in-theory        88175
times-derived    1
----------------------------------------------------------------
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))))) and ((((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) and E) or (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     125
proof            (modus-ponens tm-747 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       337
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88175.        (((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))))) and ((((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) and E) or (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-747, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88176
in-theory        88176
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 F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G))))))
theorem-size     75
proof            (modus-ponens tm-708 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88176.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G)))))), M:tm-708, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88177
in-theory        88177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     63
proof            (modus-ponens tm-665 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-88177.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-665, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88178
in-theory        88178
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (E or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C))))))
theorem-size     51
proof            (modus-ponens tm-623 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
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-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-88178.        ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (E or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))), M:tm-623, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88179
in-theory        88179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-622 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-48.           (((A -> (B and 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-88179.        ((A -> (B -> (C or B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-622, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88180
in-theory        88180
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (F or E)))
theorem-size     55
proof            (modus-ponens tm-609 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88180.        (((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))))) and (E -> (F or E))), M:tm-609, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88181
in-theory        88181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     59
proof            (modus-ponens tm-605 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-88181.        ((A -> ((B -> (C or B)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-605, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88182
in-theory        88182
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (F or E)) and ((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     105
proof            (modus-ponens tm-595 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88182.        (((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))))) and ((E -> (F or E)) and ((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-595, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88183
in-theory        88183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-550 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-48.           (((A -> (B and 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-88183.        (((A -> (B or A)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-550, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88184
in-theory        88184
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-540 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-88184.        ((A or (B -> (C or B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-540, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88185
in-theory        88185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-530 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-48.           (((A -> (B and 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-88185.        ((A or (B -> (B or C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-530, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88186
in-theory        88186
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     59
proof            (modus-ponens tm-520 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-88186.        ((A or (B -> (C -> (B and C)))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-520, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88187
in-theory        88187
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-510 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-48.           (((A -> (B and 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-88187.        ((A or ((B and C) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-510, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88188
in-theory        88188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-500 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-48.           (((A -> (B and 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-88188.        ((A or ((B and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-500, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88189
in-theory        88189
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G))))))
theorem-size     65
proof            (modus-ponens tm-490 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88189.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G)))))), M:tm-490, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88190
in-theory        88190
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-480 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-48.           (((A -> (B and 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-88190.        ((A or (B -> (C -> B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-480, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88191
in-theory        88191
times-derived    1
----------------------------------------------------------------
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)))) or E))
theorem-size     51
proof            (modus-ponens tm-470 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
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-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-88191.        ((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)))) or E)), M:tm-470, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88192
in-theory        88192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-469 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-48.           (((A -> (B and 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-88192.        ((A -> (B -> (B or C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-469, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88193
in-theory        88193
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (E or F)))
theorem-size     55
proof            (modus-ponens tm-456 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88193.        (((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))))) and (E -> (E or F))), M:tm-456, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88194
in-theory        88194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     59
proof            (modus-ponens tm-453 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-88194.        ((A -> ((B -> (B or C)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-453, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88195
in-theory        88195
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (E or F)) and ((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     105
proof            (modus-ponens tm-443 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88195.        (((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))))) and ((E -> (E or F)) and ((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-443, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88196
in-theory        88196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-409 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-88196.        (((A -> (A or B)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-409, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88197
in-theory        88197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     59
proof            (modus-ponens tm-400 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-88197.        (((A -> (B -> (A and B))) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-400, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88198
in-theory        88198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-391 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-48.           (((A -> (B and 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-88198.        ((((A and B) -> B) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-391, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88199
in-theory        88199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-382 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-48.           (((A -> (B and 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-88199.        ((((A and B) -> A) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-382, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88200
in-theory        88200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G))))))
theorem-size     65
proof            (modus-ponens tm-373 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88200.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G)))))), M:tm-373, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88201
in-theory        88201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-364 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-48.           (((A -> (B and 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-88201.        (((A -> (B -> A)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-364, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88202
in-theory        88202
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (E -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))) and E)))
theorem-size     53
proof            (modus-ponens tm-355 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
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-48.           (((A -> (B and 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-88202.        ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (E -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))) and E))), M:tm-355, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88203
in-theory        88203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     59
proof            (modus-ponens tm-354 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-88203.        ((A -> (B -> (C -> (B and C)))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-354, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88204
in-theory        88204
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (F -> (E and F))))
theorem-size     57
proof            (modus-ponens tm-341 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88204.        (((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))))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88205
in-theory        88205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E))))))
theorem-size     59
proof            (modus-ponens tm-338 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88205.        (((A -> B) -> (A -> (A and B))) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E)))))), M:tm-338, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88206
in-theory        88206
times-derived    1
----------------------------------------------------------------
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))))) and ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))))
theorem-size     123
proof            (modus-ponens tm-328 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       333
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88206.        (((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))))) and ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C))))))), M:tm-328, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88207
in-theory        88207
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (F -> (E and F))) and ((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     107
proof            (modus-ponens tm-327 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88207.        (((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))))) and ((E -> (F -> (E and F))) and ((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-327, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88208
in-theory        88208
times-derived    1
----------------------------------------------------------------
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))))) and (((E and F) -> F) and ((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     105
proof            (modus-ponens tm-326 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88208.        (((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))))) and (((E and F) -> F) and ((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-326, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88209
in-theory        88209
times-derived    1
----------------------------------------------------------------
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))))) and (((E and F) -> E) and ((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     105
proof            (modus-ponens tm-325 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88209.        (((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))))) and (((E and F) -> E) and ((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-325, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88210
in-theory        88210
times-derived    1
----------------------------------------------------------------
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))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((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     113
proof            (modus-ponens tm-324 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       337
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88210.        (((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))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((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-324, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88211
in-theory        88211
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (F -> E)) and ((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     105
proof            (modus-ponens tm-323 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88211.        (((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))))) and ((E -> (F -> E)) and ((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-323, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88212
in-theory        88212
times-derived    1
----------------------------------------------------------------
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))))) and ((E and F) -> F))
theorem-size     55
proof            (modus-ponens tm-322 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88212.        (((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))))) and ((E and F) -> F)), M:tm-322, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88213
in-theory        88213
times-derived    1
----------------------------------------------------------------
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))))) and ((E and F) -> E))
theorem-size     55
proof            (modus-ponens tm-320 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88213.        (((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))))) and ((E and F) -> E)), M:tm-320, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88214
in-theory        88214
times-derived    1
----------------------------------------------------------------
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))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     63
proof            (modus-ponens tm-318 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88214.        (((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))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88215
in-theory        88215
times-derived    1
----------------------------------------------------------------
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))))) and ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))))))
theorem-size     97
proof            (modus-ponens tm-316 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
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-48.           (((A -> (B and 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-88215.        (((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))))) and ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))))), M:tm-316, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88216
in-theory        88216
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (F -> E)))
theorem-size     55
proof            (modus-ponens tm-315 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88216.        (((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))))) and (E -> (F -> E))), M:tm-315, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88217
in-theory        88217
times-derived    1
----------------------------------------------------------------
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))))) and (((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))) -> (not (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))))))
theorem-size     125
proof            (modus-ponens tm-313 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       319
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88217.        (((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))))) and (((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))) -> (not (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))))))), M:tm-313, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88218
in-theory        88218
times-derived    1
----------------------------------------------------------------
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))))) and (((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))) -> E) -> (((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C))))) -> E)))
theorem-size     129
proof            (modus-ponens tm-312 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       327
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88218.        (((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))))) and (((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))) -> E) -> (((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C))))) -> E))), M:tm-312, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88219
in-theory        88219
times-derived    1
----------------------------------------------------------------
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))))) and (E or ((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     101
proof            (modus-ponens tm-311 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88219.        (((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))))) and (E or ((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-311, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88220
in-theory        88220
times-derived    1
----------------------------------------------------------------
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))))) and (((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))))) or E))
theorem-size     101
proof            (modus-ponens tm-310 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88220.        (((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))))) and (((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))))) or E)), M:tm-310, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88221
in-theory        88221
times-derived    1
----------------------------------------------------------------
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))))) and (E -> (((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))))) and E)))
theorem-size     103
proof            (modus-ponens tm-309 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88221.        (((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))))) and (E -> (((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))))) and E))), M:tm-309, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88222
in-theory        88222
times-derived    1
----------------------------------------------------------------
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))))) and (((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 or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (A and ((B -> C) -> ((D or B) -> C))))))
theorem-size     123
proof            (modus-ponens tm-306 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       323
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88222.        (((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))))) and (((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 or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (A and ((B -> C) -> ((D or B) -> C)))))), M:tm-306, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88223
in-theory        88223
times-derived    1
----------------------------------------------------------------
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))))) and (E -> ((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     101
proof            (modus-ponens tm-305 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88223.        (((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))))) and (E -> ((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-305, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88224
in-theory        88224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-303 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-88224.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-303, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88225
in-theory        88225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     59
proof            (modus-ponens tm-270 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-4 tm-8)
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-48.           (((A -> (B and 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-88225.        ((A -> (((B and C) -> C) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-270, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88226
in-theory        88226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     59
proof            (modus-ponens tm-239 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-3 tm-8)
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-48.           (((A -> (B and 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-88226.        ((A -> (((B and C) -> B) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-239, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88227
in-theory        88227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G))))))
theorem-size     67
proof            (modus-ponens tm-210 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88227.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G)))))), M:tm-210, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88228
in-theory        88228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     59
proof            (modus-ponens tm-183 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-88228.        ((A -> ((B -> (C -> B)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-183, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88229
in-theory        88229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-157 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-48.           (((A -> (B and 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-88229.        ((A -> ((B and C) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-157, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88230
in-theory        88230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     65
proof            (modus-ponens tm-147 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88230.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-147, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88231
in-theory        88231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-134 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-48.           (((A -> (B and 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-88231.        ((A -> ((B and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-134, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88232
in-theory        88232
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     65
proof            (modus-ponens tm-125 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88232.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-125, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88233
in-theory        88233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G))))))
theorem-size     65
proof            (modus-ponens tm-113 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88233.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G)))))), M:tm-113, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88234
in-theory        88234
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     69
proof            (modus-ponens tm-105 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88234.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-105, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88235
in-theory        88235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E))))))
theorem-size     57
proof            (modus-ponens tm-95 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88235.        (((A -> B) -> (A -> A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E)))))), M:tm-95, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88236
in-theory        88236
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (E -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C))))))
theorem-size     51
proof            (modus-ponens tm-84 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-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-88236.        ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (E -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))), M:tm-84, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88237
in-theory        88237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-83 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-88237.        ((A -> (B -> (C -> B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-83, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88238
in-theory        88238
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D))))))
theorem-size     55
proof            (modus-ponens tm-76 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-10 tm-8)
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-48.           (((A -> (B and 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-88238.        (((not (not A)) -> A) and ((B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D)))))), M:tm-76, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88239
in-theory        88239
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))))) or (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     75
proof            (modus-ponens tm-73 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-8 tm-10 tm-5)
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-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-88239.        (((not (not (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))))) or (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-73, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88240
in-theory        88240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E))))))
theorem-size     61
proof            (modus-ponens tm-69 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-9 tm-8)
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-48.           (((A -> (B and 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-88240.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E)))))), M:tm-69, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88241
in-theory        88241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     63
proof            (modus-ponens tm-54 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-88241.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-54, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88242
in-theory        88242
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) or (D or (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B)))))
theorem-size     71
proof            (modus-ponens tm-50 tm-962 ((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       241
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-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-88242.        (((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) or (D or (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B))))), M:tm-50, m:tm-962, u:((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88243
in-theory        88243
times-derived    1
----------------------------------------------------------------
theorem          ((A or (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     51
proof            (modus-ponens tm-49 tm-962 ((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       221
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-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-88243.        ((A or (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-49, m:tm-962, u:((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88244
in-theory        88244
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D)))))) or (B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D)))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D)))))
theorem-size     75
proof            (modus-ponens tm-47 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-8 tm-4 tm-5)
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-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-88244.        (((A and (B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D)))))) or (B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D)))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D))))), M:tm-47, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88245
in-theory        88245
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) and E) or (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     75
proof            (modus-ponens tm-46 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-8 tm-3 tm-5)
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-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-88245.        ((((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) and E) or (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-46, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88246
in-theory        88246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E))))))
theorem-size     55
proof            (modus-ponens tm-42 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-88246.        ((A -> (B or A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E)))))), M:tm-42, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88247
in-theory        88247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E))))))
theorem-size     55
proof            (modus-ponens tm-32 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-88247.        ((A -> (A or B)) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E)))))), M:tm-32, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88248
in-theory        88248
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C))))))
theorem-size     73
proof            (modus-ponens tm-24 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
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-48.           (((A -> (B and 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-88248.        ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))), M:tm-24, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88249
in-theory        88249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E))))))
theorem-size     57
proof            (modus-ponens tm-23 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-88249.        ((A -> (B -> (A and B))) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E)))))), M:tm-23, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88250
in-theory        88250
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E))))))
theorem-size     55
proof            (modus-ponens tm-22 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-4 tm-8)
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-48.           (((A -> (B and 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-88250.        (((A and B) -> B) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E)))))), M:tm-22, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88251
in-theory        88251
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E))))))
theorem-size     55
proof            (modus-ponens tm-21 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-3 tm-8)
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-48.           (((A -> (B and 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-88251.        (((A and B) -> A) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E)))))), M:tm-21, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88252
in-theory        88252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F))))))
theorem-size     63
proof            (modus-ponens tm-20 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
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-48.           (((A -> (B and 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-88252.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> (D and ((E -> F) -> ((G or E) -> F))))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> (D and ((E -> F) -> ((G or E) -> F)))))), M:tm-20, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88253
in-theory        88253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E))))))
theorem-size     55
proof            (modus-ponens tm-19 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-48.           (((A -> (B and 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-88253.        ((A -> (B -> A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> (C and ((D -> E) -> ((F or D) -> E))))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> (C and ((D -> E) -> ((F or D) -> E)))))), M:tm-19, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88254
in-theory        88254
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))))
theorem-size     47
proof            (modus-ponens tm-12 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       211
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-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-88254.        ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))))), M:tm-12, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88255
in-theory        88255
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))) -> (not (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))))))
theorem-size     75
proof            (modus-ponens tm-9 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-9 tm-8 tm-5)
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-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-88255.        (((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))) -> (not (A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))))), M:tm-9, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88256
in-theory        88256
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and ((B -> C) -> ((A or B) -> C)))) -> E) -> (((D or (((B -> C) -> ((A or B) -> C)) -> (D and ((B -> C) -> ((A or B) -> C))))) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and ((B -> C) -> ((A or B) -> C))))) -> E))
theorem-size     79
proof            (modus-ponens tm-8 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-8 tm-5)
proof-size       231
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88256.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and ((B -> C) -> ((A or B) -> C)))) -> E) -> (((D or (((B -> C) -> ((A or B) -> C)) -> (D and ((B -> C) -> ((A or B) -> C))))) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D and ((B -> C) -> ((A or B) -> C))))) -> E)), M:tm-8, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-88257
in-theory        88257
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D))))))
theorem-size     51
proof            (modus-ponens tm-7 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-7 tm-8 tm-5)
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-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-88257.        (A or ((B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D)))))), M:tm-7, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88258
in-theory        88258
times-derived    1
----------------------------------------------------------------
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))))) or E)
theorem-size     51
proof            (modus-ponens tm-6 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-6 tm-8 tm-5)
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-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-88258.        (((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))))) or E), M:tm-6, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88259
in-theory        88259
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D))))) and A))
theorem-size     53
proof            (modus-ponens tm-5 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-88259.        (A -> (((B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D))))) and A)), M:tm-5, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88260
in-theory        88260
times-derived    1
----------------------------------------------------------------
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 or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (A and ((B -> C) -> ((D or B) -> C)))))
theorem-size     73
proof            (modus-ponens tm-2 tm-962 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
axioms-used      (tm-2 tm-8 tm-5)
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-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-88260.        (((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 or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (A and ((B -> C) -> ((D or B) -> C))))), M:tm-2, m:tm-962, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))
================================================================
tm-name          tm-88261
in-theory        88261
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D))))))
theorem-size     51
proof            (modus-ponens tm-1 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       195
proof-steps      9
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88261.        (A -> ((B or (((C -> D) -> ((E or C) -> D)) -> (B and ((C -> D) -> ((E or C) -> D))))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> (B and ((C -> D) -> ((E or C) -> D)))))), M:tm-1, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-88262
in-theory        88262
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     55
proof            (modus-ponens tm-930 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
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-88262.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-930, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88263
in-theory        88263
times-derived    1
----------------------------------------------------------------
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)) and (((((B -> C) -> ((D or B) -> C)) -> E) or ((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     95
proof            (modus-ponens tm-920 tm-963 ((A (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4)
proof-size       297
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-4.            ((A and B) -> B), axiom
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-88263.        ((((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)) and (((((B -> C) -> ((D or B) -> C)) -> E) or ((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-920, m:tm-963, u:((A (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88264
in-theory        88264
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     55
proof            (modus-ponens tm-893 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-88264.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-893, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88265
in-theory        88265
times-derived    1
----------------------------------------------------------------
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)) and (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or ((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     97
proof            (modus-ponens tm-882 tm-963 ((A (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
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-88265.        ((((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)) and (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or ((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-882, m:tm-963, u:((A (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88266
in-theory        88266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     59
proof            (modus-ponens tm-855 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
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-88266.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-855, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88267
in-theory        88267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     53
proof            (modus-ponens tm-808 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88267.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-808, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88268
in-theory        88268
times-derived    1
----------------------------------------------------------------
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)) and (((F and ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E))) or ((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     111
proof            (modus-ponens tm-798 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88268.        ((((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)) and (((F and ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E))) or ((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-798, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88269
in-theory        88269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     53
proof            (modus-ponens tm-757 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88269.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-757, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88270
in-theory        88270
times-derived    1
----------------------------------------------------------------
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)) and (((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) and F) or ((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     111
proof            (modus-ponens tm-747 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88270.        ((((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)) and (((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) and F) or ((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-747, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88271
in-theory        88271
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)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))
theorem-size     67
proof            (modus-ponens tm-708 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       277
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88271.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))), M:tm-708, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88272
in-theory        88272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     55
proof            (modus-ponens tm-665 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88272.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-665, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88273
in-theory        88273
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (F or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     43
proof            (modus-ponens tm-623 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88273.        (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (F or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-623, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88274
in-theory        88274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-622 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88274.        ((A -> (B -> (C or B))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-622, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88275
in-theory        88275
times-derived    1
----------------------------------------------------------------
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)) and (F -> (G or F)))
theorem-size     47
proof            (modus-ponens tm-609 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88275.        ((((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)) and (F -> (G or F))), M:tm-609, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88276
in-theory        88276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     51
proof            (modus-ponens tm-605 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88276.        ((A -> ((B -> (C or B)) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-605, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88277
in-theory        88277
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G or F)) and (((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     89
proof            (modus-ponens tm-595 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88277.        ((((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)) and ((F -> (G or F)) and (((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-595, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88278
in-theory        88278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-550 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88278.        (((A -> (B or A)) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-550, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88279
in-theory        88279
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-540 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88279.        ((A or (B -> (C or B))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-540, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88280
in-theory        88280
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-530 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88280.        ((A or (B -> (B or C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-530, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88281
in-theory        88281
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     51
proof            (modus-ponens tm-520 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88281.        ((A or (B -> (C -> (B and C)))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-520, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88282
in-theory        88282
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-510 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88282.        ((A or ((B and C) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-510, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88283
in-theory        88283
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-500 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88283.        ((A or ((B and C) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-500, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88284
in-theory        88284
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))
theorem-size     57
proof            (modus-ponens tm-490 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88284.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))), M:tm-490, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88285
in-theory        88285
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-480 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88285.        ((A or (B -> (C -> B))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-480, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88286
in-theory        88286
times-derived    1
----------------------------------------------------------------
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) or F))
theorem-size     43
proof            (modus-ponens tm-470 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88286.        (((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) or F)), M:tm-470, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88287
in-theory        88287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-469 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88287.        ((A -> (B -> (B or C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-469, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88288
in-theory        88288
times-derived    1
----------------------------------------------------------------
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)) and (F -> (F or G)))
theorem-size     47
proof            (modus-ponens tm-456 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88288.        ((((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)) and (F -> (F or G))), M:tm-456, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88289
in-theory        88289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     51
proof            (modus-ponens tm-453 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88289.        ((A -> ((B -> (B or C)) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-453, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88290
in-theory        88290
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (F or G)) and (((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     89
proof            (modus-ponens tm-443 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88290.        ((((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)) and ((F -> (F or G)) and (((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-443, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88291
in-theory        88291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-409 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88291.        (((A -> (A or B)) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-409, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88292
in-theory        88292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     51
proof            (modus-ponens tm-400 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88292.        (((A -> (B -> (A and B))) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-400, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88293
in-theory        88293
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-391 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88293.        ((((A and B) -> B) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-391, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88294
in-theory        88294
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-382 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88294.        ((((A and B) -> A) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-382, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88295
in-theory        88295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))
theorem-size     57
proof            (modus-ponens tm-373 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88295.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))), M:tm-373, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88296
in-theory        88296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-364 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88296.        (((A -> (B -> A)) or C) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-364, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88297
in-theory        88297
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (F -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E) and F)))
theorem-size     45
proof            (modus-ponens tm-355 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       213
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88297.        (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (F -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E) and F))), M:tm-355, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88298
in-theory        88298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     51
proof            (modus-ponens tm-354 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88298.        ((A -> (B -> (C -> (B and C)))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-354, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88299
in-theory        88299
times-derived    1
----------------------------------------------------------------
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)) and (F -> (G -> (F and G))))
theorem-size     49
proof            (modus-ponens tm-341 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88299.        ((((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)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88300
in-theory        88300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-338 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88300.        (((A -> B) -> (A -> (A and B))) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-338, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88301
in-theory        88301
times-derived    1
----------------------------------------------------------------
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)) and (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))
theorem-size     109
proof            (modus-ponens tm-328 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       303
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88301.        ((((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)) and (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))), M:tm-328, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88302
in-theory        88302
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G -> (F and G))) and (((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     91
proof            (modus-ponens tm-327 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88302.        ((((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)) and ((F -> (G -> (F and G))) and (((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-327, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88303
in-theory        88303
times-derived    1
----------------------------------------------------------------
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)) and (((F and G) -> G) and (((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     89
proof            (modus-ponens tm-326 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88303.        ((((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)) and (((F and G) -> G) and (((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-326, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88304
in-theory        88304
times-derived    1
----------------------------------------------------------------
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)) and (((F and G) -> F) and (((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     89
proof            (modus-ponens tm-325 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88304.        ((((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)) and (((F and G) -> F) and (((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-325, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88305
in-theory        88305
times-derived    1
----------------------------------------------------------------
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)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((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     97
proof            (modus-ponens tm-324 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-88305.        ((((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)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((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-324, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88306
in-theory        88306
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G -> F)) and (((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     89
proof            (modus-ponens tm-323 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88306.        ((((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)) and ((F -> (G -> F)) and (((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-323, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88307
in-theory        88307
times-derived    1
----------------------------------------------------------------
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)) and ((F and G) -> G))
theorem-size     47
proof            (modus-ponens tm-322 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88307.        ((((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)) and ((F and G) -> G)), M:tm-322, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88308
in-theory        88308
times-derived    1
----------------------------------------------------------------
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)) and ((F and G) -> F))
theorem-size     47
proof            (modus-ponens tm-320 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88308.        ((((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)) and ((F and G) -> F)), M:tm-320, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88309
in-theory        88309
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     55
proof            (modus-ponens tm-318 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88309.        ((((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)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88310
in-theory        88310
times-derived    1
----------------------------------------------------------------
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)) and (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E))))
theorem-size     93
proof            (modus-ponens tm-316 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88310.        ((((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)) and (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)))), M:tm-316, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88311
in-theory        88311
times-derived    1
----------------------------------------------------------------
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)) and (F -> (G -> F)))
theorem-size     47
proof            (modus-ponens tm-315 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88311.        ((((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)) and (F -> (G -> F))), M:tm-315, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88312
in-theory        88312
times-derived    1
----------------------------------------------------------------
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)) and ((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)))))
theorem-size     111
proof            (modus-ponens tm-313 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88312.        ((((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)) and ((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E))))), M:tm-313, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88313
in-theory        88313
times-derived    1
----------------------------------------------------------------
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)) and (((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E) -> F) -> ((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F)))
theorem-size     103
proof            (modus-ponens tm-312 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       285
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88313.        ((((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)) and (((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E) -> F) -> ((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F))), M:tm-312, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88314
in-theory        88314
times-derived    1
----------------------------------------------------------------
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)) and (F or (((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     85
proof            (modus-ponens tm-311 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88314.        ((((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)) and (F or (((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-311, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88315
in-theory        88315
times-derived    1
----------------------------------------------------------------
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)) and ((((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)) or F))
theorem-size     85
proof            (modus-ponens tm-310 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88315.        ((((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)) and ((((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)) or F)), M:tm-310, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88316
in-theory        88316
times-derived    1
----------------------------------------------------------------
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)) and (F -> ((((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)) and F)))
theorem-size     87
proof            (modus-ponens tm-309 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88316.        ((((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)) and (F -> ((((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)) and F))), M:tm-309, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88317
in-theory        88317
times-derived    1
----------------------------------------------------------------
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)) and ((((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)))) -> (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> E)))
theorem-size     109
proof            (modus-ponens tm-306 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Em)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-306.          ((A -> (B -> C)) -> ((A -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88317.        ((((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)) and ((((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)))) -> (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> E))), M:tm-306, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Em))
================================================================
tm-name          tm-88318
in-theory        88318
times-derived    1
----------------------------------------------------------------
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)) and (F -> (((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     85
proof            (modus-ponens tm-305 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88318.        ((((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)) and (F -> (((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-305, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88319
in-theory        88319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     53
proof            (modus-ponens tm-303 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88319.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-303, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88320
in-theory        88320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     51
proof            (modus-ponens tm-270 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88320.        ((A -> (((B and C) -> C) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-270, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88321
in-theory        88321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     51
proof            (modus-ponens tm-239 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88321.        ((A -> (((B and C) -> B) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-239, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88322
in-theory        88322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))
theorem-size     59
proof            (modus-ponens tm-210 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88322.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))), M:tm-210, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88323
in-theory        88323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     51
proof            (modus-ponens tm-183 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88323.        ((A -> ((B -> (C -> B)) and A)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-183, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88324
in-theory        88324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-157 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88324.        ((A -> ((B and C) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-157, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88325
in-theory        88325
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     57
proof            (modus-ponens tm-147 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88325.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-147, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88326
in-theory        88326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-134 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88326.        ((A -> ((B and C) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-134, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88327
in-theory        88327
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     57
proof            (modus-ponens tm-125 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88327.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-125, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88328
in-theory        88328
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> (E -> F))) or (((B -> C) -> ((D or B) -> C)) -> (E -> F))) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> F)))
theorem-size     61
proof            (modus-ponens tm-114 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> C D))) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> C D)))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (Em (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       247
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88328.        (((A and (((B -> C) -> ((D or B) -> C)) -> (E -> F))) or (((B -> C) -> ((D or B) -> C)) -> (E -> F))) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> F))), M:tm-114, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> C D))) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> C D)))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (Em (-> C D)))
================================================================
tm-name          tm-88329
in-theory        88329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))
theorem-size     57
proof            (modus-ponens tm-113 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88329.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))), M:tm-113, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88330
in-theory        88330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     61
proof            (modus-ponens tm-105 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       259
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88330.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-105, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88331
in-theory        88331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-95 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88331.        (((A -> B) -> (A -> A)) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-95, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88332
in-theory        88332
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (F -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     43
proof            (modus-ponens tm-84 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88332.        (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (F -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-84, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88333
in-theory        88333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     49
proof            (modus-ponens tm-83 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88333.        ((A -> (B -> (C -> B))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-83, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88334
in-theory        88334
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     47
proof            (modus-ponens tm-76 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88334.        (((not (not A)) -> A) and (((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-76, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88335
in-theory        88335
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)))) or ((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     69
proof            (modus-ponens tm-73 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-8 tm-10 tm-4)
proof-size       221
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88335.        (((not (not ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)))) or ((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-73, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88336
in-theory        88336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     53
proof            (modus-ponens tm-69 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88336.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-69, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88337
in-theory        88337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     55
proof            (modus-ponens tm-54 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4)
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-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88337.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-54, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88338
in-theory        88338
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or ((E and (((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     53
proof            (modus-ponens tm-50 tm-963 ((A (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-8 tm-7 tm-4)
proof-size       207
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88338.        (((((A -> B) -> ((C or A) -> B)) -> D) or ((E and (((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-50, m:tm-963, u:((A (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88339
in-theory        88339
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or ((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     55
proof            (modus-ponens tm-49 tm-963 ((A (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-8 tm-6 tm-4)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88339.        (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or ((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-49, m:tm-963, u:((A (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88340
in-theory        88340
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F))) or ((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))
theorem-size     69
proof            (modus-ponens tm-47 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-8 tm-4)
proof-size       221
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88340.        (((A and ((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F))) or ((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)), M:tm-47, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88341
in-theory        88341
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) and F) or ((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     69
proof            (modus-ponens tm-46 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-8 tm-3 tm-4)
proof-size       221
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88341.        (((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) and F) or ((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-46, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88342
in-theory        88342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     47
proof            (modus-ponens tm-42 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88342.        ((A -> (B or A)) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-42, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88343
in-theory        88343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     47
proof            (modus-ponens tm-32 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88343.        ((A -> (A or B)) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-32, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88344
in-theory        88344
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     67
proof            (modus-ponens tm-24 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-88344.        (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-24, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88345
in-theory        88345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-23 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88345.        ((A -> (B -> (A and B))) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-23, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88346
in-theory        88346
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     47
proof            (modus-ponens tm-22 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88346.        (((A and B) -> B) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-22, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88347
in-theory        88347
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     47
proof            (modus-ponens tm-21 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88347.        (((A and B) -> A) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-21, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88348
in-theory        88348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     55
proof            (modus-ponens tm-20 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88348.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (((E -> F) -> ((G or E) -> F)) -> H)) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-20, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88349
in-theory        88349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     47
proof            (modus-ponens tm-19 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88349.        ((A -> (B -> A)) and (((C and (((D -> E) -> ((F or D) -> E)) -> G)) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-19, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88350
in-theory        88350
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)))
theorem-size     51
proof            (modus-ponens tm-12 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       199
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88350.        (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E))), M:tm-12, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88351
in-theory        88351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E))))
theorem-size     69
proof            (modus-ponens tm-9 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-9 tm-8 tm-4)
proof-size       203
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88351.        ((((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not ((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)))), M:tm-9, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88352
in-theory        88352
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> ((((F and (((B -> C) -> ((A or B) -> C)) -> D)) or (((B -> C) -> ((A or B) -> C)) -> D)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))
theorem-size     61
proof            (modus-ponens tm-8 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-8 tm-4)
proof-size       197
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88352.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> ((((F and (((B -> C) -> ((A or B) -> C)) -> D)) or (((B -> C) -> ((A or B) -> C)) -> D)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)), M:tm-8, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-88353
in-theory        88353
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     43
proof            (modus-ponens tm-7 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-7 tm-8 tm-4)
proof-size       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88353.        (A or (((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-7, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88354
in-theory        88354
times-derived    1
----------------------------------------------------------------
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)) or F)
theorem-size     43
proof            (modus-ponens tm-6 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-6 tm-8 tm-4)
proof-size       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88354.        ((((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)) or F), M:tm-6, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88355
in-theory        88355
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A))
theorem-size     45
proof            (modus-ponens tm-5 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-88355.        (A -> ((((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A)), M:tm-5, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88356
in-theory        88356
times-derived    1
----------------------------------------------------------------
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)))) -> (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> E))
theorem-size     67
proof            (modus-ponens tm-2 tm-963 ((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Em)))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       203
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88356.        ((((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)))) -> (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> E)), M:tm-2, m:tm-963, u:((A (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Em))
================================================================
tm-name          tm-88357
in-theory        88357
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     43
proof            (modus-ponens tm-1 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88357.        (A -> (((B and (((C -> D) -> ((E or C) -> D)) -> F)) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-1, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-88358
in-theory        88358
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     55
proof            (modus-ponens tm-930 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
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-88358.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-930, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88359
in-theory        88359
times-derived    1
----------------------------------------------------------------
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)) and (((((A -> B) -> ((C or A) -> B)) -> D) 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     95
proof            (modus-ponens tm-920 tm-964 ((A (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-3)
proof-size       297
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-3.            ((A and B) -> A), axiom
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-88359.        (((((((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)) and (((((A -> B) -> ((C or A) -> B)) -> D) 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-920, m:tm-964, u:((A (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88360
in-theory        88360
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     55
proof            (modus-ponens tm-893 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-88360.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-893, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88361
in-theory        88361
times-derived    1
----------------------------------------------------------------
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)) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) 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     97
proof            (modus-ponens tm-882 tm-964 ((A (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
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-88361.        (((((((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)) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) 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-882, m:tm-964, u:((A (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88362
in-theory        88362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     59
proof            (modus-ponens tm-855 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       247
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-88362.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-855, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88363
in-theory        88363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     53
proof            (modus-ponens tm-808 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-88363.        (((A -> B) -> (((C and A) or A) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-808, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88364
in-theory        88364
times-derived    1
----------------------------------------------------------------
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)) and (((F and (((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D))) 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     111
proof            (modus-ponens tm-798 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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-4 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
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-88364.        (((((((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)) and (((F and (((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D))) 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-798, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88365
in-theory        88365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     53
proof            (modus-ponens tm-757 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       227
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-88365.        (((A -> B) -> (((A and C) or A) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-757, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88366
in-theory        88366
times-derived    1
----------------------------------------------------------------
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)) and ((((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) and F) 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     111
proof            (modus-ponens tm-747 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-88366.        (((((((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)) and ((((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) and F) 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-747, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88367
in-theory        88367
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) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     67
proof            (modus-ponens tm-708 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       277
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88367.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-708, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88368
in-theory        88368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     55
proof            (modus-ponens tm-665 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88368.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-665, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88369
in-theory        88369
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (F or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     43
proof            (modus-ponens tm-623 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88369.        ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (F or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-623, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88370
in-theory        88370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-622 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88370.        ((A -> (B -> (C or B))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-622, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88371
in-theory        88371
times-derived    1
----------------------------------------------------------------
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)) and (F -> (G or F)))
theorem-size     47
proof            (modus-ponens tm-609 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88371.        (((((((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)) and (F -> (G or F))), M:tm-609, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88372
in-theory        88372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-605 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88372.        ((A -> ((B -> (C or B)) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-605, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88373
in-theory        88373
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G or F)) 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     89
proof            (modus-ponens tm-595 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-88373.        (((((((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)) and ((F -> (G or F)) 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-595, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88374
in-theory        88374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-550 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88374.        (((A -> (B or A)) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-550, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88375
in-theory        88375
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-540 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88375.        ((A or (B -> (C or B))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-540, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88376
in-theory        88376
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-530 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88376.        ((A or (B -> (B or C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-530, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88377
in-theory        88377
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-520 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88377.        ((A or (B -> (C -> (B and C)))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-520, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88378
in-theory        88378
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-510 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88378.        ((A or ((B and C) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-510, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88379
in-theory        88379
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-500 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88379.        ((A or ((B and C) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-500, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88380
in-theory        88380
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     57
proof            (modus-ponens tm-490 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88380.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-490, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88381
in-theory        88381
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-480 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88381.        ((A or (B -> (C -> B))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-480, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88382
in-theory        88382
times-derived    1
----------------------------------------------------------------
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) or F))
theorem-size     43
proof            (modus-ponens tm-470 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88382.        ((((((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) or F)), M:tm-470, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88383
in-theory        88383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-469 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88383.        ((A -> (B -> (B or C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-469, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88384
in-theory        88384
times-derived    1
----------------------------------------------------------------
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)) and (F -> (F or G)))
theorem-size     47
proof            (modus-ponens tm-456 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88384.        (((((((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)) and (F -> (F or G))), M:tm-456, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88385
in-theory        88385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-453 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88385.        ((A -> ((B -> (B or C)) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-453, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88386
in-theory        88386
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (F or G)) 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     89
proof            (modus-ponens tm-443 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-88386.        (((((((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)) and ((F -> (F or G)) 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-443, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88387
in-theory        88387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-409 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88387.        (((A -> (A or B)) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-409, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88388
in-theory        88388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-400 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88388.        (((A -> (B -> (A and B))) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-400, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88389
in-theory        88389
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-391 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88389.        ((((A and B) -> B) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-391, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88390
in-theory        88390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-382 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88390.        ((((A and B) -> A) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-382, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88391
in-theory        88391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     57
proof            (modus-ponens tm-373 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88391.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-373, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88392
in-theory        88392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-364 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88392.        (((A -> (B -> A)) or C) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-364, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88393
in-theory        88393
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (F -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and F)))
theorem-size     45
proof            (modus-ponens tm-355 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       213
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88393.        ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (F -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and F))), M:tm-355, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88394
in-theory        88394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-354 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88394.        ((A -> (B -> (C -> (B and C)))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-354, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88395
in-theory        88395
times-derived    1
----------------------------------------------------------------
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)) and (F -> (G -> (F and G))))
theorem-size     49
proof            (modus-ponens tm-341 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88395.        (((((((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)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88396
in-theory        88396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     51
proof            (modus-ponens tm-338 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88396.        (((A -> B) -> (A -> (A and B))) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-338, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88397
in-theory        88397
times-derived    1
----------------------------------------------------------------
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)) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     109
proof            (modus-ponens tm-328 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       303
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88397.        (((((((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)) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-328, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88398
in-theory        88398
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G -> (F and G))) 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     91
proof            (modus-ponens tm-327 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-88398.        (((((((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)) and ((F -> (G -> (F and G))) 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-327, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88399
in-theory        88399
times-derived    1
----------------------------------------------------------------
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)) and (((F and G) -> G) 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     89
proof            (modus-ponens tm-326 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-88399.        (((((((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)) and (((F and G) -> G) 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-326, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88400
in-theory        88400
times-derived    1
----------------------------------------------------------------
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)) and (((F and G) -> F) 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     89
proof            (modus-ponens tm-325 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
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-88400.        (((((((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)) and (((F and G) -> F) 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-325, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88401
in-theory        88401
times-derived    1
----------------------------------------------------------------
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)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) 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     97
proof            (modus-ponens tm-324 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-3.            ((A and B) -> A), axiom
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-88401.        (((((((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)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) 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-324, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88402
in-theory        88402
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G -> F)) 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     89
proof            (modus-ponens tm-323 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-88402.        (((((((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)) and ((F -> (G -> F)) 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-323, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88403
in-theory        88403
times-derived    1
----------------------------------------------------------------
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)) and ((F and G) -> G))
theorem-size     47
proof            (modus-ponens tm-322 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88403.        (((((((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)) and ((F and G) -> G)), M:tm-322, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88404
in-theory        88404
times-derived    1
----------------------------------------------------------------
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)) and ((F and G) -> F))
theorem-size     47
proof            (modus-ponens tm-320 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88404.        (((((((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)) and ((F and G) -> F)), M:tm-320, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88405
in-theory        88405
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     55
proof            (modus-ponens tm-318 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88405.        (((((((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)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88406
in-theory        88406
times-derived    1
----------------------------------------------------------------
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)) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     93
proof            (modus-ponens tm-316 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88406.        (((((((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)) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-316, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88407
in-theory        88407
times-derived    1
----------------------------------------------------------------
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)) and (F -> (G -> F)))
theorem-size     47
proof            (modus-ponens tm-315 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88407.        (((((((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)) and (F -> (G -> F))), M:tm-315, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88408
in-theory        88408
times-derived    1
----------------------------------------------------------------
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)) and (((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((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) and E) or (((A -> B) -> ((C or A) -> B)) -> D)))))
theorem-size     111
proof            (modus-ponens tm-313 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88408.        (((((((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)) and (((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((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) and E) or (((A -> B) -> ((C or A) -> B)) -> D))))), M:tm-313, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88409
in-theory        88409
times-derived    1
----------------------------------------------------------------
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)) and (((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> F) -> (((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> F)))
theorem-size     103
proof            (modus-ponens tm-312 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       285
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88409.        (((((((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)) and (((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> F) -> (((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> F))), M:tm-312, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88410
in-theory        88410
times-derived    1
----------------------------------------------------------------
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)) and (F 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     85
proof            (modus-ponens tm-311 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-88410.        (((((((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)) and (F 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-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88411
in-theory        88411
times-derived    1
----------------------------------------------------------------
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)) 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)) or F))
theorem-size     85
proof            (modus-ponens tm-310 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-88411.        (((((((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)) 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)) or F)), M:tm-310, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88412
in-theory        88412
times-derived    1
----------------------------------------------------------------
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)) and (F -> (((((((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)) and F)))
theorem-size     87
proof            (modus-ponens tm-309 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88412.        (((((((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)) and (F -> (((((((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)) and F))), M:tm-309, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88413
in-theory        88413
times-derived    1
----------------------------------------------------------------
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)) 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)))) -> ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> D)))
theorem-size     109
proof            (modus-ponens tm-306 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-306.          ((A -> (B -> C)) -> ((A -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88413.        (((((((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)) 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)))) -> ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> D))), M:tm-306, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm))
================================================================
tm-name          tm-88414
in-theory        88414
times-derived    1
----------------------------------------------------------------
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)) and (F -> ((((((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     85
proof            (modus-ponens tm-305 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-88414.        (((((((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)) and (F -> ((((((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-305, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88415
in-theory        88415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     53
proof            (modus-ponens tm-303 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88415.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-303, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88416
in-theory        88416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-270 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88416.        ((A -> (((B and C) -> C) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-270, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88417
in-theory        88417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-239 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88417.        ((A -> (((B and C) -> B) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-239, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88418
in-theory        88418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     59
proof            (modus-ponens tm-210 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88418.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-210, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88419
in-theory        88419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-183 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88419.        ((A -> ((B -> (C -> B)) and A)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-183, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88420
in-theory        88420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-157 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88420.        ((A -> ((B and C) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-157, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88421
in-theory        88421
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     57
proof            (modus-ponens tm-147 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88421.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-147, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88422
in-theory        88422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-134 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88422.        ((A -> ((B and C) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-134, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88423
in-theory        88423
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     57
proof            (modus-ponens tm-125 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88423.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-125, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88424
in-theory        88424
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> (D -> E)) and F) or (((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     61
proof            (modus-ponens tm-114 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D)) Em) (-> (-> (-> 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 tm-3)
proof-size       247
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88424.        ((((((A -> B) -> ((C or A) -> B)) -> (D -> E)) and F) or (((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-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D)) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D)))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (Dm (-> C D)))
================================================================
tm-name          tm-88425
in-theory        88425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     57
proof            (modus-ponens tm-113 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88425.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-113, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88426
in-theory        88426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     61
proof            (modus-ponens tm-105 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       259
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88426.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-105, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88427
in-theory        88427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     49
proof            (modus-ponens tm-95 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88427.        (((A -> B) -> (A -> A)) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-95, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88428
in-theory        88428
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (F -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     43
proof            (modus-ponens tm-84 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88428.        ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (F -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-84, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88429
in-theory        88429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-83 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88429.        ((A -> (B -> (C -> B))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-83, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88430
in-theory        88430
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     47
proof            (modus-ponens tm-76 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88430.        (((not (not A)) -> A) and ((((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-76, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88431
in-theory        88431
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)))) 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     69
proof            (modus-ponens tm-73 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-8 tm-10 tm-3)
proof-size       221
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88431.        (((not (not (((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)))) 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-73, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88432
in-theory        88432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     53
proof            (modus-ponens tm-69 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88432.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-69, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88433
in-theory        88433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     55
proof            (modus-ponens tm-54 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88433.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-54, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88434
in-theory        88434
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) 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     53
proof            (modus-ponens tm-50 tm-964 ((A (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-8 tm-7 tm-3)
proof-size       207
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88434.        (((((A -> B) -> ((C or A) -> B)) -> D) 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-50, m:tm-964, u:((A (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88435
in-theory        88435
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) 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     55
proof            (modus-ponens tm-49 tm-964 ((A (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-8 tm-6 tm-3)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88435.        ((((((A -> B) -> ((C or A) -> B)) -> D) and E) 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-49, m:tm-964, u:((A (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88436
in-theory        88436
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E))) or (((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))
theorem-size     69
proof            (modus-ponens tm-47 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       221
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88436.        (((A and (((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E))) or (((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)), M:tm-47, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88437
in-theory        88437
times-derived    1
----------------------------------------------------------------
theorem          ((((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) and F) 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     69
proof            (modus-ponens tm-46 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       221
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88437.        ((((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) and F) 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-46, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88438
in-theory        88438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     47
proof            (modus-ponens tm-42 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88438.        ((A -> (B or A)) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-42, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88439
in-theory        88439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     47
proof            (modus-ponens tm-32 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88439.        ((A -> (A or B)) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-32, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88440
in-theory        88440
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((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-24 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
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-88440.        ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-24, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88441
in-theory        88441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     49
proof            (modus-ponens tm-23 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88441.        ((A -> (B -> (A and B))) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-23, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88442
in-theory        88442
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     47
proof            (modus-ponens tm-22 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88442.        (((A and B) -> B) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-22, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88443
in-theory        88443
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     47
proof            (modus-ponens tm-21 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88443.        (((A and B) -> A) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-21, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88444
in-theory        88444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     55
proof            (modus-ponens tm-20 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88444.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((((D -> E) -> ((F or D) -> E)) -> G) and H) or (((D -> E) -> ((F or D) -> E)) -> G)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-20, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88445
in-theory        88445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     47
proof            (modus-ponens tm-19 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88445.        ((A -> (B -> A)) and ((((((C -> D) -> ((E or C) -> D)) -> F) and G) or (((C -> D) -> ((E or C) -> D)) -> F)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-19, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88446
in-theory        88446
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     51
proof            (modus-ponens tm-12 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       199
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88446.        ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-12, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88447
in-theory        88447
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((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) and E) or (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     69
proof            (modus-ponens tm-9 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-9 tm-8 tm-3)
proof-size       203
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88447.        (((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((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) and E) or (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-9, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88448
in-theory        88448
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((((((B -> C) -> ((A or B) -> C)) -> D) and F) or (((B -> C) -> ((A or B) -> C)) -> D)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))
theorem-size     61
proof            (modus-ponens tm-8 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       197
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88448.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((((((B -> C) -> ((A or B) -> C)) -> D) and F) or (((B -> C) -> ((A or B) -> C)) -> D)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)), M:tm-8, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-88449
in-theory        88449
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     43
proof            (modus-ponens tm-7 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-7 tm-8 tm-3)
proof-size       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88449.        (A or ((((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-7, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88450
in-theory        88450
times-derived    1
----------------------------------------------------------------
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)) or F)
theorem-size     43
proof            (modus-ponens tm-6 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-6 tm-8 tm-3)
proof-size       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88450.        (((((((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)) or F), M:tm-6, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88451
in-theory        88451
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))
theorem-size     45
proof            (modus-ponens tm-5 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       175
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88451.        (A -> (((((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)), M:tm-5, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88452
in-theory        88452
times-derived    1
----------------------------------------------------------------
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)))) -> ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> D))
theorem-size     67
proof            (modus-ponens tm-2 tm-964 ((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       203
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88452.        (((((((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)))) -> ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> D)), M:tm-2, m:tm-964, u:((A (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm))
================================================================
tm-name          tm-88453
in-theory        88453
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     43
proof            (modus-ponens tm-1 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88453.        (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) and F) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-1, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88454
in-theory        88454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     27
proof            (modus-ponens tm-965 tm-34 ((Am (-> (-> A B) (-> (-> (or C A) B) (-> (-> A B) (-> (or C A) B))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (-> (-> A B) (-> (or C A) B)))))
axioms-used      (tm-8 tm-2 tm-7 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-88454.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) -> ((A or B) -> C)))), M:tm-965, m:tm-34, u:((Am (-> (-> A B) (-> (-> (or C A) B) (-> (-> A B) (-> (or C A) B))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (-> (-> A B) (-> (or C A) B))))
================================================================
tm-name          tm-88455
in-theory        88455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (((B -> C) -> ((A or B) -> C)) and (B -> C))))
theorem-size     31
proof            (modus-ponens tm-965 tm-38 ((Am (-> (-> A B) (-> (-> (or C A) B) (and (-> (-> A B) (-> (or C A) B)) (-> A B))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> A B)))))
axioms-used      (tm-8 tm-2 tm-7 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-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-88455.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (((B -> C) -> ((A or B) -> C)) and (B -> C)))), M:tm-965, m:tm-38, u:((Am (-> (-> A B) (-> (-> (or C A) B) (and (-> (-> A B) (-> (or C A) B)) (-> A B))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> A B))))
================================================================
tm-name          tm-88456
in-theory        88456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D -> (B -> C))))
theorem-size     23
proof            (modus-ponens tm-965 tm-81 ((Am (-> (-> A B) (-> (-> (or C A) B) (-> Dm (-> A B))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (-> Dm (-> A B)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-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-88456.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D -> (B -> C)))), M:tm-965, m:tm-81, u:((Am (-> (-> A B) (-> (-> (or C A) B) (-> Dm (-> A B))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (-> Dm (-> A B))))
================================================================
tm-name          tm-88457
in-theory        88457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C -> D)) -> ((A or B) -> (C -> D)))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     31
proof            (modus-ponens tm-965 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> (-> (or C Cm) (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) (-> (or C Cm) (-> Dm Em)))) (A Cm) (B (-> Dm Em)) (D (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88457.        (((A -> B) or ((B -> (C -> D)) -> ((A or B) -> (C -> D)))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-965, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> (-> (or C Cm) (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) (-> (or C Cm) (-> Dm Em)))) (A Cm) (B (-> Dm Em)) (D (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-88458
in-theory        88458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D -> ((B -> C) and D))))
theorem-size     25
proof            (modus-ponens tm-965 tm-352 ((Am (-> (-> A B) (-> (-> (or C A) B) (-> Dm (and (-> A B) Dm))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (-> Dm (and (-> A B) Dm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88458.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D -> ((B -> C) and D)))), M:tm-965, m:tm-352, u:((Am (-> (-> A B) (-> (-> (or C A) B) (-> Dm (and (-> A B) Dm))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (-> Dm (and (-> A B) Dm))))
================================================================
tm-name          tm-88459
in-theory        88459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) or D)))
theorem-size     23
proof            (modus-ponens tm-965 tm-467 ((Am (-> (-> A B) (-> (-> (or C A) B) (or (-> A B) Dm)))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (or (-> A B) Dm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-6)
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-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-88459.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) or D))), M:tm-965, m:tm-467, u:((Am (-> (-> A B) (-> (-> (or C A) B) (or (-> A B) Dm)))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (or (-> A B) Dm)))
================================================================
tm-name          tm-88460
in-theory        88460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D or (B -> C))))
theorem-size     23
proof            (modus-ponens tm-965 tm-620 ((Am (-> (-> A B) (-> (-> (or C A) B) (or Dm (-> A B))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (or Dm (-> A B)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-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-88460.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D or (B -> C)))), M:tm-965, m:tm-620, u:((Am (-> (-> A B) (-> (-> (or C A) B) (or Dm (-> A B))))) (Bm (-> (-> A B) (-> (or C A) B))) (Cm (-> A B)) (D (or Dm (-> A B))))
================================================================
tm-name          tm-88461
in-theory        88461
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     61
proof            (modus-ponens tm-930 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-88461.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-930, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88462
in-theory        88462
times-derived    1
----------------------------------------------------------------
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))) and (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) or (((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     111
proof            (modus-ponens tm-920 tm-965 ((A (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       341
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-88462.        (((((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))) and (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) or (((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-920, m:tm-965, u:((A (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88463
in-theory        88463
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     61
proof            (modus-ponens tm-893 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-88463.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-893, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88464
in-theory        88464
times-derived    1
----------------------------------------------------------------
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))) and ((((A -> B) -> (((C or A) -> B) -> D)) or (((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     107
proof            (modus-ponens tm-882 tm-965 ((A (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       337
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-88464.        (((((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))) and ((((A -> B) -> (((C or A) -> B) -> D)) or (((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-882, m:tm-965, u:((A (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88465
in-theory        88465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     65
proof            (modus-ponens tm-855 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       281
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-88465.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-855, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88466
in-theory        88466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     59
proof            (modus-ponens tm-808 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-88466.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-808, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88467
in-theory        88467
times-derived    1
----------------------------------------------------------------
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))) and (((E and (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)))) or (((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     125
proof            (modus-ponens tm-798 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       349
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-88467.        (((((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))) and (((E and (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)))) or (((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-798, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88468
in-theory        88468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     59
proof            (modus-ponens tm-757 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88468.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-757, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88469
in-theory        88469
times-derived    1
----------------------------------------------------------------
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))) and ((((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) and E) or (((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     125
proof            (modus-ponens tm-747 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       349
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88469.        (((((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))) and ((((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) and E) or (((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-747, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88470
in-theory        88470
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)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H))))
theorem-size     73
proof            (modus-ponens tm-708 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       311
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-88470.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H)))), M:tm-708, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88471
in-theory        88471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     61
proof            (modus-ponens tm-665 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88471.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-665, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88472
in-theory        88472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (E or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))))
theorem-size     49
proof            (modus-ponens tm-623 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88472.        ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (E or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))), M:tm-623, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88473
in-theory        88473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-622 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88473.        ((A -> (B -> (C or B))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-622, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88474
in-theory        88474
times-derived    1
----------------------------------------------------------------
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))) and (E -> (F or E)))
theorem-size     53
proof            (modus-ponens tm-609 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88474.        (((((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))) and (E -> (F or E))), M:tm-609, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88475
in-theory        88475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-605 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88475.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-605, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88476
in-theory        88476
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F or E)) 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     101
proof            (modus-ponens tm-595 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88476.        (((((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))) and ((E -> (F or E)) 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-595, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88477
in-theory        88477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-550 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88477.        (((A -> (B or A)) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-550, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88478
in-theory        88478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-540 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88478.        ((A or (B -> (C or B))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-540, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88479
in-theory        88479
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-530 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88479.        ((A or (B -> (B or C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-530, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88480
in-theory        88480
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-520 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88480.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-520, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88481
in-theory        88481
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-510 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88481.        ((A or ((B and C) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-510, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88482
in-theory        88482
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-500 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88482.        ((A or ((B and C) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-500, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88483
in-theory        88483
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H))))
theorem-size     63
proof            (modus-ponens tm-490 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88483.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H)))), M:tm-490, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88484
in-theory        88484
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-480 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88484.        ((A or (B -> (C -> B))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-480, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88485
in-theory        88485
times-derived    1
----------------------------------------------------------------
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)) or E))
theorem-size     49
proof            (modus-ponens tm-470 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88485.        ((((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)) or E)), M:tm-470, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88486
in-theory        88486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-469 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88486.        ((A -> (B -> (B or C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-469, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88487
in-theory        88487
times-derived    1
----------------------------------------------------------------
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))) and (E -> (E or F)))
theorem-size     53
proof            (modus-ponens tm-456 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88487.        (((((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))) and (E -> (E or F))), M:tm-456, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88488
in-theory        88488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-453 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88488.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-453, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88489
in-theory        88489
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (E or F)) 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     101
proof            (modus-ponens tm-443 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88489.        (((((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))) and ((E -> (E or F)) 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-443, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88490
in-theory        88490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-409 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88490.        (((A -> (A or B)) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-409, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88491
in-theory        88491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-400 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88491.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-400, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88492
in-theory        88492
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-391 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88492.        ((((A and B) -> B) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-391, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88493
in-theory        88493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-382 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88493.        ((((A and B) -> A) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-382, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88494
in-theory        88494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H))))
theorem-size     63
proof            (modus-ponens tm-373 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88494.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H)))), M:tm-373, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88495
in-theory        88495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-364 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88495.        (((A -> (B -> A)) or C) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-364, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88496
in-theory        88496
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (E -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)) and E)))
theorem-size     51
proof            (modus-ponens tm-355 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       247
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88496.        ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (E -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)) and E))), M:tm-355, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88497
in-theory        88497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-354 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88497.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-354, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88498
in-theory        88498
times-derived    1
----------------------------------------------------------------
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))) and (E -> (F -> (E and F))))
theorem-size     55
proof            (modus-ponens tm-341 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88498.        (((((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))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88499
in-theory        88499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F))))
theorem-size     57
proof            (modus-ponens tm-338 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       257
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88499.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F)))), M:tm-338, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88500
in-theory        88500
times-derived    1
----------------------------------------------------------------
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))) and ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))))
theorem-size     123
proof            (modus-ponens tm-328 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       345
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88500.        (((((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))) and ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))))), M:tm-328, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88501
in-theory        88501
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F -> (E and F))) 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     103
proof            (modus-ponens tm-327 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       321
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88501.        (((((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))) and ((E -> (F -> (E and F))) 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-327, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88502
in-theory        88502
times-derived    1
----------------------------------------------------------------
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))) and (((E and F) -> F) 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     101
proof            (modus-ponens tm-326 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88502.        (((((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))) and (((E and F) -> F) 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-326, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88503
in-theory        88503
times-derived    1
----------------------------------------------------------------
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))) and (((E and F) -> E) 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     101
proof            (modus-ponens tm-325 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88503.        (((((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))) and (((E and F) -> E) 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-325, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88504
in-theory        88504
times-derived    1
----------------------------------------------------------------
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))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) 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     109
proof            (modus-ponens tm-324 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       345
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88504.        (((((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))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) 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-324, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88505
in-theory        88505
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F -> E)) 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     101
proof            (modus-ponens tm-323 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88505.        (((((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))) and ((E -> (F -> E)) 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-323, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88506
in-theory        88506
times-derived    1
----------------------------------------------------------------
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))) and ((E and F) -> F))
theorem-size     53
proof            (modus-ponens tm-322 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88506.        (((((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))) and ((E and F) -> F)), M:tm-322, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88507
in-theory        88507
times-derived    1
----------------------------------------------------------------
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))) and ((E and F) -> E))
theorem-size     53
proof            (modus-ponens tm-320 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88507.        (((((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))) and ((E and F) -> E)), M:tm-320, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88508
in-theory        88508
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     61
proof            (modus-ponens tm-318 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88508.        (((((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))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88509
in-theory        88509
times-derived    1
----------------------------------------------------------------
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))) and ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)))))
theorem-size     103
proof            (modus-ponens tm-316 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       319
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88509.        (((((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))) and ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))))), M:tm-316, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88510
in-theory        88510
times-derived    1
----------------------------------------------------------------
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))) and (E -> (F -> E)))
theorem-size     53
proof            (modus-ponens tm-315 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88510.        (((((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))) and (E -> (F -> E))), M:tm-315, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88511
in-theory        88511
times-derived    1
----------------------------------------------------------------
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))) and (((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))) -> (not (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))))))
theorem-size     125
proof            (modus-ponens tm-313 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       331
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88511.        (((((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))) and (((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))) -> (not (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)))))), M:tm-313, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88512
in-theory        88512
times-derived    1
----------------------------------------------------------------
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))) and (((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)) -> E) -> (((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))) -> E)))
theorem-size     119
proof            (modus-ponens tm-312 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       329
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88512.        (((((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))) and (((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)) -> E) -> (((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))) -> E))), M:tm-312, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88513
in-theory        88513
times-derived    1
----------------------------------------------------------------
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))) and (E or ((((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     97
proof            (modus-ponens tm-311 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88513.        (((((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))) and (E or ((((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-311, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88514
in-theory        88514
times-derived    1
----------------------------------------------------------------
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))) 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))) or E))
theorem-size     97
proof            (modus-ponens tm-310 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88514.        (((((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))) 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))) or E)), M:tm-310, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88515
in-theory        88515
times-derived    1
----------------------------------------------------------------
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))) and (E -> (((((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))) and E)))
theorem-size     99
proof            (modus-ponens tm-309 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       295
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88515.        (((((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))) and (E -> (((((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))) and E))), M:tm-309, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88516
in-theory        88516
times-derived    1
----------------------------------------------------------------
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))) 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) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((A -> B) -> D))))
theorem-size     123
proof            (modus-ponens tm-306 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> Am Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       335
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88516.        (((((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))) 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) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((A -> B) -> D)))), M:tm-306, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> Am Bm) Dm)))
================================================================
tm-name          tm-88517
in-theory        88517
times-derived    1
----------------------------------------------------------------
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))) and (E -> ((((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     97
proof            (modus-ponens tm-305 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88517.        (((((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))) and (E -> ((((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-305, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88518
in-theory        88518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     59
proof            (modus-ponens tm-303 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       257
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88518.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-303, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88519
in-theory        88519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-270 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88519.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-270, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88520
in-theory        88520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-239 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88520.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-239, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88521
in-theory        88521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H))))
theorem-size     65
proof            (modus-ponens tm-210 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       281
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88521.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H)))), M:tm-210, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88522
in-theory        88522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-183 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88522.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-183, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88523
in-theory        88523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-157 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88523.        ((A -> ((B and C) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-157, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88524
in-theory        88524
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     63
proof            (modus-ponens tm-147 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88524.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-147, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88525
in-theory        88525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-134 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88525.        ((A -> ((B and C) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-134, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88526
in-theory        88526
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     63
proof            (modus-ponens tm-125 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88526.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-125, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88527
in-theory        88527
times-derived    1
----------------------------------------------------------------
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)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     61
proof            (modus-ponens tm-114 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> Am Bm)) (D Dm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       275
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88527.        ((((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)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-114, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> Am Bm)) (D Dm))
================================================================
tm-name          tm-88528
in-theory        88528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H))))
theorem-size     63
proof            (modus-ponens tm-113 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88528.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H)))), M:tm-113, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88529
in-theory        88529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     67
proof            (modus-ponens tm-105 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       293
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88529.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-105, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88530
in-theory        88530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F))))
theorem-size     55
proof            (modus-ponens tm-95 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88530.        (((A -> B) -> (A -> A)) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F)))), M:tm-95, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88531
in-theory        88531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (E -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))))
theorem-size     49
proof            (modus-ponens tm-84 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88531.        ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (E -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))), M:tm-84, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88532
in-theory        88532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-83 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88532.        ((A -> (B -> (C -> B))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-83, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88533
in-theory        88533
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E))))
theorem-size     53
proof            (modus-ponens tm-76 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88533.        (((not (not A)) -> A) and ((((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E)))), M:tm-76, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88534
in-theory        88534
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))))) or (((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     77
proof            (modus-ponens tm-73 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       257
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88534.        (((not (not (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))))) or (((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-73, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88535
in-theory        88535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F))))
theorem-size     59
proof            (modus-ponens tm-69 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88535.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F)))), M:tm-69, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88536
in-theory        88536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     61
proof            (modus-ponens tm-54 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88536.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-54, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88537
in-theory        88537
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) or (((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     63
proof            (modus-ponens tm-50 tm-965 ((A (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-7 tm-2)
proof-size       245
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88537.        (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) or (((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-50, m:tm-965, u:((A (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88538
in-theory        88538
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C or A) -> B) -> D)) or (((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     59
proof            (modus-ponens tm-49 tm-965 ((A (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-6 tm-2)
proof-size       241
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88538.        ((((A -> B) -> (((C or A) -> B) -> D)) or (((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-49, m:tm-965, u:((A (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88539
in-theory        88539
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E)))) or (((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E)))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E)))
theorem-size     77
proof            (modus-ponens tm-47 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       257
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88539.        (((A and (((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E)))) or (((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E)))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E))), M:tm-47, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88540
in-theory        88540
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) and E) or (((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     77
proof            (modus-ponens tm-46 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       257
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88540.        ((((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) and E) or (((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-46, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88541
in-theory        88541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F))))
theorem-size     53
proof            (modus-ponens tm-42 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88541.        ((A -> (B or A)) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F)))), M:tm-42, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88542
in-theory        88542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F))))
theorem-size     53
proof            (modus-ponens tm-32 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88542.        ((A -> (A or B)) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F)))), M:tm-32, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88543
in-theory        88543
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))))
theorem-size     75
proof            (modus-ponens tm-24 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-88543.        ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))), M:tm-24, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88544
in-theory        88544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F))))
theorem-size     55
proof            (modus-ponens tm-23 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88544.        ((A -> (B -> (A and B))) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F)))), M:tm-23, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88545
in-theory        88545
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F))))
theorem-size     53
proof            (modus-ponens tm-22 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88545.        (((A and B) -> B) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F)))), M:tm-22, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88546
in-theory        88546
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F))))
theorem-size     53
proof            (modus-ponens tm-21 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88546.        (((A and B) -> A) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F)))), M:tm-21, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88547
in-theory        88547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G))))
theorem-size     61
proof            (modus-ponens tm-20 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88547.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (((F or D) -> E) -> G)) or (((D -> E) -> ((F or D) -> E)) -> ((D -> E) -> G))) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> ((D -> E) -> G)))), M:tm-20, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88548
in-theory        88548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F))))
theorem-size     53
proof            (modus-ponens tm-19 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88548.        ((A -> (B -> A)) and ((((C -> D) -> (((E or C) -> D) -> F)) or (((C -> D) -> ((E or C) -> D)) -> ((C -> D) -> F))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> ((C -> D) -> F)))), M:tm-19, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88549
in-theory        88549
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))))
theorem-size     55
proof            (modus-ponens tm-12 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88549.        ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)))), M:tm-12, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88550
in-theory        88550
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))) -> (not (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)))))
theorem-size     77
proof            (modus-ponens tm-9 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88550.        (((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))) -> (not (((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))))), M:tm-9, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88551
in-theory        88551
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> D)) -> E) -> (((((B -> C) -> (((A or B) -> C) -> D)) or (((B -> C) -> ((A or B) -> C)) -> ((B -> C) -> D))) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> D))) -> E))
theorem-size     71
proof            (modus-ponens tm-8 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-2)
proof-size       235
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88551.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> D)) -> E) -> (((((B -> C) -> (((A or B) -> C) -> D)) or (((B -> C) -> ((A or B) -> C)) -> ((B -> C) -> D))) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> D))) -> E)), M:tm-8, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-88552
in-theory        88552
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E))))
theorem-size     49
proof            (modus-ponens tm-7 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88552.        (A or ((((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E)))), M:tm-7, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88553
in-theory        88553
times-derived    1
----------------------------------------------------------------
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))) or E)
theorem-size     49
proof            (modus-ponens tm-6 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88553.        (((((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))) or E), M:tm-6, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88554
in-theory        88554
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E))) and A))
theorem-size     51
proof            (modus-ponens tm-5 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88554.        (A -> (((((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E))) and A)), M:tm-5, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88555
in-theory        88555
times-derived    1
----------------------------------------------------------------
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) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((A -> B) -> D)))
theorem-size     75
proof            (modus-ponens tm-2 tm-965 ((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> Am Bm) Dm))))
axioms-used      (tm-2 tm-8)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88555.        (((((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) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((A -> B) -> D))), M:tm-2, m:tm-965, u:((A (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm)))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> Am Bm) Dm)))
================================================================
tm-name          tm-88556
in-theory        88556
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E))))
theorem-size     49
proof            (modus-ponens tm-1 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88556.        (A -> ((((B -> C) -> (((D or B) -> C) -> E)) or (((B -> C) -> ((D or B) -> C)) -> ((B -> C) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((B -> C) -> E)))), M:tm-1, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-88557
in-theory        88557
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     43
proof            (modus-ponens tm-930 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-88557.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-930, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88558
in-theory        88558
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((((B -> C) -> ((D or B) -> C)) -> A) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))
theorem-size     71
proof            (modus-ponens tm-920 tm-966 ((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-88558.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((((B -> C) -> ((D or B) -> C)) -> A) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))), M:tm-920, m:tm-966, u:((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88559
in-theory        88559
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     43
proof            (modus-ponens tm-893 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-88559.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-893, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88560
in-theory        88560
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((A or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))
theorem-size     61
proof            (modus-ponens tm-882 tm-966 ((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-88560.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((A or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))), M:tm-882, m:tm-966, u:((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88561
in-theory        88561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     47
proof            (modus-ponens tm-855 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-88561.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-855, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88562
in-theory        88562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     41
proof            (modus-ponens tm-808 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-88562.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-808, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88563
in-theory        88563
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((E and (A or (((B -> C) -> ((D or B) -> C)) -> A))) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))
theorem-size     75
proof            (modus-ponens tm-798 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-88563.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((E and (A or (((B -> C) -> ((D or B) -> C)) -> A))) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))), M:tm-798, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88564
in-theory        88564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     41
proof            (modus-ponens tm-757 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88564.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-757, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88565
in-theory        88565
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((((A or (((B -> C) -> ((D or B) -> C)) -> A)) and E) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))
theorem-size     75
proof            (modus-ponens tm-747 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88565.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((((A or (((B -> C) -> ((D or B) -> C)) -> A)) and E) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))), M:tm-747, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88566
in-theory        88566
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 F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E)))
theorem-size     55
proof            (modus-ponens tm-708 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-1.            (A -> (B -> A)), 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-88566.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E))), M:tm-708, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88567
in-theory        88567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     43
proof            (modus-ponens tm-665 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-88567.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-665, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88568
in-theory        88568
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (E or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))
theorem-size     31
proof            (modus-ponens tm-623 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88568.        ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (E or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))), M:tm-623, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88569
in-theory        88569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-622 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88569.        ((A -> (B -> (C or B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-622, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88570
in-theory        88570
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (F or E)))
theorem-size     35
proof            (modus-ponens tm-609 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88570.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (F or E))), M:tm-609, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88571
in-theory        88571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     39
proof            (modus-ponens tm-605 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88571.        ((A -> ((B -> (C or B)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-605, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88572
in-theory        88572
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (F or E)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     65
proof            (modus-ponens tm-595 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88572.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (F or E)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-595, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88573
in-theory        88573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-550 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88573.        (((A -> (B or A)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-550, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88574
in-theory        88574
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-540 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88574.        ((A or (B -> (C or B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-540, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88575
in-theory        88575
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-530 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88575.        ((A or (B -> (B or C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-530, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88576
in-theory        88576
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     39
proof            (modus-ponens tm-520 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88576.        ((A or (B -> (C -> (B and C)))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-520, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88577
in-theory        88577
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-510 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88577.        ((A or ((B and C) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-510, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88578
in-theory        88578
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-500 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88578.        ((A or ((B and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-500, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88579
in-theory        88579
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E)))
theorem-size     45
proof            (modus-ponens tm-490 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88579.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E))), M:tm-490, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88580
in-theory        88580
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-480 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88580.        ((A or (B -> (C -> B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-480, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88581
in-theory        88581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A) or E))
theorem-size     31
proof            (modus-ponens tm-470 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88581.        ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A) or E)), M:tm-470, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88582
in-theory        88582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-469 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88582.        ((A -> (B -> (B or C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-469, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88583
in-theory        88583
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (E or F)))
theorem-size     35
proof            (modus-ponens tm-456 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88583.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (E or F))), M:tm-456, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88584
in-theory        88584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     39
proof            (modus-ponens tm-453 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88584.        ((A -> ((B -> (B or C)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-453, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88585
in-theory        88585
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (E or F)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     65
proof            (modus-ponens tm-443 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88585.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (E or F)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-443, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88586
in-theory        88586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-409 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88586.        (((A -> (A or B)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-409, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88587
in-theory        88587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     39
proof            (modus-ponens tm-400 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88587.        (((A -> (B -> (A and B))) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-400, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88588
in-theory        88588
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-391 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88588.        ((((A and B) -> B) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-391, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88589
in-theory        88589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-382 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88589.        ((((A and B) -> A) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-382, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88590
in-theory        88590
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E)))
theorem-size     45
proof            (modus-ponens tm-373 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88590.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E))), M:tm-373, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88591
in-theory        88591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-364 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88591.        (((A -> (B -> A)) or C) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-364, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88592
in-theory        88592
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (E -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A) and E)))
theorem-size     33
proof            (modus-ponens tm-355 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88592.        ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (E -> ((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A) and E))), M:tm-355, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88593
in-theory        88593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     39
proof            (modus-ponens tm-354 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88593.        ((A -> (B -> (C -> (B and C)))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-354, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88594
in-theory        88594
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (F -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-341 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88594.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88595
in-theory        88595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C)))
theorem-size     39
proof            (modus-ponens tm-338 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88595.        (((A -> B) -> (A -> (A and B))) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C))), M:tm-338, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88596
in-theory        88596
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     73
proof            (modus-ponens tm-328 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88596.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-328, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88597
in-theory        88597
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (F -> (E and F))) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     67
proof            (modus-ponens tm-327 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88597.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (F -> (E and F))) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-327, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88598
in-theory        88598
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((E and F) -> F) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     65
proof            (modus-ponens tm-326 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88598.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((E and F) -> F) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-326, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88599
in-theory        88599
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((E and F) -> E) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     65
proof            (modus-ponens tm-325 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88599.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((E and F) -> E) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-325, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88600
in-theory        88600
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     73
proof            (modus-ponens tm-324 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88600.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-324, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88601
in-theory        88601
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (F -> E)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     65
proof            (modus-ponens tm-323 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88601.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (F -> E)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-323, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88602
in-theory        88602
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E and F) -> F))
theorem-size     35
proof            (modus-ponens tm-322 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88602.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E and F) -> F)), M:tm-322, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88603
in-theory        88603
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E and F) -> E))
theorem-size     35
proof            (modus-ponens tm-320 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88603.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E and F) -> E)), M:tm-320, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88604
in-theory        88604
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-318 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88604.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88605
in-theory        88605
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (A or (((B -> C) -> ((D or B) -> C)) -> A))))
theorem-size     57
proof            (modus-ponens tm-316 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
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-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-88605.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (A or (((B -> C) -> ((D or B) -> C)) -> A)))), M:tm-316, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88606
in-theory        88606
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (F -> E)))
theorem-size     35
proof            (modus-ponens tm-315 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88606.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (F -> E))), M:tm-315, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88607
in-theory        88607
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))) -> (not (A or (((B -> C) -> ((D or B) -> C)) -> A)))))
theorem-size     75
proof            (modus-ponens tm-313 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88607.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))) -> (not (A or (((B -> C) -> ((D or B) -> C)) -> A))))), M:tm-313, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88608
in-theory        88608
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A) -> E) -> (((A or (((B -> C) -> ((D or B) -> C)) -> A)) or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) -> E)))
theorem-size     79
proof            (modus-ponens tm-312 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), 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-88608.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A) -> E) -> (((A or (((B -> C) -> ((D or B) -> C)) -> A)) or (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) -> E))), M:tm-312, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88609
in-theory        88609
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E or ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     61
proof            (modus-ponens tm-311 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88609.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E or ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-311, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88610
in-theory        88610
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) or E))
theorem-size     61
proof            (modus-ponens tm-310 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88610.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) or E)), M:tm-310, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88611
in-theory        88611
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and E)))
theorem-size     63
proof            (modus-ponens tm-309 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88611.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and E))), M:tm-309, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88612
in-theory        88612
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> A)))
theorem-size     73
proof            (modus-ponens tm-306 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Am)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88612.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> A))), M:tm-306, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Am))
================================================================
tm-name          tm-88613
in-theory        88613
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))))
theorem-size     61
proof            (modus-ponens tm-305 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88613.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) and (E -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))), M:tm-305, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88614
in-theory        88614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     41
proof            (modus-ponens tm-303 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), 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-88614.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-303, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88615
in-theory        88615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     39
proof            (modus-ponens tm-270 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88615.        ((A -> (((B and C) -> C) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-270, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88616
in-theory        88616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     39
proof            (modus-ponens tm-239 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88616.        ((A -> (((B and C) -> B) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-239, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88617
in-theory        88617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E)))
theorem-size     47
proof            (modus-ponens tm-210 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88617.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E))), M:tm-210, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88618
in-theory        88618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     39
proof            (modus-ponens tm-183 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88618.        ((A -> ((B -> (C -> B)) and A)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-183, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88619
in-theory        88619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-157 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88619.        ((A -> ((B and C) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-157, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88620
in-theory        88620
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     45
proof            (modus-ponens tm-147 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88620.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-147, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88621
in-theory        88621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-134 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88621.        ((A -> ((B and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-134, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88622
in-theory        88622
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     45
proof            (modus-ponens tm-125 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88622.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-125, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88623
in-theory        88623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C -> D) -> ((E or C) -> D)) -> (A -> B))) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) -> A) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B)))
theorem-size     49
proof            (modus-ponens tm-114 tm-966 ((A (or (-> C D) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> C D)))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (Am (-> C D))))
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-14.           (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88623.        (((A -> B) or (((C -> D) -> ((E or C) -> D)) -> (A -> B))) -> ((((E -> C) or ((C -> D) -> ((E or C) -> D))) -> A) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B))), M:tm-114, m:tm-966, u:((A (or (-> C D) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> C D)))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (Am (-> C D)))
================================================================
tm-name          tm-88624
in-theory        88624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E)))
theorem-size     45
proof            (modus-ponens tm-113 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88624.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E))), M:tm-113, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88625
in-theory        88625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     49
proof            (modus-ponens tm-105 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88625.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-105, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88626
in-theory        88626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C)))
theorem-size     37
proof            (modus-ponens tm-95 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88626.        (((A -> B) -> (A -> A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C))), M:tm-95, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88627
in-theory        88627
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (E -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))
theorem-size     31
proof            (modus-ponens tm-84 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-2 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88627.        ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (E -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))), M:tm-84, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88628
in-theory        88628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     37
proof            (modus-ponens tm-83 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88628.        ((A -> (B -> (C -> B))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-83, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88629
in-theory        88629
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (((C -> D) -> ((E or C) -> D)) -> B)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B)))
theorem-size     35
proof            (modus-ponens tm-76 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88629.        (((not (not A)) -> A) and ((B or (((C -> D) -> ((E or C) -> D)) -> B)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B))), M:tm-76, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88630
in-theory        88630
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (((B -> C) -> ((D or B) -> C)) -> A)))) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))
theorem-size     45
proof            (modus-ponens tm-73 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88630.        (((not (not (A or (((B -> C) -> ((D or B) -> C)) -> A)))) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)), M:tm-73, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88631
in-theory        88631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C)))
theorem-size     41
proof            (modus-ponens tm-69 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88631.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C))), M:tm-69, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88632
in-theory        88632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     43
proof            (modus-ponens tm-54 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88632.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-54, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88633
in-theory        88633
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (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-50 tm-966 ((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88633.        (((((A -> B) -> ((C or A) -> B)) -> D) or (D or (((A -> B) -> ((C or A) -> B)) -> D))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-50, m:tm-966, u:((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88634
in-theory        88634
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))
theorem-size     31
proof            (modus-ponens tm-49 tm-966 ((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-8 tm-6 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-1.            (A -> (B -> A)), 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-88634.        ((A or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)), M:tm-49, m:tm-966, u:((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88635
in-theory        88635
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (((C -> D) -> ((E or C) -> D)) -> B))) or (B or (((C -> D) -> ((E or C) -> D)) -> B))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B))
theorem-size     45
proof            (modus-ponens tm-47 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88635.        (((A and (B or (((C -> D) -> ((E or C) -> D)) -> B))) or (B or (((C -> D) -> ((E or C) -> D)) -> B))) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B)), M:tm-47, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88636
in-theory        88636
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (((B -> C) -> ((D or B) -> C)) -> A)) and E) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))
theorem-size     45
proof            (modus-ponens tm-46 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88636.        ((((A or (((B -> C) -> ((D or B) -> C)) -> A)) and E) or (A or (((B -> C) -> ((D or B) -> C)) -> A))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)), M:tm-46, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88637
in-theory        88637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C)))
theorem-size     35
proof            (modus-ponens tm-42 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88637.        ((A -> (B or A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C))), M:tm-42, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88638
in-theory        88638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C)))
theorem-size     35
proof            (modus-ponens tm-32 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88638.        ((A -> (A or B)) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C))), M:tm-32, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88639
in-theory        88639
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))
theorem-size     43
proof            (modus-ponens tm-24 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
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-1.            (A -> (B -> A)), 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-88639.        ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))), M:tm-24, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88640
in-theory        88640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C)))
theorem-size     37
proof            (modus-ponens tm-23 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), 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-88640.        ((A -> (B -> (A and B))) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C))), M:tm-23, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88641
in-theory        88641
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C)))
theorem-size     35
proof            (modus-ponens tm-22 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88641.        (((A and B) -> B) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C))), M:tm-22, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88642
in-theory        88642
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C)))
theorem-size     35
proof            (modus-ponens tm-21 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88642.        (((A and B) -> A) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C))), M:tm-21, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88643
in-theory        88643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D)))
theorem-size     43
proof            (modus-ponens tm-20 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), 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-88643.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((E -> F) -> ((G or E) -> F)) -> D)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> D))), M:tm-20, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88644
in-theory        88644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C)))
theorem-size     35
proof            (modus-ponens tm-19 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), 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-88644.        ((A -> (B -> A)) and ((C or (((D -> E) -> ((F or D) -> E)) -> C)) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> C))), M:tm-19, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88645
in-theory        88645
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (A or (((B -> C) -> ((D or B) -> C)) -> A)))
theorem-size     27
proof            (modus-ponens tm-12 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
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-12.           ((A -> B) -> (A -> A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88645.        ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (A or (((B -> C) -> ((D or B) -> C)) -> A))), M:tm-12, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88646
in-theory        88646
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))) -> (not (A or (((B -> C) -> ((D or B) -> C)) -> A))))
theorem-size     45
proof            (modus-ponens tm-9 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       169
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88646.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))) -> (not (A or (((B -> C) -> ((D or B) -> C)) -> A)))), M:tm-9, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88647
in-theory        88647
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((D or (((B -> C) -> ((A or B) -> C)) -> D)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))
theorem-size     49
proof            (modus-ponens tm-8 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
axioms-used      (tm-8 tm-1)
proof-size       175
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88647.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((D or (((B -> C) -> ((A or B) -> C)) -> D)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)), M:tm-8, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-88648
in-theory        88648
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (((C -> D) -> ((E or C) -> D)) -> B)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B)))
theorem-size     31
proof            (modus-ponens tm-7 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       149
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88648.        (A or ((B or (((C -> D) -> ((E or C) -> D)) -> B)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B))), M:tm-7, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88649
in-theory        88649
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) or E)
theorem-size     31
proof            (modus-ponens tm-6 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       149
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88649.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)) or E), M:tm-6, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88650
in-theory        88650
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (((C -> D) -> ((E or C) -> D)) -> B)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B)) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), 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-88650.        (A -> (((B or (((C -> D) -> ((E or C) -> D)) -> B)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B)) and A)), M:tm-5, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88651
in-theory        88651
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> A))
theorem-size     43
proof            (modus-ponens tm-2 tm-966 ((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Am)))
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-1.            (A -> (B -> A)), 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-88651.        (((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> A)), M:tm-2, m:tm-966, u:((A (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am))) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Am))
================================================================
tm-name          tm-88652
in-theory        88652
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (((C -> D) -> ((E or C) -> D)) -> B)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B)))
theorem-size     31
proof            (modus-ponens tm-1 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-1 tm-8)
proof-size       149
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88652.        (A -> ((B or (((C -> D) -> ((E or C) -> D)) -> B)) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> B))), M:tm-1, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-88653
in-theory        88653
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-930 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-88653.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-930, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88654
in-theory        88654
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-893 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-88654.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-893, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88655
in-theory        88655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-855 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-88655.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-855, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88656
in-theory        88656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-808 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-88656.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-808, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88657
in-theory        88657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-757 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88657.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-757, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88658
in-theory        88658
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     59
proof            (modus-ponens tm-708 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88658.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-708, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88659
in-theory        88659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-665 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88659.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-665, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88660
in-theory        88660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-622 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88660.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-622, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88661
in-theory        88661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G)))
theorem-size     39
proof            (modus-ponens tm-609 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88661.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88662
in-theory        88662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-605 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-88662.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-605, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88663
in-theory        88663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-595 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-88663.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-595, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88664
in-theory        88664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-550 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88664.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-550, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88665
in-theory        88665
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-540 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88665.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-540, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88666
in-theory        88666
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-530 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88666.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-530, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88667
in-theory        88667
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-520 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88667.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-520, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88668
in-theory        88668
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-510 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88668.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-510, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88669
in-theory        88669
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-500 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88669.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-500, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88670
in-theory        88670
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-490 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88670.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-490, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88671
in-theory        88671
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-480 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88671.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-480, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88672
in-theory        88672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-469 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88672.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-469, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88673
in-theory        88673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H)))
theorem-size     39
proof            (modus-ponens tm-456 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88673.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88674
in-theory        88674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-453 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88674.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-453, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88675
in-theory        88675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-443 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88675.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-443, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88676
in-theory        88676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-409 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88676.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-409, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88677
in-theory        88677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-400 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88677.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-400, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88678
in-theory        88678
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-391 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88678.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-391, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88679
in-theory        88679
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-382 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88679.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-382, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88680
in-theory        88680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-373 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88680.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-373, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88681
in-theory        88681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-364 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88681.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-364, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88682
in-theory        88682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-354 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88682.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-354, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88683
in-theory        88683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H))))
theorem-size     41
proof            (modus-ponens tm-341 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88683.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88684
in-theory        88684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) 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-338 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88684.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-338, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88685
in-theory        88685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     75
proof            (modus-ponens tm-327 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88685.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-327, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88686
in-theory        88686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-326 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88686.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-326, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88687
in-theory        88687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-325 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88687.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-325, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88688
in-theory        88688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     81
proof            (modus-ponens tm-324 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88688.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-324, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88689
in-theory        88689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-323 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88689.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-323, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88690
in-theory        88690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H))
theorem-size     39
proof            (modus-ponens tm-322 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88690.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88691
in-theory        88691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G))
theorem-size     39
proof            (modus-ponens tm-320 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88691.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88692
in-theory        88692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     47
proof            (modus-ponens tm-318 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88692.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88693
in-theory        88693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G)))
theorem-size     39
proof            (modus-ponens tm-315 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88693.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88694
in-theory        88694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-311 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88694.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-311, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88695
in-theory        88695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G))
theorem-size     69
proof            (modus-ponens tm-310 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88695.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)), M:tm-310, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88696
in-theory        88696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G)))
theorem-size     71
proof            (modus-ponens tm-309 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88696.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G))), M:tm-309, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88697
in-theory        88697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     61
proof            (modus-ponens tm-308 tm-967 ((A (-> Am (or Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-88697.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-308, m:tm-967, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-88698
in-theory        88698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (A -> (B or A)))
theorem-size     39
proof            (modus-ponens tm-307 tm-967 ((A (-> Am (or Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88698.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (A -> (B or A))), M:tm-307, m:tm-967, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-88699
in-theory        88699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-305 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88699.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-305, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88700
in-theory        88700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-303 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88700.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-303, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88701
in-theory        88701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-270 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88701.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-270, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88702
in-theory        88702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-239 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88702.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-239, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88703
in-theory        88703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-210 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88703.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-210, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88704
in-theory        88704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-183 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88704.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-183, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88705
in-theory        88705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-157 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88705.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-157, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88706
in-theory        88706
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-147 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88706.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-147, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88707
in-theory        88707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-134 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88707.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-134, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88708
in-theory        88708
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-125 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88708.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-125, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88709
in-theory        88709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-113 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88709.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-113, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88710
in-theory        88710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     53
proof            (modus-ponens tm-105 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88710.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-105, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88711
in-theory        88711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-95 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88711.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-95, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88712
in-theory        88712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-83 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88712.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-83, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88713
in-theory        88713
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or 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-76 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88713.        (((not (not A)) -> A) and ((B -> (C or B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-76, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88714
in-theory        88714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) 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-69 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88714.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-69, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88715
in-theory        88715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-54 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88715.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-54, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88716
in-theory        88716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-42 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-88716.        ((A -> (B or A)) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-42, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88717
in-theory        88717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-32 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-88717.        ((A -> (A or B)) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-32, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88718
in-theory        88718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-23 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-88718.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-23, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88719
in-theory        88719
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-22 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-88719.        (((A and B) -> B) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-22, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88720
in-theory        88720
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-21 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-88720.        (((A and B) -> A) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-21, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88721
in-theory        88721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-20 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-88721.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-20, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88722
in-theory        88722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-19 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-88722.        ((A -> (B -> A)) and ((C -> (D or C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-19, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88723
in-theory        88723
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-7 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88723.        (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-7, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88724
in-theory        88724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)
theorem-size     35
proof            (modus-ponens tm-6 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88724.        (((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G), M:tm-6, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88725
in-theory        88725
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))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88725.        (A -> (((B -> (C or B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and A)), M:tm-5, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88726
in-theory        88726
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-1 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88726.        (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-1, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88727
in-theory        88727
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-930 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-88727.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-930, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88728
in-theory        88728
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-893 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-88728.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-893, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88729
in-theory        88729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-855 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-88729.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-855, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88730
in-theory        88730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-808 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-88730.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-808, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88731
in-theory        88731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-757 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88731.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-757, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88732
in-theory        88732
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     59
proof            (modus-ponens tm-708 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88732.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-708, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88733
in-theory        88733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-665 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88733.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-665, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88734
in-theory        88734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-622 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88734.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-622, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88735
in-theory        88735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G)))
theorem-size     39
proof            (modus-ponens tm-609 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88735.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88736
in-theory        88736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-605 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88736.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-605, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88737
in-theory        88737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-595 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88737.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-595, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88738
in-theory        88738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-550 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88738.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-550, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88739
in-theory        88739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-540 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88739.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-540, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88740
in-theory        88740
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-530 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88740.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-530, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88741
in-theory        88741
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-520 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88741.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-520, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88742
in-theory        88742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-510 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88742.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-510, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88743
in-theory        88743
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-500 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88743.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-500, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88744
in-theory        88744
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-490 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88744.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-490, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88745
in-theory        88745
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-480 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88745.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-480, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88746
in-theory        88746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-469 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88746.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-469, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88747
in-theory        88747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H)))
theorem-size     39
proof            (modus-ponens tm-456 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88747.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88748
in-theory        88748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-453 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-88748.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-453, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88749
in-theory        88749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-443 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-88749.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-443, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88750
in-theory        88750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-409 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88750.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-409, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88751
in-theory        88751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-400 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88751.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-400, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88752
in-theory        88752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-391 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88752.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-391, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88753
in-theory        88753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-382 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88753.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-382, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88754
in-theory        88754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-373 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88754.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-373, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88755
in-theory        88755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-364 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88755.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-364, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88756
in-theory        88756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-354 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88756.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-354, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88757
in-theory        88757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H))))
theorem-size     41
proof            (modus-ponens tm-341 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88757.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88758
in-theory        88758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (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-338 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88758.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-338, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88759
in-theory        88759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     75
proof            (modus-ponens tm-327 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88759.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-327, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88760
in-theory        88760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-326 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88760.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-326, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88761
in-theory        88761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-325 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88761.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-325, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88762
in-theory        88762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     81
proof            (modus-ponens tm-324 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88762.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-324, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88763
in-theory        88763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-323 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88763.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-323, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88764
in-theory        88764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H))
theorem-size     39
proof            (modus-ponens tm-322 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88764.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88765
in-theory        88765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G))
theorem-size     39
proof            (modus-ponens tm-320 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88765.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88766
in-theory        88766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     47
proof            (modus-ponens tm-318 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88766.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88767
in-theory        88767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G)))
theorem-size     39
proof            (modus-ponens tm-315 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88767.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88768
in-theory        88768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-311 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88768.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-311, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88769
in-theory        88769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G))
theorem-size     69
proof            (modus-ponens tm-310 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88769.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)), M:tm-310, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88770
in-theory        88770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G)))
theorem-size     71
proof            (modus-ponens tm-309 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88770.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G))), M:tm-309, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88771
in-theory        88771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     61
proof            (modus-ponens tm-308 tm-968 ((A (-> Am (or Am Bm))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-88771.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-308, m:tm-968, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-88772
in-theory        88772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (A -> (A or B)))
theorem-size     39
proof            (modus-ponens tm-307 tm-968 ((A (-> Am (or Am Bm))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88772.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (A -> (A or B))), M:tm-307, m:tm-968, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-88773
in-theory        88773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-305 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88773.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-305, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88774
in-theory        88774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-303 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88774.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-303, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88775
in-theory        88775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-270 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88775.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-270, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88776
in-theory        88776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-239 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88776.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-239, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88777
in-theory        88777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-210 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88777.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-210, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88778
in-theory        88778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-183 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88778.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-183, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88779
in-theory        88779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-157 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88779.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-157, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88780
in-theory        88780
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-147 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88780.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-147, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88781
in-theory        88781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-134 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88781.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-134, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88782
in-theory        88782
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-125 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88782.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-125, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88783
in-theory        88783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-113 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88783.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-113, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88784
in-theory        88784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     53
proof            (modus-ponens tm-105 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88784.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-105, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88785
in-theory        88785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-95 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88785.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-95, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88786
in-theory        88786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-83 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88786.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-83, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88787
in-theory        88787
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> 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     39
proof            (modus-ponens tm-76 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88787.        (((not (not A)) -> 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-76, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88788
in-theory        88788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) 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-69 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88788.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-69, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88789
in-theory        88789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-54 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88789.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-54, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88790
in-theory        88790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-42 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-88790.        ((A -> (B or A)) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-42, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88791
in-theory        88791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-32 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-88791.        ((A -> (A or B)) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-32, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88792
in-theory        88792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-23 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-88792.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-23, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88793
in-theory        88793
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-22 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-88793.        (((A and B) -> B) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-22, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88794
in-theory        88794
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-21 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-88794.        (((A and B) -> A) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-21, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88795
in-theory        88795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-20 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-88795.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-20, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88796
in-theory        88796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-19 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-88796.        ((A -> (B -> A)) and ((C -> (C or D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-19, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88797
in-theory        88797
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-7 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88797.        (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-7, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88798
in-theory        88798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)
theorem-size     35
proof            (modus-ponens tm-6 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88798.        (((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G), M:tm-6, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88799
in-theory        88799
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))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88799.        (A -> (((B -> (B or C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and A)), M:tm-5, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88800
in-theory        88800
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-1 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88800.        (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-1, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-88801
in-theory        88801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((A -> B) -> ((C or A) -> B)))))
theorem-size     47
proof            (modus-ponens tm-969 tm-1 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-88801.        ((((A -> B) -> ((C or A) -> B)) -> (D -> ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((A -> B) -> ((C or A) -> B))))), M:tm-969, m:tm-1, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-88802
in-theory        88802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B))))
theorem-size     51
proof            (modus-ponens tm-969 tm-2 ((Am (-> A Cm)) (Bm (or C A)) (B Cm) (D (-> (-> (-> A Cm) (or C A)) (-> (-> A Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       185
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-88802.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B)))), M:tm-969, 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-88803
in-theory        88803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (((A -> B) -> ((C or A) -> B)) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((A -> B) -> ((C or A) -> B)) and D))))
theorem-size     51
proof            (modus-ponens tm-969 tm-5 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> A B) (-> (or C A) B)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       179
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-88803.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (((A -> B) -> ((C or A) -> B)) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((A -> B) -> ((C or A) -> B)) and D)))), M:tm-969, m:tm-5, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> A B) (-> (or C A) B)) Bm))))
================================================================
tm-name          tm-88804
in-theory        88804
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) or D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) or D)))
theorem-size     47
proof            (modus-ponens tm-969 tm-6 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> A B) (-> (or C A) B)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-88804.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) or D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) or D))), M:tm-969, m:tm-6, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> A B) (-> (or C A) B)) Bm)))
================================================================
tm-name          tm-88805
in-theory        88805
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D or ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((A -> B) -> ((C or A) -> B)))))
theorem-size     47
proof            (modus-ponens tm-969 tm-7 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-88805.        ((((A -> B) -> ((C or A) -> B)) -> (D or ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((A -> B) -> ((C or A) -> B))))), M:tm-969, m:tm-7, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-88806
in-theory        88806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D))))
theorem-size     63
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
proof-size       197
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-88806.        ((((A -> B) -> ((C or A) -> B)) -> ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D)))), M:tm-969, 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-88807
in-theory        88807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-9 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> (-> A B) (not (-> (or C A) B))) (not (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-88807.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B))))), M:tm-969, 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-88808
in-theory        88808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> D))))
theorem-size     35
proof            (modus-ponens tm-969 tm-11 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-88808.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> D)))), M:tm-969, m:tm-11, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-88809
in-theory        88809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (A -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (A -> B))))
theorem-size     39
proof            (modus-ponens tm-969 tm-12 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> A B)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88809.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (A -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (A -> B)))), M:tm-969, m:tm-12, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> A B))))
================================================================
tm-name          tm-88810
in-theory        88810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     51
proof            (modus-ponens tm-969 tm-14 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-88810.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-969, m:tm-14, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-88811
in-theory        88811
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D and E) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D and E) -> D)))
theorem-size     35
proof            (modus-ponens tm-969 tm-16 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-88811.        ((((A -> B) -> ((C or A) -> B)) -> ((D and E) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D and E) -> D))), M:tm-969, m:tm-16, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-88812
in-theory        88812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D and E) -> E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D and E) -> E)))
theorem-size     35
proof            (modus-ponens tm-969 tm-18 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-88812.        ((((A -> B) -> ((C or A) -> B)) -> ((D and E) -> E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D and E) -> E))), M:tm-969, m:tm-18, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-88813
in-theory        88813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-19 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> (or C A) B))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-88813.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88814
in-theory        88814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     71
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-88814.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88815
in-theory        88815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D and E) -> D) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and E) -> D) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-21 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-88815.        ((((A -> B) -> ((C or A) -> B)) -> (((D and E) -> D) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and E) -> D) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88816
in-theory        88816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D and E) -> E) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and E) -> E) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-22 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-88816.        ((((A -> B) -> ((C or A) -> B)) -> (((D and E) -> E) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and E) -> E) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88817
in-theory        88817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-88817.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88818
in-theory        88818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((A -> B) and ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((A -> B) and ((C or A) -> B)))))
theorem-size     51
proof            (modus-ponens tm-969 tm-24 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (and (-> A B) (-> (or C A) B))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88818.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((A -> B) and ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((A -> B) and ((C or A) -> B))))), M:tm-969, 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-88819
in-theory        88819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (D and E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-969 tm-25 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (and Bm Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-88819.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (D and E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (D and E))))), M:tm-969, m:tm-25, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-88820
in-theory        88820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-32 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-88820.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88821
in-theory        88821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (D or E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (D or E))))
theorem-size     35
proof            (modus-ponens tm-969 tm-33 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-88821.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (D or E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (D or E)))), M:tm-969, m:tm-33, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-88822
in-theory        88822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-42 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-88822.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88823
in-theory        88823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (E or D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E or D))))
theorem-size     35
proof            (modus-ponens tm-969 tm-43 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-88823.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (E or D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E or D)))), M:tm-969, m:tm-43, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-88824
in-theory        88824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((B or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((B or (A -> B)) -> ((C or A) -> B))))
theorem-size     47
proof            (modus-ponens tm-969 tm-44 ((A Am) (B Bm) (Cm (-> (or C Am) Bm)) (D (-> (or Bm (-> Am Bm)) (-> (or C Am) Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-88824.        ((((A -> B) -> ((C or A) -> B)) -> ((B or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((B or (A -> B)) -> ((C or A) -> B)))), M:tm-969, 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-88825
in-theory        88825
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C)))) and (((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C)))))
theorem-size     89
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
proof-size       261
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-88825.        (((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C)))) and (((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C))))), M:tm-969, 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-88826
in-theory        88826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B))))
theorem-size     55
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-88826.        ((((A -> B) -> ((C or A) -> B)) -> ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B)))), M:tm-969, 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-88827
in-theory        88827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B))))
theorem-size     55
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-88827.        ((((A -> B) -> ((C or A) -> B)) -> (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B)))), M:tm-969, 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-88828
in-theory        88828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> ((C or A) -> (B and A))) -> ((B or (A -> (B and A))) -> ((C or A) -> (B and A)))) and (((C -> A) or ((A -> (B and A)) -> ((C or A) -> (B and A)))) -> ((B or (A -> (B and A))) -> ((C or A) -> (B and A)))))
theorem-size     63
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-88828.        ((((A -> (B and A)) -> ((C or A) -> (B and A))) -> ((B or (A -> (B and A))) -> ((C or A) -> (B and A)))) and (((C -> A) or ((A -> (B and A)) -> ((C or A) -> (B and A)))) -> ((B or (A -> (B and A))) -> ((C or A) -> (B and A))))), M:tm-969, 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-88829
in-theory        88829
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B)))) and (((D -> (A -> B)) or (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B)))))
theorem-size     101
proof            (modus-ponens tm-969 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-2 tm-5 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-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-88829.        (((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B)))) and (((D -> (A -> B)) or (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B))))), M:tm-969, 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-88830
in-theory        88830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     71
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-88830.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88831
in-theory        88831
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> ((B or A) -> (B or A))) -> ((A -> (B or A)) -> ((A or (B or A)) -> (B or A)))) and (((B -> A) or ((A -> (B or A)) -> ((B or A) -> (B or A)))) -> ((A -> (B or A)) -> ((A or (B or A)) -> (B or A)))))
theorem-size     63
proof            (modus-ponens tm-969 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-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-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-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-88831.        ((((A -> (B or A)) -> ((B or A) -> (B or A))) -> ((A -> (B or A)) -> ((A or (B or A)) -> (B or A)))) and (((B -> A) or ((A -> (B or A)) -> ((B or A) -> (B or A)))) -> ((A -> (B or A)) -> ((A or (B or A)) -> (B or A))))), M:tm-969, 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-88832
in-theory        88832
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-969 tm-56 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88832.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-969, m:tm-56, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-88833
in-theory        88833
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> ((C or (A -> (not B))) -> (not A))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (A -> (not B))) -> (not A)))) and (((C -> (A -> (not B))) or (((A -> (not B)) -> (not A)) -> ((C or (A -> (not B))) -> (not A)))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (A -> (not B))) -> (not A)))))
theorem-size     86
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-9)
proof-size       254
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-88833.        (((((A -> (not B)) -> (not A)) -> ((C or (A -> (not B))) -> (not A))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (A -> (not B))) -> (not A)))) and (((C -> (A -> (not B))) or (((A -> (not B)) -> (not A)) -> ((C or (A -> (not B))) -> (not A)))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (A -> (not B))) -> (not A))))), M:tm-969, 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-88834
in-theory        88834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     67
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-88834.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88835
in-theory        88835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     47
proof            (modus-ponens tm-969 tm-71 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88835.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-969, m:tm-71, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-88836
in-theory        88836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((not (not (A -> B))) or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((not (not (A -> B))) or (A -> B)) -> ((C or A) -> B))))
theorem-size     55
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-88836.        ((((A -> B) -> ((C or A) -> B)) -> (((not (not (A -> B))) or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((not (not (A -> B))) or (A -> B)) -> ((C or A) -> B)))), M:tm-969, 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-88837
in-theory        88837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((not (not D)) -> D) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((not (not D)) -> D) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-76 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-88837.        ((((A -> B) -> ((C or A) -> B)) -> (((not (not D)) -> D) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((not (not D)) -> D) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88838
in-theory        88838
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((not (not D)) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((not (not D)) -> D)))
theorem-size     35
proof            (modus-ponens tm-969 tm-78 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88838.        ((((A -> B) -> ((C or A) -> B)) -> ((not (not D)) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((not (not D)) -> D))), M:tm-969, m:tm-78, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-88839
in-theory        88839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> ((C or A) -> (B -> A))) -> ((D or (A -> (B -> A))) -> ((C or A) -> (B -> A)))) and (((C -> A) or ((A -> (B -> A)) -> ((C or A) -> (B -> A)))) -> ((D or (A -> (B -> A))) -> ((C or A) -> (B -> A)))))
theorem-size     63
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88839.        ((((A -> (B -> A)) -> ((C or A) -> (B -> A))) -> ((D or (A -> (B -> A))) -> ((C or A) -> (B -> A)))) and (((C -> A) or ((A -> (B -> A)) -> ((C or A) -> (B -> A)))) -> ((D or (A -> (B -> A))) -> ((C or A) -> (B -> A))))), M:tm-969, 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-88840
in-theory        88840
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 tm-83 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> (or C A) B))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-88840.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88841
in-theory        88841
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (D -> ((C or A) -> B)))))
theorem-size     47
proof            (modus-ponens tm-969 tm-84 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (-> (or C A) B))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-88841.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (D -> ((C or A) -> B))))), M:tm-969, m:tm-84, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (-> (or C A) B)))))
================================================================
tm-name          tm-88842
in-theory        88842
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F -> E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (F -> E)))))
theorem-size     39
proof            (modus-ponens tm-969 tm-85 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88842.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F -> E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (F -> E))))), M:tm-969, m:tm-85, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-88843
in-theory        88843
times-derived    4
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((C or A) -> B))))
theorem-size     43
proof            (modus-ponens tm-969 tm-86 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> A B) (-> (or C 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-88843.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((C or A) -> B)))), M:tm-969, m:tm-86, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> A B) (-> (or C A) B))))
================================================================
tm-name          tm-88844
in-theory        88844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> ((B or A) -> A)) -> (((A -> C) or (A -> A)) -> ((B or A) -> A))) and (((B -> A) or ((A -> A) -> ((B or A) -> A))) -> (((A -> C) or (A -> A)) -> ((B or A) -> A))))
theorem-size     51
proof            (modus-ponens tm-969 tm-92 ((A Am) (B Am) (Bm (-> (or C Am) Am)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> (or C Am) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-88844.        ((((A -> A) -> ((B or A) -> A)) -> (((A -> C) or (A -> A)) -> ((B or A) -> A))) and (((B -> A) or ((A -> A) -> ((B or A) -> A))) -> (((A -> C) or (A -> A)) -> ((B or A) -> A)))), M:tm-969, 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-88845
in-theory        88845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (D -> D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> (D -> D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 tm-95 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> (or C A) B))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-88845.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (D -> D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> (D -> D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88846
in-theory        88846
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (D -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (D -> D))))
theorem-size     39
proof            (modus-ponens tm-969 tm-97 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-88846.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (D -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (D -> D)))), M:tm-969, m:tm-97, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-88847
in-theory        88847
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> ((D or (A -> (B -> C))) -> (A -> C))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (A -> (B -> C))) -> (A -> C)))) and (((D -> (A -> (B -> C))) or (((A -> (B -> C)) -> (A -> C)) -> ((D or (A -> (B -> C))) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (A -> (B -> C))) -> (A -> C)))))
theorem-size     115
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
proof-size       327
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-88847.        (((((A -> (B -> C)) -> (A -> C)) -> ((D or (A -> (B -> C))) -> (A -> C))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (A -> (B -> C))) -> (A -> C)))) and (((D -> (A -> (B -> C))) or (((A -> (B -> C)) -> (A -> C)) -> ((D or (A -> (B -> C))) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (A -> (B -> C))) -> (A -> C))))), M:tm-969, 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-88848
in-theory        88848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     83
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-88848.        ((((A -> B) -> ((C or A) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88849
in-theory        88849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     63
proof            (modus-ponens tm-969 tm-107 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88849.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-969, 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-88850
in-theory        88850
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))) and (((D -> (A -> (B -> C))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))))
theorem-size     131
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1)
proof-size       331
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-88850.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))) and (((D -> (A -> (B -> C))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))), M:tm-969, 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-88851
in-theory        88851
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-88851.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88852
in-theory        88852
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((D or A) -> (B -> C))) -> ((A -> (B -> C)) -> (((D or A) -> B) -> ((D or A) -> C)))) and (((D -> A) or ((A -> (B -> C)) -> ((D or A) -> (B -> C)))) -> ((A -> (B -> C)) -> (((D or A) -> B) -> ((D or A) -> C)))))
theorem-size     67
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-88852.        ((((A -> (B -> C)) -> ((D or A) -> (B -> C))) -> ((A -> (B -> C)) -> (((D or A) -> B) -> ((D or A) -> C)))) and (((D -> A) or ((A -> (B -> C)) -> ((D or A) -> (B -> C)))) -> ((A -> (B -> C)) -> (((D or A) -> B) -> ((D or A) -> C))))), M:tm-969, 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-88853
in-theory        88853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     55
proof            (modus-ponens tm-969 tm-115 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-88853.        ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-969, m:tm-115, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-88854
in-theory        88854
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> ((D or ((A -> B) and C)) -> B)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((A -> B) and C)) -> B))) and (((D -> ((A -> B) and C)) or ((((A -> B) and C) -> B) -> ((D or ((A -> B) and C)) -> B))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((A -> B) and C)) -> B))))
theorem-size     95
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-3)
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-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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-88854.        ((((((A -> B) and C) -> B) -> ((D or ((A -> B) and C)) -> B)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((A -> B) and C)) -> B))) and (((D -> ((A -> B) and C)) or ((((A -> B) and C) -> B) -> ((D or ((A -> B) and C)) -> B))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((A -> B) and C)) -> B)))), M:tm-969, 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-88855
in-theory        88855
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-88855.        ((((A -> B) -> ((C or A) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88856
in-theory        88856
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     55
proof            (modus-ponens tm-969 tm-127 ((Am (-> (-> A B) (-> (or C A) B))) (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       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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88856.        ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-969, 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-88857
in-theory        88857
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> ((C or (A and B)) -> A)) -> ((D or ((A and B) -> A)) -> ((C or (A and B)) -> A))) and (((C -> (A and B)) or (((A and B) -> A) -> ((C or (A and B)) -> A))) -> ((D or ((A and B) -> A)) -> ((C or (A and B)) -> A))))
theorem-size     65
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-88857.        (((((A and B) -> A) -> ((C or (A and B)) -> A)) -> ((D or ((A and B) -> A)) -> ((C or (A and B)) -> A))) and (((C -> (A and B)) or (((A and B) -> A) -> ((C or (A and B)) -> A))) -> ((D or ((A and B) -> A)) -> ((C or (A and B)) -> A)))), M:tm-969, 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-88858
in-theory        88858
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-88858.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88859
in-theory        88859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E and F) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E and F) -> E))))
theorem-size     39
proof            (modus-ponens tm-969 tm-136 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-88859.        ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E and F) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E and F) -> E)))), M:tm-969, m:tm-136, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-88860
in-theory        88860
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> ((D or (A and (B -> C))) -> C)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (A and (B -> C))) -> C))) and (((D -> (A and (B -> C))) or (((A and (B -> C)) -> C) -> ((D or (A and (B -> C))) -> C))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (A and (B -> C))) -> C))))
theorem-size     95
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-4)
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-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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-88860.        (((((A and (B -> C)) -> C) -> ((D or (A and (B -> C))) -> C)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (A and (B -> C))) -> C))) and (((D -> (A and (B -> C))) or (((A and (B -> C)) -> C) -> ((D or (A and (B -> C))) -> C))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (A and (B -> C))) -> C)))), M:tm-969, 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-88861
in-theory        88861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-88861.        ((((A -> B) -> ((C or A) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88862
in-theory        88862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     55
proof            (modus-ponens tm-969 tm-149 ((Am (-> (-> A B) (-> (or C A) B))) (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       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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88862.        ((((A -> B) -> ((C or A) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-969, 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-88863
in-theory        88863
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> ((C or (A and B)) -> B)) -> ((D or ((A and B) -> B)) -> ((C or (A and B)) -> B))) and (((C -> (A and B)) or (((A and B) -> B) -> ((C or (A and B)) -> B))) -> ((D or ((A and B) -> B)) -> ((C or (A and B)) -> B))))
theorem-size     65
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-88863.        (((((A and B) -> B) -> ((C or (A and B)) -> B)) -> ((D or ((A and B) -> B)) -> ((C or (A and B)) -> B))) and (((C -> (A and B)) or (((A and B) -> B) -> ((C or (A and B)) -> B))) -> ((D or ((A and B) -> B)) -> ((C or (A and B)) -> B)))), M:tm-969, 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-88864
in-theory        88864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-88864.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88865
in-theory        88865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E and F) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E and F) -> F))))
theorem-size     39
proof            (modus-ponens tm-969 tm-159 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-88865.        ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E and F) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E and F) -> F)))), M:tm-969, m:tm-159, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-88866
in-theory        88866
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-88866.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88867
in-theory        88867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> E)) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (F -> E)) and D))))
theorem-size     43
proof            (modus-ponens tm-969 tm-184 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm Cm)) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-88867.        ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> E)) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (F -> E)) and D)))), M:tm-969, m:tm-184, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-88868
in-theory        88868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     79
proof            (modus-ponens tm-969 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-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-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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-88868.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88869
in-theory        88869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     59
proof            (modus-ponens tm-969 tm-211 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
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-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-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-88869.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-969, 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-88870
in-theory        88870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-2 tm-5 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-88870.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88871
in-theory        88871
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (((E and F) -> E) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((E and F) -> E) and D))))
theorem-size     43
proof            (modus-ponens tm-969 tm-240 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Cm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88871.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (((E and F) -> E) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((E and F) -> E) and D)))), M:tm-969, m:tm-240, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-88872
in-theory        88872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-2 tm-5 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-88872.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88873
in-theory        88873
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (((E and F) -> F) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((E and F) -> F) and D))))
theorem-size     43
proof            (modus-ponens tm-969 tm-271 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88873.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (((E and F) -> F) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((E and F) -> F) and D)))), M:tm-969, m:tm-271, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-88874
in-theory        88874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     67
proof            (modus-ponens tm-969 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-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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-88874.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88875
in-theory        88875
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> (E and F))) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     47
proof            (modus-ponens tm-969 tm-304 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88875.        ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> (E and F))) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-969, m:tm-304, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-88876
in-theory        88876
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> ((A -> B) -> ((C or A) -> B))))))
theorem-size     67
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-88876.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> ((A -> B) -> ((C or A) -> B)))))), M:tm-969, 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-88877
in-theory        88877
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (C or A)) -> ((A -> B) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (C or A)) -> ((A -> B) -> B)))))
theorem-size     71
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-88877.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (C or A)) -> ((A -> B) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (C or A)) -> ((A -> B) -> B))))), M:tm-969, 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-88878
in-theory        88878
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (((A -> B) -> ((C or A) -> B)) and D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (((A -> B) -> ((C or A) -> B)) and D)))))
theorem-size     71
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-88878.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (((A -> B) -> ((C or A) -> B)) and D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (((A -> B) -> ((C or A) -> B)) and D))))), M:tm-969, 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-88879
in-theory        88879
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> ((C or A) -> B)) or D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> ((C or A) -> B)) or D))))
theorem-size     67
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-88879.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> ((C or A) -> B)) or D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> ((C or A) -> B)) or D)))), M:tm-969, 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-88880
in-theory        88880
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D or ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D or ((A -> B) -> ((C or A) -> B))))))
theorem-size     67
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-88880.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D or ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D or ((A -> B) -> ((C or A) -> B)))))), M:tm-969, 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-88881
in-theory        88881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D)))))
theorem-size     83
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-88881.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D))))), M:tm-969, 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-88882
in-theory        88882
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B))))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-88882.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B)))))), M:tm-969, 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-88883
in-theory        88883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> D)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-315 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (-> Cm Bm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-88883.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> D))))), M:tm-969, 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-88884
in-theory        88884
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> (A -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> (A -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-88884.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> (A -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> (A -> B))))), M:tm-969, 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-88885
in-theory        88885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     71
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-88885.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-969, 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-88886
in-theory        88886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> D))))
theorem-size     55
proof            (modus-ponens tm-969 tm-320 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-88886.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> D)))), M:tm-969, 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-88887
in-theory        88887
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> E))))
theorem-size     55
proof            (modus-ponens tm-969 tm-322 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-88887.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> E)))), M:tm-969, 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-88888
in-theory        88888
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B))))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-88888.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B)))))), M:tm-969, 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-88889
in-theory        88889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B))))))
theorem-size     91
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
proof-size       297
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-88889.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))))), M:tm-969, 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-88890
in-theory        88890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> D) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> D) and ((A -> B) -> ((C or A) -> B))))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-88890.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> D) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> D) and ((A -> B) -> ((C or A) -> B)))))), M:tm-969, 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-88891
in-theory        88891
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> E) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> E) and ((A -> B) -> ((C or A) -> B))))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-88891.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> E) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> E) and ((A -> B) -> ((C or A) -> B)))))), M:tm-969, 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-88892
in-theory        88892
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B))))))
theorem-size     79
proof            (modus-ponens tm-969 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-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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-88892.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B)))))), M:tm-969, 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-88893
in-theory        88893
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> ((A -> B) and ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> ((A -> B) and ((C or A) -> B))))))
theorem-size     71
proof            (modus-ponens tm-969 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-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-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-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-88893.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> ((A -> B) and ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> ((A -> B) and ((C or A) -> B)))))), M:tm-969, 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-88894
in-theory        88894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> ((C or A) -> (A and B))) -> (((A -> B) or (A -> (A and B))) -> ((C or A) -> (A and B)))) and (((C -> A) or ((A -> (A and B)) -> ((C or A) -> (A and B)))) -> (((A -> B) or (A -> (A and B))) -> ((C or A) -> (A and B)))))
theorem-size     67
proof            (modus-ponens tm-969 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-2 tm-5 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-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-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-88894.        ((((A -> (A and B)) -> ((C or A) -> (A and B))) -> (((A -> B) or (A -> (A and B))) -> ((C or A) -> (A and B)))) and (((C -> A) or ((A -> (A and B)) -> ((C or A) -> (A and B)))) -> (((A -> B) or (A -> (A and B))) -> ((C or A) -> (A and B))))), M:tm-969, 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-88895
in-theory        88895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-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-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-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-88895.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88896
in-theory        88896
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (D -> (D and E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (D -> (D and E)))))
theorem-size     43
proof            (modus-ponens tm-969 tm-340 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 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-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-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-88896.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (D -> (D and E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (D -> (D and E))))), M:tm-969, m:tm-340, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-88897
in-theory        88897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> (D and E))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> (D and E))))))
theorem-size     59
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-88897.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> (D and E))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> (D and E)))))), M:tm-969, 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-88898
in-theory        88898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> ((C or A) -> (B -> (A and B)))) -> ((D or (A -> (B -> (A and B)))) -> ((C or A) -> (B -> (A and B))))) and (((C -> A) or ((A -> (B -> (A and B))) -> ((C or A) -> (B -> (A and B))))) -> ((D or (A -> (B -> (A and B)))) -> ((C or A) -> (B -> (A and B))))))
theorem-size     79
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> 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-88898.        ((((A -> (B -> (A and B))) -> ((C or A) -> (B -> (A and B)))) -> ((D or (A -> (B -> (A and B)))) -> ((C or A) -> (B -> (A and B))))) and (((C -> A) or ((A -> (B -> (A and B))) -> ((C or A) -> (B -> (A and B))))) -> ((D or (A -> (B -> (A and B)))) -> ((C or A) -> (B -> (A and B)))))), M:tm-969, 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-88899
in-theory        88899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-88899.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88900
in-theory        88900
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D -> (((C or A) -> B) and D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (D -> (((C or A) -> B) and D)))))
theorem-size     51
proof            (modus-ponens tm-969 tm-355 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (and (-> (or C A) B) Cm))))))
axioms-used      (tm-2 tm-5 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-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-1.            (A -> (B -> 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-88900.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D -> (((C or A) -> B) and D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (D -> (((C or A) -> B) and D))))), M:tm-969, 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-88901
in-theory        88901
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F -> (E and F))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (F -> (E and F))))))
theorem-size     43
proof            (modus-ponens tm-969 tm-356 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm (and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> 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-88901.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F -> (E and F))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (F -> (E and F)))))), M:tm-969, m:tm-356, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-88902
in-theory        88902
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> D)) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> D)) or F) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-88902.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> D)) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> D)) or F) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88903
in-theory        88903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> D)) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> D)) or F)))
theorem-size     39
proof            (modus-ponens tm-969 tm-365 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-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-88903.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> D)) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> D)) or F))), M:tm-969, m:tm-365, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-88904
in-theory        88904
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-88904.        ((((A -> B) -> ((C or A) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88905
in-theory        88905
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     55
proof            (modus-ponens tm-969 tm-374 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88905.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-969, m:tm-374, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-88906
in-theory        88906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D and E) -> D) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D and E) -> D) or F) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-88906.        ((((A -> B) -> ((C or A) -> B)) -> ((((D and E) -> D) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D and E) -> D) or F) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88907
in-theory        88907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D and E) -> D) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and E) -> D) or F)))
theorem-size     39
proof            (modus-ponens tm-969 tm-383 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 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-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-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-88907.        ((((A -> B) -> ((C or A) -> B)) -> (((D and E) -> D) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and E) -> D) or F))), M:tm-969, m:tm-383, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-88908
in-theory        88908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D and E) -> E) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D and E) -> E) or F) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-88908.        ((((A -> B) -> ((C or A) -> B)) -> ((((D and E) -> E) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D and E) -> E) or F) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88909
in-theory        88909
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D and E) -> E) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and E) -> E) or F)))
theorem-size     39
proof            (modus-ponens tm-969 tm-392 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 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-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-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-88909.        ((((A -> B) -> ((C or A) -> B)) -> (((D and E) -> E) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D and E) -> E) or F))), M:tm-969, m:tm-392, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-88910
in-theory        88910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-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-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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-88910.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88911
in-theory        88911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (D and E))) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (D and E))) or F)))
theorem-size     43
proof            (modus-ponens tm-969 tm-401 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
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-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-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-88911.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (D and E))) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (D and E))) or F))), M:tm-969, m:tm-401, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-88912
in-theory        88912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> (D or E)) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (D or E)) or F) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-88912.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> (D or E)) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (D or E)) or F) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88913
in-theory        88913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (D or E)) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (D or E)) or F)))
theorem-size     39
proof            (modus-ponens tm-969 tm-410 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-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-88913.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (D or E)) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (D or E)) or F))), M:tm-969, m:tm-410, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-88914
in-theory        88914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B))))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-88914.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B)))))), M:tm-969, 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-88915
in-theory        88915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-88915.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88916
in-theory        88916
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (E or F)) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (E or F)) and D))))
theorem-size     43
proof            (modus-ponens tm-969 tm-454 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
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-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-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-88916.        ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (E or F)) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (E or F)) and D)))), M:tm-969, m:tm-454, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-88917
in-theory        88917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (D or E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (D or E)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-456 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-88917.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (D or E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (D or E))))), M:tm-969, 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-88918
in-theory        88918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A -> B) or A) -> B)) -> ((A -> B) -> B)) and ((((A -> B) -> A) or ((A -> B) -> (((A -> B) or A) -> B))) -> ((A -> B) -> B)))
theorem-size     41
proof            (modus-ponens tm-969 tm-464 ((Am (-> Bm Cm)) (C (-> Bm Cm)) (A Bm) (B Cm) (D (-> (-> Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-88918.        ((((A -> B) -> (((A -> B) or A) -> B)) -> ((A -> B) -> B)) and ((((A -> B) -> A) or ((A -> B) -> (((A -> B) or A) -> B))) -> ((A -> B) -> B))), M:tm-969, m:tm-464, u:((Am (-> Bm Cm)) (C (-> Bm Cm)) (A Bm) (B Cm) (D (-> (-> Bm Cm) Cm)))
================================================================
tm-name          tm-88919
in-theory        88919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> ((C or A) -> (A or B))) -> ((D or (A -> (A or B))) -> ((C or A) -> (A or B)))) and (((C -> A) or ((A -> (A or B)) -> ((C or A) -> (A or B)))) -> ((D or (A -> (A or B))) -> ((C or A) -> (A or B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-88919.        ((((A -> (A or B)) -> ((C or A) -> (A or B))) -> ((D or (A -> (A or B))) -> ((C or A) -> (A or B)))) and (((C -> A) or ((A -> (A or B)) -> ((C or A) -> (A or B)))) -> ((D or (A -> (A or B))) -> ((C or A) -> (A or B))))), M:tm-969, 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-88920
in-theory        88920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (E or F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (E or F))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-88920.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (E or F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (E or F))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88921
in-theory        88921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (((C or A) -> B) or D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (((C or A) -> B) or D))))
theorem-size     47
proof            (modus-ponens tm-969 tm-470 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or (-> (or C A) B) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-88921.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (((C or A) -> B) or D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (((C or A) -> B) or D)))), M:tm-969, m:tm-470, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or (-> (or C A) B) Cm))))
================================================================
tm-name          tm-88922
in-theory        88922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (E or F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (E or F)))))
theorem-size     39
proof            (modus-ponens tm-969 tm-471 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-88922.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (E or F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (E or F))))), M:tm-969, m:tm-471, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-88923
in-theory        88923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-88923.        ((((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88924
in-theory        88924
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F -> E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or (E -> (F -> E)))))
theorem-size     39
proof            (modus-ponens tm-969 tm-481 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-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-88924.        ((((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F -> E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or (E -> (F -> E))))), M:tm-969, m:tm-481, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-88925
in-theory        88925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-88925.        ((((A -> B) -> ((C or A) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88926
in-theory        88926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     55
proof            (modus-ponens tm-969 tm-491 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88926.        ((((A -> B) -> ((C or A) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-969, m:tm-491, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-88927
in-theory        88927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-88927.        ((((A -> B) -> ((C or A) -> B)) -> ((D or ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88928
in-theory        88928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D or ((E and F) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((E and F) -> E))))
theorem-size     39
proof            (modus-ponens tm-969 tm-501 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 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-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-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-88928.        ((((A -> B) -> ((C or A) -> B)) -> (D or ((E and F) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((E and F) -> E)))), M:tm-969, m:tm-501, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-88929
in-theory        88929
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-88929.        ((((A -> B) -> ((C or A) -> B)) -> ((D or ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88930
in-theory        88930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D or ((E and F) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((E and F) -> F))))
theorem-size     39
proof            (modus-ponens tm-969 tm-511 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 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-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-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-88930.        ((((A -> B) -> ((C or A) -> B)) -> (D or ((E and F) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((E and F) -> F)))), M:tm-969, m:tm-511, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-88931
in-theory        88931
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-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-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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-88931.        ((((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88932
in-theory        88932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F -> (E and F))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or (E -> (F -> (E and F))))))
theorem-size     43
proof            (modus-ponens tm-969 tm-521 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm (and Cm 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-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-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-88932.        ((((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F -> (E and F))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or (E -> (F -> (E and F)))))), M:tm-969, m:tm-521, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-88933
in-theory        88933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (E or F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (E -> (E or F))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-88933.        ((((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (E or F))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (E -> (E or F))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88934
in-theory        88934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D or (E -> (E or F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or (E -> (E or F)))))
theorem-size     39
proof            (modus-ponens tm-969 tm-531 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 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-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-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-88934.        ((((A -> B) -> ((C or A) -> B)) -> (D or (E -> (E or F)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or (E -> (E or F))))), M:tm-969, m:tm-531, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-88935
in-theory        88935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F or E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (E -> (F or E))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-88935.        ((((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F or E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (E -> (F or E))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88936
in-theory        88936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F or E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or (E -> (F or E)))))
theorem-size     39
proof            (modus-ponens tm-969 tm-541 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-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-88936.        ((((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F or E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or (E -> (F or E))))), M:tm-969, m:tm-541, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-88937
in-theory        88937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E or D)) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E or D)) or F) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-88937.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E or D)) or F) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E or D)) or F) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88938
in-theory        88938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E or D)) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E or D)) or F)))
theorem-size     39
proof            (modus-ponens tm-969 tm-551 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 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-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-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-88938.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E or D)) or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E or D)) or F))), M:tm-969, m:tm-551, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-88939
in-theory        88939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B))))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-88939.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B)))))), M:tm-969, 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-88940
in-theory        88940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     63
proof            (modus-ponens tm-969 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-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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-88940.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88941
in-theory        88941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F or E)) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (F or E)) and D))))
theorem-size     43
proof            (modus-ponens tm-969 tm-606 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
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-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-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-88941.        ((((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F or E)) and D))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((E -> (F or E)) and D)))), M:tm-969, m:tm-606, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-88942
in-theory        88942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E or D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E or D)))))
theorem-size     55
proof            (modus-ponens tm-969 tm-609 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-88942.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E or D)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E or D))))), M:tm-969, 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-88943
in-theory        88943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> ((C or A) -> (B or A))) -> ((D or (A -> (B or A))) -> ((C or A) -> (B or A)))) and (((C -> A) or ((A -> (B or A)) -> ((C or A) -> (B or A)))) -> ((D or (A -> (B or A))) -> ((C or A) -> (B or A)))))
theorem-size     63
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-88943.        ((((A -> (B or A)) -> ((C or A) -> (B or A))) -> ((D or (A -> (B or A))) -> ((C or A) -> (B or A)))) and (((C -> A) or ((A -> (B or A)) -> ((C or A) -> (B or A)))) -> ((D or (A -> (B or A))) -> ((C or A) -> (B or A))))), M:tm-969, 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-88944
in-theory        88944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F or E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (F or E))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     59
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-88944.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F or E))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (E -> (F or E))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88945
in-theory        88945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D or ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (D or ((C or A) -> B)))))
theorem-size     47
proof            (modus-ponens tm-969 tm-623 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or Cm (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-88945.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D or ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> (D or ((C or A) -> B))))), M:tm-969, m:tm-623, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or Cm (-> (or C A) B)))))
================================================================
tm-name          tm-88946
in-theory        88946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F or E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (F or E)))))
theorem-size     39
proof            (modus-ponens tm-969 tm-624 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-88946.        ((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F or E)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> (F or E))))), M:tm-969, m:tm-624, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-88947
in-theory        88947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((B or (A -> B)) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((B or (A -> B)) -> ((C or A) -> B)))))
theorem-size     67
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-88947.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((B or (A -> B)) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((B or (A -> B)) -> ((C or A) -> B))))), M:tm-969, 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-88948
in-theory        88948
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> ((D or (A or (B -> A))) -> C)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((D or (A or (B -> A))) -> C))) and (((D -> (A or (B -> A))) or (((A or (B -> A)) -> C) -> ((D or (A or (B -> A))) -> C))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((D or (A or (B -> A))) -> C))))
theorem-size     91
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-88948.        (((((A or (B -> A)) -> C) -> ((D or (A or (B -> A))) -> C)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((D or (A or (B -> A))) -> C))) and (((D -> (A or (B -> A))) or (((A or (B -> A)) -> C) -> ((D or (A or (B -> A))) -> C))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((D or (A or (B -> A))) -> C)))), M:tm-969, 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-88949
in-theory        88949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     71
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-88949.        ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88950
in-theory        88950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     51
proof            (modus-ponens tm-969 tm-667 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-88950.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-969, m:tm-667, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-88951
in-theory        88951
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> ((((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))))) and (((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) -> ((((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     125
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
proof-size       361
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-88951.        (((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> ((((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))))) and (((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) -> ((((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-969, 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-88952
in-theory        88952
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) and (((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))))
theorem-size     77
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1)
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-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-1.            (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-88952.        (((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) and (((D -> (A -> B)) or (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))))), M:tm-969, 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-88953
in-theory        88953
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) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))) and (((E -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> ((E 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)) -> ((E or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))))
theorem-size     171
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
proof-size       401
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-88953.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> ((E 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)) -> ((E or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))) and (((E -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> ((E 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)) -> ((E or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)))), M:tm-969, 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-88954
in-theory        88954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     95
proof            (modus-ponens tm-969 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-2 tm-5 tm-8)
proof-size       303
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-88954.        ((((A -> B) -> ((C or A) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88955
in-theory        88955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88955.        ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-969, 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-88956
in-theory        88956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-3)
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-88956.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B))))), M:tm-969, 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-88957
in-theory        88957
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> ((D or ((A and B) or A)) -> C)) -> (((A -> C) or (((A and B) or A) -> C)) -> ((D or ((A and B) or A)) -> C))) and (((D -> ((A and B) or A)) or ((((A and B) or A) -> C) -> ((D or ((A and B) or A)) -> C))) -> (((A -> C) or (((A and B) or A) -> C)) -> ((D or ((A and B) or A)) -> C))))
theorem-size     87
proof            (modus-ponens tm-969 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-2 tm-5 tm-8 tm-3)
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-88957.        ((((((A and B) or A) -> C) -> ((D or ((A and B) or A)) -> C)) -> (((A -> C) or (((A and B) or A) -> C)) -> ((D or ((A and B) or A)) -> C))) and (((D -> ((A and B) or A)) or ((((A and B) or A) -> C) -> ((D or ((A and B) or A)) -> C))) -> (((A -> C) or (((A and B) or A) -> C)) -> ((D or ((A and B) or A)) -> C)))), M:tm-969, 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-88958
in-theory        88958
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     67
proof            (modus-ponens tm-969 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-88958.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, 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-88959
in-theory        88959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (((D and F) or D) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     47
proof            (modus-ponens tm-969 tm-759 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-88959.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (((D and F) or D) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-969, m:tm-759, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-88960
in-theory        88960
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-969 tm-798 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (or (and Cm (-> A B)) (-> A B)) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-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-4.            ((A and B) -> B), axiom
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-88960.        ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B))))), M:tm-969, m:tm-798, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (or (and Cm (-> A B)) (-> A B)) (-> (or C A) B)))))
================================================================
tm-name          tm-88961
in-theory        88961
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or B) -> C) -> ((D or ((A and B) or B)) -> C)) -> (((B -> C) or (((A and B) or B) -> C)) -> ((D or ((A and B) or B)) -> C))) and (((D -> ((A and B) or B)) or ((((A and B) or B) -> C) -> ((D or ((A and B) or B)) -> C))) -> (((B -> C) or (((A and B) or B) -> C)) -> ((D or ((A and B) or B)) -> C))))
theorem-size     87
proof            (modus-ponens tm-969 tm-805 ((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or C (or (and Am Bm) Bm)) Cm)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or C (or (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-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-4.            ((A and B) -> B), axiom
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-88961.        ((((((A and B) or B) -> C) -> ((D or ((A and B) or B)) -> C)) -> (((B -> C) or (((A and B) or B) -> C)) -> ((D or ((A and B) or B)) -> C))) and (((D -> ((A and B) or B)) or ((((A and B) or B) -> C) -> ((D or ((A and B) or B)) -> C))) -> (((B -> C) or (((A and B) or B) -> C)) -> ((D or ((A and B) or B)) -> C)))), M:tm-969, m:tm-805, u:((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or C (or (and Am Bm) Bm)) Cm)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or C (or (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-88962
in-theory        88962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     67
proof            (modus-ponens tm-969 tm-808 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-88962.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, m:tm-808, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-88963
in-theory        88963
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (((F and D) or D) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (((F and D) or D) -> E))))
theorem-size     47
proof            (modus-ponens tm-969 tm-810 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-88963.        ((((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (((F and D) or D) -> E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (((F and D) or D) -> E)))), M:tm-969, m:tm-810, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-88964
in-theory        88964
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> ((C or A) -> (B and A))) -> (((A -> (B and A)) -> ((C or A) -> (B and A))) and ((B or (A -> (B and A))) -> ((C or A) -> (B and A))))) and (((C -> A) or ((A -> (B and A)) -> ((C or A) -> (B and A)))) -> (((A -> (B and A)) -> ((C or A) -> (B and A))) and ((B or (A -> (B and A))) -> ((C or A) -> (B and A))))))
theorem-size     91
proof            (modus-ponens tm-969 tm-844 ((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (and (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am))) (-> (or Bm (-> Am (and Bm Am))) (-> (or C Am) (and Bm Am)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       303
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-48.           (((A -> (B and 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-88964.        ((((A -> (B and A)) -> ((C or A) -> (B and A))) -> (((A -> (B and A)) -> ((C or A) -> (B and A))) and ((B or (A -> (B and A))) -> ((C or A) -> (B and A))))) and (((C -> A) or ((A -> (B and A)) -> ((C or A) -> (B and A)))) -> (((A -> (B and A)) -> ((C or A) -> (B and A))) and ((B or (A -> (B and A))) -> ((C or A) -> (B and A)))))), M:tm-969, m:tm-844, u:((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (and (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am))) (-> (or Bm (-> Am (and Bm Am))) (-> (or C Am) (and Bm Am))))))
================================================================
tm-name          tm-88965
in-theory        88965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> ((C or A) -> (B and A))) -> ((A -> (B and A)) -> ((C or A) -> (B and A)))) and (((C -> A) or ((A -> (B and A)) -> ((C or A) -> (B and A)))) -> ((A -> (B and A)) -> ((C or A) -> (B and A)))))
theorem-size     59
proof            (modus-ponens tm-969 tm-850 ((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-88965.        ((((A -> (B and A)) -> ((C or A) -> (B and A))) -> ((A -> (B and A)) -> ((C or A) -> (B and A)))) and (((C -> A) or ((A -> (B and A)) -> ((C or A) -> (B and A)))) -> ((A -> (B and A)) -> ((C or A) -> (B and A))))), M:tm-969, m:tm-850, u:((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am)))))
================================================================
tm-name          tm-88966
in-theory        88966
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (A and B))) -> C) -> ((D or (A or (B -> (A and B)))) -> C)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((D or (A or (B -> (A and B)))) -> C))) and (((D -> (A or (B -> (A and B)))) or (((A or (B -> (A and B))) -> C) -> ((D or (A or (B -> (A and B)))) -> C))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((D or (A or (B -> (A and B)))) -> C))))
theorem-size     113
proof            (modus-ponens tm-969 tm-852 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or C (or Am (-> Bm (and Am Bm)))) Cm)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or C (or Am (-> Bm (and Am Bm)))) Cm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-88966.        (((((A or (B -> (A and B))) -> C) -> ((D or (A or (B -> (A and B)))) -> C)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((D or (A or (B -> (A and B)))) -> C))) and (((D -> (A or (B -> (A and B)))) or (((A or (B -> (A and B))) -> C) -> ((D or (A or (B -> (A and B)))) -> C))) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((D or (A or (B -> (A and B)))) -> C)))), M:tm-969, m:tm-852, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or C (or Am (-> Bm (and Am Bm)))) Cm)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or C (or Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-88967
in-theory        88967
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     79
proof            (modus-ponens tm-969 tm-855 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A B) (-> (or C A) B))))))
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-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-48.           (((A -> (B and 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-88967.        ((((A -> B) -> ((C or A) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, m:tm-855, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-88968
in-theory        88968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))
theorem-size     59
proof            (modus-ponens tm-969 tm-857 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
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-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-1.            (A -> (B -> A)), 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-88968.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))), M:tm-969, m:tm-857, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-88969
in-theory        88969
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (A or B)) -> C) -> ((D or (A or (A or B))) -> C)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (A or (A or B))) -> C))) and (((D -> (A or (A or B))) or (((A or (A or B)) -> C) -> ((D or (A or (A or B))) -> C))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (A or (A or B))) -> C))))
theorem-size     91
proof            (modus-ponens tm-969 tm-890 ((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or C (or Am (or Am Bm))) Cm)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or C (or Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-88969.        (((((A or (A or B)) -> C) -> ((D or (A or (A or B))) -> C)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (A or (A or B))) -> C))) and (((D -> (A or (A or B))) or (((A or (A or B)) -> C) -> ((D or (A or (A or B))) -> C))) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (A or (A or B))) -> C)))), M:tm-969, m:tm-890, u:((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or C (or Am (or Am Bm))) Cm)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or C (or Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-88970
in-theory        88970
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     71
proof            (modus-ponens tm-969 tm-893 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-88970.        ((((A -> B) -> ((C or A) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, m:tm-893, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-88971
in-theory        88971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D or E) -> F) -> ((D or (D or E)) -> F))))
theorem-size     51
proof            (modus-ponens tm-969 tm-895 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-88971.        ((((A -> B) -> ((C or A) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))), M:tm-969, m:tm-895, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-88972
in-theory        88972
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B or A)) -> C) -> ((D or (A or (B or A))) -> C)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((D or (A or (B or A))) -> C))) and (((D -> (A or (B or A))) or (((A or (B or A)) -> C) -> ((D or (A or (B or A))) -> C))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((D or (A or (B or A))) -> C))))
theorem-size     91
proof            (modus-ponens tm-969 tm-927 ((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or C (or Am (or Bm Am))) Cm)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or C (or Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-88972.        (((((A or (B or A)) -> C) -> ((D or (A or (B or A))) -> C)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((D or (A or (B or A))) -> C))) and (((D -> (A or (B or A))) or (((A or (B or A)) -> C) -> ((D or (A or (B or A))) -> C))) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((D or (A or (B or A))) -> C)))), M:tm-969, m:tm-927, u:((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or C (or Am (or Bm Am))) Cm)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or C (or Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-88973
in-theory        88973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     71
proof            (modus-ponens tm-969 tm-930 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-88973.        ((((A -> B) -> ((C or A) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, m:tm-930, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-88974
in-theory        88974
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D or E) -> F) -> ((E or (D or E)) -> F))))
theorem-size     51
proof            (modus-ponens tm-969 tm-932 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-88974.        ((((A -> B) -> ((C or A) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))), M:tm-969, m:tm-932, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-88975
in-theory        88975
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B))))) and (((D -> (A -> B)) or (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B))))))
theorem-size     145
proof            (modus-ponens tm-969 tm-969 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       387
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-88975.        (((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B))))) and (((D -> (A -> B)) or (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B)))))), M:tm-969, m:tm-969, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-88976
in-theory        88976
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     53
proof            (modus-ponens tm-930 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-88976.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-930, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88977
in-theory        88977
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     53
proof            (modus-ponens tm-893 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-88977.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-893, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88978
in-theory        88978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     57
proof            (modus-ponens tm-855 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       243
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-88978.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-855, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88979
in-theory        88979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B))))))
theorem-size     69
proof            (modus-ponens tm-850 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       267
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-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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-88979.        ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B)))))), M:tm-850, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
================================================================
tm-name          tm-88980
in-theory        88980
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B)))))) and ((D or (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))) -> ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B)))))))
theorem-size     141
proof            (modus-ponens tm-844 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       353
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88980.        (((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B)))))) and ((D or (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))) -> ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and ((A -> B) -> ((C or A) -> B))))))), M:tm-844, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
================================================================
tm-name          tm-88981
in-theory        88981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     51
proof            (modus-ponens tm-808 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-88981.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-808, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88982
in-theory        88982
times-derived    1
----------------------------------------------------------------
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))) and (((E and (((A -> B) -> ((C or A) -> B)) -> D)) or (((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     93
proof            (modus-ponens tm-798 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> 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 tm-4)
proof-size       287
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88982.        (((((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))) and (((E and (((A -> B) -> ((C or A) -> B)) -> D)) or (((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-798, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88983
in-theory        88983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     51
proof            (modus-ponens tm-757 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88983.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-757, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88984
in-theory        88984
times-derived    1
----------------------------------------------------------------
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))) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((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     93
proof            (modus-ponens tm-747 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> 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 tm-3)
proof-size       287
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-88984.        (((((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))) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((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-747, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88985
in-theory        88985
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) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     65
proof            (modus-ponens tm-708 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       273
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88985.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-708, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88986
in-theory        88986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))))
theorem-size     51
proof            (modus-ponens tm-703 tm-969 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       267
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88986.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))), M:tm-703, m:tm-969, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C)))))
================================================================
tm-name          tm-88987
in-theory        88987
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) and (((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))) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))))
theorem-size     115
proof            (modus-ponens tm-697 tm-969 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       351
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-88987.        (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) and (((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))) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))))), M:tm-697, m:tm-969, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C)))))
================================================================
tm-name          tm-88988
in-theory        88988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     53
proof            (modus-ponens tm-665 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88988.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-665, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88989
in-theory        88989
times-derived    1
----------------------------------------------------------------
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))) and ((D or (((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     81
proof            (modus-ponens tm-654 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (and (-> (-> (-> 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 tm-1)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-88989.        (((((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))) and ((D or (((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-654, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88990
in-theory        88990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (E or ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     41
proof            (modus-ponens tm-623 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88990.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (E or ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-623, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-88991
in-theory        88991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-622 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88991.        ((A -> (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-622, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88992
in-theory        88992
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C))))) -> ((((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E or ((B -> C) -> ((D or B) -> C))))))
theorem-size     71
proof            (modus-ponens tm-619 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (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 tm-2 tm-5)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88992.        ((A or (((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C))))) -> ((((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E or ((B -> C) -> ((D or B) -> C)))))), M:tm-619, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
================================================================
tm-name          tm-88993
in-theory        88993
times-derived    1
----------------------------------------------------------------
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))) and (E -> (F or E)))
theorem-size     45
proof            (modus-ponens tm-609 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-88993.        (((((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))) and (E -> (F or E))), M:tm-609, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88994
in-theory        88994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     49
proof            (modus-ponens tm-605 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88994.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-605, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88995
in-theory        88995
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F or E)) 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     85
proof            (modus-ponens tm-595 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-88995.        (((((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))) and ((E -> (F or E)) 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-595, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88996
in-theory        88996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-550 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88996.        (((A -> (B or A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-550, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88997
in-theory        88997
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-540 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88997.        ((A or (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-540, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88998
in-theory        88998
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-530 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88998.        ((A or (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-530, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-88999
in-theory        88999
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     49
proof            (modus-ponens tm-520 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-88999.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-520, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89000
in-theory        89000
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-510 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89000.        ((A or ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-510, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89001
in-theory        89001
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-500 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89001.        ((A or ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-500, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89002
in-theory        89002
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     55
proof            (modus-ponens tm-490 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89002.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-490, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89003
in-theory        89003
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-480 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89003.        ((A or (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-480, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89004
in-theory        89004
times-derived    1
----------------------------------------------------------------
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)) or E))
theorem-size     41
proof            (modus-ponens tm-470 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89004.        ((((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)) or E)), M:tm-470, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89005
in-theory        89005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-469 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89005.        ((A -> (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-469, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89006
in-theory        89006
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E))) -> ((((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (((B -> C) -> ((D or B) -> C)) or E))))
theorem-size     71
proof            (modus-ponens tm-466 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (-> (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 tm-2 tm-5)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89006.        ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E))) -> ((((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E)) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (((B -> C) -> ((D or B) -> C)) or E)))), M:tm-466, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)))))
================================================================
tm-name          tm-89007
in-theory        89007
times-derived    1
----------------------------------------------------------------
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))) and (E -> (E or F)))
theorem-size     45
proof            (modus-ponens tm-456 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-89007.        (((((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))) and (E -> (E or F))), M:tm-456, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89008
in-theory        89008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     49
proof            (modus-ponens tm-453 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89008.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-453, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89009
in-theory        89009
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (E or F)) 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     85
proof            (modus-ponens tm-443 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-89009.        (((((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))) and ((E -> (E or F)) 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-443, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89010
in-theory        89010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-409 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89010.        (((A -> (A or B)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-409, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89011
in-theory        89011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     49
proof            (modus-ponens tm-400 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89011.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-400, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89012
in-theory        89012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-391 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89012.        ((((A and B) -> B) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-391, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89013
in-theory        89013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-382 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89013.        ((((A and B) -> A) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-382, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89014
in-theory        89014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     55
proof            (modus-ponens tm-373 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89014.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-373, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89015
in-theory        89015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-364 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89015.        (((A -> (B -> A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-364, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89016
in-theory        89016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> (((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and E)))
theorem-size     43
proof            (modus-ponens tm-355 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89016.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> (((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and E))), M:tm-355, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89017
in-theory        89017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     49
proof            (modus-ponens tm-354 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89017.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-354, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89018
in-theory        89018
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E)))) -> ((((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E -> (((B -> C) -> ((D or B) -> C)) and E)))))
theorem-size     77
proof            (modus-ponens tm-351 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))) (-> (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 tm-2)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89018.        ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E)))) -> ((((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E -> (((B -> C) -> ((D or B) -> C)) and E))))), M:tm-351, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))))))
================================================================
tm-name          tm-89019
in-theory        89019
times-derived    1
----------------------------------------------------------------
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))) and (E -> (F -> (E and F))))
theorem-size     47
proof            (modus-ponens tm-341 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-89019.        (((((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))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89020
in-theory        89020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     49
proof            (modus-ponens tm-338 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-89020.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-338, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89021
in-theory        89021
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))) -> ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and D))))
theorem-size     81
proof            (modus-ponens tm-335 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (-> (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       263
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89021.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and D))) -> ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and D)))), M:tm-335, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)))))
================================================================
tm-name          tm-89022
in-theory        89022
times-derived    1
----------------------------------------------------------------
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))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))))
theorem-size     91
proof            (modus-ponens tm-328 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> 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       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-328.          ((A -> 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-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-89022.        (((((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))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))), M:tm-328, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89023
in-theory        89023
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F -> (E and F))) 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     87
proof            (modus-ponens tm-327 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-89023.        (((((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))) and ((E -> (F -> (E and F))) 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-327, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89024
in-theory        89024
times-derived    1
----------------------------------------------------------------
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))) and (((E and F) -> F) 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     85
proof            (modus-ponens tm-326 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-89024.        (((((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))) and (((E and F) -> F) 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-326, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89025
in-theory        89025
times-derived    1
----------------------------------------------------------------
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))) and (((E and F) -> E) 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     85
proof            (modus-ponens tm-325 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-89025.        (((((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))) and (((E and F) -> E) 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-325, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89026
in-theory        89026
times-derived    1
----------------------------------------------------------------
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))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) 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     93
proof            (modus-ponens tm-324 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-89026.        (((((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))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) 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-324, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89027
in-theory        89027
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F -> E)) 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     85
proof            (modus-ponens tm-323 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-89027.        (((((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))) and ((E -> (F -> E)) 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-323, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89028
in-theory        89028
times-derived    1
----------------------------------------------------------------
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))) and ((E and F) -> F))
theorem-size     45
proof            (modus-ponens tm-322 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-89028.        (((((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))) and ((E and F) -> F)), M:tm-322, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89029
in-theory        89029
times-derived    1
----------------------------------------------------------------
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))) and ((E and F) -> E))
theorem-size     45
proof            (modus-ponens tm-320 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-89029.        (((((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))) and ((E and F) -> E)), M:tm-320, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89030
in-theory        89030
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     53
proof            (modus-ponens tm-318 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-89030.        (((((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))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89031
in-theory        89031
times-derived    1
----------------------------------------------------------------
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))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     63
proof            (modus-ponens tm-316 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> 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       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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89031.        (((((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))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-316, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89032
in-theory        89032
times-derived    1
----------------------------------------------------------------
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))) and (E -> (F -> E)))
theorem-size     45
proof            (modus-ponens tm-315 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-89032.        (((((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))) and (E -> (F -> E))), M:tm-315, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89033
in-theory        89033
times-derived    1
----------------------------------------------------------------
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))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))) -> (not (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     93
proof            (modus-ponens tm-313 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-89033.        (((((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))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))) -> (not (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-313, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89034
in-theory        89034
times-derived    1
----------------------------------------------------------------
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))) and ((((((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 ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> E)))
theorem-size     111
proof            (modus-ponens tm-312 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> 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       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-312.          ((A -> B) -> ((A -> B) and ((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-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-89034.        (((((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))) and ((((((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 ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> E))), M:tm-312, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89035
in-theory        89035
times-derived    1
----------------------------------------------------------------
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))) and (E or ((((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     81
proof            (modus-ponens tm-311 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-7.            (A -> (B or 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-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-89035.        (((((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))) and (E or ((((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-311, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89036
in-theory        89036
times-derived    1
----------------------------------------------------------------
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))) 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))) or E))
theorem-size     81
proof            (modus-ponens tm-310 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-6.            (A -> (A or 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-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-89036.        (((((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))) 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))) or E)), M:tm-310, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89037
in-theory        89037
times-derived    1
----------------------------------------------------------------
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))) and (E -> (((((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))) and E)))
theorem-size     83
proof            (modus-ponens tm-309 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-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-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-89037.        (((((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))) and (E -> (((((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))) and E))), M:tm-309, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89038
in-theory        89038
times-derived    1
----------------------------------------------------------------
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))) and (E -> ((((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     81
proof            (modus-ponens tm-305 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-1.            (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-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-89038.        (((((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))) and (E -> ((((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-305, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89039
in-theory        89039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     51
proof            (modus-ponens tm-303 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89039.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-303, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89040
in-theory        89040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     49
proof            (modus-ponens tm-270 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89040.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-270, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89041
in-theory        89041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     49
proof            (modus-ponens tm-239 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89041.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-239, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89042
in-theory        89042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     57
proof            (modus-ponens tm-210 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       243
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89042.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-210, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89043
in-theory        89043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     49
proof            (modus-ponens tm-183 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89043.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-183, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89044
in-theory        89044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-157 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89044.        ((A -> ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-157, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89045
in-theory        89045
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     55
proof            (modus-ponens tm-147 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89045.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-147, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89046
in-theory        89046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-134 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89046.        ((A -> ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-134, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89047
in-theory        89047
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     55
proof            (modus-ponens tm-125 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89047.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-125, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89048
in-theory        89048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     55
proof            (modus-ponens tm-113 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89048.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-113, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89049
in-theory        89049
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C)))))
theorem-size     77
proof            (modus-ponens tm-110 tm-969 ((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (-> (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 tm-5)
proof-size       277
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89049.        ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C))))), M:tm-110, m:tm-969, u:((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))))))
================================================================
tm-name          tm-89050
in-theory        89050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     59
proof            (modus-ponens tm-105 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89050.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-105, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89051
in-theory        89051
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))) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> B)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> B))))
theorem-size     69
proof            (modus-ponens tm-102 tm-969 ((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> Am Bm) Bm)) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Bm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       281
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89051.        (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (C or A))) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> B))) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> B)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> B)))), M:tm-102, m:tm-969, u:((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> Am Bm) Bm)) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Bm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Bm)))))
================================================================
tm-name          tm-89052
in-theory        89052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     47
proof            (modus-ponens tm-95 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89052.        (((A -> B) -> (A -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-95, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89053
in-theory        89053
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-92 tm-969 ((Dm (-> (-> Am Bm) (-> (or Cm Am) Bm))) (A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       249
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89053.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((C or A) -> B))))), M:tm-92, m:tm-969, u:((Dm (-> (-> Am Bm) (-> (or Cm Am) Bm))) (A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-89054
in-theory        89054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     41
proof            (modus-ponens tm-84 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89054.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-84, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89055
in-theory        89055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     47
proof            (modus-ponens tm-83 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89055.        ((A -> (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-83, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89056
in-theory        89056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C))))) -> ((((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E -> ((B -> C) -> ((D or B) -> C))))))
theorem-size     71
proof            (modus-ponens tm-80 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89056.        ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C))))) -> ((((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E -> ((B -> C) -> ((D or B) -> C)))))), M:tm-80, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
================================================================
tm-name          tm-89057
in-theory        89057
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> ((D or B) -> C)) -> E) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))
theorem-size     45
proof            (modus-ponens tm-76 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89057.        (((not (not A)) -> A) and ((((B -> C) -> ((D or B) -> C)) -> E) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))), M:tm-76, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89058
in-theory        89058
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> ((C or A) -> B)) -> D))) or (((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     53
proof            (modus-ponens tm-73 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-89058.        (((not (not (((A -> B) -> ((C or A) -> B)) -> D))) or (((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-73, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89059
in-theory        89059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     51
proof            (modus-ponens tm-69 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89059.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-69, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89060
in-theory        89060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     53
proof            (modus-ponens tm-54 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89060.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-54, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89061
in-theory        89061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C)))))
theorem-size     75
proof            (modus-ponens tm-51 tm-969 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89061.        (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))), M:tm-51, m:tm-969, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-89062
in-theory        89062
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> ((((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C))))))
theorem-size     71
proof            (modus-ponens tm-48 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       229
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89062.        ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> ((((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))), M:tm-48, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
================================================================
tm-name          tm-89063
in-theory        89063
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     53
proof            (modus-ponens tm-47 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-89063.        (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-47, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89064
in-theory        89064
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((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     53
proof            (modus-ponens tm-46 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-89064.        ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((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-46, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89065
in-theory        89065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))))
theorem-size     63
proof            (modus-ponens tm-45 tm-969 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C))))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89065.        ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))), M:tm-45, m:tm-969, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C)))))
================================================================
tm-name          tm-89066
in-theory        89066
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((((B -> C) -> ((D or B) -> C)) -> A) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)))
theorem-size     41
proof            (modus-ponens tm-44 tm-969 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89066.        ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> ((((B -> C) -> ((D or B) -> C)) -> A) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))), M:tm-44, m:tm-969, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89067
in-theory        89067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     45
proof            (modus-ponens tm-42 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-89067.        ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-42, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89068
in-theory        89068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     45
proof            (modus-ponens tm-32 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-89068.        ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-32, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89069
in-theory        89069
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     51
proof            (modus-ponens tm-24 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> 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       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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89069.        ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-24, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89070
in-theory        89070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     47
proof            (modus-ponens tm-23 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-89070.        ((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-23, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89071
in-theory        89071
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     45
proof            (modus-ponens tm-22 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-89071.        (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-22, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89072
in-theory        89072
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     45
proof            (modus-ponens tm-21 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-89072.        (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-21, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89073
in-theory        89073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     53
proof            (modus-ponens tm-20 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89073.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> ((((D -> E) -> ((F or D) -> E)) -> G) and (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-20, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89074
in-theory        89074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     45
proof            (modus-ponens tm-19 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-89074.        ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> ((((C -> D) -> ((E or C) -> D)) -> F) and (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-19, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89075
in-theory        89075
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))) -> (not (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     53
proof            (modus-ponens tm-9 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-8)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89075.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))) -> (not (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-9, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89076
in-theory        89076
times-derived    1
----------------------------------------------------------------
theorem          ((((((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 ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> E))
theorem-size     71
proof            (modus-ponens tm-8 tm-969 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       205
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89076.        ((((((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 ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> E)), M:tm-8, m:tm-969, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-89077
in-theory        89077
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))
theorem-size     41
proof            (modus-ponens tm-7 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-8)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89077.        (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))), M:tm-7, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89078
in-theory        89078
times-derived    1
----------------------------------------------------------------
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))) or E)
theorem-size     41
proof            (modus-ponens tm-6 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-8)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89078.        (((((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))) or E), M:tm-6, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89079
in-theory        89079
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and A))
theorem-size     43
proof            (modus-ponens tm-5 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89079.        (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and A)), M:tm-5, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89080
in-theory        89080
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))
theorem-size     41
proof            (modus-ponens tm-1 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-8)
proof-size       167
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89080.        (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> ((((B -> C) -> ((D or B) -> C)) -> E) and (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))), M:tm-1, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-89081
in-theory        89081
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-930 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-89081.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-930, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89082
in-theory        89082
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-893 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-89082.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-893, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89083
in-theory        89083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     53
proof            (modus-ponens tm-855 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-89083.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-855, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89084
in-theory        89084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-808 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-89084.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-808, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89085
in-theory        89085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-757 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89085.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-757, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89086
in-theory        89086
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     61
proof            (modus-ponens tm-708 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-89086.        (((((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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-708, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89087
in-theory        89087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-665 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89087.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-665, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89088
in-theory        89088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-622 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89088.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-622, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89089
in-theory        89089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G)))
theorem-size     41
proof            (modus-ponens tm-609 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89089.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89090
in-theory        89090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-605 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89090.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-605, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89091
in-theory        89091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and ((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     77
proof            (modus-ponens tm-595 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89091.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and ((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-595, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89092
in-theory        89092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-550 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89092.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-550, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89093
in-theory        89093
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-540 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89093.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-540, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89094
in-theory        89094
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-530 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89094.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-530, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89095
in-theory        89095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-520 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89095.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-520, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89096
in-theory        89096
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-510 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89096.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-510, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89097
in-theory        89097
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-500 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89097.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-500, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89098
in-theory        89098
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-490 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89098.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-490, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89099
in-theory        89099
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-480 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89099.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-480, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89100
in-theory        89100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-469 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89100.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-469, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89101
in-theory        89101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H)))
theorem-size     41
proof            (modus-ponens tm-456 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89101.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89102
in-theory        89102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-453 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89102.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-453, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89103
in-theory        89103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and ((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     77
proof            (modus-ponens tm-443 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89103.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and ((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-443, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89104
in-theory        89104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-409 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89104.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-409, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89105
in-theory        89105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-400 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89105.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-400, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89106
in-theory        89106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-391 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89106.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-391, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89107
in-theory        89107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-382 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89107.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-382, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89108
in-theory        89108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-373 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89108.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-373, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89109
in-theory        89109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-364 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89109.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-364, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89110
in-theory        89110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-354 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89110.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-354, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89111
in-theory        89111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H))))
theorem-size     43
proof            (modus-ponens tm-341 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89111.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89112
in-theory        89112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) 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-338 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89112.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-338, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89113
in-theory        89113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and ((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     79
proof            (modus-ponens tm-327 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-89113.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and ((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-327, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89114
in-theory        89114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and ((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     77
proof            (modus-ponens tm-326 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89114.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and ((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-326, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89115
in-theory        89115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and ((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     77
proof            (modus-ponens tm-325 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89115.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and ((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-325, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89116
in-theory        89116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((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     85
proof            (modus-ponens tm-324 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-8)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89116.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((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-324, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89117
in-theory        89117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and ((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     77
proof            (modus-ponens tm-323 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89117.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and ((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-323, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89118
in-theory        89118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H))
theorem-size     41
proof            (modus-ponens tm-322 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89118.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89119
in-theory        89119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G))
theorem-size     41
proof            (modus-ponens tm-320 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89119.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89120
in-theory        89120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     49
proof            (modus-ponens tm-318 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89120.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89121
in-theory        89121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G)))
theorem-size     41
proof            (modus-ponens tm-315 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89121.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89122
in-theory        89122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or ((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     73
proof            (modus-ponens tm-311 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89122.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or ((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-311, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89123
in-theory        89123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G))
theorem-size     73
proof            (modus-ponens tm-310 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89123.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)), M:tm-310, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89124
in-theory        89124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G)))
theorem-size     75
proof            (modus-ponens tm-309 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89124.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G))), M:tm-309, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89125
in-theory        89125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     63
proof            (modus-ponens tm-308 tm-970 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89125.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-308, m:tm-970, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-89126
in-theory        89126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (A -> (B -> (A and B))))
theorem-size     43
proof            (modus-ponens tm-307 tm-970 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89126.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-970, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-89127
in-theory        89127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((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     73
proof            (modus-ponens tm-305 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89127.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((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-305, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89128
in-theory        89128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-303 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-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-89128.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-303, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89129
in-theory        89129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-270 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89129.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-270, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89130
in-theory        89130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-239 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89130.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-239, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89131
in-theory        89131
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     53
proof            (modus-ponens tm-210 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89131.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-210, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89132
in-theory        89132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-183 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89132.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-183, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89133
in-theory        89133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-157 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89133.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-157, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89134
in-theory        89134
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 F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-147 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89134.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-147, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89135
in-theory        89135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-134 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89135.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-134, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89136
in-theory        89136
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 F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-125 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89136.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-125, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89137
in-theory        89137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-113 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89137.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-113, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89138
in-theory        89138
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 F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     55
proof            (modus-ponens tm-105 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89138.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-105, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89139
in-theory        89139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and 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-95 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89139.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-95, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89140
in-theory        89140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-83 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89140.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-83, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89141
in-theory        89141
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((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     41
proof            (modus-ponens tm-76 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-10 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89141.        (((not (not A)) -> A) and ((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-76, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89142
in-theory        89142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     47
proof            (modus-ponens tm-69 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89142.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-69, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89143
in-theory        89143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-54 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-89143.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-54, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89144
in-theory        89144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-42 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89144.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-42, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89145
in-theory        89145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-32 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89145.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-32, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89146
in-theory        89146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and 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-23 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-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-89146.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-23, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89147
in-theory        89147
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-22 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89147.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-22, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89148
in-theory        89148
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-21 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89148.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-21, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89149
in-theory        89149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-20 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-20.           (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89149.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-20, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89150
in-theory        89150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-19 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89150.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-19, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89151
in-theory        89151
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-7 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       155
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89151.        (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-7, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89152
in-theory        89152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)
theorem-size     37
proof            (modus-ponens tm-6 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       155
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89152.        (((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G), M:tm-6, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89153
in-theory        89153
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))) and A))
theorem-size     39
proof            (modus-ponens tm-5 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-89153.        (A -> (((B -> (C -> (B and C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and A)), M:tm-5, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89154
in-theory        89154
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-1 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       155
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89154.        (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-1, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89155
in-theory        89155
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-930 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-89155.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-930, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89156
in-theory        89156
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-893 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-89156.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-893, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89157
in-theory        89157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-855 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-89157.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-855, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89158
in-theory        89158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-808 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-89158.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-808, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89159
in-theory        89159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-757 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89159.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-757, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89160
in-theory        89160
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     59
proof            (modus-ponens tm-708 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89160.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-708, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89161
in-theory        89161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-665 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89161.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-665, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89162
in-theory        89162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-622 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89162.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-622, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89163
in-theory        89163
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G)))
theorem-size     39
proof            (modus-ponens tm-609 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89163.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89164
in-theory        89164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-605 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89164.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-605, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89165
in-theory        89165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-595 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89165.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-595, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89166
in-theory        89166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-550 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89166.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-550, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89167
in-theory        89167
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-540 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89167.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-540, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89168
in-theory        89168
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-530 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89168.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-530, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89169
in-theory        89169
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-520 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89169.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-520, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89170
in-theory        89170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-510 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89170.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-510, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89171
in-theory        89171
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-500 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89171.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-500, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89172
in-theory        89172
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-490 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89172.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-490, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89173
in-theory        89173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-480 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89173.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-480, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89174
in-theory        89174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-469 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89174.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-469, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89175
in-theory        89175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H)))
theorem-size     39
proof            (modus-ponens tm-456 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89175.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89176
in-theory        89176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-453 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89176.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-453, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89177
in-theory        89177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-443 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89177.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-443, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89178
in-theory        89178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-409 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89178.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-409, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89179
in-theory        89179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-400 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89179.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-400, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89180
in-theory        89180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-391 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89180.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-391, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89181
in-theory        89181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-382 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89181.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-382, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89182
in-theory        89182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-373 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89182.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-373, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89183
in-theory        89183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-364 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89183.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-364, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89184
in-theory        89184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-354 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89184.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-354, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89185
in-theory        89185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H))))
theorem-size     41
proof            (modus-ponens tm-341 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89185.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89186
in-theory        89186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> 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-338 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89186.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-338, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89187
in-theory        89187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     75
proof            (modus-ponens tm-327 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89187.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-327, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89188
in-theory        89188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-326 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-89188.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-326, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89189
in-theory        89189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-325 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89189.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-325, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89190
in-theory        89190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     81
proof            (modus-ponens tm-324 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89190.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-324, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89191
in-theory        89191
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-323 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89191.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-323, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89192
in-theory        89192
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H))
theorem-size     39
proof            (modus-ponens tm-322 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89192.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89193
in-theory        89193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G))
theorem-size     39
proof            (modus-ponens tm-320 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89193.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89194
in-theory        89194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     47
proof            (modus-ponens tm-318 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89194.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89195
in-theory        89195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G)))
theorem-size     39
proof            (modus-ponens tm-315 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89195.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89196
in-theory        89196
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-311 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89196.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-311, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89197
in-theory        89197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G))
theorem-size     69
proof            (modus-ponens tm-310 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89197.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)), M:tm-310, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89198
in-theory        89198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G)))
theorem-size     71
proof            (modus-ponens tm-309 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89198.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G))), M:tm-309, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89199
in-theory        89199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     61
proof            (modus-ponens tm-308 tm-971 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-22.           (A -> (((B and C) -> C) and A)), 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-89199.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-308, m:tm-971, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-89200
in-theory        89200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((A and B) -> B))
theorem-size     39
proof            (modus-ponens tm-307 tm-971 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 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-3.            ((A and B) -> A), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89200.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((A and B) -> B)), M:tm-307, m:tm-971, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-89201
in-theory        89201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-305 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89201.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-305, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89202
in-theory        89202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-303 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89202.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-303, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89203
in-theory        89203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-270 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-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-89203.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-270, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89204
in-theory        89204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-239 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89204.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-239, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89205
in-theory        89205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-210 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89205.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-210, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89206
in-theory        89206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-183 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89206.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-183, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89207
in-theory        89207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-157 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89207.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-157, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89208
in-theory        89208
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-147 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89208.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-147, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89209
in-theory        89209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-134 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89209.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-134, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89210
in-theory        89210
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-125 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-8)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89210.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-125, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89211
in-theory        89211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-113 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89211.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-113, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89212
in-theory        89212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     53
proof            (modus-ponens tm-105 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89212.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-105, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89213
in-theory        89213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-95 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89213.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-95, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89214
in-theory        89214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-83 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89214.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-83, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89215
in-theory        89215
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) 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-76 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89215.        (((not (not A)) -> A) and (((B and C) -> C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-76, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89216
in-theory        89216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) 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-69 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89216.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-69, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89217
in-theory        89217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-54 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89217.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-54, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89218
in-theory        89218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-42 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-89218.        ((A -> (B or A)) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-42, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89219
in-theory        89219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-32 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-89219.        ((A -> (A or B)) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-32, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89220
in-theory        89220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-23 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-89220.        ((A -> (B -> (A and B))) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-23, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89221
in-theory        89221
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-22 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-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-89221.        (((A and B) -> B) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-22, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89222
in-theory        89222
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-21 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-89222.        (((A and B) -> A) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-21, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89223
in-theory        89223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-20 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89223.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-20, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89224
in-theory        89224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-19 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-89224.        ((A -> (B -> A)) and (((C and D) -> D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-19, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89225
in-theory        89225
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-7 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89225.        (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-7, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89226
in-theory        89226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)
theorem-size     35
proof            (modus-ponens tm-6 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89226.        ((((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G), M:tm-6, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89227
in-theory        89227
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))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89227.        (A -> ((((B and C) -> C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and A)), M:tm-5, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89228
in-theory        89228
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-1 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89228.        (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-1, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89229
in-theory        89229
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-930 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-89229.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-930, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89230
in-theory        89230
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-893 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-89230.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-893, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89231
in-theory        89231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-855 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-89231.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-855, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89232
in-theory        89232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-808 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-89232.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-808, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89233
in-theory        89233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-757 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89233.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-757, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89234
in-theory        89234
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     59
proof            (modus-ponens tm-708 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89234.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-708, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89235
in-theory        89235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-665 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89235.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-665, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89236
in-theory        89236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-622 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89236.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-622, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89237
in-theory        89237
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G)))
theorem-size     39
proof            (modus-ponens tm-609 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89237.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89238
in-theory        89238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-605 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89238.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-605, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89239
in-theory        89239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-595 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89239.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-595, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89240
in-theory        89240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-550 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89240.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-550, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89241
in-theory        89241
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-540 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89241.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-540, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89242
in-theory        89242
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-530 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89242.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-530, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89243
in-theory        89243
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-520 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89243.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-520, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89244
in-theory        89244
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-510 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89244.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-510, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89245
in-theory        89245
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-500 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89245.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-500, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89246
in-theory        89246
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-490 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89246.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-490, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89247
in-theory        89247
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-480 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89247.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-480, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89248
in-theory        89248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-469 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89248.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-469, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89249
in-theory        89249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H)))
theorem-size     39
proof            (modus-ponens tm-456 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89249.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89250
in-theory        89250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-453 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89250.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-453, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89251
in-theory        89251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-443 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89251.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-443, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89252
in-theory        89252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-409 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89252.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-409, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89253
in-theory        89253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-400 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89253.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-400, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89254
in-theory        89254
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-391 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89254.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-391, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89255
in-theory        89255
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-382 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89255.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-382, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89256
in-theory        89256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-373 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89256.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-373, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89257
in-theory        89257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-364 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89257.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-364, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89258
in-theory        89258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-354 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89258.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-354, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89259
in-theory        89259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H))))
theorem-size     41
proof            (modus-ponens tm-341 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89259.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89260
in-theory        89260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) 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-338 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89260.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-338, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89261
in-theory        89261
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     75
proof            (modus-ponens tm-327 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89261.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-327, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89262
in-theory        89262
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-326 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89262.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-326, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89263
in-theory        89263
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-325 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-89263.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-325, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89264
in-theory        89264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     81
proof            (modus-ponens tm-324 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89264.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-324, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89265
in-theory        89265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-323 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89265.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-323, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89266
in-theory        89266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H))
theorem-size     39
proof            (modus-ponens tm-322 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89266.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89267
in-theory        89267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G))
theorem-size     39
proof            (modus-ponens tm-320 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89267.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89268
in-theory        89268
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     47
proof            (modus-ponens tm-318 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89268.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89269
in-theory        89269
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G)))
theorem-size     39
proof            (modus-ponens tm-315 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89269.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89270
in-theory        89270
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-311 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89270.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-311, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89271
in-theory        89271
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G))
theorem-size     69
proof            (modus-ponens tm-310 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89271.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)), M:tm-310, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89272
in-theory        89272
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G)))
theorem-size     71
proof            (modus-ponens tm-309 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89272.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G))), M:tm-309, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89273
in-theory        89273
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     61
proof            (modus-ponens tm-308 tm-972 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-89273.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-308, m:tm-972, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-89274
in-theory        89274
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((A and B) -> A))
theorem-size     39
proof            (modus-ponens tm-307 tm-972 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89274.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((A and B) -> A)), M:tm-307, m:tm-972, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-89275
in-theory        89275
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-305 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89275.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-305, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89276
in-theory        89276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-303 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89276.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-303, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89277
in-theory        89277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-270 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89277.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-270, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89278
in-theory        89278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-239 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-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-89278.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-239, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89279
in-theory        89279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-210 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89279.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-210, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89280
in-theory        89280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-183 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89280.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-183, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89281
in-theory        89281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-157 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89281.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-157, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89282
in-theory        89282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-147 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-8)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89282.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-147, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89283
in-theory        89283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-134 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89283.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-134, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89284
in-theory        89284
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-125 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89284.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-125, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89285
in-theory        89285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-113 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89285.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-113, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89286
in-theory        89286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     53
proof            (modus-ponens tm-105 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89286.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-105, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89287
in-theory        89287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-95 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89287.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-95, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89288
in-theory        89288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-83 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89288.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-83, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89289
in-theory        89289
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> 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-76 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89289.        (((not (not A)) -> A) and (((B and C) -> B) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-76, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89290
in-theory        89290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) 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-69 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89290.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-69, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89291
in-theory        89291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-54 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89291.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-54, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89292
in-theory        89292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-42 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-89292.        ((A -> (B or A)) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-42, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89293
in-theory        89293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-32 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-89293.        ((A -> (A or B)) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-32, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89294
in-theory        89294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-23 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-89294.        ((A -> (B -> (A and B))) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-23, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89295
in-theory        89295
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-22 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-89295.        (((A and B) -> B) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-22, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89296
in-theory        89296
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-21 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-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-89296.        (((A and B) -> A) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-21, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89297
in-theory        89297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-20 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89297.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-20, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89298
in-theory        89298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-19 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-89298.        ((A -> (B -> A)) and (((C and D) -> C) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-19, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89299
in-theory        89299
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-7 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89299.        (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-7, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89300
in-theory        89300
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)
theorem-size     35
proof            (modus-ponens tm-6 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89300.        ((((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G), M:tm-6, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89301
in-theory        89301
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))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89301.        (A -> ((((B and C) -> B) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and A)), M:tm-5, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89302
in-theory        89302
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-1 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89302.        (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-1, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89303
in-theory        89303
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-930 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-89303.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-930, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89304
in-theory        89304
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-893 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-89304.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-893, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89305
in-theory        89305
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 ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     59
proof            (modus-ponens tm-855 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-89305.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-855, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89306
in-theory        89306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     53
proof            (modus-ponens tm-808 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-89306.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-808, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89307
in-theory        89307
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     53
proof            (modus-ponens tm-757 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89307.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-757, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89308
in-theory        89308
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 H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     67
proof            (modus-ponens tm-708 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       285
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89308.        (((((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 H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-708, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89309
in-theory        89309
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-665 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89309.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-665, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89310
in-theory        89310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-622 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89310.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-622, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89311
in-theory        89311
times-derived    1
----------------------------------------------------------------
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))) and (H -> (I or H)))
theorem-size     47
proof            (modus-ponens tm-609 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89311.        ((((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))) and (H -> (I or H))), M:tm-609, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89312
in-theory        89312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-605 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89312.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-605, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89313
in-theory        89313
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (I or H)) and (((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     89
proof            (modus-ponens tm-595 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89313.        ((((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))) and ((H -> (I or H)) and (((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-595, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89314
in-theory        89314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-550 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89314.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-550, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89315
in-theory        89315
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-540 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89315.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-540, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89316
in-theory        89316
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-530 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89316.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-530, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89317
in-theory        89317
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-520 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89317.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-520, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89318
in-theory        89318
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-510 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89318.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-510, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89319
in-theory        89319
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-500 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89319.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-500, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89320
in-theory        89320
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 H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-490 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89320.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-490, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89321
in-theory        89321
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-480 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89321.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-480, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89322
in-theory        89322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-469 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89322.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-469, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89323
in-theory        89323
times-derived    1
----------------------------------------------------------------
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))) and (H -> (H or I)))
theorem-size     47
proof            (modus-ponens tm-456 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89323.        ((((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))) and (H -> (H or I))), M:tm-456, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89324
in-theory        89324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-453 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89324.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-453, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89325
in-theory        89325
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (H or I)) and (((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     89
proof            (modus-ponens tm-443 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89325.        ((((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))) and ((H -> (H or I)) and (((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-443, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89326
in-theory        89326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-409 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89326.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-409, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89327
in-theory        89327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-400 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89327.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-400, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89328
in-theory        89328
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-391 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89328.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-391, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89329
in-theory        89329
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-382 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89329.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-382, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89330
in-theory        89330
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 H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-373 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89330.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-373, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89331
in-theory        89331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-364 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89331.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-364, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89332
in-theory        89332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-354 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89332.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-354, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89333
in-theory        89333
times-derived    1
----------------------------------------------------------------
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))) and (H -> (I -> (H and I))))
theorem-size     49
proof            (modus-ponens tm-341 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89333.        ((((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))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89334
in-theory        89334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-338 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89334.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-338, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89335
in-theory        89335
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (I -> (H and I))) and (((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     91
proof            (modus-ponens tm-327 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89335.        ((((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))) and ((H -> (I -> (H and I))) and (((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-327, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89336
in-theory        89336
times-derived    1
----------------------------------------------------------------
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))) and (((H and I) -> I) and (((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     89
proof            (modus-ponens tm-326 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89336.        ((((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))) and (((H and I) -> I) and (((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-326, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89337
in-theory        89337
times-derived    1
----------------------------------------------------------------
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))) and (((H and I) -> H) and (((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     89
proof            (modus-ponens tm-325 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89337.        ((((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))) and (((H and I) -> H) and (((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-325, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89338
in-theory        89338
times-derived    1
----------------------------------------------------------------
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))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((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     97
proof            (modus-ponens tm-324 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-89338.        ((((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))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((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-324, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89339
in-theory        89339
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (I -> H)) and (((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     89
proof            (modus-ponens tm-323 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89339.        ((((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))) and ((H -> (I -> H)) and (((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-323, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89340
in-theory        89340
times-derived    1
----------------------------------------------------------------
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))) and ((H and I) -> I))
theorem-size     47
proof            (modus-ponens tm-322 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89340.        ((((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))) and ((H and I) -> I)), M:tm-322, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89341
in-theory        89341
times-derived    1
----------------------------------------------------------------
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))) and ((H and I) -> H))
theorem-size     47
proof            (modus-ponens tm-320 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89341.        ((((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))) and ((H and I) -> H)), M:tm-320, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89342
in-theory        89342
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     55
proof            (modus-ponens tm-318 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89342.        ((((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))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89343
in-theory        89343
times-derived    1
----------------------------------------------------------------
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))) and (H -> (I -> H)))
theorem-size     47
proof            (modus-ponens tm-315 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89343.        ((((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))) and (H -> (I -> H))), M:tm-315, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89344
in-theory        89344
times-derived    1
----------------------------------------------------------------
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))) and (H or (((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     85
proof            (modus-ponens tm-311 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89344.        ((((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))) and (H or (((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-311, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89345
in-theory        89345
times-derived    1
----------------------------------------------------------------
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))) and ((((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))) or H))
theorem-size     85
proof            (modus-ponens tm-310 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89345.        ((((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))) and ((((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))) or H)), M:tm-310, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89346
in-theory        89346
times-derived    1
----------------------------------------------------------------
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))) and (H -> ((((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))) and H)))
theorem-size     87
proof            (modus-ponens tm-309 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-8)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89346.        ((((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))) and (H -> ((((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))) and H))), M:tm-309, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89347
in-theory        89347
times-derived    1
----------------------------------------------------------------
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))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     69
proof            (modus-ponens tm-308 tm-973 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89347.        ((((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))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-308, m:tm-973, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))
================================================================
tm-name          tm-89348
in-theory        89348
times-derived    1
----------------------------------------------------------------
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))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     55
proof            (modus-ponens tm-307 tm-973 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89348.        ((((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))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-973, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))
================================================================
tm-name          tm-89349
in-theory        89349
times-derived    1
----------------------------------------------------------------
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))) and (H -> (((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     85
proof            (modus-ponens tm-305 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89349.        ((((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))) and (H -> (((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-305, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89350
in-theory        89350
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     53
proof            (modus-ponens tm-303 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89350.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-303, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89351
in-theory        89351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-270 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89351.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-270, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89352
in-theory        89352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-239 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89352.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-239, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89353
in-theory        89353
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 H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     59
proof            (modus-ponens tm-210 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-89353.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-210, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89354
in-theory        89354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-183 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89354.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-183, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89355
in-theory        89355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-157 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89355.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-157, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89356
in-theory        89356
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     57
proof            (modus-ponens tm-147 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89356.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-147, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89357
in-theory        89357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-134 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89357.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-134, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89358
in-theory        89358
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     57
proof            (modus-ponens tm-125 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89358.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-125, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89359
in-theory        89359
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 H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-113 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89359.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-113, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89360
in-theory        89360
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     61
proof            (modus-ponens tm-105 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89360.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-105, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89361
in-theory        89361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-95 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89361.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-95, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89362
in-theory        89362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-83 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89362.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-83, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89363
in-theory        89363
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((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     47
proof            (modus-ponens tm-76 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89363.        (((not (not A)) -> A) and (((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-76, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89364
in-theory        89364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     53
proof            (modus-ponens tm-69 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89364.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-69, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89365
in-theory        89365
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-54 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89365.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-54, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89366
in-theory        89366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-42 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-42.           (A -> ((B -> (C or B)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89366.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-42, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89367
in-theory        89367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-32 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-32.           (A -> ((B -> (B or C)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89367.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-32, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89368
in-theory        89368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-23 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89368.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-23, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89369
in-theory        89369
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-22 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89369.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-22, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89370
in-theory        89370
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-21 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89370.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-21, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89371
in-theory        89371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-20 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-89371.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-20, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89372
in-theory        89372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-19 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-19.           (A -> ((B -> (C -> B)) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89372.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-19, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89373
in-theory        89373
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-7 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89373.        (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-7, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89374
in-theory        89374
times-derived    1
----------------------------------------------------------------
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))) or H)
theorem-size     43
proof            (modus-ponens tm-6 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-8)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89374.        ((((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))) or H), M:tm-6, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89375
in-theory        89375
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))) and A))
theorem-size     45
proof            (modus-ponens tm-5 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       183
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-89375.        (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))) and A)), M:tm-5, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89376
in-theory        89376
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-1 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-8)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89376.        (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-1, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-89377
in-theory        89377
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-930 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-89377.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-930, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89378
in-theory        89378
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-893 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-89378.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-893, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89379
in-theory        89379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-855 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-89379.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-855, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89380
in-theory        89380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-808 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-89380.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-808, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89381
in-theory        89381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-757 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89381.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-757, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89382
in-theory        89382
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 G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     59
proof            (modus-ponens tm-708 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89382.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-708, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89383
in-theory        89383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-665 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89383.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-665, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89384
in-theory        89384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-622 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89384.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-622, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89385
in-theory        89385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G)))
theorem-size     39
proof            (modus-ponens tm-609 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89385.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89386
in-theory        89386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-605 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89386.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-605, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89387
in-theory        89387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-595 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89387.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H or G)) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-595, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89388
in-theory        89388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-550 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89388.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-550, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89389
in-theory        89389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-540 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89389.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-540, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89390
in-theory        89390
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-530 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89390.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-530, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89391
in-theory        89391
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-520 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89391.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-520, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89392
in-theory        89392
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-510 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89392.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-510, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89393
in-theory        89393
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-500 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89393.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-500, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89394
in-theory        89394
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-490 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89394.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-490, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89395
in-theory        89395
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-480 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89395.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-480, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89396
in-theory        89396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-469 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89396.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-469, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89397
in-theory        89397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H)))
theorem-size     39
proof            (modus-ponens tm-456 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89397.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89398
in-theory        89398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-453 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89398.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-453, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89399
in-theory        89399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-443 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89399.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (G or H)) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-443, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89400
in-theory        89400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-409 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89400.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-409, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89401
in-theory        89401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-400 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89401.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-400, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89402
in-theory        89402
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-391 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89402.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-391, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89403
in-theory        89403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-382 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89403.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-382, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89404
in-theory        89404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-373 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89404.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-373, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89405
in-theory        89405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-364 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89405.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-364, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89406
in-theory        89406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-354 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89406.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-354, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89407
in-theory        89407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H))))
theorem-size     41
proof            (modus-ponens tm-341 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89407.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89408
in-theory        89408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) 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-338 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89408.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-338, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89409
in-theory        89409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     75
proof            (modus-ponens tm-327 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89409.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-327, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89410
in-theory        89410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-326 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89410.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> H) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-326, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89411
in-theory        89411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-325 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89411.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G and H) -> G) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-325, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89412
in-theory        89412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     81
proof            (modus-ponens tm-324 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89412.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-324, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89413
in-theory        89413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-323 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-89413.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> G)) and ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-323, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89414
in-theory        89414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H))
theorem-size     39
proof            (modus-ponens tm-322 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89414.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89415
in-theory        89415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G))
theorem-size     39
proof            (modus-ponens tm-320 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89415.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89416
in-theory        89416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     47
proof            (modus-ponens tm-318 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89416.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89417
in-theory        89417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G)))
theorem-size     39
proof            (modus-ponens tm-315 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89417.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89418
in-theory        89418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-311 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89418.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G or ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-311, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89419
in-theory        89419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G))
theorem-size     69
proof            (modus-ponens tm-310 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89419.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)), M:tm-310, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89420
in-theory        89420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G)))
theorem-size     71
proof            (modus-ponens tm-309 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89420.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and G))), M:tm-309, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89421
in-theory        89421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     61
proof            (modus-ponens tm-308 tm-974 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89421.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-308, m:tm-974, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-89422
in-theory        89422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (A -> (B -> A)))
theorem-size     39
proof            (modus-ponens tm-307 tm-974 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89422.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (A -> (B -> A))), M:tm-307, m:tm-974, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))
================================================================
tm-name          tm-89423
in-theory        89423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-305 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89423.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and (G -> ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))), M:tm-305, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89424
in-theory        89424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-303 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89424.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-303, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89425
in-theory        89425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-270 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89425.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-270, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89426
in-theory        89426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-239 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89426.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-239, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89427
in-theory        89427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-210 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89427.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-210, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89428
in-theory        89428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-183 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-89428.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-183, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89429
in-theory        89429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-157 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89429.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-157, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89430
in-theory        89430
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-147 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89430.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-147, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89431
in-theory        89431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-134 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89431.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-134, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89432
in-theory        89432
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-125 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89432.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-125, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89433
in-theory        89433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-113 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89433.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-113, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89434
in-theory        89434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     53
proof            (modus-ponens tm-105 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89434.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-105, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89435
in-theory        89435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-95 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89435.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-95, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89436
in-theory        89436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-83 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89436.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-83, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89437
in-theory        89437
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> 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-76 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89437.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-76, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89438
in-theory        89438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) 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-69 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89438.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-69, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89439
in-theory        89439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-54 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89439.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-54, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89440
in-theory        89440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-42 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-89440.        ((A -> (B or A)) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-42, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89441
in-theory        89441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-32 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-89441.        ((A -> (A or B)) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-32, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89442
in-theory        89442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-23 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-89442.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-23, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89443
in-theory        89443
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-22 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-89443.        (((A and B) -> B) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-22, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89444
in-theory        89444
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-21 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-89444.        (((A and B) -> A) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-21, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89445
in-theory        89445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-20 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-89445.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-20, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89446
in-theory        89446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-19 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-89446.        ((A -> (B -> A)) and ((C -> (D -> C)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-19, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89447
in-theory        89447
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-7 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89447.        (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-7, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89448
in-theory        89448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G)
theorem-size     35
proof            (modus-ponens tm-6 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89448.        (((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) or G), M:tm-6, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89449
in-theory        89449
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))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89449.        (A -> (((B -> (C -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and A)), M:tm-5, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89450
in-theory        89450
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-1 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       147
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89450.        (A -> ((B -> (C -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-1, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-89451
in-theory        89451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> ((A -> B) -> ((C or A) -> B))))
theorem-size     21
proof            (modus-ponens tm-975 tm-1 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> A B) (-> (or C A) B))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89451.        (((A -> B) -> ((C or A) -> B)) -> (D -> ((A -> B) -> ((C or A) -> B)))), M:tm-975, m:tm-1, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-89452
in-theory        89452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B)))
theorem-size     23
proof            (modus-ponens tm-975 tm-2 ((Am (-> A Cm)) (Bm (or C A)) (B Cm) (D (-> (-> (-> A Cm) (or C A)) (-> (-> A Cm) Cm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89452.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B))), M:tm-975, 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-89453
in-theory        89453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (((A -> B) -> ((C or A) -> B)) and D)))
theorem-size     23
proof            (modus-ponens tm-975 tm-5 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> A B) (-> (or C A) B)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-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-5.            (A -> (B -> (A and B))), axiom
tm-89453.        (((A -> B) -> ((C or A) -> B)) -> (D -> (((A -> B) -> ((C or A) -> B)) and D))), M:tm-975, m:tm-5, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> A B) (-> (or C A) B)) Bm))))
================================================================
tm-name          tm-89454
in-theory        89454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) or D))
theorem-size     21
proof            (modus-ponens tm-975 tm-6 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> A B) (-> (or C A) B)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-89454.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) or D)), M:tm-975, m:tm-6, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> A B) (-> (or C A) B)) Bm)))
================================================================
tm-name          tm-89455
in-theory        89455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D or ((A -> B) -> ((C or A) -> B))))
theorem-size     21
proof            (modus-ponens tm-975 tm-7 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-89455.        (((A -> B) -> ((C or A) -> B)) -> (D or ((A -> B) -> ((C or A) -> B)))), M:tm-975, m:tm-7, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-89456
in-theory        89456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D)))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 tm-8)
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-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-89456.        (((A -> B) -> ((C or A) -> B)) -> ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D))), M:tm-975, 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-89457
in-theory        89457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B))))
theorem-size     25
proof            (modus-ponens tm-975 tm-9 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> (-> A B) (not (-> (or C A) B))) (not (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-89457.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B)))), M:tm-975, 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-89458
in-theory        89458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-975 tm-11 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 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-12.           ((A -> B) -> (A -> A)), M: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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-89458.        (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> D))), M:tm-975, m:tm-11, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-89459
in-theory        89459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (A -> B)))
theorem-size     17
proof            (modus-ponens tm-975 tm-12 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> A B)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89459.        (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (A -> B))), M:tm-975, m:tm-12, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> A B))))
================================================================
tm-name          tm-89460
in-theory        89460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-975 tm-14 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-89460.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-975, m:tm-14, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-89461
in-theory        89461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-975 tm-16 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-89461.        (((A -> B) -> ((C or A) -> B)) -> ((D and E) -> D)), M:tm-975, m:tm-16, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-89462
in-theory        89462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-975 tm-18 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Cm))))
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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-89462.        (((A -> B) -> ((C or A) -> B)) -> ((D and E) -> E)), M:tm-975, m:tm-18, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-89463
in-theory        89463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-975 tm-19 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 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-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-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-89463.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89464
in-theory        89464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89464.        (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89465
in-theory        89465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D and E) -> D) and ((A -> B) -> ((C or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-975 tm-21 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-89465.        (((A -> B) -> ((C or A) -> B)) -> (((D and E) -> D) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89466
in-theory        89466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D and E) -> E) and ((A -> B) -> ((C or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-975 tm-22 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-89466.        (((A -> B) -> ((C or A) -> B)) -> (((D and E) -> E) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89467
in-theory        89467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-89467.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89468
in-theory        89468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((A -> B) and ((C or A) -> B))))
theorem-size     23
proof            (modus-ponens tm-975 tm-24 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (and (-> A B) (-> (or C A) B))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-89468.        (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((A -> B) and ((C or A) -> B)))), M:tm-975, 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-89469
in-theory        89469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-975 tm-25 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-89469.        (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (D and E)))), M:tm-975, m:tm-25, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-89470
in-theory        89470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-975 tm-32 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-89470.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89471
in-theory        89471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-975 tm-33 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-89471.        (((A -> B) -> ((C or A) -> B)) -> (D -> (D or E))), M:tm-975, m:tm-33, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-89472
in-theory        89472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-975 tm-42 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-89472.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89473
in-theory        89473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-975 tm-43 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-89473.        (((A -> B) -> ((C or A) -> B)) -> (D -> (E or D))), M:tm-975, m:tm-43, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-89474
in-theory        89474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((B or (A -> B)) -> ((C or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-975 tm-44 ((A Am) (B Bm) (Cm (-> (or C Am) Bm)) (D (-> (or Bm (-> Am Bm)) (-> (or C Am) Bm)))))
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-12.           ((A -> B) -> (A -> A)), M: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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-89474.        (((A -> B) -> ((C or A) -> B)) -> ((B or (A -> B)) -> ((C or A) -> B))), M:tm-975, 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-89475
in-theory        89475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-975 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-2 tm-1 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-89475.        ((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (A -> B)) -> (A -> C)))), M:tm-975, 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-89476
in-theory        89476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-89476.        (((A -> B) -> ((C or A) -> B)) -> ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B))), M:tm-975, 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-89477
in-theory        89477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-89477.        (((A -> B) -> ((C or A) -> B)) -> (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B))), M:tm-975, 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-89478
in-theory        89478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or A) -> (B and A))) -> ((B or (A -> (B and A))) -> ((C or A) -> (B and A))))
theorem-size     29
proof            (modus-ponens tm-975 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-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-12.           ((A -> B) -> (A -> A)), M: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-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-89478.        (((A -> (B and A)) -> ((C or A) -> (B and A))) -> ((B or (A -> (B and A))) -> ((C or A) -> (B and A)))), M:tm-975, 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-89479
in-theory        89479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B))))
theorem-size     47
proof            (modus-ponens tm-975 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-2 tm-1 tm-8)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89479.        ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B)))), M:tm-975, 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-89480
in-theory        89480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89480.        (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89481
in-theory        89481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> ((B or A) -> (B or A))) -> ((A -> (B or A)) -> ((A or (B or A)) -> (B or A))))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 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-12.           ((A -> B) -> (A -> A)), M: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-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-89481.        (((A -> (B or A)) -> ((B or A) -> (B or A))) -> ((A -> (B or A)) -> ((A or (B or A)) -> (B or A)))), M:tm-975, 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-89482
in-theory        89482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-975 tm-56 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89482.        (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-975, m:tm-56, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-89483
in-theory        89483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> ((C or (A -> (not B))) -> (not A))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (A -> (not B))) -> (not A))))
theorem-size     39
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-9)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89483.        ((((A -> (not B)) -> (not A)) -> ((C or (A -> (not B))) -> (not A))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (A -> (not B))) -> (not A)))), M:tm-975, 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-89484
in-theory        89484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     31
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-89484.        (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89485
in-theory        89485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-975 tm-71 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89485.        (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-975, m:tm-71, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-89486
in-theory        89486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((not (not (A -> B))) or (A -> B)) -> ((C or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-89486.        (((A -> B) -> ((C or A) -> B)) -> (((not (not (A -> B))) or (A -> B)) -> ((C or A) -> B))), M:tm-975, 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-89487
in-theory        89487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((not (not D)) -> D) and ((A -> B) -> ((C or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-975 tm-76 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-89487.        (((A -> B) -> ((C or A) -> B)) -> (((not (not D)) -> D) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89488
in-theory        89488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-975 tm-78 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-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-89488.        (((A -> B) -> ((C or A) -> B)) -> ((not (not D)) -> D)), M:tm-975, m:tm-78, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-89489
in-theory        89489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> ((C or A) -> (B -> A))) -> ((D or (A -> (B -> A))) -> ((C or A) -> (B -> A))))
theorem-size     29
proof            (modus-ponens tm-975 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-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-12.           ((A -> B) -> (A -> A)), M: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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-89489.        (((A -> (B -> A)) -> ((C or A) -> (B -> A))) -> ((D or (A -> (B -> A))) -> ((C or A) -> (B -> A)))), M:tm-975, 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-89490
in-theory        89490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 tm-83 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89490.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89491
in-theory        89491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D -> ((C or A) -> B))))
theorem-size     21
proof            (modus-ponens tm-975 tm-84 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (-> (or C A) B))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-89491.        (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D -> ((C or A) -> B)))), M:tm-975, m:tm-84, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (-> (or C A) B)))))
================================================================
tm-name          tm-89492
in-theory        89492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-975 tm-85 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89492.        (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F -> E)))), M:tm-975, m:tm-85, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-89493
in-theory        89493
times-derived    4
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B)))
theorem-size     19
proof            (modus-ponens tm-975 tm-86 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> A B) (-> (or C A) B)))))
axioms-used      (tm-2 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-89493.        (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B))), M:tm-975, m:tm-86, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> A B) (-> (or C A) B))))
================================================================
tm-name          tm-89494
in-theory        89494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> ((B or A) -> A)) -> (((A -> C) or (A -> A)) -> ((B or A) -> A)))
theorem-size     23
proof            (modus-ponens tm-975 tm-92 ((A Am) (B Am) (Bm (-> (or C Am) Am)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> (or C Am) 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-12.           ((A -> B) -> (A -> A)), M: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-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-89494.        (((A -> A) -> ((B or A) -> A)) -> (((A -> C) or (A -> A)) -> ((B or A) -> A))), M:tm-975, 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-89495
in-theory        89495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (D -> D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 tm-95 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> (or C A) B))))))
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-12.           ((A -> B) -> (A -> A)), M: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-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-89495.        (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (D -> D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89496
in-theory        89496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-975 tm-97 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-89496.        (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (D -> D))), M:tm-975, m:tm-97, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-89497
in-theory        89497
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> ((D or (A -> (B -> C))) -> (A -> C))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (A -> (B -> C))) -> (A -> C))))
theorem-size     53
proof            (modus-ponens tm-975 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-2 tm-1 tm-8)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-89497.        ((((A -> (B -> C)) -> (A -> C)) -> ((D or (A -> (B -> C))) -> (A -> C))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (A -> (B -> C))) -> (A -> C)))), M:tm-975, 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-89498
in-theory        89498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     39
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-89498.        (((A -> B) -> ((C or A) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89499
in-theory        89499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-975 tm-107 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-13.           (((A -> (B -> C)) -> (A -> 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-89499.        (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-975, 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-89500
in-theory        89500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-975 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-2 tm-1 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-14.           (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-89500.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((D or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-975, 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-89501
in-theory        89501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89501.        (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89502
in-theory        89502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((D or A) -> (B -> C))) -> ((A -> (B -> C)) -> (((D or A) -> B) -> ((D or A) -> C))))
theorem-size     31
proof            (modus-ponens tm-975 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-2 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-14.           (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-89502.        (((A -> (B -> C)) -> ((D or A) -> (B -> C))) -> ((A -> (B -> C)) -> (((D or A) -> B) -> ((D or A) -> C)))), M:tm-975, 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-89503
in-theory        89503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-975 tm-115 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-14.           (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-89503.        (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-975, m:tm-115, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-89504
in-theory        89504
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> ((D or ((A -> B) and C)) -> B)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((A -> B) and C)) -> B)))
theorem-size     43
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-3)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-89504.        (((((A -> B) and C) -> B) -> ((D or ((A -> B) and C)) -> B)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((A -> B) and C)) -> B))), M:tm-975, 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-89505
in-theory        89505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89505.        (((A -> B) -> ((C or A) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89506
in-theory        89506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-975 tm-127 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-89506.        (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-975, 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-89507
in-theory        89507
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> ((C or (A and B)) -> A)) -> ((D or ((A and B) -> A)) -> ((C or (A and B)) -> A)))
theorem-size     29
proof            (modus-ponens tm-975 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-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-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A 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-89507.        ((((A and B) -> A) -> ((C or (A and B)) -> A)) -> ((D or ((A and B) -> A)) -> ((C or (A and B)) -> A))), M:tm-975, 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-89508
in-theory        89508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-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-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-89508.        (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89509
in-theory        89509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-975 tm-136 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A 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-89509.        (((A -> B) -> ((C or A) -> B)) -> (D -> ((E and F) -> E))), M:tm-975, m:tm-136, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-89510
in-theory        89510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> ((D or (A and (B -> C))) -> C)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (A and (B -> C))) -> C)))
theorem-size     43
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-4)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-89510.        ((((A and (B -> C)) -> C) -> ((D or (A and (B -> C))) -> C)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (A and (B -> C))) -> C))), M:tm-975, 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-89511
in-theory        89511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89511.        (((A -> B) -> ((C or A) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89512
in-theory        89512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-975 tm-149 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-89512.        (((A -> B) -> ((C or A) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-975, 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-89513
in-theory        89513
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> ((C or (A and B)) -> B)) -> ((D or ((A and B) -> B)) -> ((C or (A and B)) -> B)))
theorem-size     29
proof            (modus-ponens tm-975 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-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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A 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-89513.        ((((A and B) -> B) -> ((C or (A and B)) -> B)) -> ((D or ((A and B) -> B)) -> ((C or (A and B)) -> B))), M:tm-975, 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-89514
in-theory        89514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-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-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-89514.        (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89515
in-theory        89515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-975 tm-159 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A 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-89515.        (((A -> B) -> ((C or A) -> B)) -> (D -> ((E and F) -> F))), M:tm-975, m:tm-159, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-89516
in-theory        89516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-975 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-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-12.           ((A -> B) -> (A -> A)), M: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-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-89516.        (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89517
in-theory        89517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-975 tm-184 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm Cm)) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89517.        (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> E)) and D))), M:tm-975, m:tm-184, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-89518
in-theory        89518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-89518.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89519
in-theory        89519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-975 tm-211 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-89519.        (((A -> B) -> ((C or A) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-975, 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-89520
in-theory        89520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-89520.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89521
in-theory        89521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-975 tm-240 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-89521.        (((A -> B) -> ((C or A) -> B)) -> (D -> (((E and F) -> E) and D))), M:tm-975, m:tm-240, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-89522
in-theory        89522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-89522.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89523
in-theory        89523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-975 tm-271 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-89523.        (((A -> B) -> ((C or A) -> B)) -> (D -> (((E and F) -> F) and D))), M:tm-975, m:tm-271, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-89524
in-theory        89524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     31
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-89524.        (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89525
in-theory        89525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-975 tm-304 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
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-89525.        (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-975, m:tm-304, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-89526
in-theory        89526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> ((A -> B) -> ((C or A) -> B)))))
theorem-size     31
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 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-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-5.            (A -> (B -> (A and B))), axiom
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-89526.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> ((A -> B) -> ((C or A) -> B))))), M:tm-975, 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-89527
in-theory        89527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (C or A)) -> ((A -> B) -> B))))
theorem-size     33
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-89527.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (C or A)) -> ((A -> B) -> B)))), M:tm-975, 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-89528
in-theory        89528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (((A -> B) -> ((C or A) -> B)) and D))))
theorem-size     33
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-89528.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (((A -> B) -> ((C or A) -> B)) and D)))), M:tm-975, 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-89529
in-theory        89529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> ((C or A) -> B)) or D)))
theorem-size     31
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-89529.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> ((C or A) -> B)) or D))), M:tm-975, 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-89530
in-theory        89530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D or ((A -> B) -> ((C or A) -> B)))))
theorem-size     31
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-89530.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D or ((A -> B) -> ((C or A) -> B))))), M:tm-975, 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-89531
in-theory        89531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D))))
theorem-size     39
proof            (modus-ponens tm-975 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-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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
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-89531.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((((C or A) -> B) -> D) -> (((A -> B) or ((C or A) -> B)) -> D)))), M:tm-975, 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-89532
in-theory        89532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B)))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-9)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-89532.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((A -> B) -> (not ((C or A) -> B))) -> (not (A -> B))))), M:tm-975, 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-89533
in-theory        89533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-975 tm-315 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
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-89533.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> D)))), M:tm-975, 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-89534
in-theory        89534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> (A -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
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-89534.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> (A -> B)))), M:tm-975, 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-89535
in-theory        89535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       213
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
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-89535.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-975, 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-89536
in-theory        89536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> D)))
theorem-size     25
proof            (modus-ponens tm-975 tm-320 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-89536.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> D))), M:tm-975, 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-89537
in-theory        89537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> E)))
theorem-size     25
proof            (modus-ponens tm-975 tm-322 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-89537.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D and E) -> E))), M:tm-975, 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-89538
in-theory        89538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
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-89538.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-975, 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-89539
in-theory        89539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     43
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       229
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-89539.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((C or A) -> B))))), M:tm-975, 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-89540
in-theory        89540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> D) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     35
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-89540.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> D) and ((A -> B) -> ((C or A) -> B))))), M:tm-975, 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-89541
in-theory        89541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> E) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-89541.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and E) -> E) and ((A -> B) -> ((C or A) -> B))))), M:tm-975, 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-89542
in-theory        89542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-89542.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> ((C or A) -> B))))), M:tm-975, 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-89543
in-theory        89543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> ((A -> B) and ((C or A) -> B)))))
theorem-size     33
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-89543.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((A -> B) -> ((A -> B) and ((C or A) -> B))))), M:tm-975, 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-89544
in-theory        89544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> ((C or A) -> (A and B))) -> (((A -> B) or (A -> (A and B))) -> ((C or A) -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
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-89544.        (((A -> (A and B)) -> ((C or A) -> (A and B))) -> (((A -> B) or (A -> (A and B))) -> ((C or A) -> (A and B)))), M:tm-975, 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-89545
in-theory        89545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-89545.        (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89546
in-theory        89546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-975 tm-340 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
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-89546.        (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (D -> (D and E)))), M:tm-975, m:tm-340, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-89547
in-theory        89547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 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-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-5.            (A -> (B -> (A and B))), axiom
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-89547.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E -> (D and E))))), M:tm-975, 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-89548
in-theory        89548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> ((C or A) -> (B -> (A and B)))) -> ((D or (A -> (B -> (A and B)))) -> ((C or A) -> (B -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and 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-89548.        (((A -> (B -> (A and B))) -> ((C or A) -> (B -> (A and B)))) -> ((D or (A -> (B -> (A and B)))) -> ((C or A) -> (B -> (A and B))))), M:tm-975, 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-89549
in-theory        89549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-975 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-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-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and 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-89549.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89550
in-theory        89550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D -> (((C or A) -> B) and D))))
theorem-size     23
proof            (modus-ponens tm-975 tm-355 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (and (-> (or C A) B) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-89550.        (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D -> (((C or A) -> B) and D)))), M:tm-975, 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-89551
in-theory        89551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-975 tm-356 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and 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-89551.        (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F -> (E and F))))), M:tm-975, m:tm-356, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-89552
in-theory        89552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> D)) or F) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89552.        (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> D)) or F) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89553
in-theory        89553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-975 tm-365 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (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-89553.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> D)) or F)), M:tm-975, m:tm-365, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-89554
in-theory        89554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89554.        (((A -> B) -> ((C or A) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89555
in-theory        89555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-975 tm-374 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (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-89555.        (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-975, m:tm-374, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-89556
in-theory        89556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D and E) -> D) or F) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-6 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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-89556.        (((A -> B) -> ((C or A) -> B)) -> ((((D and E) -> D) or F) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89557
in-theory        89557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-975 tm-383 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-89557.        (((A -> B) -> ((C or A) -> B)) -> (((D and E) -> D) or F)), M:tm-975, m:tm-383, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-89558
in-theory        89558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D and E) -> E) or F) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-6 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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-89558.        (((A -> B) -> ((C or A) -> B)) -> ((((D and E) -> E) or F) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89559
in-theory        89559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-975 tm-392 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-89559.        (((A -> B) -> ((C or A) -> B)) -> (((D and E) -> E) or F)), M:tm-975, m:tm-392, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-89560
in-theory        89560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> ((C or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-89560.        (((A -> B) -> ((C or A) -> B)) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89561
in-theory        89561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-975 tm-401 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89561.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (D and E))) or F)), M:tm-975, m:tm-401, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-89562
in-theory        89562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> (D or E)) or F) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-89562.        (((A -> B) -> ((C or A) -> B)) -> (((D -> (D or E)) or F) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89563
in-theory        89563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-975 tm-410 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A 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-89563.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (D or E)) or F)), M:tm-975, m:tm-410, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-89564
in-theory        89564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-89564.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> ((C or A) -> B))))), M:tm-975, 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-89565
in-theory        89565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-89565.        (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89566
in-theory        89566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-975 tm-454 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-89566.        (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (E or F)) and D))), M:tm-975, m:tm-454, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-89567
in-theory        89567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (D or E))))
theorem-size     25
proof            (modus-ponens tm-975 tm-456 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-89567.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (D or E)))), M:tm-975, 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-89568
in-theory        89568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A -> B) or A) -> B)) -> ((A -> B) -> B))
theorem-size     17
proof            (modus-ponens tm-975 tm-464 ((Am (-> Bm Cm)) (C (-> Bm Cm)) (A Bm) (B Cm) (D (-> (-> Bm Cm) Cm))))
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-13.           (((A -> (B -> C)) -> (A -> 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-89568.        (((A -> B) -> (((A -> B) or A) -> B)) -> ((A -> B) -> B)), M:tm-975, m:tm-464, u:((Am (-> Bm Cm)) (C (-> Bm Cm)) (A Bm) (B Cm) (D (-> (-> Bm Cm) Cm)))
================================================================
tm-name          tm-89569
in-theory        89569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> ((C or A) -> (A or B))) -> ((D or (A -> (A or B))) -> ((C or A) -> (A or B))))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-6)
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-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-6.            (A -> (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-89569.        (((A -> (A or B)) -> ((C or A) -> (A or B))) -> ((D or (A -> (A or B))) -> ((C or A) -> (A or B)))), M:tm-975, 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-89570
in-theory        89570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (E or F))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89570.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (E or F))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89571
in-theory        89571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (((C or A) -> B) or D)))
theorem-size     21
proof            (modus-ponens tm-975 tm-470 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or (-> (or C A) B) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-89571.        (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (((C or A) -> B) or D))), M:tm-975, m:tm-470, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or (-> (or C A) B) Cm))))
================================================================
tm-name          tm-89572
in-theory        89572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-975 tm-471 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (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-89572.        (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (E or F)))), M:tm-975, m:tm-471, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-89573
in-theory        89573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89573.        (((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F -> E))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89574
in-theory        89574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-975 tm-481 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (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-89574.        (((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F -> E)))), M:tm-975, m:tm-481, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-89575
in-theory        89575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89575.        (((A -> B) -> ((C or A) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89576
in-theory        89576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-975 tm-491 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-35.           (A 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-89576.        (((A -> B) -> ((C or A) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-975, m:tm-491, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-89577
in-theory        89577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D or ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-7 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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-89577.        (((A -> B) -> ((C or A) -> B)) -> ((D or ((E and F) -> E)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89578
in-theory        89578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-975 tm-501 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-89578.        (((A -> B) -> ((C or A) -> B)) -> (D or ((E and F) -> E))), M:tm-975, m:tm-501, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-89579
in-theory        89579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D or ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-7 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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-89579.        (((A -> B) -> ((C or A) -> B)) -> ((D or ((E and F) -> F)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89580
in-theory        89580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-975 tm-511 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-89580.        (((A -> B) -> ((C or A) -> B)) -> (D or ((E and F) -> F))), M:tm-975, m:tm-511, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-89581
in-theory        89581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-89581.        (((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89582
in-theory        89582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-975 tm-521 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89582.        (((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F -> (E and F))))), M:tm-975, m:tm-521, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-89583
in-theory        89583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (E or F))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-89583.        (((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (E or F))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89584
in-theory        89584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-975 tm-531 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A 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-89584.        (((A -> B) -> ((C or A) -> B)) -> (D or (E -> (E or F)))), M:tm-975, m:tm-531, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-89585
in-theory        89585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F or E))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-89585.        (((A -> B) -> ((C or A) -> B)) -> ((D or (E -> (F or E))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89586
in-theory        89586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-975 tm-541 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B 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-89586.        (((A -> B) -> ((C or A) -> B)) -> (D or (E -> (F or E)))), M:tm-975, m:tm-541, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-89587
in-theory        89587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> (E or D)) or F) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-89587.        (((A -> B) -> ((C or A) -> B)) -> (((D -> (E or D)) or F) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89588
in-theory        89588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-975 tm-551 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B 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-89588.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E or D)) or F)), M:tm-975, m:tm-551, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-89589
in-theory        89589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-89589.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> ((C or A) -> B))))), M:tm-975, 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-89590
in-theory        89590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-89590.        (((A -> B) -> ((C or A) -> B)) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89591
in-theory        89591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-975 tm-606 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-89591.        (((A -> B) -> ((C or A) -> B)) -> (D -> ((E -> (F or E)) and D))), M:tm-975, m:tm-606, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-89592
in-theory        89592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E or D))))
theorem-size     25
proof            (modus-ponens tm-975 tm-609 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       181
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-89592.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (D -> (E or D)))), M:tm-975, 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-89593
in-theory        89593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> ((C or A) -> (B or A))) -> ((D or (A -> (B or A))) -> ((C or A) -> (B or A))))
theorem-size     29
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-7)
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-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-7.            (A -> (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-89593.        (((A -> (B or A)) -> ((C or A) -> (B or A))) -> ((D or (A -> (B or A))) -> ((C or A) -> (B or A)))), M:tm-975, 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-89594
in-theory        89594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F or E))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89594.        (((A -> B) -> ((C or A) -> B)) -> ((D -> (E -> (F or E))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89595
in-theory        89595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D or ((C or A) -> B))))
theorem-size     21
proof            (modus-ponens tm-975 tm-623 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or Cm (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-89595.        (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (D or ((C or A) -> B)))), M:tm-975, m:tm-623, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or Cm (-> (or C A) B)))))
================================================================
tm-name          tm-89596
in-theory        89596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-975 tm-624 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (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-89596.        (((A -> B) -> ((C or A) -> B)) -> (D -> (E -> (F or E)))), M:tm-975, m:tm-624, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-89597
in-theory        89597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((B or (A -> B)) -> ((C or A) -> B))))
theorem-size     31
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       211
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
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-89597.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((B or (A -> B)) -> ((C or A) -> B)))), M:tm-975, 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-89598
in-theory        89598
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> ((D or (A or (B -> A))) -> C)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((D or (A or (B -> A))) -> C)))
theorem-size     41
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-89598.        ((((A or (B -> A)) -> C) -> ((D or (A or (B -> A))) -> C)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((D or (A or (B -> A))) -> C))), M:tm-975, 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-89599
in-theory        89599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-89599.        (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89600
in-theory        89600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-975 tm-667 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 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-12.           ((A -> B) -> (A -> A)), M: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-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-89600.        (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-975, m:tm-667, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-89601
in-theory        89601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> ((((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     59
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       275
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
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-89601.        ((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> ((((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-975, 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-89602
in-theory        89602
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8)
proof-size       231
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-89602.        ((((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C))) -> (((A -> B) -> (A -> C)) -> ((D or (A -> B)) -> (A -> C)))), M:tm-975, 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-89603
in-theory        89603
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) -> (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     77
proof            (modus-ponens tm-975 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-2 tm-1 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-89603.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> ((E 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)) -> ((E or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))), M:tm-975, 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-89604
in-theory        89604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     45
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-89604.        (((A -> B) -> ((C or A) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89605
in-theory        89605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-975 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-89605.        (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-975, 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-89606
in-theory        89606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-89606.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> ((C or A) -> B)))), M:tm-975, 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-89607
in-theory        89607
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> ((D or ((A and B) or A)) -> C)) -> (((A -> C) or (((A and B) or A) -> C)) -> ((D or ((A and B) or A)) -> C)))
theorem-size     39
proof            (modus-ponens tm-975 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-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-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-89607.        (((((A and B) or A) -> C) -> ((D or ((A and B) or A)) -> C)) -> (((A -> C) or (((A and B) or A) -> C)) -> ((D or ((A and B) or A)) -> C))), M:tm-975, 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-89608
in-theory        89608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     31
proof            (modus-ponens tm-975 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-2 tm-1 tm-8 tm-5 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-12.           ((A -> B) -> (A -> A)), M: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-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-89608.        (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, 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-89609
in-theory        89609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-975 tm-759 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-3.            ((A and B) -> A), axiom
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-89609.        (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-975, m:tm-759, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-89610
in-theory        89610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-975 tm-798 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (or (and Cm (-> A B)) (-> A B)) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-89610.        (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and (((D and (A -> B)) or (A -> B)) -> ((C or A) -> B)))), M:tm-975, m:tm-798, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (or (and Cm (-> A B)) (-> A B)) (-> (or C A) B)))))
================================================================
tm-name          tm-89611
in-theory        89611
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> ((D or ((A and B) or B)) -> C)) -> (((B -> C) or (((A and B) or B) -> C)) -> ((D or ((A and B) or B)) -> C)))
theorem-size     39
proof            (modus-ponens tm-975 tm-805 ((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or C (or (and Am Bm) Bm)) Cm)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or C (or (and Am Bm) Bm)) Cm)))))
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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A and B) -> B), axiom
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-89611.        (((((A and B) or B) -> C) -> ((D or ((A and B) or B)) -> C)) -> (((B -> C) or (((A and B) or B) -> C)) -> ((D or ((A and B) or B)) -> C))), M:tm-975, m:tm-805, u:((A (or (and Am Bm) Bm)) (B Cm) (Dm (-> (or C (or (and Am Bm) Bm)) Cm)) (D (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) (-> (or C (or (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-89612
in-theory        89612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     31
proof            (modus-ponens tm-975 tm-808 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-89612.        (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> (((F and D) or D) -> E)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, m:tm-808, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-89613
in-theory        89613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-975 tm-810 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 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-12.           ((A -> B) -> (A -> A)), M: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-4.            ((A and B) -> B), axiom
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-89613.        (((A -> B) -> ((C or A) -> B)) -> ((D -> E) -> (((F and D) or D) -> E))), M:tm-975, m:tm-810, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-89614
in-theory        89614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or A) -> (B and A))) -> (((A -> (B and A)) -> ((C or A) -> (B and A))) and ((B or (A -> (B and A))) -> ((C or A) -> (B and A)))))
theorem-size     43
proof            (modus-ponens tm-975 tm-844 ((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (and (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am))) (-> (or Bm (-> Am (and Bm Am))) (-> (or C Am) (and Bm Am)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       235
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-89614.        (((A -> (B and A)) -> ((C or A) -> (B and A))) -> (((A -> (B and A)) -> ((C or A) -> (B and A))) and ((B or (A -> (B and A))) -> ((C or A) -> (B and A))))), M:tm-975, m:tm-844, u:((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (and (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am))) (-> (or Bm (-> Am (and Bm Am))) (-> (or C Am) (and Bm Am))))))
================================================================
tm-name          tm-89615
in-theory        89615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or A) -> (B and A))) -> ((A -> (B and A)) -> ((C or A) -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-975 tm-850 ((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-89615.        (((A -> (B and A)) -> ((C or A) -> (B and A))) -> ((A -> (B and A)) -> ((C or A) -> (B and A)))), M:tm-975, m:tm-850, u:((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (-> (-> Am (and Bm Am)) (-> (or C Am) (and Bm Am)))))
================================================================
tm-name          tm-89616
in-theory        89616
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> ((D or (A or (B -> (A and B)))) -> C)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((D or (A or (B -> (A and B)))) -> C)))
theorem-size     51
proof            (modus-ponens tm-975 tm-852 ((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or C (or Am (-> Bm (and Am Bm)))) Cm)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or C (or Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-89616.        ((((A or (B -> (A and B))) -> C) -> ((D or (A or (B -> (A and B)))) -> C)) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> ((D or (A or (B -> (A and B)))) -> C))), M:tm-975, m:tm-852, u:((A (or Am (-> Bm (and Am Bm)))) (B Cm) (Dm (-> (or C (or Am (-> Bm (and Am Bm)))) Cm)) (D (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) (-> (or C (or Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-89617
in-theory        89617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-975 tm-855 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-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-89617.        (((A -> B) -> ((C or A) -> B)) -> ((((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, m:tm-855, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-89618
in-theory        89618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-975 tm-857 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-89618.        (((A -> B) -> ((C or A) -> B)) -> (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-975, m:tm-857, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-89619
in-theory        89619
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> ((D or (A or (A or B))) -> C)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (A or (A or B))) -> C)))
theorem-size     41
proof            (modus-ponens tm-975 tm-890 ((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or C (or Am (or Am Bm))) Cm)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or C (or Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-89619.        ((((A or (A or B)) -> C) -> ((D or (A or (A or B))) -> C)) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or (A or (A or B))) -> C))), M:tm-975, m:tm-890, u:((A (or Am (or Am Bm))) (B Cm) (Dm (-> (or C (or Am (or Am Bm))) Cm)) (D (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) (-> (or C (or Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-89620
in-theory        89620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-975 tm-893 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-89620.        (((A -> B) -> ((C or A) -> B)) -> ((((D or E) -> F) -> ((D or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, m:tm-893, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-89621
in-theory        89621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-975 tm-895 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 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-12.           ((A -> B) -> (A -> A)), M: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-6.            (A -> (A or B)), axiom
tm-49.           (((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-89621.        (((A -> B) -> ((C or A) -> B)) -> (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-975, m:tm-895, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-89622
in-theory        89622
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> ((D or (A or (B or A))) -> C)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((D or (A or (B or A))) -> C)))
theorem-size     41
proof            (modus-ponens tm-975 tm-927 ((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or C (or Am (or Bm Am))) Cm)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or C (or Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-89622.        ((((A or (B or A)) -> C) -> ((D or (A or (B or A))) -> C)) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> ((D or (A or (B or A))) -> C))), M:tm-975, m:tm-927, u:((A (or Am (or Bm Am))) (B Cm) (Dm (-> (or C (or Am (or Bm Am))) Cm)) (D (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) (-> (or C (or Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-89623
in-theory        89623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-975 tm-930 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-89623.        (((A -> B) -> ((C or A) -> B)) -> ((((D or E) -> F) -> ((E or (D or E)) -> F)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, m:tm-930, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-89624
in-theory        89624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-975 tm-932 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 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-12.           ((A -> B) -> (A -> A)), M: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-7.            (A -> (B or A)), axiom
tm-50.           (((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-89624.        (((A -> B) -> ((C or A) -> B)) -> (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-975, m:tm-932, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-89625
in-theory        89625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B)))))
theorem-size     69
proof            (modus-ponens tm-975 tm-969 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       291
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
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-89625.        ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or (A -> B)) -> ((C or A) -> B))))), M:tm-975, m:tm-969, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-89626
in-theory        89626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))))
theorem-size     43
proof            (modus-ponens tm-975 tm-975 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       245
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89626.        ((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))), M:tm-975, m:tm-975, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm)))))
================================================================
tm-name          tm-89627
in-theory        89627
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))) and (((D -> (A -> B)) or (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))))
theorem-size     93
proof            (modus-ponens tm-969 tm-975 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       315
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
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-89627.        (((((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))) and (((D -> (A -> B)) or (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> ((D or (A -> B)) -> ((C or A) -> B))))), M:tm-969, m:tm-975, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm)))))
================================================================
tm-name          tm-89628
in-theory        89628
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-930 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89628.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-930, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89629
in-theory        89629
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-893 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89629.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-893, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89630
in-theory        89630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     41
proof            (modus-ponens tm-855 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89630.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-855, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89631
in-theory        89631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))))
theorem-size     43
proof            (modus-ponens tm-850 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       221
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89631.        ((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))), M:tm-850, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-89632
in-theory        89632
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))) and ((D or (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))) -> (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))))
theorem-size     89
proof            (modus-ponens tm-844 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89632.        (((((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))) and ((D or (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B))))) -> (((A -> B) -> ((C or A) -> B)) -> (D and ((A -> B) -> ((C or A) -> B)))))), M:tm-844, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-89633
in-theory        89633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-808 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89633.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-808, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89634
in-theory        89634
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((E and (((A -> B) -> ((C or A) -> B)) -> D)) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     61
proof            (modus-ponens tm-798 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89634.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((E and (((A -> B) -> ((C or A) -> B)) -> D)) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-798, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89635
in-theory        89635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-757 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89635.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-757, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89636
in-theory        89636
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((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)) -> (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     61
proof            (modus-ponens tm-747 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89636.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((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)) -> (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-747, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89637
in-theory        89637
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) -> (((E -> F) -> ((G or E) -> F)) -> H)))
theorem-size     49
proof            (modus-ponens tm-708 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89637.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H))), M:tm-708, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89638
in-theory        89638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)))
theorem-size     31
proof            (modus-ponens tm-703 tm-975 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       227
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89638.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))), M:tm-703, m:tm-975, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-89639
in-theory        89639
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> (((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))) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))))
theorem-size     75
proof            (modus-ponens tm-697 tm-975 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89639.        (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> (((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))) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)))), M:tm-697, m:tm-975, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-89640
in-theory        89640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-665 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89640.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-665, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89641
in-theory        89641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((D or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     49
proof            (modus-ponens tm-654 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89641.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((D or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-654, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89642
in-theory        89642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (E or (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     25
proof            (modus-ponens tm-623 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
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-12.           ((A -> B) -> (A -> A)), M: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-89642.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (E or (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-623, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89643
in-theory        89643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-622 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89643.        ((A -> (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-622, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89644
in-theory        89644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C))))) -> (((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-619 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89644.        ((A or (((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C))))) -> (((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C))))), M:tm-619, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-89645
in-theory        89645
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (F or E)))
theorem-size     29
proof            (modus-ponens tm-609 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89645.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89646
in-theory        89646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-605 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89646.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-605, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89647
in-theory        89647
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (F or E)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     53
proof            (modus-ponens tm-595 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89647.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (F or E)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-595, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89648
in-theory        89648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-550 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89648.        (((A -> (B or A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-550, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89649
in-theory        89649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-540 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89649.        ((A or (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-540, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89650
in-theory        89650
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-530 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89650.        ((A or (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-530, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89651
in-theory        89651
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-520 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89651.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-520, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89652
in-theory        89652
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-510 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89652.        ((A or ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-510, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89653
in-theory        89653
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-500 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89653.        ((A or ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-500, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89654
in-theory        89654
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H)))
theorem-size     39
proof            (modus-ponens tm-490 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89654.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H))), M:tm-490, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89655
in-theory        89655
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-480 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
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-12.           ((A -> B) -> (A -> A)), M: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-89655.        ((A or (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-480, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89656
in-theory        89656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-470 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
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-12.           ((A -> B) -> (A -> A)), M: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-89656.        ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) or E)), M:tm-470, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89657
in-theory        89657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-469 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89657.        ((A -> (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-469, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89658
in-theory        89658
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E))) -> (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E)))
theorem-size     45
proof            (modus-ponens tm-466 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89658.        ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E))) -> (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E))), M:tm-466, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))))
================================================================
tm-name          tm-89659
in-theory        89659
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (E or F)))
theorem-size     29
proof            (modus-ponens tm-456 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89659.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89660
in-theory        89660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-453 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89660.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-453, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89661
in-theory        89661
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (E or F)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     53
proof            (modus-ponens tm-443 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89661.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (E or F)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-443, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89662
in-theory        89662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-409 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89662.        (((A -> (A or B)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-409, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89663
in-theory        89663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-400 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89663.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-400, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89664
in-theory        89664
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-391 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89664.        ((((A and B) -> B) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-391, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89665
in-theory        89665
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-382 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89665.        ((((A and B) -> A) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-382, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89666
in-theory        89666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H)))
theorem-size     39
proof            (modus-ponens tm-373 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89666.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H))), M:tm-373, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89667
in-theory        89667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-364 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
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-12.           ((A -> B) -> (A -> A)), M: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-89667.        (((A -> (B -> A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-364, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89668
in-theory        89668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> ((((A -> B) -> ((C or A) -> B)) -> D) and E)))
theorem-size     27
proof            (modus-ponens tm-355 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89668.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> ((((A -> B) -> ((C or A) -> B)) -> D) and E))), M:tm-355, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89669
in-theory        89669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-354 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-12.           ((A -> B) -> (A -> A)), M: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-89669.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-354, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89670
in-theory        89670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E)))) -> (((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E))))
theorem-size     49
proof            (modus-ponens tm-351 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89670.        ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E)))) -> (((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E)))), M:tm-351, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)))))
================================================================
tm-name          tm-89671
in-theory        89671
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (F -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-341 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89671.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89672
in-theory        89672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F)))
theorem-size     33
proof            (modus-ponens tm-338 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89672.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F))), M:tm-338, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89673
in-theory        89673
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))) -> (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and D)))
theorem-size     55
proof            (modus-ponens tm-335 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       217
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89673.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and D))) -> (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and D))), M:tm-335, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))))
================================================================
tm-name          tm-89674
in-theory        89674
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     59
proof            (modus-ponens tm-328 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
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-328.          ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89674.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-328, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89675
in-theory        89675
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     55
proof            (modus-ponens tm-327 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89675.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-327, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89676
in-theory        89676
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((E and F) -> F) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     53
proof            (modus-ponens tm-326 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89676.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((E and F) -> F) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-326, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89677
in-theory        89677
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((E and F) -> E) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     53
proof            (modus-ponens tm-325 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89677.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((E and F) -> E) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-325, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89678
in-theory        89678
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     61
proof            (modus-ponens tm-324 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89678.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-324, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89679
in-theory        89679
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (F -> E)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     53
proof            (modus-ponens tm-323 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89679.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (F -> E)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-323, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89680
in-theory        89680
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E and F) -> F))
theorem-size     29
proof            (modus-ponens tm-322 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89680.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89681
in-theory        89681
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E and F) -> E))
theorem-size     29
proof            (modus-ponens tm-320 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89681.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89682
in-theory        89682
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-318 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89682.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89683
in-theory        89683
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     47
proof            (modus-ponens tm-316 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89683.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((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-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89684
in-theory        89684
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (F -> E)))
theorem-size     29
proof            (modus-ponens tm-315 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89684.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89685
in-theory        89685
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((A -> B) -> ((C or A) -> B)) -> D))) -> (not (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     61
proof            (modus-ponens tm-313 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89685.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((A -> B) -> ((C or A) -> B)) -> D))) -> (not (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-313, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89686
in-theory        89686
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> E) -> (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> D)) -> E)))
theorem-size     63
proof            (modus-ponens tm-312 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
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-312.          ((A -> B) -> ((A -> B) and ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89686.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> E) -> (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> D)) -> E))), M:tm-312, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89687
in-theory        89687
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E or ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     49
proof            (modus-ponens tm-311 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89687.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E or ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-311, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89688
in-theory        89688
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) or E))
theorem-size     49
proof            (modus-ponens tm-310 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89688.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) or E)), M:tm-310, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89689
in-theory        89689
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and E)))
theorem-size     51
proof            (modus-ponens tm-309 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89689.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and E))), M:tm-309, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89690
in-theory        89690
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> ((A -> B) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)))
theorem-size     59
proof            (modus-ponens tm-306 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (C Dm)))
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-306.          ((A -> (B -> C)) -> ((A -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89690.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> ((A -> B) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D))), M:tm-306, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (C Dm))
================================================================
tm-name          tm-89691
in-theory        89691
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     49
proof            (modus-ponens tm-305 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89691.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) and (E -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-305, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89692
in-theory        89692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-303 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89692.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-303, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89693
in-theory        89693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-270 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89693.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-270, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89694
in-theory        89694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-239 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89694.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-239, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89695
in-theory        89695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H)))
theorem-size     41
proof            (modus-ponens tm-210 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89695.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H))), M:tm-210, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89696
in-theory        89696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-183 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-12.           ((A -> B) -> (A -> A)), M: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-89696.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-183, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89697
in-theory        89697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-157 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89697.        ((A -> ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-157, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89698
in-theory        89698
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     39
proof            (modus-ponens tm-147 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89698.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-147, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89699
in-theory        89699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-134 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89699.        ((A -> ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-134, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89700
in-theory        89700
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     39
proof            (modus-ponens tm-125 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89700.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-125, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89701
in-theory        89701
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> E)))
theorem-size     37
proof            (modus-ponens tm-114 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> C D))))
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-14.           (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89701.        ((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> E))), M:tm-114, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> C D)))
================================================================
tm-name          tm-89702
in-theory        89702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H)))
theorem-size     39
proof            (modus-ponens tm-113 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-12.           ((A -> B) -> (A -> A)), M: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-89702.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H))), M:tm-113, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89703
in-theory        89703
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C)))) -> (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C))))
theorem-size     49
proof            (modus-ponens tm-110 tm-975 ((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       229
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89703.        ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C)))) -> (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C)))), M:tm-110, m:tm-975, u:((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm)))))
================================================================
tm-name          tm-89704
in-theory        89704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     43
proof            (modus-ponens tm-105 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-12.           ((A -> B) -> (A -> A)), M: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-89704.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-105, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89705
in-theory        89705
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))) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> B)))
theorem-size     49
proof            (modus-ponens tm-102 tm-975 ((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> Am Bm) Bm)) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89705.        (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (C or A))) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> B))) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> B))), M:tm-102, m:tm-975, u:((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> Am Bm) Bm)) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-89706
in-theory        89706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F)))
theorem-size     31
proof            (modus-ponens tm-95 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-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-89706.        (((A -> B) -> (A -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F))), M:tm-95, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89707
in-theory        89707
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B))))
theorem-size     51
proof            (modus-ponens tm-92 tm-975 ((Dm (-> (-> Am Bm) (-> (or Cm Am) Bm))) (A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
axioms-used      (tm-8 tm-2 tm-1)
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-1.            (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-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-89707.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B)))), M:tm-92, m:tm-975, u:((Dm (-> (-> Am Bm) (-> (or Cm Am) Bm))) (A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) (-> (or Cm Am) Bm)))))
================================================================
tm-name          tm-89708
in-theory        89708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     25
proof            (modus-ponens tm-84 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
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-12.           ((A -> B) -> (A -> A)), M: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-89708.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-84, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89709
in-theory        89709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-83 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89709.        ((A -> (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-83, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89710
in-theory        89710
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C))))) -> (((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-80 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89710.        ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C))))) -> (((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C))))), M:tm-80, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-89711
in-theory        89711
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> ((D or B) -> C)) -> E) -> (((B -> C) -> ((D or B) -> C)) -> E)))
theorem-size     29
proof            (modus-ponens tm-76 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89711.        (((not (not A)) -> A) and ((((B -> C) -> ((D or B) -> C)) -> E) -> (((B -> C) -> ((D or B) -> C)) -> E))), M:tm-76, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89712
in-theory        89712
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> ((C or A) -> B)) -> D))) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D))
theorem-size     37
proof            (modus-ponens tm-73 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89712.        (((not (not (((A -> B) -> ((C or A) -> B)) -> D))) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D)), M:tm-73, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89713
in-theory        89713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F)))
theorem-size     35
proof            (modus-ponens tm-69 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89713.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F))), M:tm-69, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89714
in-theory        89714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((C or A) -> B))))
theorem-size     49
proof            (modus-ponens tm-55 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (C (-> (-> Am Bm) (-> (or Cm Am) Bm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89714.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((C or A) -> B)))), M:tm-55, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (C (-> (-> Am Bm) (-> (or Cm Am) Bm))))
================================================================
tm-name          tm-89715
in-theory        89715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-54 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89715.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-54, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89716
in-theory        89716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C))))
theorem-size     49
proof            (modus-ponens tm-51 tm-975 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       203
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-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-89716.        (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))), M:tm-51, m:tm-975, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm)))))
================================================================
tm-name          tm-89717
in-theory        89717
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-48 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) 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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89717.        ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))), M:tm-48, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-89718
in-theory        89718
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((B -> C) -> ((D or B) -> C)) -> E))
theorem-size     37
proof            (modus-ponens tm-47 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89718.        (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((B -> C) -> ((D or B) -> C)) -> E)), M:tm-47, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89719
in-theory        89719
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D))
theorem-size     37
proof            (modus-ponens tm-46 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89719.        ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D)), M:tm-46, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89720
in-theory        89720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)))
theorem-size     43
proof            (modus-ponens tm-45 tm-975 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C)))))
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89720.        ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))), M:tm-45, m:tm-975, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-89721
in-theory        89721
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((B -> C) -> ((D or B) -> C)) -> A))
theorem-size     25
proof            (modus-ponens tm-44 tm-975 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89721.        ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((B -> C) -> ((D or B) -> C)) -> A)), M:tm-44, m:tm-975, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89722
in-theory        89722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-42 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89722.        ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F))), M:tm-42, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89723
in-theory        89723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-32 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89723.        ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F))), M:tm-32, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89724
in-theory        89724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     35
proof            (modus-ponens tm-24 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89724.        ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-24, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89725
in-theory        89725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F)))
theorem-size     31
proof            (modus-ponens tm-23 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89725.        ((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F))), M:tm-23, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89726
in-theory        89726
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-22 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89726.        (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F))), M:tm-22, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89727
in-theory        89727
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-21 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89727.        (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F))), M:tm-21, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89728
in-theory        89728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-20 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89728.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((D -> E) -> ((F or D) -> E)) -> G))), M:tm-20, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89729
in-theory        89729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-19 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-19.           (A -> ((B -> (C -> B)) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89729.        ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((C -> D) -> ((E or C) -> D)) -> F))), M:tm-19, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89730
in-theory        89730
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((A -> B) -> ((C or A) -> B)) -> D))) -> (not (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     37
proof            (modus-ponens tm-9 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-9 tm-2 tm-1 tm-8)
proof-size       149
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89730.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((A -> B) -> ((C or A) -> B)) -> D))) -> (not (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-9, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89731
in-theory        89731
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> E) -> (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> D)) -> E))
theorem-size     39
proof            (modus-ponens tm-8 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-89731.        (((((A -> B) -> ((C or A) -> B)) -> D) -> E) -> (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> D)) -> E)), M:tm-8, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))
================================================================
tm-name          tm-89732
in-theory        89732
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((B -> C) -> ((D or B) -> C)) -> E)))
theorem-size     25
proof            (modus-ponens tm-7 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-8)
proof-size       131
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89732.        (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((B -> C) -> ((D or B) -> C)) -> E))), M:tm-7, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89733
in-theory        89733
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) or E)
theorem-size     25
proof            (modus-ponens tm-6 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-8)
proof-size       131
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89733.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)) or E), M:tm-6, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89734
in-theory        89734
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((B -> C) -> ((D or B) -> C)) -> E)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-89734.        (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((B -> C) -> ((D or B) -> C)) -> E)) and A)), M:tm-5, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89735
in-theory        89735
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((A -> B) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D))
theorem-size     35
proof            (modus-ponens tm-2 tm-975 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (C Dm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       149
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89735.        (((((A -> B) -> ((C or A) -> B)) -> D) -> ((A -> B) -> ((C or A) -> B))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)), M:tm-2, m:tm-975, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (C Dm))
================================================================
tm-name          tm-89736
in-theory        89736
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((B -> C) -> ((D or B) -> C)) -> E)))
theorem-size     25
proof            (modus-ponens tm-1 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-1 tm-2 tm-8)
proof-size       131
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89736.        (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((B -> C) -> ((D or B) -> C)) -> E))), M:tm-1, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89737
in-theory        89737
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     55
proof            (modus-ponens tm-930 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-89737.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-930, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89738
in-theory        89738
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     55
proof            (modus-ponens tm-893 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-9)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-89738.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-893, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89739
in-theory        89739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     59
proof            (modus-ponens tm-855 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-89739.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-855, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89740
in-theory        89740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     53
proof            (modus-ponens tm-808 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9)
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-4.            ((A and B) -> B), axiom
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-89740.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-808, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89741
in-theory        89741
times-derived    1
----------------------------------------------------------------
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))) and (((E and ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))) or ((((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     114
proof            (modus-ponens tm-798 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
proof-size       292
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-89741.        ((((((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))) and (((E and ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))) or ((((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-798, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89742
in-theory        89742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     53
proof            (modus-ponens tm-757 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89742.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-757, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89743
in-theory        89743
times-derived    1
----------------------------------------------------------------
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))) and (((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) and E) or ((((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     114
proof            (modus-ponens tm-747 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       292
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89743.        ((((((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))) and (((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) and E) or ((((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-747, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89744
in-theory        89744
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) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H))))
theorem-size     67
proof            (modus-ponens tm-708 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       259
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89744.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H)))), M:tm-708, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89745
in-theory        89745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     55
proof            (modus-ponens tm-665 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89745.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-665, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89746
in-theory        89746
times-derived    1
----------------------------------------------------------------
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))) and (((not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or ((((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     100
proof            (modus-ponens tm-654 tm-976 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (C (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       284
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89746.        ((((((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))) and (((not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or ((((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-654, m:tm-976, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (C (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89747
in-theory        89747
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (E or (not (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-623 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-8)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89747.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (E or (not (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-623, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89748
in-theory        89748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-622 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89748.        ((A -> (B -> (C or B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-622, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89749
in-theory        89749
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> ((C or A) -> B)) -> (D or ((A -> B) -> ((C or A) -> B)))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((A -> B) -> ((C or A) -> B)))))))
theorem-size     49
proof            (modus-ponens tm-618 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or C (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or C (-> (-> Am Bm) (-> (or Cm Am) Bm))))))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or C (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
axioms-used      (tm-9 tm-1 tm-7 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89749.        (not ((((A -> B) -> ((C or A) -> B)) -> (D or ((A -> B) -> ((C or A) -> B)))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((A -> B) -> ((C or A) -> B))))))), M:tm-618, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or C (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or C (-> (-> Am Bm) (-> (or Cm Am) Bm))))))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or C (-> (-> Am Bm) (-> (or Cm Am) Bm)))))
================================================================
tm-name          tm-89750
in-theory        89750
times-derived    1
----------------------------------------------------------------
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))) and (E -> (F or E)))
theorem-size     47
proof            (modus-ponens tm-609 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89750.        ((((((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))) and (E -> (F or E))), M:tm-609, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89751
in-theory        89751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     51
proof            (modus-ponens tm-605 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89751.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-605, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89752
in-theory        89752
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F or E)) 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     89
proof            (modus-ponens tm-595 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89752.        ((((((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))) and ((E -> (F or E)) 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-595, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89753
in-theory        89753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-550 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89753.        (((A -> (B or A)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-550, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89754
in-theory        89754
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-540 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89754.        ((A or (B -> (C or B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-540, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89755
in-theory        89755
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-530 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89755.        ((A or (B -> (B or C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-530, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89756
in-theory        89756
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     51
proof            (modus-ponens tm-520 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89756.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-520, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89757
in-theory        89757
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-510 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89757.        ((A or ((B and C) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-510, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89758
in-theory        89758
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-500 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89758.        ((A or ((B and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-500, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89759
in-theory        89759
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H))))
theorem-size     57
proof            (modus-ponens tm-490 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-8)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89759.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H)))), M:tm-490, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89760
in-theory        89760
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-480 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89760.        ((A or (B -> (C -> B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-480, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89761
in-theory        89761
times-derived    1
----------------------------------------------------------------
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)) or E))
theorem-size     43
proof            (modus-ponens tm-470 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-8)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89761.        (((((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)) or E)), M:tm-470, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89762
in-theory        89762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-469 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89762.        ((A -> (B -> (B or C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-469, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89763
in-theory        89763
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) or D)) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) or D)))))
theorem-size     49
proof            (modus-ponens tm-465 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) C)) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) C))))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) C))))
axioms-used      (tm-9 tm-1 tm-6 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89763.        (not ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) or D)) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) or D))))), M:tm-465, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) C)) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) C))))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) C)))
================================================================
tm-name          tm-89764
in-theory        89764
times-derived    1
----------------------------------------------------------------
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))) and (E -> (E or F)))
theorem-size     47
proof            (modus-ponens tm-456 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89764.        ((((((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))) and (E -> (E or F))), M:tm-456, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89765
in-theory        89765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     51
proof            (modus-ponens tm-453 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89765.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-453, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89766
in-theory        89766
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (E or F)) 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     89
proof            (modus-ponens tm-443 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89766.        ((((((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))) and ((E -> (E or F)) 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-443, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89767
in-theory        89767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-409 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89767.        (((A -> (A or B)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-409, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89768
in-theory        89768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     51
proof            (modus-ponens tm-400 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89768.        (((A -> (B -> (A and B))) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-400, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89769
in-theory        89769
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-391 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89769.        ((((A and B) -> B) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-391, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89770
in-theory        89770
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-382 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89770.        ((((A and B) -> A) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-382, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89771
in-theory        89771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H))))
theorem-size     57
proof            (modus-ponens tm-373 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-8)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89771.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H)))), M:tm-373, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89772
in-theory        89772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-364 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89772.        (((A -> (B -> A)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-364, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89773
in-theory        89773
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (E -> ((not (((A -> B) -> ((C or A) -> B)) -> D)) and E)))
theorem-size     45
proof            (modus-ponens tm-355 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89773.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (E -> ((not (((A -> B) -> ((C or A) -> B)) -> D)) and E))), M:tm-355, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89774
in-theory        89774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     51
proof            (modus-ponens tm-354 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89774.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-354, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89775
in-theory        89775
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> ((C or A) -> B)) -> (D -> (((A -> B) -> ((C or A) -> B)) and D))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((A -> B) -> ((C or A) -> B)) and D))))))
theorem-size     53
proof            (modus-ponens tm-350 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) C))) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> C (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) C)))))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> C (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-8)
proof-size       203
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89775.        (not ((((A -> B) -> ((C or A) -> B)) -> (D -> (((A -> B) -> ((C or A) -> B)) and D))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (((A -> B) -> ((C or A) -> B)) and D)))))), M:tm-350, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) C))) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> C (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) C)))))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> C (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) C))))
================================================================
tm-name          tm-89776
in-theory        89776
times-derived    1
----------------------------------------------------------------
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))) and (E -> (F -> (E and F))))
theorem-size     49
proof            (modus-ponens tm-341 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89776.        ((((((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))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89777
in-theory        89777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F))))
theorem-size     51
proof            (modus-ponens tm-338 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-9 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89777.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F)))), M:tm-338, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89778
in-theory        89778
times-derived    1
----------------------------------------------------------------
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))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) and (not (((A -> B) -> ((C or A) -> B)) -> D)))))
theorem-size     112
proof            (modus-ponens tm-328 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       288
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89778.        ((((((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))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) and (not (((A -> B) -> ((C or A) -> B)) -> D))))), M:tm-328, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89779
in-theory        89779
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F -> (E and F))) 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     91
proof            (modus-ponens tm-327 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89779.        ((((((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))) and ((E -> (F -> (E and F))) 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-327, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89780
in-theory        89780
times-derived    1
----------------------------------------------------------------
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))) and (((E and F) -> F) 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     89
proof            (modus-ponens tm-326 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89780.        ((((((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))) and (((E and F) -> F) 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-326, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89781
in-theory        89781
times-derived    1
----------------------------------------------------------------
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))) and (((E and F) -> E) 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     89
proof            (modus-ponens tm-325 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89781.        ((((((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))) and (((E and F) -> E) 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-325, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89782
in-theory        89782
times-derived    1
----------------------------------------------------------------
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))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) 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     97
proof            (modus-ponens tm-324 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89782.        ((((((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))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) 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-324, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89783
in-theory        89783
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F -> E)) 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     89
proof            (modus-ponens tm-323 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89783.        ((((((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))) and ((E -> (F -> E)) 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-323, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89784
in-theory        89784
times-derived    1
----------------------------------------------------------------
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))) and ((E and F) -> F))
theorem-size     47
proof            (modus-ponens tm-322 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89784.        ((((((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))) and ((E and F) -> F)), M:tm-322, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89785
in-theory        89785
times-derived    1
----------------------------------------------------------------
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))) and ((E and F) -> E))
theorem-size     47
proof            (modus-ponens tm-320 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89785.        ((((((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))) and ((E and F) -> E)), M:tm-320, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89786
in-theory        89786
times-derived    1
----------------------------------------------------------------
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))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     55
proof            (modus-ponens tm-318 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89786.        ((((((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))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89787
in-theory        89787
times-derived    1
----------------------------------------------------------------
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))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))))
theorem-size     99
proof            (modus-ponens tm-316 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89787.        ((((((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))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))), M:tm-316, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89788
in-theory        89788
times-derived    1
----------------------------------------------------------------
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))) and (E -> (F -> E)))
theorem-size     47
proof            (modus-ponens tm-315 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89788.        ((((((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))) and (E -> (F -> E))), M:tm-315, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89789
in-theory        89789
times-derived    1
----------------------------------------------------------------
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))) and ((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (not (not (((A -> B) -> ((C or A) -> B)) -> D)))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))))
theorem-size     114
proof            (modus-ponens tm-313 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       274
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-89789.        ((((((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))) and ((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (not (not (((A -> B) -> ((C or A) -> B)) -> D)))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))))), M:tm-313, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89790
in-theory        89790
times-derived    1
----------------------------------------------------------------
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))) and (((not (((A -> B) -> ((C or A) -> B)) -> D)) -> E) -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) or (not (((A -> B) -> ((C or A) -> B)) -> D))) -> E)))
theorem-size     100
proof            (modus-ponens tm-312 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       264
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89790.        ((((((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))) and (((not (((A -> B) -> ((C or A) -> B)) -> D)) -> E) -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) or (not (((A -> B) -> ((C or A) -> B)) -> D))) -> E))), M:tm-312, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89791
in-theory        89791
times-derived    1
----------------------------------------------------------------
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))) and (E or (((((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     85
proof            (modus-ponens tm-311 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89791.        ((((((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))) and (E or (((((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-311, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89792
in-theory        89792
times-derived    1
----------------------------------------------------------------
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))) 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))) or E))
theorem-size     85
proof            (modus-ponens tm-310 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89792.        ((((((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))) 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))) or E)), M:tm-310, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89793
in-theory        89793
times-derived    1
----------------------------------------------------------------
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))) and (E -> ((((((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))) and E)))
theorem-size     87
proof            (modus-ponens tm-309 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89793.        ((((((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))) and (E -> ((((((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))) and E))), M:tm-309, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89794
in-theory        89794
times-derived    1
----------------------------------------------------------------
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))) and (E -> (((((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     85
proof            (modus-ponens tm-305 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89794.        ((((((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))) and (E -> (((((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-305, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89795
in-theory        89795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     53
proof            (modus-ponens tm-303 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89795.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-303, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89796
in-theory        89796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     51
proof            (modus-ponens tm-270 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89796.        ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-270, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89797
in-theory        89797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     51
proof            (modus-ponens tm-239 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89797.        ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-239, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89798
in-theory        89798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H))))
theorem-size     59
proof            (modus-ponens tm-210 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-9 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89798.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H)))), M:tm-210, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89799
in-theory        89799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     51
proof            (modus-ponens tm-183 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89799.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-183, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89800
in-theory        89800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-157 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89800.        ((A -> ((B and C) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-157, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89801
in-theory        89801
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     57
proof            (modus-ponens tm-147 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-8)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89801.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-147, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89802
in-theory        89802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-134 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89802.        ((A -> ((B and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-134, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89803
in-theory        89803
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     57
proof            (modus-ponens tm-125 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-8)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89803.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-125, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89804
in-theory        89804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H))))
theorem-size     57
proof            (modus-ponens tm-113 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-8)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89804.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H)))), M:tm-113, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89805
in-theory        89805
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B))))))
theorem-size     53
proof            (modus-ponens tm-109 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm)))))) (B (-> Am Bm)) (C (or Cm Am)) (D Bm) (Dm (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-9 tm-1 tm-2 tm-8)
proof-size       221
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89805.        (not ((((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> (C or A)) -> ((A -> B) -> B)))))), M:tm-109, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm)))))) (B (-> Am Bm)) (C (or Cm Am)) (D Bm) (Dm (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-89806
in-theory        89806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     61
proof            (modus-ponens tm-105 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       241
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89806.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-105, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89807
in-theory        89807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F))))
theorem-size     49
proof            (modus-ponens tm-95 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89807.        (((A -> B) -> (A -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F)))), M:tm-95, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89808
in-theory        89808
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (E -> (not (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-84 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89808.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (E -> (not (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-84, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89809
in-theory        89809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     49
proof            (modus-ponens tm-83 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89809.        ((A -> (B -> (C -> B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-83, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89810
in-theory        89810
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> ((C or A) -> B)) -> (D -> ((A -> B) -> ((C or A) -> B)))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((A -> B) -> ((C or A) -> B)))))))
theorem-size     49
proof            (modus-ponens tm-79 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> C (-> (-> Am Bm) (-> (or Cm Am) Bm))))))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> C (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
axioms-used      (tm-9 tm-1 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89810.        (not ((((A -> B) -> ((C or A) -> B)) -> (D -> ((A -> B) -> ((C or A) -> B)))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> ((A -> B) -> ((C or A) -> B))))))), M:tm-79, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> C (-> (-> Am Bm) (-> (or Cm Am) Bm))))))) (B (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> C (-> (-> Am Bm) (-> (or Cm Am) Bm)))))
================================================================
tm-name          tm-89811
in-theory        89811
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not (((B -> C) -> ((D or B) -> C)) -> E))))
theorem-size     47
proof            (modus-ponens tm-76 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89811.        (((not (not A)) -> A) and (((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not (((B -> C) -> ((D or B) -> C)) -> E)))), M:tm-76, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89812
in-theory        89812
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))) or ((((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     72
proof            (modus-ponens tm-73 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-8 tm-10 tm-9)
proof-size       206
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89812.        (((not (not ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))) or ((((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-73, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89813
in-theory        89813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F))))
theorem-size     53
proof            (modus-ponens tm-69 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       191
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-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-89813.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F)))), M:tm-69, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89814
in-theory        89814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     55
proof            (modus-ponens tm-54 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       197
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89814.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-54, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89815
in-theory        89815
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))) or ((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))) -> (not (((B -> C) -> ((D or B) -> C)) -> E)))
theorem-size     72
proof            (modus-ponens tm-47 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-9)
proof-size       206
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89815.        (((A and ((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))) or ((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))) -> (not (((B -> C) -> ((D or B) -> C)) -> E))), M:tm-47, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89816
in-theory        89816
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) and E) or ((((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     72
proof            (modus-ponens tm-46 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       206
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89816.        (((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) and E) or ((((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-46, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89817
in-theory        89817
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) or ((((B -> C) -> ((A or B) -> C)) -> D) -> (not (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))) -> (not (((B -> C) -> ((A or B) -> C)) -> D)))
theorem-size     58
proof            (modus-ponens tm-44 tm-976 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (C (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       194
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89817.        (((not (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) or ((((B -> C) -> ((A or B) -> C)) -> D) -> (not (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))) -> (not (((B -> C) -> ((A or B) -> C)) -> D))), M:tm-44, m:tm-976, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (C (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89818
in-theory        89818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F))))
theorem-size     47
proof            (modus-ponens tm-42 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89818.        ((A -> (B or A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F)))), M:tm-42, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89819
in-theory        89819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F))))
theorem-size     47
proof            (modus-ponens tm-32 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89819.        ((A -> (A or B)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F)))), M:tm-32, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89820
in-theory        89820
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) and (not (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     70
proof            (modus-ponens tm-24 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       204
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89820.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) and (not (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-24, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89821
in-theory        89821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F))))
theorem-size     49
proof            (modus-ponens tm-23 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       179
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89821.        ((A -> (B -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F)))), M:tm-23, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89822
in-theory        89822
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F))))
theorem-size     47
proof            (modus-ponens tm-22 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89822.        (((A and B) -> B) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F)))), M:tm-22, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89823
in-theory        89823
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F))))
theorem-size     47
proof            (modus-ponens tm-21 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89823.        (((A and B) -> A) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F)))), M:tm-21, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89824
in-theory        89824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G))))
theorem-size     55
proof            (modus-ponens tm-20 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       197
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89824.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (not (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) -> (not (((D -> E) -> ((F or D) -> E)) -> G)))), M:tm-20, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89825
in-theory        89825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F))))
theorem-size     47
proof            (modus-ponens tm-19 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89825.        ((A -> (B -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (not (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) -> (not (((C -> D) -> ((E or C) -> D)) -> F)))), M:tm-19, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89826
in-theory        89826
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     57
proof            (modus-ponens tm-12 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8)
proof-size       187
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89826.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-12, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89827
in-theory        89827
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (not (not (((A -> B) -> ((C or A) -> B)) -> D)))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))))
theorem-size     72
proof            (modus-ponens tm-9 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-9 tm-8)
proof-size       188
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89827.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (not (not (((A -> B) -> ((C or A) -> B)) -> D)))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))), M:tm-9, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89828
in-theory        89828
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A -> B) -> ((C or A) -> B)) -> D)) -> E) -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) or (not (((A -> B) -> ((C or A) -> B)) -> D))) -> E))
theorem-size     58
proof            (modus-ponens tm-8 tm-976 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-8 tm-9)
proof-size       176
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89828.        (((not (((A -> B) -> ((C or A) -> B)) -> D)) -> E) -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) or (not (((A -> B) -> ((C or A) -> B)) -> D))) -> E)), M:tm-8, m:tm-976, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-89829
in-theory        89829
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not (((B -> C) -> ((D or B) -> C)) -> E))))
theorem-size     43
proof            (modus-ponens tm-7 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-7 tm-9 tm-8)
proof-size       153
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89829.        (A or (((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not (((B -> C) -> ((D or B) -> C)) -> E)))), M:tm-7, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89830
in-theory        89830
times-derived    1
----------------------------------------------------------------
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))) or E)
theorem-size     43
proof            (modus-ponens tm-6 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-6 tm-9 tm-8)
proof-size       153
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89830.        ((((((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))) or E), M:tm-6, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89831
in-theory        89831
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not (((B -> C) -> ((D or B) -> C)) -> E))) and A))
theorem-size     45
proof            (modus-ponens tm-5 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       157
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89831.        (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not (((B -> C) -> ((D or B) -> C)) -> E))) and A)), M:tm-5, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89832
in-theory        89832
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not (((B -> C) -> ((D or B) -> C)) -> E))))
theorem-size     43
proof            (modus-ponens tm-1 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-1 tm-9 tm-8)
proof-size       153
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-89832.        (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (not (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> (not (((B -> C) -> ((D or B) -> C)) -> E)))), M:tm-1, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-89833
in-theory        89833
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     45
proof            (modus-ponens tm-977 tm-1 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-1)
proof-size       163
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-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-1.            (A -> (B -> A)), axiom
tm-89833.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-1, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89834
in-theory        89834
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) or (((C -> A) or ((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     63
proof            (modus-ponens tm-977 tm-2 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> Bm Cm)) (E (-> (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       189
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-89834.        (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) or (((C -> A) or ((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-977, m:tm-2, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> Bm Cm)) (E (-> (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm))))
================================================================
tm-name          tm-89835
in-theory        89835
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and E)))
theorem-size     47
proof            (modus-ponens tm-977 tm-5 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) Bm)))))
axioms-used      (tm-8 tm-5)
proof-size       167
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-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-5.            (A -> (B -> (A and B))), axiom
tm-89835.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and E))), M:tm-977, m:tm-5, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) Bm))))
================================================================
tm-name          tm-89836
in-theory        89836
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) or E))
theorem-size     45
proof            (modus-ponens tm-977 tm-6 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) Bm))))
axioms-used      (tm-8 tm-6)
proof-size       163
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-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-6.            (A -> (A or B)), axiom
tm-89836.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) or E)), M:tm-977, m:tm-6, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) Bm)))
================================================================
tm-name          tm-89837
in-theory        89837
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     45
proof            (modus-ponens tm-977 tm-7 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-7)
proof-size       163
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-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-7.            (A -> (B or A)), axiom
tm-89837.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-7, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89838
in-theory        89838
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((D -> E) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or D) -> E)))
theorem-size     49
proof            (modus-ponens tm-977 tm-8 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (-> Bm Cm) (-> (or (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) Cm)))))
axioms-used      (tm-8)
proof-size       175
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-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-89838.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((D -> E) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or D) -> E))), M:tm-977, m:tm-8, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (-> Bm Cm) (-> (or (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) Cm))))
================================================================
tm-name          tm-89839
in-theory        89839
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not D)) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))))
theorem-size     59
proof            (modus-ponens tm-977 tm-9 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (not Bm)) (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))))
axioms-used      (tm-8 tm-9)
proof-size       183
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-89839.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not D)) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))), M:tm-977, m:tm-9, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (not Bm)) (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
================================================================
tm-name          tm-89840
in-theory        89840
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-977 tm-11 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1)
proof-size       163
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-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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-89840.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> E))), M:tm-977, m:tm-11, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-89841
in-theory        89841
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     55
proof            (modus-ponens tm-977 tm-12 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       193
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89841.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-12, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89842
in-theory        89842
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-977 tm-14 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-89842.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-977, m:tm-14, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-89843
in-theory        89843
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-977 tm-16 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       163
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-89843.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E and F) -> E)), M:tm-977, m:tm-16, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-89844
in-theory        89844
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-977 tm-18 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       163
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-89844.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E and F) -> F)), M:tm-977, m:tm-18, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-89845
in-theory        89845
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-977 tm-19 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       183
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-89845.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-19, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89846
in-theory        89846
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     57
proof            (modus-ponens tm-977 tm-20 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-89846.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-20, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89847
in-theory        89847
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and F) -> E) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-977 tm-21 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (and Bm Cm) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       183
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-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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-89847.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and F) -> E) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-21, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (and Bm Cm) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89848
in-theory        89848
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and F) -> F) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-977 tm-22 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (and Bm Cm) Cm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       183
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-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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-89848.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and F) -> F) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-22, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (and Bm Cm) Cm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89849
in-theory        89849
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (E and F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-23 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-89849.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (E and F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-23, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89850
in-theory        89850
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D)))
theorem-size     57
proof            (modus-ponens tm-977 tm-24 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       199
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-89850.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D))), M:tm-977, m:tm-24, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm))))
================================================================
tm-name          tm-89851
in-theory        89851
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-977 tm-25 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       169
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-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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-89851.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (E and F)))), M:tm-977, m:tm-25, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-89852
in-theory        89852
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (E or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-977 tm-32 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (or Bm Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       183
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-89852.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (E or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-32, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (or Bm Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89853
in-theory        89853
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-977 tm-33 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       163
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-89853.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (E or F))), M:tm-977, m:tm-33, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-89854
in-theory        89854
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F or E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-977 tm-42 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (or Cm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       183
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-89854.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F or E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-42, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (or Cm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89855
in-theory        89855
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-977 tm-43 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       163
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-89855.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F or E))), M:tm-977, m:tm-43, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-89856
in-theory        89856
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((((C -> A) or ((A -> B) -> ((C or A) -> B))) and E) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))
theorem-size     59
proof            (modus-ponens tm-977 tm-46 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm))))
axioms-used      (tm-8 tm-3)
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-89856.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((((C -> A) or ((A -> B) -> ((C or A) -> B))) and E) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)), M:tm-977, m:tm-46, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm)))
================================================================
tm-name          tm-89857
in-theory        89857
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and ((C -> A) or ((A -> B) -> ((C or A) -> B)))) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))
theorem-size     59
proof            (modus-ponens tm-977 tm-47 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (and Cm (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm))))
axioms-used      (tm-8 tm-4)
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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-89857.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and ((C -> A) or ((A -> B) -> ((C or A) -> B)))) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)), M:tm-977, m:tm-47, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (and Cm (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm)))
================================================================
tm-name          tm-89858
in-theory        89858
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))
theorem-size     47
proof            (modus-ponens tm-977 tm-49 ((Am (-> A B)) (Bm (-> (-> B C) (-> (or A B) C))) (D Cm) (E (-> (or (-> A B) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm))))
axioms-used      (tm-8 tm-6)
proof-size       191
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-89858.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)), M:tm-977, m:tm-49, u:((Am (-> A B)) (Bm (-> (-> B C) (-> (or A B) C))) (D Cm) (E (-> (or (-> A B) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm)))
================================================================
tm-name          tm-89859
in-theory        89859
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))
theorem-size     53
proof            (modus-ponens tm-977 tm-50 ((Am (-> A B)) (Bm (-> (-> B C) (-> (or A B) C))) (D Cm) (E (-> (or (-> (-> B C) (-> (or A B) C)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm))))
axioms-used      (tm-8 tm-7)
proof-size       197
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-89859.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)), M:tm-977, m:tm-50, u:((Am (-> A B)) (Bm (-> (-> B C) (-> (or A B) C))) (D Cm) (E (-> (or (-> (-> B C) (-> (or A B) C)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm)))
================================================================
tm-name          tm-89860
in-theory        89860
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     57
proof            (modus-ponens tm-977 tm-54 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5)
proof-size       207
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-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-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-89860.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-54, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89861
in-theory        89861
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-977 tm-56 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1)
proof-size       187
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-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-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-89861.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-977, m:tm-56, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-89862
in-theory        89862
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (D -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     72
proof            (modus-ponens tm-977 tm-57 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       210
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-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-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-89862.        (((((A -> B) -> ((C or A) -> B)) -> (not (D -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-57, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89863
in-theory        89863
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D)))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     76
proof            (modus-ponens tm-977 tm-61 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       218
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-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-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-89863.        (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D)))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-61, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89864
in-theory        89864
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) or D))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) or D)))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     72
proof            (modus-ponens tm-977 tm-62 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (or (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-6)
proof-size       210
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-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-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-89864.        (((((A -> B) -> ((C or A) -> B)) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) or D))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) or D)))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-62, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (or (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89865
in-theory        89865
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (D or ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D or ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     72
proof            (modus-ponens tm-977 tm-63 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (or Bm (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-7)
proof-size       210
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-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-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-89865.        (((((A -> B) -> ((C or A) -> B)) -> (not (D or ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D or ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-63, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (or Bm (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89866
in-theory        89866
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> ((E -> (not F)) -> (not E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     55
proof            (modus-ponens tm-977 tm-69 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-9)
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-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-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-89866.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> ((E -> (not F)) -> (not E))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-69, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89867
in-theory        89867
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     39
proof            (modus-ponens tm-977 tm-71 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       181
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-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-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-89867.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-977, m:tm-71, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-89868
in-theory        89868
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((not (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))
theorem-size     59
proof            (modus-ponens tm-977 tm-73 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (not (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm))))
axioms-used      (tm-8 tm-10)
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-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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-89868.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((not (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)), M:tm-977, m:tm-73, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (not (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm)))
================================================================
tm-name          tm-89869
in-theory        89869
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((not (not E)) -> E) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-977 tm-76 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (not (not Bm)) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-10)
proof-size       183
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-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-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-89869.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((not (not E)) -> E) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-76, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (not (not Bm)) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89870
in-theory        89870
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((not (not E)) -> E))
theorem-size     33
proof            (modus-ponens tm-977 tm-78 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-10)
proof-size       163
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-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-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-89870.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((not (not E)) -> E)), M:tm-977, m:tm-78, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-89871
in-theory        89871
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (E -> D)))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (E -> D))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     52
proof            (modus-ponens tm-977 tm-79 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (-> Cm Bm)))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       204
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-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-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-89871.        (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (E -> D)))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (E -> D))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-79, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (-> Cm Bm)))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89872
in-theory        89872
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (G -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-83 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-89872.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (G -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-83, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89873
in-theory        89873
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (E -> D)))
theorem-size     45
proof            (modus-ponens tm-977 tm-84 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       197
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-89873.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (E -> D))), M:tm-977, m:tm-84, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> Cm Bm))))
================================================================
tm-name          tm-89874
in-theory        89874
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (G -> F))))
theorem-size     35
proof            (modus-ponens tm-977 tm-85 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1)
proof-size       179
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-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-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-89874.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (G -> F)))), M:tm-977, m:tm-85, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-89875
in-theory        89875
times-derived    3
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     43
proof            (modus-ponens tm-977 tm-86 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-89875.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-977, m:tm-86, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))
================================================================
tm-name          tm-89876
in-theory        89876
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> E)))
theorem-size     49
proof            (modus-ponens tm-977 tm-87 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> Bm Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       211
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-89876.        (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> E))), M:tm-977, m:tm-87, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> Bm Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> Bm Cm))))
================================================================
tm-name          tm-89877
in-theory        89877
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> (E -> E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-95 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-89877.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> (E -> E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-95, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89878
in-theory        89878
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> (E -> E)))
theorem-size     35
proof            (modus-ponens tm-977 tm-97 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       187
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-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-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-89878.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> (E -> E))), M:tm-977, m:tm-97, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-89879
in-theory        89879
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((D -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E))
theorem-size     75
proof            (modus-ponens tm-977 tm-98 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (-> Bm (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       261
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-89879.        (((((A -> B) -> ((C or A) -> B)) -> ((D -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E)), M:tm-977, m:tm-98, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (-> Bm (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm)))
================================================================
tm-name          tm-89880
in-theory        89880
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     71
proof            (modus-ponens tm-977 tm-99 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       263
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-89880.        (((((A -> B) -> ((C or A) -> B)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-977, m:tm-99, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)))
================================================================
tm-name          tm-89881
in-theory        89881
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     63
proof            (modus-ponens tm-977 tm-105 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       251
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-89881.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-105, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89882
in-theory        89882
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-977 tm-107 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       231
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-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-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-89882.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-977, m:tm-107, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-89883
in-theory        89883
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     68
proof            (modus-ponens tm-977 tm-109 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-2)
proof-size       244
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-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-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-89883.        (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-109, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89884
in-theory        89884
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     59
proof            (modus-ponens tm-977 tm-113 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       231
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-89884.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-113, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89885
in-theory        89885
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> F))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> F)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (D -> F))))
theorem-size     57
proof            (modus-ponens tm-977 tm-114 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> Bm (-> Cm Dm))) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
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-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-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-89885.        (((((A -> B) -> ((C or A) -> B)) -> (D -> (E -> F))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> (E -> F)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> E) -> (D -> F)))), M:tm-977, m:tm-114, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> Bm (-> Cm Dm))) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-89886
in-theory        89886
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-977 tm-115 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       211
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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-89886.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-977, m:tm-115, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-89887
in-theory        89887
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     59
proof            (modus-ponens tm-977 tm-125 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       231
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-89887.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-125, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89888
in-theory        89888
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     43
proof            (modus-ponens tm-977 tm-127 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       211
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-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-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-89888.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-977, m:tm-127, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-89889
in-theory        89889
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not ((D and E) -> D))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D and E) -> D)))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     52
proof            (modus-ponens tm-977 tm-130 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> (and Bm Cm) Bm))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-3)
proof-size       204
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-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-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-89889.        (((((A -> B) -> ((C or A) -> B)) -> (not ((D and E) -> D))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D and E) -> D)))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-130, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> (and Bm Cm) Bm))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89890
in-theory        89890
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F and G) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-134 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-89890.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F and G) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-134, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89891
in-theory        89891
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D and E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     47
proof            (modus-ponens tm-977 tm-135 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (and Bm Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       199
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-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-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-89891.        (((((A -> B) -> ((C or A) -> B)) -> (D and E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-977, m:tm-135, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (and Bm Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)))
================================================================
tm-name          tm-89892
in-theory        89892
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-977 tm-136 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       179
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-89892.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F and G) -> F))), M:tm-977, m:tm-136, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-89893
in-theory        89893
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     59
proof            (modus-ponens tm-977 tm-147 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       231
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-89893.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-147, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89894
in-theory        89894
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     43
proof            (modus-ponens tm-977 tm-149 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       211
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-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-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-89894.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-977, m:tm-149, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-89895
in-theory        89895
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not ((D and E) -> E))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D and E) -> E)))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     52
proof            (modus-ponens tm-977 tm-153 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> (and Bm Cm) Cm))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-4)
proof-size       204
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-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-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-89895.        (((((A -> B) -> ((C or A) -> B)) -> (not ((D and E) -> E))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D and E) -> E)))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-153, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> (and Bm Cm) Cm))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89896
in-theory        89896
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F and G) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-157 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-89896.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F and G) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-157, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89897
in-theory        89897
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D and E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E))
theorem-size     47
proof            (modus-ponens tm-977 tm-158 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (and Bm Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       199
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-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-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-89897.        (((((A -> B) -> ((C or A) -> B)) -> (D and E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D and E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E)), M:tm-977, m:tm-158, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (and Bm Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm)))
================================================================
tm-name          tm-89898
in-theory        89898
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F and G) -> G)))
theorem-size     35
proof            (modus-ponens tm-977 tm-159 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       179
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-89898.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F and G) -> G))), M:tm-977, m:tm-159, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-89899
in-theory        89899
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (E -> D)) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (E -> D)) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     80
proof            (modus-ponens tm-977 tm-179 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> Bm (-> Cm Bm)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1)
proof-size       238
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-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-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-89899.        (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (E -> D)) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (E -> D)) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-179, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> Bm (-> Cm Bm)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89900
in-theory        89900
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (G -> F)) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-977 tm-183 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-89900.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (G -> F)) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-183, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89901
in-theory        89901
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (G -> F)) and E)))
theorem-size     37
proof            (modus-ponens tm-977 tm-184 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       187
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-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-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-89901.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (G -> F)) and E))), M:tm-977, m:tm-184, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-89902
in-theory        89902
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     96
proof            (modus-ponens tm-977 tm-206 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-5 tm-2)
proof-size       278
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-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-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-89902.        (((((A -> B) -> ((C or A) -> B)) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-206, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89903
in-theory        89903
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     61
proof            (modus-ponens tm-977 tm-210 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       239
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-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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-89903.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-210, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89904
in-theory        89904
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     45
proof            (modus-ponens tm-977 tm-211 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       219
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-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-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-89904.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-977, m:tm-211, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-89905
in-theory        89905
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (((D and E) -> D) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (((D and E) -> D) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     80
proof            (modus-ponens tm-977 tm-235 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> (and Bm Cm) Bm) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-5 tm-3)
proof-size       238
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-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-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-89905.        (((((A -> B) -> ((C or A) -> B)) -> (not (((D and E) -> D) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (((D and E) -> D) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-235, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> (and Bm Cm) Bm) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89906
in-theory        89906
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (((F and G) -> F) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-977 tm-239 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-89906.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (((F and G) -> F) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-239, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89907
in-theory        89907
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (((F and G) -> F) and E)))
theorem-size     37
proof            (modus-ponens tm-977 tm-240 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       187
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-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-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-89907.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (((F and G) -> F) and E))), M:tm-977, m:tm-240, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-89908
in-theory        89908
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (((D and E) -> E) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (((D and E) -> E) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     80
proof            (modus-ponens tm-977 tm-266 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> (and Bm Cm) Cm) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-5 tm-4)
proof-size       238
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-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-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-89908.        (((((A -> B) -> ((C or A) -> B)) -> (not (((D and E) -> E) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (((D and E) -> E) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-266, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> (and Bm Cm) Cm) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89909
in-theory        89909
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (((F and G) -> G) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-977 tm-270 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-89909.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (((F and G) -> G) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-270, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89910
in-theory        89910
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (((F and G) -> G) and E)))
theorem-size     37
proof            (modus-ponens tm-977 tm-271 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       187
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-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-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-89910.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (((F and G) -> G) and E))), M:tm-977, m:tm-271, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-89911
in-theory        89911
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (E -> (D and E))) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (E -> (D and E))) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     84
proof            (modus-ponens tm-977 tm-299 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> Bm (-> Cm (and Bm Cm))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       248
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-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-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-89911.        (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (E -> (D and E))) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (E -> (D and E))) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-299, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> Bm (-> Cm (and Bm Cm))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89912
in-theory        89912
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (G -> (F and G))) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     55
proof            (modus-ponens tm-977 tm-303 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5)
proof-size       215
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-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-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-89912.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (G -> (F and G))) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-303, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89913
in-theory        89913
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     39
proof            (modus-ponens tm-977 tm-304 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       195
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-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-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-89913.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (G -> (F and G))) and E))), M:tm-977, m:tm-304, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-89914
in-theory        89914
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-977 tm-305 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       215
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-89914.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-977, m:tm-305, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
================================================================
tm-name          tm-89915
in-theory        89915
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> E))) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> E)) and ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E))))
theorem-size     81
proof            (modus-ponens tm-977 tm-306 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> Bm Cm)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> Bm Cm)) (-> (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       255
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-89915.        (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> E))) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D -> E)) and ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E)))), M:tm-977, m:tm-306, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> Bm Cm)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> Bm Cm)) (-> (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm)))))
================================================================
tm-name          tm-89916
in-theory        89916
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and E))))
theorem-size     63
proof            (modus-ponens tm-977 tm-309 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       221
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-89916.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and E)))), M:tm-977, m:tm-309, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) Bm)))))
================================================================
tm-name          tm-89917
in-theory        89917
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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) or E)))
theorem-size     61
proof            (modus-ponens tm-977 tm-310 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (or (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       215
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-89917.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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) or E))), M:tm-977, m:tm-310, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (or (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) Bm))))
================================================================
tm-name          tm-89918
in-theory        89918
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-977 tm-311 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (or Bm (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       215
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-89918.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-977, m:tm-311, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (or Bm (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
================================================================
tm-name          tm-89919
in-theory        89919
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((D -> E) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or D) -> E))))
theorem-size     65
proof            (modus-ponens tm-977 tm-312 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (-> Bm Cm) (-> (or (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       237
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
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-89919.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((D -> E) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or D) -> E)))), M:tm-977, m:tm-312, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (-> Bm Cm) (-> (or (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) Cm)))))
================================================================
tm-name          tm-89920
in-theory        89920
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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))) -> (not D)) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))))
theorem-size     75
proof            (modus-ponens tm-977 tm-313 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (not Bm)) (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       243
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-89920.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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))) -> (not D)) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))))), M:tm-977, m:tm-313, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (not Bm)) (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))))
================================================================
tm-name          tm-89921
in-theory        89921
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> (F -> E))))
theorem-size     49
proof            (modus-ponens tm-977 tm-315 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-89921.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> (F -> E)))), M:tm-977, m:tm-315, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-89922
in-theory        89922
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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))) -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))))
theorem-size     71
proof            (modus-ponens tm-977 tm-316 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (or (-> A B) (-> (-> B C) (-> (or A B) C))))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       249
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-89922.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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))) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))), M:tm-977, m:tm-316, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
================================================================
tm-name          tm-89923
in-theory        89923
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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     57
proof            (modus-ponens tm-977 tm-318 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       249
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-89923.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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-977, m:tm-318, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-89924
in-theory        89924
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E and F) -> E)))
theorem-size     49
proof            (modus-ponens tm-977 tm-320 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-89924.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E and F) -> E))), M:tm-977, m:tm-320, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-89925
in-theory        89925
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E and F) -> F)))
theorem-size     49
proof            (modus-ponens tm-977 tm-322 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-89925.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E and F) -> F))), M:tm-977, m:tm-322, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-89926
in-theory        89926
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E -> (F -> E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     65
proof            (modus-ponens tm-977 tm-323 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> Bm (-> Cm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-89926.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E -> (F -> E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-977, m:tm-323, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> Bm (-> Cm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
================================================================
tm-name          tm-89927
in-theory        89927
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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 (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     73
proof            (modus-ponens tm-977 tm-324 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       271
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-89927.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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 (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-977, m:tm-324, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
================================================================
tm-name          tm-89928
in-theory        89928
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (((E and F) -> E) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     65
proof            (modus-ponens tm-977 tm-325 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> (and Bm Cm) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-89928.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (((E and F) -> E) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-977, m:tm-325, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> (and Bm Cm) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
================================================================
tm-name          tm-89929
in-theory        89929
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (((E and F) -> F) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     65
proof            (modus-ponens tm-977 tm-326 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> (and Bm Cm) Cm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-89929.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (((E and F) -> F) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-977, m:tm-326, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> (and Bm Cm) Cm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
================================================================
tm-name          tm-89930
in-theory        89930
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E -> (F -> (E and F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     67
proof            (modus-ponens tm-977 tm-327 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       247
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-89930.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E -> (F -> (E and F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-977, m:tm-327, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
================================================================
tm-name          tm-89931
in-theory        89931
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D))))
theorem-size     73
proof            (modus-ponens tm-977 tm-328 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       257
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-89931.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D)))), M:tm-977, m:tm-328, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)))))
================================================================
tm-name          tm-89932
in-theory        89932
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> (E -> (E and F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-977 tm-338 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-89932.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> (E -> (E and F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-338, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89933
in-theory        89933
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> (E -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-977 tm-340 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       195
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-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-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-89933.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> (E -> (E and F)))), M:tm-977, m:tm-340, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-89934
in-theory        89934
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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     51
proof            (modus-ponens tm-977 tm-341 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-89934.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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-977, m:tm-341, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-89935
in-theory        89935
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((D -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D)) -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D)) -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E))
theorem-size     79
proof            (modus-ponens tm-977 tm-349 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (-> Bm (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)) Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       271
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-89935.        (((((A -> B) -> ((C or A) -> B)) -> ((D -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D)) -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) and D)) -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E)), M:tm-977, m:tm-349, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (-> Bm (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm)) Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm)))
================================================================
tm-name          tm-89936
in-theory        89936
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (E -> (D and E))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (E -> (D and E)))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     56
proof            (modus-ponens tm-977 tm-350 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (-> Cm (and Bm Cm))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-5)
proof-size       214
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-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-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-89936.        (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (E -> (D and E))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (E -> (D and E)))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-350, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (-> Cm (and Bm Cm))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89937
in-theory        89937
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (G -> (F and G)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-977 tm-354 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-89937.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (G -> (F and G)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-354, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89938
in-theory        89938
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (E -> (D and E))))
theorem-size     47
proof            (modus-ponens tm-977 tm-355 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       205
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-89938.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (E -> (D and E)))), M:tm-977, m:tm-355, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-89939
in-theory        89939
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (G -> (F and G)))))
theorem-size     37
proof            (modus-ponens tm-977 tm-356 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       187
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-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-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and 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-89939.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (G -> (F and G))))), M:tm-977, m:tm-356, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-89940
in-theory        89940
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> E)) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-364 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-89940.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> E)) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-364, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89941
in-theory        89941
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> E)) or G))
theorem-size     35
proof            (modus-ponens tm-977 tm-365 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       179
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-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-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-89941.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> E)) or G)), M:tm-977, m:tm-365, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-89942
in-theory        89942
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     59
proof            (modus-ponens tm-977 tm-373 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       231
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-89942.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-373, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89943
in-theory        89943
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     43
proof            (modus-ponens tm-977 tm-374 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       211
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-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-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-89943.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-977, m:tm-374, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-89944
in-theory        89944
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E and F) -> E) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-382 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> (and Bm Cm) Bm) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-89944.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E and F) -> E) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-382, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> (and Bm Cm) Bm) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89945
in-theory        89945
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and F) -> E) or G))
theorem-size     35
proof            (modus-ponens tm-977 tm-383 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       179
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-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-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-89945.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and F) -> E) or G)), M:tm-977, m:tm-383, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-89946
in-theory        89946
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E and F) -> F) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-391 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> (and Bm Cm) Cm) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6 tm-4)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-89946.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E and F) -> F) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-391, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> (and Bm Cm) Cm) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89947
in-theory        89947
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and F) -> F) or G))
theorem-size     35
proof            (modus-ponens tm-977 tm-392 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       179
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-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-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-89947.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E and F) -> F) or G)), M:tm-977, m:tm-392, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-89948
in-theory        89948
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> (E and F))) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-977 tm-400 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-89948.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F -> (E and F))) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-400, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89949
in-theory        89949
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (E and F))) or G))
theorem-size     37
proof            (modus-ponens tm-977 tm-401 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       187
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-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-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-89949.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (E and F))) or G)), M:tm-977, m:tm-401, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-89950
in-theory        89950
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (E or F)) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-409 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> Bm (or Bm Cm)) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-89950.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (E or F)) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-409, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> Bm (or Bm Cm)) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89951
in-theory        89951
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (E or F)) or G))
theorem-size     35
proof            (modus-ponens tm-977 tm-410 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       179
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-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-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-89951.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (E or F)) or G)), M:tm-977, m:tm-410, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-89952
in-theory        89952
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E -> (E or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     65
proof            (modus-ponens tm-977 tm-443 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> Bm (or Bm Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-89952.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E -> (E or F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-977, m:tm-443, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> Bm (or Bm Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
================================================================
tm-name          tm-89953
in-theory        89953
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (D or E)) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (D or E)) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     80
proof            (modus-ponens tm-977 tm-449 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> Bm (or Bm Cm)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6)
proof-size       238
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-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-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-89953.        (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (D or E)) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (D or E)) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-449, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> Bm (or Bm Cm)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89954
in-theory        89954
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (F or G)) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-977 tm-453 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-89954.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (F or G)) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-453, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89955
in-theory        89955
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (F or G)) and E)))
theorem-size     37
proof            (modus-ponens tm-977 tm-454 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       187
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-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-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-89955.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (F or G)) and E))), M:tm-977, m:tm-454, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-89956
in-theory        89956
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> (E or F))))
theorem-size     49
proof            (modus-ponens tm-977 tm-456 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-89956.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> (E or F)))), M:tm-977, m:tm-456, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-89957
in-theory        89957
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or D) -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or D) -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E))
theorem-size     75
proof            (modus-ponens tm-977 tm-464 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (or (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       261
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-89957.        (((((A -> B) -> ((C or A) -> B)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or D) -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or D) -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E)), M:tm-977, m:tm-464, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (or (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm)))
================================================================
tm-name          tm-89958
in-theory        89958
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (D or E)))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (D or E))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     52
proof            (modus-ponens tm-977 tm-465 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (or Bm Cm)))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-6)
proof-size       204
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-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-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-89958.        (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (D or E)))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (D or E))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-465, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (or Bm Cm)))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89959
in-theory        89959
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (F or G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-469 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (or Cm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-89959.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (F or G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-469, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (or Cm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89960
in-theory        89960
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or E)))
theorem-size     45
proof            (modus-ponens tm-977 tm-470 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       197
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-89960.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or E))), M:tm-977, m:tm-470, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (or Bm Cm))))
================================================================
tm-name          tm-89961
in-theory        89961
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (F or G))))
theorem-size     35
proof            (modus-ponens tm-977 tm-471 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       179
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-89961.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (F or G)))), M:tm-977, m:tm-471, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-89962
in-theory        89962
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or (F -> (G -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-480 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> Cm (-> Dm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-89962.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or (F -> (G -> F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-480, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> Cm (-> Dm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89963
in-theory        89963
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (F -> (G -> F))))
theorem-size     35
proof            (modus-ponens tm-977 tm-481 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       179
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-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-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-89963.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (F -> (G -> F)))), M:tm-977, m:tm-481, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-89964
in-theory        89964
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     59
proof            (modus-ponens tm-977 tm-490 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       231
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-89964.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-490, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89965
in-theory        89965
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-977 tm-491 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       211
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-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-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-89965.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-977, m:tm-491, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-89966
in-theory        89966
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or ((F and G) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-500 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> (and Cm Dm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-89966.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or ((F and G) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-500, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> (and Cm Dm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89967
in-theory        89967
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or ((F and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-977 tm-501 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       179
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-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-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-89967.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or ((F and G) -> F))), M:tm-977, m:tm-501, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-89968
in-theory        89968
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or ((F and G) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-510 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> (and Cm Dm) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7 tm-4)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-89968.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or ((F and G) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-510, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> (and Cm Dm) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89969
in-theory        89969
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or ((F and G) -> G)))
theorem-size     35
proof            (modus-ponens tm-977 tm-511 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       179
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-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-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-89969.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or ((F and G) -> G))), M:tm-977, m:tm-511, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-89970
in-theory        89970
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or (F -> (G -> (F and G)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-977 tm-520 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-89970.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or (F -> (G -> (F and G)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-520, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89971
in-theory        89971
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (F -> (G -> (F and G)))))
theorem-size     37
proof            (modus-ponens tm-977 tm-521 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       187
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-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-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-89971.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (F -> (G -> (F and G))))), M:tm-977, m:tm-521, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-89972
in-theory        89972
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or (F -> (F or G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-530 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> Cm (or Cm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-89972.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or (F -> (F or G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-530, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> Cm (or Cm Dm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89973
in-theory        89973
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (F -> (F or G))))
theorem-size     35
proof            (modus-ponens tm-977 tm-531 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       179
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-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-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-89973.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (F -> (F or G)))), M:tm-977, m:tm-531, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-89974
in-theory        89974
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or (F -> (G or F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-540 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> Cm (or Dm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-89974.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or (F -> (G or F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-540, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> Cm (or Dm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89975
in-theory        89975
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (F -> (G or F))))
theorem-size     35
proof            (modus-ponens tm-977 tm-541 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       179
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-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-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-89975.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or (F -> (G or F)))), M:tm-977, m:tm-541, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-89976
in-theory        89976
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F or E)) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-550 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> Bm (or Cm Bm)) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-89976.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F or E)) or G) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-550, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> Bm (or Cm Bm)) Dm) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89977
in-theory        89977
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F or E)) or G))
theorem-size     35
proof            (modus-ponens tm-977 tm-551 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       179
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-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-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-89977.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F or E)) or G)), M:tm-977, m:tm-551, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-89978
in-theory        89978
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E -> (F or E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     65
proof            (modus-ponens tm-977 tm-595 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> Bm (or Cm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-89978.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((E -> (F or E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-977, m:tm-595, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (and (-> Bm (or Cm Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
================================================================
tm-name          tm-89979
in-theory        89979
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (E or D)) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (E or D)) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     80
proof            (modus-ponens tm-977 tm-601 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> Bm (or Cm Bm)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7)
proof-size       238
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-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-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-89979.        (((((A -> B) -> ((C or A) -> B)) -> (not ((D -> (E or D)) and ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not ((D -> (E or D)) and ((C -> A) or ((A -> B) -> ((C or A) -> B))))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-601, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (and (-> Bm (or Cm Bm)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89980
in-theory        89980
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (G or F)) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-977 tm-605 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       207
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-89980.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> ((F -> (G or F)) and E)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-605, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89981
in-theory        89981
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (G or F)) and E)))
theorem-size     37
proof            (modus-ponens tm-977 tm-606 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       187
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-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-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-89981.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> ((F -> (G or F)) and E))), M:tm-977, m:tm-606, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-89982
in-theory        89982
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> (F or E))))
theorem-size     49
proof            (modus-ponens tm-977 tm-609 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-89982.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (E -> (F or E)))), M:tm-977, m:tm-609, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-89983
in-theory        89983
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((D or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E))
theorem-size     75
proof            (modus-ponens tm-977 tm-617 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (or Bm (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       261
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-89983.        (((((A -> B) -> ((C or A) -> B)) -> ((D or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> E)) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> E))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E)), M:tm-977, m:tm-617, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (-> (or Bm (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm)) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm)))
================================================================
tm-name          tm-89984
in-theory        89984
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (E or D)))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (E or D))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     52
proof            (modus-ponens tm-977 tm-618 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (or Cm Bm)))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-7)
proof-size       204
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-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-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-89984.        (((((A -> B) -> ((C or A) -> B)) -> (not (D -> (E or D)))) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (not (D -> (E or D))))) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-977, m:tm-618, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D (not (-> Bm (or Cm Bm)))) (E (not (or (-> A B) (-> (-> B C) (-> (or A B) C))))))
================================================================
tm-name          tm-89985
in-theory        89985
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (G or F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     51
proof            (modus-ponens tm-977 tm-622 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (or Dm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       199
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-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-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-89985.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> (F -> (G or F))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-622, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> Bm (-> Cm (or Dm Cm))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89986
in-theory        89986
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (E or D)))
theorem-size     45
proof            (modus-ponens tm-977 tm-623 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       197
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-89986.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (E or D))), M:tm-977, m:tm-623, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) (or Cm Bm))))
================================================================
tm-name          tm-89987
in-theory        89987
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (G or F))))
theorem-size     35
proof            (modus-ponens tm-977 tm-624 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       179
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-89987.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E -> (F -> (G or F)))), M:tm-977, m:tm-624, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-89988
in-theory        89988
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     57
proof            (modus-ponens tm-977 tm-665 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       225
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-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-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-89988.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-665, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89989
in-theory        89989
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-977 tm-667 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1)
proof-size       205
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-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-1.            (A -> (B -> A)), 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-89989.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-977, m:tm-667, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-89990
in-theory        89990
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     69
proof            (modus-ponens tm-977 tm-708 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       269
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-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-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-89990.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-708, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89991
in-theory        89991
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     53
proof            (modus-ponens tm-977 tm-710 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       249
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-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-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-89991.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-977, m:tm-710, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-89992
in-theory        89992
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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))) and E) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)))
theorem-size     75
proof            (modus-ponens tm-977 tm-747 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       261
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-89992.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((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))) and E) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))), M:tm-977, m:tm-747, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (and (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm))))
================================================================
tm-name          tm-89993
in-theory        89993
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> (((E and G) or E) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     55
proof            (modus-ponens tm-977 tm-757 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       219
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-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-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-89993.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> (((E and G) or E) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-757, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89994
in-theory        89994
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     39
proof            (modus-ponens tm-977 tm-759 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       199
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-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-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-89994.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> (((E and G) or E) -> F))), M:tm-977, m:tm-759, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-89995
in-theory        89995
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (((E and ((C -> A) or ((A -> B) -> ((C or A) -> B)))) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)))
theorem-size     75
proof            (modus-ponens tm-977 tm-798 ((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (and Cm (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       261
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-89995.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (((E and ((C -> A) or ((A -> B) -> ((C or A) -> B)))) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))), M:tm-977, m:tm-798, u:((Am (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (D Bm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Bm) (-> (or (and Cm (or (-> A B) (-> (-> B C) (-> (or A B) C)))) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Bm))))
================================================================
tm-name          tm-89996
in-theory        89996
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> (((G and E) or E) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     55
proof            (modus-ponens tm-977 tm-808 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       219
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-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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
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-89996.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> (((G and E) or E) -> F)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-808, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89997
in-theory        89997
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     39
proof            (modus-ponens tm-977 tm-810 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       199
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-89997.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E -> F) -> (((G and E) or E) -> F))), M:tm-977, m:tm-810, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-89998
in-theory        89998
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     61
proof            (modus-ponens tm-977 tm-855 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5)
proof-size       239
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-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-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-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-89998.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-855, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-89999
in-theory        89999
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     45
proof            (modus-ponens tm-977 tm-857 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       219
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-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-1.            (A -> (B -> A)), 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-89999.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-977, m:tm-857, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-90000
in-theory        90000
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (((C -> A) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)))
theorem-size     63
proof            (modus-ponens tm-977 tm-882 ((Am (-> A B)) (Bm (-> (-> B C) (-> (or A B) C))) (D Cm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm) (-> (or (-> A B) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-90000.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and (((C -> A) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))), M:tm-977, m:tm-882, u:((Am (-> A B)) (Bm (-> (-> B C) (-> (or A B) C))) (D Cm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm) (-> (or (-> A B) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm))))
================================================================
tm-name          tm-90001
in-theory        90001
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     57
proof            (modus-ponens tm-977 tm-893 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       225
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-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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-90001.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E or F) -> G) -> ((E or (E or F)) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-893, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-90002
in-theory        90002
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-977 tm-895 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       205
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-90002.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-977, m:tm-895, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-90003
in-theory        90003
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)))
theorem-size     69
proof            (modus-ponens tm-977 tm-920 ((Am (-> A B)) (Bm (-> (-> B C) (-> (or A B) C))) (D Cm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm) (-> (or (-> (-> B C) (-> (or A B) C)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       261
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-90003.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))), M:tm-977, m:tm-920, u:((Am (-> A B)) (Bm (-> (-> B C) (-> (or A B) C))) (D Cm) (E (and (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) Cm) (-> (or (-> (-> B C) (-> (or A B) C)) (or (-> A B) (-> (-> B C) (-> (or A B) C)))) Cm))))
================================================================
tm-name          tm-90004
in-theory        90004
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     57
proof            (modus-ponens tm-977 tm-930 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       225
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-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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-90004.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E or F) -> G) -> ((F or (E or F)) -> G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-930, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-90005
in-theory        90005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-977 tm-932 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       205
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-90005.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-977, m:tm-932, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-90006
in-theory        90006
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D)) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D)))
theorem-size     79
proof            (modus-ponens tm-975 tm-977 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       293
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-90006.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D)) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D))), M:tm-975, m:tm-977, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm))))
================================================================
tm-name          tm-90007
in-theory        90007
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D)) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D))) and (((E -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D))))
theorem-size     175
proof            (modus-ponens tm-969 tm-977 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       409
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-90007.        ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D)) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D))) and (((E -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> ((E or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> D)))), M:tm-969, m:tm-977, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm))))
================================================================
tm-name          tm-90008
in-theory        90008
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     61
proof            (modus-ponens tm-930 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90008.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-930, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90009
in-theory        90009
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     61
proof            (modus-ponens tm-893 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90009.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-893, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90010
in-theory        90010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     65
proof            (modus-ponens tm-855 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8)
proof-size       243
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90010.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-855, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90011
in-theory        90011
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))))
theorem-size     79
proof            (modus-ponens tm-850 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       269
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90011.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))), M:tm-850, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
================================================================
tm-name          tm-90012
in-theory        90012
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))) and ((E or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))))
theorem-size     161
proof            (modus-ponens tm-844 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       365
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90012.        ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))) and ((E or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (E and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))))), M:tm-844, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
================================================================
tm-name          tm-90013
in-theory        90013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     59
proof            (modus-ponens tm-808 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90013.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-808, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90014
in-theory        90014
times-derived    1
----------------------------------------------------------------
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)) and (((F and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E)) or ((((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     115
proof            (modus-ponens tm-798 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90014.        ((((((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)) and (((F and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E)) or ((((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-798, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90015
in-theory        90015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     59
proof            (modus-ponens tm-757 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-90015.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-757, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90016
in-theory        90016
times-derived    1
----------------------------------------------------------------
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)) and (((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) and F) or ((((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     115
proof            (modus-ponens tm-747 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-90016.        ((((((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)) and (((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) and F) or ((((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-747, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90017
in-theory        90017
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I)))
theorem-size     73
proof            (modus-ponens tm-708 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       273
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-90017.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I))), M:tm-708, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90018
in-theory        90018
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)))
theorem-size     75
proof            (modus-ponens tm-703 tm-977 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       283
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-90018.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))), M:tm-703, m:tm-977, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C))))
================================================================
tm-name          tm-90019
in-theory        90019
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E)) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))))
theorem-size     169
proof            (modus-ponens tm-697 tm-977 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       397
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-90019.        ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E)) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)))), M:tm-697, m:tm-977, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C))))
================================================================
tm-name          tm-90020
in-theory        90020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     61
proof            (modus-ponens tm-665 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-90020.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-665, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90021
in-theory        90021
times-derived    1
----------------------------------------------------------------
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)) and ((E or ((((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     97
proof            (modus-ponens tm-654 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (B Em) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-90021.        ((((((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)) and ((E or ((((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-654, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (B Em) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90022
in-theory        90022
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (F or (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)))
theorem-size     49
proof            (modus-ponens tm-623 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90022.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (F or (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))), M:tm-623, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90023
in-theory        90023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-622 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-90023.        ((A -> (B -> (C or B))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-622, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90024
in-theory        90024
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (F or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> (F or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E))))
theorem-size     81
proof            (modus-ponens tm-619 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (or B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       241
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90024.        ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (F or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> (F or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)))), M:tm-619, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (or B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
================================================================
tm-name          tm-90025
in-theory        90025
times-derived    1
----------------------------------------------------------------
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)) and (F -> (G or F)))
theorem-size     53
proof            (modus-ponens tm-609 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-90025.        ((((((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)) and (F -> (G or F))), M:tm-609, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90026
in-theory        90026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-605 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-90026.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-605, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90027
in-theory        90027
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G or F)) and (((((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     101
proof            (modus-ponens tm-595 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-90027.        ((((((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)) and ((F -> (G or F)) and (((((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-595, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90028
in-theory        90028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-550 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-90028.        (((A -> (B or A)) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-550, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90029
in-theory        90029
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-540 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-90029.        ((A or (B -> (C or B))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-540, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90030
in-theory        90030
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-530 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-90030.        ((A or (B -> (B or C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-530, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90031
in-theory        90031
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-520 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-90031.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-520, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90032
in-theory        90032
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-510 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-90032.        ((A or ((B and C) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-510, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90033
in-theory        90033
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-500 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-90033.        ((A or ((B and C) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-500, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90034
in-theory        90034
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I)))
theorem-size     63
proof            (modus-ponens tm-490 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-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-90034.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I))), M:tm-490, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90035
in-theory        90035
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-480 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-90035.        ((A or (B -> (C -> B))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-480, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90036
in-theory        90036
times-derived    1
----------------------------------------------------------------
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) or F))
theorem-size     49
proof            (modus-ponens tm-470 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90036.        (((((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) or F)), M:tm-470, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90037
in-theory        90037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-469 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-90037.        ((A -> (B -> (B or C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-469, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90038
in-theory        90038
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) or F))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) or F)))
theorem-size     81
proof            (modus-ponens tm-466 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (or (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       241
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90038.        ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) or F))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) or F))), M:tm-466, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (or (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-90039
in-theory        90039
times-derived    1
----------------------------------------------------------------
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)) and (F -> (F or G)))
theorem-size     53
proof            (modus-ponens tm-456 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-90039.        ((((((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)) and (F -> (F or G))), M:tm-456, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90040
in-theory        90040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-453 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-90040.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-453, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90041
in-theory        90041
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (F or G)) and (((((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     101
proof            (modus-ponens tm-443 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-90041.        ((((((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)) and ((F -> (F or G)) and (((((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-443, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90042
in-theory        90042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-409 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-90042.        (((A -> (A or B)) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-409, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90043
in-theory        90043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-400 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-90043.        (((A -> (B -> (A and B))) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-400, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90044
in-theory        90044
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-391 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-90044.        ((((A and B) -> B) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-391, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90045
in-theory        90045
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-382 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-90045.        ((((A and B) -> A) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-382, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90046
in-theory        90046
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I)))
theorem-size     63
proof            (modus-ponens tm-373 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-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-90046.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I))), M:tm-373, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90047
in-theory        90047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-364 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-90047.        (((A -> (B -> A)) or C) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-364, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90048
in-theory        90048
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (F -> ((((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E) and F)))
theorem-size     51
proof            (modus-ponens tm-355 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90048.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (F -> ((((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E) and F))), M:tm-355, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90049
in-theory        90049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-354 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-90049.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-354, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90050
in-theory        90050
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (F -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) and F)))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> (F -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) and F))))
theorem-size     85
proof            (modus-ponens tm-351 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> B (and (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       253
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90050.        ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (F -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) and F)))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> (F -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) and F)))), M:tm-351, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> B (and (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
================================================================
tm-name          tm-90051
in-theory        90051
times-derived    1
----------------------------------------------------------------
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)) and (F -> (G -> (F and G))))
theorem-size     55
proof            (modus-ponens tm-341 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-90051.        ((((((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)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90052
in-theory        90052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G)))
theorem-size     57
proof            (modus-ponens tm-338 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-90052.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G))), M:tm-338, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90053
in-theory        90053
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) and E))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) and E)))
theorem-size     97
proof            (modus-ponens tm-335 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (and (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (and (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       271
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90053.        ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) and E))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) and E))), M:tm-335, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (and (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (and (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-90054
in-theory        90054
times-derived    1
----------------------------------------------------------------
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)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) and (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))))
theorem-size     113
proof            (modus-ponens tm-328 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       297
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-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-90054.        ((((((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)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) and (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)))), M:tm-328, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90055
in-theory        90055
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G -> (F and G))) and (((((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     103
proof            (modus-ponens tm-327 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       283
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-90055.        ((((((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)) and ((F -> (G -> (F and G))) and (((((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-327, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90056
in-theory        90056
times-derived    1
----------------------------------------------------------------
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)) and (((F and G) -> G) and (((((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     101
proof            (modus-ponens tm-326 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-90056.        ((((((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)) and (((F and G) -> G) and (((((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-326, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90057
in-theory        90057
times-derived    1
----------------------------------------------------------------
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)) and (((F and G) -> F) and (((((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     101
proof            (modus-ponens tm-325 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-90057.        ((((((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)) and (((F and G) -> F) and (((((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-325, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90058
in-theory        90058
times-derived    1
----------------------------------------------------------------
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)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((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     109
proof            (modus-ponens tm-324 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       307
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-90058.        ((((((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)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((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-324, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90059
in-theory        90059
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G -> F)) and (((((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     101
proof            (modus-ponens tm-323 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-90059.        ((((((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)) and ((F -> (G -> F)) and (((((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-323, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90060
in-theory        90060
times-derived    1
----------------------------------------------------------------
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)) and ((F and G) -> G))
theorem-size     53
proof            (modus-ponens tm-322 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-90060.        ((((((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)) and ((F and G) -> G)), M:tm-322, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90061
in-theory        90061
times-derived    1
----------------------------------------------------------------
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)) and ((F and G) -> F))
theorem-size     53
proof            (modus-ponens tm-320 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-90061.        ((((((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)) and ((F and G) -> F)), M:tm-320, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90062
in-theory        90062
times-derived    1
----------------------------------------------------------------
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)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     61
proof            (modus-ponens tm-318 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-90062.        ((((((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)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90063
in-theory        90063
times-derived    1
----------------------------------------------------------------
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)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E)))
theorem-size     83
proof            (modus-ponens tm-316 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-90063.        ((((((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)) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E))), M:tm-316, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90064
in-theory        90064
times-derived    1
----------------------------------------------------------------
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)) and (F -> (G -> F)))
theorem-size     53
proof            (modus-ponens tm-315 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-90064.        ((((((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)) and (F -> (G -> F))), M:tm-315, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90065
in-theory        90065
times-derived    1
----------------------------------------------------------------
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)) and ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (not (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))) -> (not ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E))))
theorem-size     115
proof            (modus-ponens tm-313 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       283
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-90065.        ((((((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)) and ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (not (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))) -> (not ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E)))), M:tm-313, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90066
in-theory        90066
times-derived    1
----------------------------------------------------------------
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)) and (((((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E) -> F) -> ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) or (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)) -> F)))
theorem-size     129
proof            (modus-ponens tm-312 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       301
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-90066.        ((((((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)) and (((((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E) -> F) -> ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) or (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)) -> F))), M:tm-312, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90067
in-theory        90067
times-derived    1
----------------------------------------------------------------
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)) and (F or (((((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     97
proof            (modus-ponens tm-311 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-90067.        ((((((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)) and (F or (((((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-311, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90068
in-theory        90068
times-derived    1
----------------------------------------------------------------
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)) and ((((((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)) or F))
theorem-size     97
proof            (modus-ponens tm-310 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-90068.        ((((((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)) and ((((((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)) or F)), M:tm-310, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90069
in-theory        90069
times-derived    1
----------------------------------------------------------------
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)) and (F -> ((((((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)) and F)))
theorem-size     99
proof            (modus-ponens tm-309 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       257
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
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-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-90069.        ((((((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)) and (F -> ((((((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)) and F))), M:tm-309, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90070
in-theory        90070
times-derived    1
----------------------------------------------------------------
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)) and ((((((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))) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> E)))
theorem-size     113
proof            (modus-ponens tm-306 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C Em)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       287
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (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-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-90070.        ((((((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)) and ((((((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))) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> E))), M:tm-306, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C Em))
================================================================
tm-name          tm-90071
in-theory        90071
times-derived    1
----------------------------------------------------------------
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)) and (F -> (((((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     97
proof            (modus-ponens tm-305 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-90071.        ((((((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)) and (F -> (((((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-305, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90072
in-theory        90072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     59
proof            (modus-ponens tm-303 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-90072.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-303, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90073
in-theory        90073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-270 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-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-90073.        ((A -> (((B and C) -> C) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-270, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90074
in-theory        90074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-239 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-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-90074.        ((A -> (((B and C) -> B) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-239, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90075
in-theory        90075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I)))
theorem-size     65
proof            (modus-ponens tm-210 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-90075.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I))), M:tm-210, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90076
in-theory        90076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-183 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-90076.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-183, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90077
in-theory        90077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-157 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-90077.        ((A -> ((B and C) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-157, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90078
in-theory        90078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     63
proof            (modus-ponens tm-147 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-90078.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-147, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90079
in-theory        90079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-134 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-90079.        ((A -> ((B and C) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-134, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90080
in-theory        90080
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     63
proof            (modus-ponens tm-125 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-90080.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-125, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90081
in-theory        90081
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (E -> F)) -> ((((((B -> C) -> ((A or B) -> C)) -> D) or (((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)) -> F)))
theorem-size     79
proof            (modus-ponens tm-114 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> C D))) (B (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (Em (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       255
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90081.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (E -> F)) -> ((((((B -> C) -> ((A or B) -> C)) -> D) or (((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)) -> F))), M:tm-114, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> C D))) (B (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (Em (-> C D)))
================================================================
tm-name          tm-90082
in-theory        90082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I)))
theorem-size     63
proof            (modus-ponens tm-113 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-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-90082.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I))), M:tm-113, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90083
in-theory        90083
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> F)) -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> F)))) -> (((((C -> D) -> ((B or C) -> D)) -> (E -> F)) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> F))) -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> F))))
theorem-size     115
proof            (modus-ponens tm-110 tm-977 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B C)) (Em (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C))) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (-> B C)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> B C))) (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       307
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90083.        ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> F)) -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> F)))) -> (((((C -> D) -> ((B or C) -> D)) -> (E -> F)) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (E -> F))) -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> F)))), M:tm-110, m:tm-977, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B C)) (Em (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C))) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (-> B C)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> B C))) (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) B) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)))))
================================================================
tm-name          tm-90084
in-theory        90084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     67
proof            (modus-ponens tm-105 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       255
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-90084.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-105, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90085
in-theory        90085
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))) -> (((((B -> C) -> ((A or B) -> C)) -> (D -> E)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)))
theorem-size     115
proof            (modus-ponens tm-102 tm-977 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B C)) (Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (-> B C)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> B C))) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)))))
axioms-used      (tm-8 tm-2)
proof-size       319
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90085.        ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))) -> (((((B -> C) -> ((A or B) -> C)) -> (D -> E)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))), M:tm-102, m:tm-977, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (-> B C)) (Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (-> B C)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> B C))) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C))))
================================================================
tm-name          tm-90086
in-theory        90086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G)))
theorem-size     55
proof            (modus-ponens tm-95 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-90086.        (((A -> B) -> (A -> A)) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G))), M:tm-95, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90087
in-theory        90087
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))
theorem-size     93
proof            (modus-ponens tm-92 tm-977 ((Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       259
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90087.        ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))), M:tm-92, m:tm-977, u:((Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-90088
in-theory        90088
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (F -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)))
theorem-size     49
proof            (modus-ponens tm-84 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90088.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (F -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))), M:tm-84, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90089
in-theory        90089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-83 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-90089.        ((A -> (B -> (C -> B))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-83, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90090
in-theory        90090
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (F -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> (F -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E))))
theorem-size     81
proof            (modus-ponens tm-80 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))))
axioms-used      (tm-8 tm-1)
proof-size       241
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90090.        ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (F -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> (F -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)))), M:tm-80, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
================================================================
tm-name          tm-90091
in-theory        90091
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F)))
theorem-size     53
proof            (modus-ponens tm-76 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-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-90091.        (((not (not A)) -> A) and (((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F))), M:tm-76, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90092
in-theory        90092
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E))) or ((((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     67
proof            (modus-ponens tm-73 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-10)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90092.        (((not (not ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E))) or ((((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-73, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90093
in-theory        90093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G)))
theorem-size     59
proof            (modus-ponens tm-69 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       205
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-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-90093.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G))), M:tm-69, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90094
in-theory        90094
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not D)) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))) -> (((((B -> C) -> ((A or B) -> C)) -> (not D)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     92
proof            (modus-ponens tm-66 tm-977 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (not B)) (Em (not (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (not B)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (not B))) (not (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))))
axioms-used      (tm-8 tm-9)
proof-size       252
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90094.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not D)) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))) -> (((((B -> C) -> ((A or B) -> C)) -> (not D)) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not D))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-66, m:tm-977, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (Dm (not B)) (Em (not (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) (not B)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (not B))) (not (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
================================================================
tm-name          tm-90095
in-theory        90095
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) or ((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> ((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))))
theorem-size     115
proof            (modus-ponens tm-55 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (B (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-2 tm-8)
proof-size       271
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90095.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> ((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) or ((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))) -> ((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))), M:tm-55, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (B (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-90096
in-theory        90096
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     61
proof            (modus-ponens tm-54 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8)
proof-size       211
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-90096.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-54, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90097
in-theory        90097
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> ((A or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> E))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> ((A or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> E)))
theorem-size     95
proof            (modus-ponens tm-51 tm-977 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm)))))
axioms-used      (tm-8)
proof-size       261
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-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-90097.        (((A -> ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> ((A or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> E))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> ((A or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> E))), M:tm-51, m:tm-977, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or C (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) Dm))))
================================================================
tm-name          tm-90098
in-theory        90098
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (A and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> (A and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E))))
theorem-size     81
proof            (modus-ponens tm-48 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))))
axioms-used      (tm-8 tm-5)
proof-size       231
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90098.        ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> (A and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)))) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> (A and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)))), M:tm-48, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (and B (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
================================================================
tm-name          tm-90099
in-theory        90099
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F)) or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F)) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F))
theorem-size     67
proof            (modus-ponens tm-47 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-4)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90099.        (((A and ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F)) or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F)) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F)), M:tm-47, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90100
in-theory        90100
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) and F) or ((((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     67
proof            (modus-ponens tm-46 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-3)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90100.        (((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) and F) or ((((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-46, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90101
in-theory        90101
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E)) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E)))
theorem-size     93
proof            (modus-ponens tm-45 tm-977 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)))))
axioms-used      (tm-8 tm-2)
proof-size       257
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90101.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> E)) or ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> E))), M:tm-45, m:tm-977, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B Dm) (Em (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C)) (D (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) C))))
================================================================
tm-name          tm-90102
in-theory        90102
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> A)) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> A))
theorem-size     49
proof            (modus-ponens tm-44 tm-977 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (B Em) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-1)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90102.        ((A or ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> A)) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> A)), M:tm-44, m:tm-977, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (B Em) (C (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90103
in-theory        90103
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G)))
theorem-size     53
proof            (modus-ponens tm-42 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-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-90103.        ((A -> (B or A)) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G))), M:tm-42, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90104
in-theory        90104
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G)))
theorem-size     53
proof            (modus-ponens tm-32 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-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-90104.        ((A -> (A or B)) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G))), M:tm-32, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90105
in-theory        90105
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) and (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)))
theorem-size     65
proof            (modus-ponens tm-24 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       207
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-90105.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) and (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))), M:tm-24, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90106
in-theory        90106
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G)))
theorem-size     55
proof            (modus-ponens tm-23 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8)
proof-size       193
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-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-90106.        ((A -> (B -> (A and B))) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G))), M:tm-23, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90107
in-theory        90107
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G)))
theorem-size     53
proof            (modus-ponens tm-22 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-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-90107.        (((A and B) -> B) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G))), M:tm-22, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90108
in-theory        90108
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G)))
theorem-size     53
proof            (modus-ponens tm-21 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-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-90108.        (((A and B) -> A) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G))), M:tm-21, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90109
in-theory        90109
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H)))
theorem-size     61
proof            (modus-ponens tm-20 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       211
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-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-90109.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G) -> H) -> (((((E -> F) -> ((D or E) -> F)) -> G) or (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> G)) -> H))), M:tm-20, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90110
in-theory        90110
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G)))
theorem-size     53
proof            (modus-ponens tm-19 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-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-90110.        ((A -> (B -> A)) and (((((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F) -> G) -> (((((D -> E) -> ((C or D) -> E)) -> F) or (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> F)) -> G))), M:tm-19, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90111
in-theory        90111
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E))
theorem-size     35
proof            (modus-ponens tm-12 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       173
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90111.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E)), M:tm-12, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90112
in-theory        90112
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (not (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))) -> (not ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E)))
theorem-size     67
proof            (modus-ponens tm-9 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-9 tm-8)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90112.        ((((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (not (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))) -> (not ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E))), M:tm-9, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90113
in-theory        90113
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) -> F) -> ((((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> E) or (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E)) -> F))
theorem-size     81
proof            (modus-ponens tm-8 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
axioms-used      (tm-8)
proof-size       207
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-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-90113.        (((((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) -> F) -> ((((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> E) or (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E)) -> F)), M:tm-8, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))
================================================================
tm-name          tm-90114
in-theory        90114
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F)))
theorem-size     49
proof            (modus-ponens tm-7 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-7 tm-8)
proof-size       167
proof-steps      7
----------------------------------------------------------------
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-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-90114.        (A or (((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F))), M:tm-7, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90115
in-theory        90115
times-derived    2
----------------------------------------------------------------
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)) or F)
theorem-size     49
proof            (modus-ponens tm-6 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-6 tm-8)
proof-size       167
proof-steps      7
----------------------------------------------------------------
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-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-90115.        ((((((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)) or F), M:tm-6, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90116
in-theory        90116
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F)) and A))
theorem-size     51
proof            (modus-ponens tm-5 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8)
proof-size       171
proof-steps      7
----------------------------------------------------------------
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-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-90116.        (A -> ((((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F)) and A)), M:tm-5, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90117
in-theory        90117
times-derived    2
----------------------------------------------------------------
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))) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> E))
theorem-size     65
proof            (modus-ponens tm-2 tm-977 ((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C Em)))
axioms-used      (tm-2 tm-8)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90117.        ((((((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))) -> (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> E)), M:tm-2, m:tm-977, u:((A (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)) (B (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))) (C Em))
================================================================
tm-name          tm-90118
in-theory        90118
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F)))
theorem-size     49
proof            (modus-ponens tm-1 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-1 tm-8)
proof-size       167
proof-steps      7
----------------------------------------------------------------
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-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-90118.        (A -> (((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E) -> F) -> (((((C -> D) -> ((B or C) -> D)) -> E) or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> E)) -> F))), M:tm-1, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-90119
in-theory        90119
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-930 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90119.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-930, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90120
in-theory        90120
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-893 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), 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-90120.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-893, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90121
in-theory        90121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     47
proof            (modus-ponens tm-855 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), 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-90121.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-855, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90122
in-theory        90122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-808 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), 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-90122.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-808, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90123
in-theory        90123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-757 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90123.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-757, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90124
in-theory        90124
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 F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     55
proof            (modus-ponens tm-708 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), 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-90124.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-708, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90125
in-theory        90125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-665 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90125.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-665, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90126
in-theory        90126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-622 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90126.        ((A -> (B -> (C or B))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-622, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90127
in-theory        90127
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90127.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90128
in-theory        90128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-605 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90128.        ((A -> ((B -> (C or B)) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-605, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90129
in-theory        90129
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G or F)) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-90129.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G or F)) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-595, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90130
in-theory        90130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-550 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90130.        (((A -> (B or A)) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-550, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90131
in-theory        90131
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-540 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90131.        ((A or (B -> (C or B))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-540, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90132
in-theory        90132
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-530 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90132.        ((A or (B -> (B or C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-530, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90133
in-theory        90133
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-520 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90133.        ((A or (B -> (C -> (B and C)))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-520, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90134
in-theory        90134
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-510 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90134.        ((A or ((B and C) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-510, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90135
in-theory        90135
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-500 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90135.        ((A or ((B and C) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-500, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90136
in-theory        90136
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-490 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90136.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-490, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90137
in-theory        90137
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-480 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90137.        ((A or (B -> (C -> B))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-480, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90138
in-theory        90138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-469 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-90138.        ((A -> (B -> (B or C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-469, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90139
in-theory        90139
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90139.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90140
in-theory        90140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-453 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-90140.        ((A -> ((B -> (B or C)) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-453, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90141
in-theory        90141
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (F or G)) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90141.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (F or G)) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-443, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90142
in-theory        90142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-409 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-90142.        (((A -> (A or B)) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-409, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90143
in-theory        90143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-400 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-90143.        (((A -> (B -> (A and B))) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-400, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90144
in-theory        90144
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-391 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-90144.        ((((A and B) -> B) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-391, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90145
in-theory        90145
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-382 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-90145.        ((((A and B) -> A) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-382, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90146
in-theory        90146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-373 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 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-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-90146.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-373, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90147
in-theory        90147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-364 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-90147.        (((A -> (B -> A)) or C) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-364, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90148
in-theory        90148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-354 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-90148.        ((A -> (B -> (C -> (B and C)))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-354, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90149
in-theory        90149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90149.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90150
in-theory        90150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     39
proof            (modus-ponens tm-338 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-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-90150.        (((A -> B) -> (A -> (A and B))) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-338, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90151
in-theory        90151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> (F and G))) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90151.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> (F and G))) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-327, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90152
in-theory        90152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and G) -> G) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90152.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and G) -> G) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-326, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90153
in-theory        90153
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and G) -> F) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90153.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and G) -> F) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-325, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90154
in-theory        90154
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-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-90154.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-324, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90155
in-theory        90155
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> F)) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90155.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> F)) and (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-323, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90156
in-theory        90156
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90156.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90157
in-theory        90157
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90157.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90158
in-theory        90158
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90158.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90159
in-theory        90159
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90159.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90160
in-theory        90160
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F or (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90160.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F or (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-311, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90161
in-theory        90161
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90161.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) or F)), M:tm-310, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90162
in-theory        90162
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90162.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and F))), M:tm-309, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90163
in-theory        90163
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90163.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-305, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90164
in-theory        90164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-303 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-90164.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-303, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90165
in-theory        90165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-270 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-90165.        ((A -> (((B and C) -> C) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-270, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90166
in-theory        90166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-239 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-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-90166.        ((A -> (((B and C) -> B) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-239, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90167
in-theory        90167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-210 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-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-90167.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-210, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90168
in-theory        90168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-183 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-90168.        ((A -> ((B -> (C -> B)) and A)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-183, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90169
in-theory        90169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-157 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-90169.        ((A -> ((B and C) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-157, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90170
in-theory        90170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     45
proof            (modus-ponens tm-147 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 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-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-90170.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-147, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90171
in-theory        90171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-134 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-90171.        ((A -> ((B and C) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-134, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90172
in-theory        90172
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     45
proof            (modus-ponens tm-125 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-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-90172.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-125, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90173
in-theory        90173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-113 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 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-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-90173.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-113, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90174
in-theory        90174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     49
proof            (modus-ponens tm-105 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-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-90174.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-105, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90175
in-theory        90175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     37
proof            (modus-ponens tm-95 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90175.        (((A -> B) -> (A -> A)) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-95, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90176
in-theory        90176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-83 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-90176.        ((A -> (B -> (C -> B))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-83, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90177
in-theory        90177
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-76 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8)
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-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-90177.        (((not (not A)) -> A) and (B or ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-76, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90178
in-theory        90178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     41
proof            (modus-ponens tm-69 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8)
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-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-90178.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-69, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90179
in-theory        90179
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-54 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), 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-90179.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-54, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90180
in-theory        90180
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-42 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90180.        ((A -> (B or A)) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-42, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90181
in-theory        90181
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-32 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-90181.        ((A -> (A or B)) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-32, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90182
in-theory        90182
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     37
proof            (modus-ponens tm-23 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-90182.        ((A -> (B -> (A and B))) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-23, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90183
in-theory        90183
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-22 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-90183.        (((A and B) -> B) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-22, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90184
in-theory        90184
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-21 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-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-90184.        (((A and B) -> A) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-21, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90185
in-theory        90185
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-20 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 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-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-90185.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-20, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90186
in-theory        90186
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-19 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-90186.        ((A -> (B -> A)) and (C or ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-19, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90187
in-theory        90187
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     31
proof            (modus-ponens tm-7 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90187.        (A or (B or ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-7, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90188
in-theory        90188
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) or F)
theorem-size     31
proof            (modus-ponens tm-6 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-6 tm-7 tm-8)
proof-size       123
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90188.        ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) or F), M:tm-6, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90189
in-theory        90189
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       127
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90189.        (A -> ((B or ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and A)), M:tm-5, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90190
in-theory        90190
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     31
proof            (modus-ponens tm-1 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-1 tm-7 tm-8)
proof-size       123
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90190.        (A -> (B or ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-1, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-90191
in-theory        90191
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-966 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> (-> B C) (-> (or D B) C)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       241
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
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-90191.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-966, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> (-> B C) (-> (or D B) C)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90192
in-theory        90192
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     51
proof            (modus-ponens tm-962 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> (-> B C) (-> (or D B) C)) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (-> (-> B C) (-> (or D B) C)))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       277
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-90192.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> C) -> ((A or B) -> C)))), M:tm-962, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> (-> B C) (-> (or D B) C)) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (-> (-> B C) (-> (or D B) C))))))
================================================================
tm-name          tm-90193
in-theory        90193
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H))
theorem-size     43
proof            (modus-ponens tm-930 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), 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-90193.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-930, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90194
in-theory        90194
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-917 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (or B C) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), 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-90194.        ((A or (B or A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-917, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (or B C) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90195
in-theory        90195
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (B or A)))
theorem-size     37
proof            (modus-ponens tm-914 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (or B C) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (or B C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-90195.        ((A or (B or A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (B or A))), M:tm-914, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (or B C) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (or B C)))))
================================================================
tm-name          tm-90196
in-theory        90196
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H))
theorem-size     43
proof            (modus-ponens tm-893 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90196.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-893, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90197
in-theory        90197
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-879 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (or B C) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90197.        ((A or (A or B)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-879, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (or B C) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90198
in-theory        90198
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B)))
theorem-size     37
proof            (modus-ponens tm-876 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (or B C) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (or B C))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90198.        ((A or (A or B)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B))), M:tm-876, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (or B C) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (or B C)))))
================================================================
tm-name          tm-90199
in-theory        90199
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G))
theorem-size     35
proof            (modus-ponens tm-874 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90199.        ((A -> (B or A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G)), M:tm-874, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90200
in-theory        90200
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G))
theorem-size     35
proof            (modus-ponens tm-872 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90200.        ((A -> (A or B)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G)), M:tm-872, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90201
in-theory        90201
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G))
theorem-size     37
proof            (modus-ponens tm-870 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90201.        ((A -> (B -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G)), M:tm-870, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90202
in-theory        90202
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G))
theorem-size     35
proof            (modus-ponens tm-869 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90202.        (((A and B) -> B) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G)), M:tm-869, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90203
in-theory        90203
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G))
theorem-size     35
proof            (modus-ponens tm-868 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90203.        (((A and B) -> A) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G)), M:tm-868, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90204
in-theory        90204
times-derived    2
----------------------------------------------------------------
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)) or H))
theorem-size     43
proof            (modus-ponens tm-867 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90204.        (((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)) or H)), M:tm-867, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90205
in-theory        90205
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G))
theorem-size     35
proof            (modus-ponens tm-866 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90205.        ((A -> (B -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G)), M:tm-866, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90206
in-theory        90206
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) or F))
theorem-size     31
proof            (modus-ponens tm-861 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 tm-7)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90206.        (A or (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) or F)), M:tm-861, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90207
in-theory        90207
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) or F)
theorem-size     31
proof            (modus-ponens tm-860 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90207.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) or F), M:tm-860, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90208
in-theory        90208
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) or F) and A))
theorem-size     33
proof            (modus-ponens tm-859 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90208.        (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) or F) and A)), M:tm-859, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90209
in-theory        90209
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) or F))
theorem-size     31
proof            (modus-ponens tm-858 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
axioms-used      (tm-8 tm-6 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90209.        (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) or F)), M:tm-858, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))
================================================================
tm-name          tm-90210
in-theory        90210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H))
theorem-size     47
proof            (modus-ponens tm-855 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90210.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-855, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90211
in-theory        90211
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-841 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> B (and C B)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       209
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90211.        ((A or (B -> (A and B))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-841, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> B (and C B)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90212
in-theory        90212
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (B -> (A and B))))
theorem-size     41
proof            (modus-ponens tm-837 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> B (and C B)) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (-> B (and C B)))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       233
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-90212.        ((A or (B -> (A and B))) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (B -> (A and B)))), M:tm-837, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> B (and C B)) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (-> B (and C B))))))
================================================================
tm-name          tm-90213
in-theory        90213
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B))
theorem-size     35
proof            (modus-ponens tm-836 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
proof-size       205
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-90213.        (((A and B) or B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B)), M:tm-836, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90214
in-theory        90214
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A))
theorem-size     35
proof            (modus-ponens tm-835 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
proof-size       205
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-90214.        (((A and B) or A) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A)), M:tm-835, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90215
in-theory        90215
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> (A -> C))))
theorem-size     49
proof            (modus-ponens tm-834 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> (-> B C) (-> B D)) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       267
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-90215.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> (A -> C)))), M:tm-834, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> (-> B C) (-> B D)) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-90216
in-theory        90216
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (B -> A)))
theorem-size     37
proof            (modus-ponens tm-833 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> B C) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (-> B C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-90216.        ((A or (B -> A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (B -> A))), M:tm-833, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> B C) (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (-> B C)))))
================================================================
tm-name          tm-90217
in-theory        90217
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C)))
theorem-size     37
proof            (modus-ponens tm-831 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90217.        ((A -> (B or A)) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C))), M:tm-831, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90218
in-theory        90218
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C)))
theorem-size     37
proof            (modus-ponens tm-829 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90218.        ((A -> (A or B)) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C))), M:tm-829, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90219
in-theory        90219
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))
theorem-size     33
proof            (modus-ponens tm-827 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90219.        (A -> (A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))), M:tm-827, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90220
in-theory        90220
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C)))
theorem-size     39
proof            (modus-ponens tm-826 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-90220.        ((A -> (B -> (A and B))) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C))), M:tm-826, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90221
in-theory        90221
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C)))
theorem-size     37
proof            (modus-ponens tm-825 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90221.        (((A and B) -> B) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C))), M:tm-825, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90222
in-theory        90222
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C)))
theorem-size     37
proof            (modus-ponens tm-824 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90222.        (((A and B) -> A) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C))), M:tm-824, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90223
in-theory        90223
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     45
proof            (modus-ponens tm-823 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       233
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-90223.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-823, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90224
in-theory        90224
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C)))
theorem-size     37
proof            (modus-ponens tm-822 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90224.        ((A -> (B -> A)) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C))), M:tm-822, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90225
in-theory        90225
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))) -> (not A))
theorem-size     35
proof            (modus-ponens tm-816 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-9 tm-6)
proof-size       187
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-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-6.            (A -> (A or B)), 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-90225.        ((A -> (not (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))) -> (not A)), M:tm-816, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90226
in-theory        90226
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 or (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and E)) -> F))
theorem-size     65
proof            (modus-ponens tm-815 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       223
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-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-6.            (A -> (A or B)), 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-90226.        (((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and E) -> F) -> ((E or (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and E)) -> F)), M:tm-815, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90227
in-theory        90227
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B)))
theorem-size     33
proof            (modus-ponens tm-814 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90227.        (A or (B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B))), M:tm-814, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90228
in-theory        90228
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) or F)
theorem-size     33
proof            (modus-ponens tm-813 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90228.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) or F), M:tm-813, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90229
in-theory        90229
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B)) and A))
theorem-size     35
proof            (modus-ponens tm-812 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90229.        (A -> ((B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B)) and A)), M:tm-812, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90230
in-theory        90230
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B)))
theorem-size     33
proof            (modus-ponens tm-811 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), 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-90230.        (A -> (B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B))), M:tm-811, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (and (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B))))
================================================================
tm-name          tm-90231
in-theory        90231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H))
theorem-size     41
proof            (modus-ponens tm-808 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), 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-90231.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-808, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90232
in-theory        90232
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-795 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-6)
proof-size       193
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), 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-90232.        (((A and B) or B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-795, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90233
in-theory        90233
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C))))) or ((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C))))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E))
theorem-size     67
proof            (modus-ponens tm-794 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-6)
proof-size       261
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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), 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-90233.        (((A and ((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C))))) or ((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C))))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E)), M:tm-794, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90234
in-theory        90234
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)) or H))
theorem-size     41
proof            (modus-ponens tm-757 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90234.        (((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)) or H)), M:tm-757, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90235
in-theory        90235
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-744 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-6)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90235.        (((A and B) or A) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-744, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90236
in-theory        90236
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) and E) or ((((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-743 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-6)
proof-size       261
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90236.        (((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) and E) or ((((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-743, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90237
in-theory        90237
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)) or I))
theorem-size     55
proof            (modus-ponens tm-708 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), 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-90237.        (((((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)) or I)), M:tm-708, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90238
in-theory        90238
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-694 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> (-> B C) (-> B D)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       237
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90238.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-694, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> (-> B C) (-> B D)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90239
in-theory        90239
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((((B -> C) -> ((A or B) -> C)) -> D) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))) -> ((((B -> C) -> ((A or B) -> C)) -> D) -> D))
theorem-size     53
proof            (modus-ponens tm-692 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90239.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or ((((B -> C) -> ((A or B) -> C)) -> D) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))) -> ((((B -> C) -> ((A or B) -> C)) -> D) -> D)), M:tm-692, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90240
in-theory        90240
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F)))
theorem-size     45
proof            (modus-ponens tm-690 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90240.        ((A -> (B or A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F))), M:tm-690, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90241
in-theory        90241
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F)))
theorem-size     45
proof            (modus-ponens tm-688 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90241.        ((A -> (A or B)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F))), M:tm-688, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90242
in-theory        90242
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> D)))
theorem-size     65
proof            (modus-ponens tm-686 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
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-5.            (A -> (B -> (A and B))), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90242.        (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> D))), M:tm-686, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90243
in-theory        90243
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F)))
theorem-size     47
proof            (modus-ponens tm-685 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90243.        ((A -> (B -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F))), M:tm-685, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90244
in-theory        90244
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F)))
theorem-size     45
proof            (modus-ponens tm-684 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 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-4.            ((A and B) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90244.        (((A and B) -> B) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F))), M:tm-684, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90245
in-theory        90245
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F)))
theorem-size     45
proof            (modus-ponens tm-683 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 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-3.            ((A and B) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90245.        (((A and B) -> A) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F))), M:tm-683, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90246
in-theory        90246
times-derived    2
----------------------------------------------------------------
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     53
proof            (modus-ponens tm-682 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       263
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90246.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-682, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90247
in-theory        90247
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F)))
theorem-size     45
proof            (modus-ponens tm-681 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90247.        ((A -> (B -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F))), M:tm-681, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90248
in-theory        90248
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     51
proof            (modus-ponens tm-676 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       235
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90248.        (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-676, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90249
in-theory        90249
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> D))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))))
theorem-size     67
proof            (modus-ponens tm-674 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-9 tm-6)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90249.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> D))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))), M:tm-674, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90250
in-theory        90250
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> D) -> E) -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) or ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) -> E))
theorem-size     57
proof            (modus-ponens tm-673 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-6)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90250.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> D) -> E) -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) or ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) -> E)), M:tm-673, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90251
in-theory        90251
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E)))
theorem-size     41
proof            (modus-ponens tm-672 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-6)
proof-size       207
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90251.        (A or (((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E))), M:tm-672, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90252
in-theory        90252
times-derived    2
----------------------------------------------------------------
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)) or E)
theorem-size     41
proof            (modus-ponens tm-671 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       207
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90252.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) or E), M:tm-671, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90253
in-theory        90253
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E)) and A))
theorem-size     43
proof            (modus-ponens tm-670 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90253.        (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E)) and A)), M:tm-670, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90254
in-theory        90254
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> D)) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))
theorem-size     65
proof            (modus-ponens tm-669 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       241
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90254.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> D)) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)), M:tm-669, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90255
in-theory        90255
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E)))
theorem-size     41
proof            (modus-ponens tm-668 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       207
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90255.        (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E))), M:tm-668, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-90256
in-theory        90256
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)) or H))
theorem-size     43
proof            (modus-ponens tm-665 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90256.        ((((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)) or H)), M:tm-665, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90257
in-theory        90257
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-651 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> B C) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90257.        ((A or (B -> A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-651, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (-> B C) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90258
in-theory        90258
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-649 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90258.        ((A -> (B or A)) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-649, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90259
in-theory        90259
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-647 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90259.        ((A -> (A or B)) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-647, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90260
in-theory        90260
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))
theorem-size     31
proof            (modus-ponens tm-645 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90260.        (A -> (A and ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))), M:tm-645, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90261
in-theory        90261
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     37
proof            (modus-ponens tm-644 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
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-5.            (A -> (B -> (A and B))), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90261.        ((A -> (B -> (A and B))) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-644, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90262
in-theory        90262
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-643 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90262.        (((A and B) -> B) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-643, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90263
in-theory        90263
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-642 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90263.        (((A and B) -> A) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-642, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90264
in-theory        90264
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-641 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90264.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-641, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90265
in-theory        90265
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     35
proof            (modus-ponens tm-640 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90265.        ((A -> (B -> A)) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-640, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90266
in-theory        90266
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F)) -> F)
theorem-size     33
proof            (modus-ponens tm-638 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (and B (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) C)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4 tm-6)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90266.        ((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F)) -> F), M:tm-638, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (and B (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) C)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90267
in-theory        90267
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) and F) -> E)
theorem-size     33
proof            (modus-ponens tm-636 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (and (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B) C) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3 tm-6)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90267.        (((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) and F) -> E), M:tm-636, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> (and (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) B) C) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90268
in-theory        90268
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> E)) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> E))
theorem-size     43
proof            (modus-ponens tm-634 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm) C)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       229
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90268.        (((((A -> B) -> ((C or A) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> E)) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> E)), M:tm-634, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (Em (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm) C)) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90269
in-theory        90269
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))) -> (not A))
theorem-size     33
proof            (modus-ponens tm-631 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-9 tm-6)
proof-size       175
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90269.        ((A -> (not ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))) -> (not A)), M:tm-631, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90270
in-theory        90270
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) -> ((F or ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> E))
theorem-size     61
proof            (modus-ponens tm-630 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       207
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90270.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) -> ((F or ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> E)), M:tm-630, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90271
in-theory        90271
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     31
proof            (modus-ponens tm-629 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-7 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90271.        (A or (B -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-629, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90272
in-theory        90272
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) or F)
theorem-size     31
proof            (modus-ponens tm-628 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90272.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) or F), M:tm-628, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90273
in-theory        90273
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and A))
theorem-size     33
proof            (modus-ponens tm-627 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       171
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90273.        (A -> ((B -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and A)), M:tm-627, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90274
in-theory        90274
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((D or B) -> C)) -> E)) -> (A -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     31
proof            (modus-ponens tm-626 tm-979 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (Em (-> C (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90274.        ((A -> (((B -> C) -> ((D or B) -> C)) -> E)) -> (A -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-626, m:tm-979, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) (Em (-> C (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90275
in-theory        90275
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     31
proof            (modus-ponens tm-625 tm-979 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))))
axioms-used      (tm-8 tm-1 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90275.        (A -> (B -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-625, m:tm-979, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-90276
in-theory        90276
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)) or H))
theorem-size     37
proof            (modus-ponens tm-622 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-90276.        ((A -> (B -> (C or B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-622, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90277
in-theory        90277
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90277.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (G or F))), M:tm-609, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90278
in-theory        90278
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)) or H))
theorem-size     39
proof            (modus-ponens tm-605 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-90278.        ((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)) or H)), M:tm-605, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90279
in-theory        90279
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (G or F)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)))
theorem-size     65
proof            (modus-ponens tm-595 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90279.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (G or F)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))), M:tm-595, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90280
in-theory        90280
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)) or H))
theorem-size     37
proof            (modus-ponens tm-550 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90280.        (((A -> (B or A)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-550, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90281
in-theory        90281
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)) or H))
theorem-size     37
proof            (modus-ponens tm-540 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-90281.        ((A or (B -> (C or B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-540, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90282
in-theory        90282
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)) or H))
theorem-size     37
proof            (modus-ponens tm-530 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90282.        ((A or (B -> (B or C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-530, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90283
in-theory        90283
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)) or H))
theorem-size     39
proof            (modus-ponens tm-520 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-90283.        ((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)) or H)), M:tm-520, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90284
in-theory        90284
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)) or H))
theorem-size     37
proof            (modus-ponens tm-510 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-90284.        ((A or ((B and C) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-510, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90285
in-theory        90285
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)) or H))
theorem-size     37
proof            (modus-ponens tm-500 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-90285.        ((A or ((B and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-500, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90286
in-theory        90286
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)) or I))
theorem-size     45
proof            (modus-ponens tm-490 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 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-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-90286.        ((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)) or I)), M:tm-490, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90287
in-theory        90287
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)) or H))
theorem-size     37
proof            (modus-ponens tm-480 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-90287.        ((A or (B -> (C -> B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-480, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90288
in-theory        90288
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)) or H))
theorem-size     37
proof            (modus-ponens tm-469 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90288.        ((A -> (B -> (B or C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-469, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90289
in-theory        90289
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90289.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (F or G))), M:tm-456, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90290
in-theory        90290
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)) or H))
theorem-size     39
proof            (modus-ponens tm-453 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90290.        ((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)) or H)), M:tm-453, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90291
in-theory        90291
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (F or G)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)))
theorem-size     65
proof            (modus-ponens tm-443 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-90291.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (F or G)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))), M:tm-443, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90292
in-theory        90292
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)) or H))
theorem-size     37
proof            (modus-ponens tm-409 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90292.        (((A -> (A or B)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-409, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90293
in-theory        90293
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)) or H))
theorem-size     39
proof            (modus-ponens tm-400 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90293.        (((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)) or H)), M:tm-400, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90294
in-theory        90294
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)) or H))
theorem-size     37
proof            (modus-ponens tm-391 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90294.        ((((A and B) -> B) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-391, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90295
in-theory        90295
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)) or H))
theorem-size     37
proof            (modus-ponens tm-382 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90295.        ((((A and B) -> A) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-382, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90296
in-theory        90296
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)) or I))
theorem-size     45
proof            (modus-ponens tm-373 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90296.        ((((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)) or I)), M:tm-373, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90297
in-theory        90297
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)) or H))
theorem-size     37
proof            (modus-ponens tm-364 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90297.        (((A -> (B -> A)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-364, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90298
in-theory        90298
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)) or H))
theorem-size     39
proof            (modus-ponens tm-354 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-90298.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-354, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90299
in-theory        90299
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90299.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (G -> (F and G)))), M:tm-341, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90300
in-theory        90300
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)) or G))
theorem-size     39
proof            (modus-ponens tm-338 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-6 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-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-90300.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G)), M:tm-338, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90301
in-theory        90301
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (G -> (F and G))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)))
theorem-size     67
proof            (modus-ponens tm-327 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90301.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (G -> (F and G))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))), M:tm-327, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90302
in-theory        90302
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (((F and G) -> G) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)))
theorem-size     65
proof            (modus-ponens tm-326 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90302.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (((F and G) -> G) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))), M:tm-326, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90303
in-theory        90303
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (((F and G) -> F) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)))
theorem-size     65
proof            (modus-ponens tm-325 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90303.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (((F and G) -> F) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))), M:tm-325, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90304
in-theory        90304
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)))
theorem-size     73
proof            (modus-ponens tm-324 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-6 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-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-90304.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))), M:tm-324, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90305
in-theory        90305
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (G -> F)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)))
theorem-size     65
proof            (modus-ponens tm-323 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90305.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (G -> F)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))), M:tm-323, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90306
in-theory        90306
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90306.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F and G) -> G)), M:tm-322, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90307
in-theory        90307
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90307.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F and G) -> F)), M:tm-320, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90308
in-theory        90308
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90308.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90309
in-theory        90309
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90309.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (G -> F))), M:tm-315, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90310
in-theory        90310
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F or (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)))
theorem-size     61
proof            (modus-ponens tm-311 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90310.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F or (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))), M:tm-311, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90311
in-theory        90311
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90311.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) or F)), M:tm-310, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90312
in-theory        90312
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90312.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and F))), M:tm-309, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90313
in-theory        90313
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)))
theorem-size     61
proof            (modus-ponens tm-305 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90313.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E) and (F -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))), M:tm-305, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90314
in-theory        90314
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)) or H))
theorem-size     41
proof            (modus-ponens tm-303 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-90314.        ((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)) or H)), M:tm-303, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90315
in-theory        90315
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)) or H))
theorem-size     39
proof            (modus-ponens tm-270 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-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-90315.        ((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)) or H)), M:tm-270, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90316
in-theory        90316
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)) or H))
theorem-size     39
proof            (modus-ponens tm-239 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
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-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-90316.        ((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)) or H)), M:tm-239, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90317
in-theory        90317
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)) or I))
theorem-size     47
proof            (modus-ponens tm-210 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-6 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-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-90317.        ((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)) or I)), M:tm-210, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90318
in-theory        90318
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)) or H))
theorem-size     39
proof            (modus-ponens tm-183 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-90318.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-183, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90319
in-theory        90319
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)) or H))
theorem-size     37
proof            (modus-ponens tm-157 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-90319.        ((A -> ((B and C) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-157, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90320
in-theory        90320
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)) or H))
theorem-size     45
proof            (modus-ponens tm-147 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 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-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-90320.        ((((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)) or H)), M:tm-147, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90321
in-theory        90321
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)) or H))
theorem-size     37
proof            (modus-ponens tm-134 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-90321.        ((A -> ((B and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-134, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90322
in-theory        90322
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)) or H))
theorem-size     45
proof            (modus-ponens tm-125 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-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-90322.        (((((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)) or H)), M:tm-125, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90323
in-theory        90323
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)) or I))
theorem-size     45
proof            (modus-ponens tm-113 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 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-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-90323.        ((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)) or I)), M:tm-113, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90324
in-theory        90324
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)) or H))
theorem-size     49
proof            (modus-ponens tm-105 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-6 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-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-90324.        ((((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)) or H)), M:tm-105, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90325
in-theory        90325
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)) or G))
theorem-size     37
proof            (modus-ponens tm-95 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-90325.        (((A -> B) -> (A -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) or G)), M:tm-95, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90326
in-theory        90326
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)) or H))
theorem-size     37
proof            (modus-ponens tm-83 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-90326.        ((A -> (B -> (C -> B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) or H)), M:tm-83, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90327
in-theory        90327
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)) or F))
theorem-size     35
proof            (modus-ponens tm-76 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-10 tm-6 tm-8)
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-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-90327.        (((not (not A)) -> A) and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) or F)), M:tm-76, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90328
in-theory        90328
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)) or G))
theorem-size     41
proof            (modus-ponens tm-69 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-9 tm-6 tm-8)
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-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-90328.        (((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)) or G)), M:tm-69, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90329
in-theory        90329
times-derived    2
----------------------------------------------------------------
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)) or H))
theorem-size     43
proof            (modus-ponens tm-54 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), 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-90329.        (((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)) or H)), M:tm-54, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-90330
in-theory        90330
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8)
proof-size       145
proof-steps      7
----------------------------------------------------------------
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-90330.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-980, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-90331
in-theory        90331
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 -> (not F)) -> (not E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       141
proof-steps      7
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-90331.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-980, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-90332
in-theory        90332
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((not (not E)) -> E))
theorem-size     33
proof            (modus-ponens tm-980 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-8 tm-10)
proof-size       129
proof-steps      7
----------------------------------------------------------------
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-10.           ((not (not A)) -> A), axiom
tm-90332.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((not (not E)) -> E)), M:tm-980, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-90333
in-theory        90333
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 -> F))))
theorem-size     35
proof            (modus-ponens tm-980 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-90333.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (G -> F)))), M:tm-980, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-90334
in-theory        90334
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 -> E)))
theorem-size     35
proof            (modus-ponens tm-980 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-90334.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (E -> E))), M:tm-980, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-90335
in-theory        90335
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 -> (F -> G)) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-980 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-90335.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-980, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-90336
in-theory        90336
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 -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-90336.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-980, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-90337
in-theory        90337
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     43
proof            (modus-ponens tm-980 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       167
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-90337.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-980, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-90338
in-theory        90338
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-980 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-90338.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F and G) -> F))), M:tm-980, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-90339
in-theory        90339
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 -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     43
proof            (modus-ponens tm-980 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       167
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-90339.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-980, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-90340
in-theory        90340
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F and G) -> G)))
theorem-size     35
proof            (modus-ponens tm-980 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-90340.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F and G) -> G))), M:tm-980, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-90341
in-theory        90341
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 -> F)) and E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-90341.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G -> F)) and E))), M:tm-980, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-90342
in-theory        90342
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 -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     45
proof            (modus-ponens tm-980 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-90342.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-980, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-90343
in-theory        90343
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and G) -> F) and E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-90343.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and G) -> F) and E))), M:tm-980, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-90344
in-theory        90344
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and G) -> G) and E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-90344.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and G) -> G) and E))), M:tm-980, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-90345
in-theory        90345
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 -> (F and G))) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-90345.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G -> (F and G))) and E))), M:tm-980, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-90346
in-theory        90346
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 -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-980 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-90346.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (E -> (E and F)))), M:tm-980, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-90347
in-theory        90347
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 -> (F and G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-90347.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (G -> (F and G))))), M:tm-980, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-90348
in-theory        90348
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)) or G))
theorem-size     35
proof            (modus-ponens tm-980 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-90348.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) or G)), M:tm-980, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-90349
in-theory        90349
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))) or H))
theorem-size     43
proof            (modus-ponens tm-980 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-90349.        (((((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))) or H)), M:tm-980, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-90350
in-theory        90350
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) or G))
theorem-size     35
proof            (modus-ponens tm-980 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-90350.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) or G)), M:tm-980, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-90351
in-theory        90351
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) or G))
theorem-size     35
proof            (modus-ponens tm-980 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-90351.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) or G)), M:tm-980, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-90352
in-theory        90352
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))) or G))
theorem-size     37
proof            (modus-ponens tm-980 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-90352.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) or G)), M:tm-980, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-90353
in-theory        90353
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)) or G))
theorem-size     35
proof            (modus-ponens tm-980 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-90353.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) or G)), M:tm-980, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-90354
in-theory        90354
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (F or G)) and E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-90354.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (F or G)) and E))), M:tm-980, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-90355
in-theory        90355
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (F or G))))
theorem-size     35
proof            (modus-ponens tm-980 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-90355.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (F or G)))), M:tm-980, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-90356
in-theory        90356
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> F))))
theorem-size     35
proof            (modus-ponens tm-980 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-90356.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> F)))), M:tm-980, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-90357
in-theory        90357
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-90357.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-980, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-90358
in-theory        90358
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-980 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-90358.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F and G) -> F))), M:tm-980, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-90359
in-theory        90359
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F and G) -> G)))
theorem-size     35
proof            (modus-ponens tm-980 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-90359.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F and G) -> G))), M:tm-980, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-90360
in-theory        90360
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (F and G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-90360.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (F and G))))), M:tm-980, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-90361
in-theory        90361
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (F or G))))
theorem-size     35
proof            (modus-ponens tm-980 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-90361.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (F or G)))), M:tm-980, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-90362
in-theory        90362
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G or F))))
theorem-size     35
proof            (modus-ponens tm-980 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-90362.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G or F)))), M:tm-980, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-90363
in-theory        90363
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)) or G))
theorem-size     35
proof            (modus-ponens tm-980 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-90363.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) or G)), M:tm-980, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-90364
in-theory        90364
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 or F)) and E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-90364.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G or F)) and E))), M:tm-980, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-90365
in-theory        90365
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 or F))))
theorem-size     35
proof            (modus-ponens tm-980 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-90365.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (G or F)))), M:tm-980, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-90366
in-theory        90366
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) -> ((F or (E -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-980 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-90366.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-980, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-90367
in-theory        90367
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 -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     53
proof            (modus-ponens tm-980 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       195
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-90367.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-980, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-90368
in-theory        90368
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 G) or E) -> F)))
theorem-size     39
proof            (modus-ponens tm-980 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-90368.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (((E and G) or E) -> F))), M:tm-980, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-90369
in-theory        90369
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 and E) or E) -> F)))
theorem-size     39
proof            (modus-ponens tm-980 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-90369.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (((G and E) or E) -> F))), M:tm-980, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-90370
in-theory        90370
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     45
proof            (modus-ponens tm-980 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-90370.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-980, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-90371
in-theory        90371
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-980 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-90371.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-980, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-90372
in-theory        90372
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-980 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-90372.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-980, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-90373
in-theory        90373
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 or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     55
proof            (modus-ponens tm-980 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       199
proof-steps      9
----------------------------------------------------------------
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-90373.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-980, 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-90374
in-theory        90374
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90374.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-980, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-90375
in-theory        90375
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     43
proof            (modus-ponens tm-980 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90375.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-980, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-90376
in-theory        90376
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) -> ((G -> H) -> ((F or G) -> H))) and E)))
theorem-size     45
proof            (modus-ponens tm-980 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-90376.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))), M:tm-980, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-90377
in-theory        90377
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-980 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90377.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G)))), M:tm-980, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-90378
in-theory        90378
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) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90378.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-980, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-90379
in-theory        90379
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> E))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90379.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> E))) -> (not E))), M:tm-980, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-90380
in-theory        90380
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)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G)))))
theorem-size     49
proof            (modus-ponens tm-980 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       185
proof-steps      9
----------------------------------------------------------------
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-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-90380.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G))))), M:tm-980, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-90381
in-theory        90381
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) -> (not E)) -> (not (E and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90381.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> (not E)) -> (not (E and F)))), M:tm-980, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-90382
in-theory        90382
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) -> (not F)) -> (not (E and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90382.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> (not F)) -> (not (E and F)))), M:tm-980, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-90383
in-theory        90383
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (E and F)))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90383.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (E and F)))) -> (not E))), M:tm-980, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-90384
in-theory        90384
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (E or F))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90384.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (E or F))) -> (not E))), M:tm-980, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-90385
in-theory        90385
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F or E))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90385.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F or E))) -> (not E))), M:tm-980, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-90386
in-theory        90386
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F))))
theorem-size     47
proof            (modus-ponens tm-980 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       181
proof-steps      9
----------------------------------------------------------------
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-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-90386.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F)))), M:tm-980, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-90387
in-theory        90387
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F))))
theorem-size     45
proof            (modus-ponens tm-980 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90387.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F)))), M:tm-980, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-90388
in-theory        90388
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G)))
theorem-size     51
proof            (modus-ponens tm-980 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       189
proof-steps      9
----------------------------------------------------------------
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-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-90388.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G))), M:tm-980, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-90389
in-theory        90389
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90389.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-980, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-90390
in-theory        90390
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 -> (not F)) -> (not E))) or G))
theorem-size     41
proof            (modus-ponens tm-980 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90390.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G)), M:tm-980, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-90391
in-theory        90391
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) -> ((F -> (not G)) -> (not F))) and E)))
theorem-size     43
proof            (modus-ponens tm-980 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-90391.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E))), M:tm-980, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-90392
in-theory        90392
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 -> (not F))) -> ((E -> F) -> (not E))))
theorem-size     43
proof            (modus-ponens tm-980 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90392.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E)))), M:tm-980, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-90393
in-theory        90393
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) -> ((F -> (not G)) -> (not F)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90393.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-980, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-90394
in-theory        90394
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((not (not E)) -> (not E)) -> (not (not (not E)))))
theorem-size     39
proof            (modus-ponens tm-980 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-8 tm-9 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90394.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((not (not E)) -> (not E)) -> (not (not (not E))))), M:tm-980, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-90395
in-theory        90395
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (((not (not E)) or E) -> F)))
theorem-size     39
proof            (modus-ponens tm-980 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-90395.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (((not (not E)) or E) -> F))), M:tm-980, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-90396
in-theory        90396
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((not (not F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-980 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90396.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((not (not F)) -> F))), M:tm-980, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-90397
in-theory        90397
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((not (not E)) -> E) or F))
theorem-size     35
proof            (modus-ponens tm-980 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90397.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((not (not E)) -> E) or F)), M:tm-980, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-90398
in-theory        90398
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((not (not F)) -> F) and E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-90398.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((not (not F)) -> F) and E))), M:tm-980, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-90399
in-theory        90399
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F)))
theorem-size     43
proof            (modus-ponens tm-980 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       167
proof-steps      9
----------------------------------------------------------------
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-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-90399.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F))), M:tm-980, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-90400
in-theory        90400
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((not (not F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-980 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90400.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((not (not F)) -> F))), M:tm-980, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-90401
in-theory        90401
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (G -> F)))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90401.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (G -> F)))) -> (not E))), M:tm-980, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-90402
in-theory        90402
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)) -> G) -> ((H or (E -> (F -> E))) -> G)))
theorem-size     45
proof            (modus-ponens tm-980 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90402.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G))), M:tm-980, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-90403
in-theory        90403
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (H -> G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90403.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (H -> G))))), M:tm-980, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-90404
in-theory        90404
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 -> F))) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90404.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (G -> F))) or H)), M:tm-980, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-90405
in-theory        90405
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 -> (H -> G))) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-90405.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G -> (H -> G))) and E))), M:tm-980, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-90406
in-theory        90406
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 -> (G -> F))))
theorem-size     37
proof            (modus-ponens tm-980 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-90406.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (E -> (G -> F)))), M:tm-980, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-90407
in-theory        90407
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 -> (H -> G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90407.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (G -> (H -> G))))), M:tm-980, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-90408
in-theory        90408
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> E))
theorem-size     31
proof            (modus-ponens tm-980 tm-86 ((A (-> Am Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90408.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> E)), M:tm-980, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-90409
in-theory        90409
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 -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90409.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> G)) -> (E -> (F -> G)))), M:tm-980, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-90410
in-theory        90410
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 F)))
theorem-size     35
proof            (modus-ponens tm-980 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90410.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and F) -> (E and F))), M:tm-980, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-90411
in-theory        90411
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 -> F)))
theorem-size     35
proof            (modus-ponens tm-980 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90411.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (E -> F))), M:tm-980, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-90412
in-theory        90412
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((not (not E)) -> (not (not E))))
theorem-size     35
proof            (modus-ponens tm-980 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90412.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((not (not E)) -> (not (not E)))), M:tm-980, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-90413
in-theory        90413
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not (E -> E))) -> (not (E -> F))))
theorem-size     41
proof            (modus-ponens tm-980 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       181
proof-steps      11
----------------------------------------------------------------
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-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-90413.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not (E -> E))) -> (not (E -> F)))), M:tm-980, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-90414
in-theory        90414
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F)))
theorem-size     43
proof            (modus-ponens tm-980 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90414.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F))), M:tm-980, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-90415
in-theory        90415
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> (F -> F))))
theorem-size     37
proof            (modus-ponens tm-980 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90415.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> (F -> F)))), M:tm-980, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-90416
in-theory        90416
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 -> E)) or G))
theorem-size     37
proof            (modus-ponens tm-980 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90416.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (E -> E)) or G)), M:tm-980, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-90417
in-theory        90417
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) -> (F -> F)) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-90417.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> G) -> (F -> F)) and E))), M:tm-980, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-90418
in-theory        90418
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) -> ((E -> F) -> E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90418.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> E) -> ((E -> F) -> E))), M:tm-980, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-90419
in-theory        90419
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) -> (F -> F))))
theorem-size     37
proof            (modus-ponens tm-980 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90419.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> G) -> (F -> F)))), M:tm-980, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-90420
in-theory        90420
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) -> G)) -> (E -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-90420.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F -> E) -> G)) -> (E -> G))), M:tm-980, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-90421
in-theory        90421
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E -> F)) -> (E -> F)))
theorem-size     37
proof            (modus-ponens tm-980 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-90421.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E -> F)) -> (E -> F))), M:tm-980, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-90422
in-theory        90422
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 -> (F -> G)) -> (E -> F))))
theorem-size     47
proof            (modus-ponens tm-980 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       227
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90422.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F)))), M:tm-980, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-90423
in-theory        90423
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)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F)))))
theorem-size     59
proof            (modus-ponens tm-980 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       237
proof-steps      11
----------------------------------------------------------------
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-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-90423.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F))))), M:tm-980, 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-90424
in-theory        90424
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 -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H)))
theorem-size     61
proof            (modus-ponens tm-980 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       243
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-90424.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H))), M:tm-980, 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-90425
in-theory        90425
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     49
proof            (modus-ponens tm-980 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       211
proof-steps      11
----------------------------------------------------------------
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-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-90425.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-980, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-90426
in-theory        90426
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 -> (F -> G)) -> (E -> G))) or H))
theorem-size     49
proof            (modus-ponens tm-980 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       211
proof-steps      11
----------------------------------------------------------------
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-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-90426.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H)), M:tm-980, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-90427
in-theory        90427
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 -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E)))
theorem-size     51
proof            (modus-ponens tm-980 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       217
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-90427.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E))), M:tm-980, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-90428
in-theory        90428
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 -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G))))
theorem-size     57
proof            (modus-ponens tm-980 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       235
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-90428.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G)))), M:tm-980, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-90429
in-theory        90429
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 -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     49
proof            (modus-ponens tm-980 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       211
proof-steps      11
----------------------------------------------------------------
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-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-90429.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-980, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-90430
in-theory        90430
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)) -> H)) -> ((E -> (F -> G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-980 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       243
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-90430.        (((((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)) -> H)) -> ((E -> (F -> G)) -> H))), M:tm-980, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-90431
in-theory        90431
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E)))
theorem-size     47
proof            (modus-ponens tm-980 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       201
proof-steps      11
----------------------------------------------------------------
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-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-90431.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E))), M:tm-980, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-90432
in-theory        90432
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))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H)))
theorem-size     61
proof            (modus-ponens tm-980 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       231
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-90432.        (((((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))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H))), M:tm-980, 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-90433
in-theory        90433
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90433.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-980, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-90434
in-theory        90434
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 -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90434.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-980, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-90435
in-theory        90435
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 -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     47
proof            (modus-ponens tm-980 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       197
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-90435.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-980, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-90436
in-theory        90436
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 -> H))) -> (E -> ((F -> G) -> (F -> H)))))
theorem-size     45
proof            (modus-ponens tm-980 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90436.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H))))), M:tm-980, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-90437
in-theory        90437
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 -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     45
proof            (modus-ponens tm-980 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-90437.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-980, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-90438
in-theory        90438
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) and E) -> F))
theorem-size     35
proof            (modus-ponens tm-980 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-90438.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) and E) -> F)), M:tm-980, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-90439
in-theory        90439
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)) -> G) and H) -> G))
theorem-size     39
proof            (modus-ponens tm-980 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-90439.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F -> E)) -> G) and H) -> G)), M:tm-980, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-90440
in-theory        90440
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))) -> H) and I) -> H))
theorem-size     47
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-90440.        (((((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))) -> H) and I) -> H)), M:tm-980, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-90441
in-theory        90441
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 G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F)))
theorem-size     49
proof            (modus-ponens tm-980 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       239
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-90441.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F))), M:tm-980, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-90442
in-theory        90442
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E)))
theorem-size     43
proof            (modus-ponens tm-980 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       207
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90442.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E))), M:tm-980, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-90443
in-theory        90443
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E))))
theorem-size     53
proof            (modus-ponens tm-980 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       213
proof-steps      11
----------------------------------------------------------------
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-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-90443.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E)))), M:tm-980, 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-90444
in-theory        90444
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H)))
theorem-size     55
proof            (modus-ponens tm-980 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       219
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-90444.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H))), M:tm-980, 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-90445
in-theory        90445
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90445.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-980, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-90446
in-theory        90446
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90446.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H)), M:tm-980, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-90447
in-theory        90447
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) and H) -> F) -> (((F -> G) and H) -> G)) and E)))
theorem-size     47
proof            (modus-ponens tm-980 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       197
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-90447.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E))), M:tm-980, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-90448
in-theory        90448
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F)))
theorem-size     51
proof            (modus-ponens tm-980 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       211
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-90448.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F))), M:tm-980, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-90449
in-theory        90449
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) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90449.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-980, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-90450
in-theory        90450
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) -> G) and H) -> G))
theorem-size     39
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-90450.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E and F) -> E) -> G) and H) -> G)), M:tm-980, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-90451
in-theory        90451
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 -> G)) -> ((E and F) -> G)))
theorem-size     41
proof            (modus-ponens tm-980 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       207
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-90451.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> (E -> G)) -> ((E and F) -> G))), M:tm-980, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-90452
in-theory        90452
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F and G) -> F))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-980 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       169
proof-steps      11
----------------------------------------------------------------
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-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-90452.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F and G) -> F))) -> (not E))), M:tm-980, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-90453
in-theory        90453
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) -> G) -> ((H or ((E and F) -> E)) -> G)))
theorem-size     45
proof            (modus-ponens tm-980 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       183
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-90453.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G))), M:tm-980, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-90454
in-theory        90454
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-980 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90454.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G and H) -> G)))), M:tm-980, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-90455
in-theory        90455
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F and G) -> F)) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90455.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F and G) -> F)) or H)), M:tm-980, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-90456
in-theory        90456
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 and H) -> G)) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-90456.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> ((G and H) -> G)) and E))), M:tm-980, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-90457
in-theory        90457
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F and G)) -> (E -> F)))
theorem-size     37
proof            (modus-ponens tm-980 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90457.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F and G)) -> (E -> F))), M:tm-980, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-90458
in-theory        90458
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 and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-980 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-90458.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> ((G and H) -> G)))), M:tm-980, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-90459
in-theory        90459
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and (E -> F)) -> F))
theorem-size     35
proof            (modus-ponens tm-980 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-90459.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and (E -> F)) -> F)), M:tm-980, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-90460
in-theory        90460
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 -> (G -> F)) -> H)) -> H))
theorem-size     39
proof            (modus-ponens tm-980 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-90460.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and ((F -> (G -> F)) -> H)) -> H)), M:tm-980, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-90461
in-theory        90461
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 -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I))
theorem-size     47
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-90461.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I)), M:tm-980, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-90462
in-theory        90462
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 and G) -> F) -> H)) -> H))
theorem-size     39
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-90462.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and (((F and G) -> F) -> H)) -> H)), M:tm-980, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-90463
in-theory        90463
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 -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G)))
theorem-size     49
proof            (modus-ponens tm-980 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       239
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-90463.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G))), M:tm-980, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-90464
in-theory        90464
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 -> G)) -> F) -> ((E and (F -> G)) -> F)))
theorem-size     43
proof            (modus-ponens tm-980 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       207
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90464.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F))), M:tm-980, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-90465
in-theory        90465
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 -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F))))
theorem-size     53
proof            (modus-ponens tm-980 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       213
proof-steps      11
----------------------------------------------------------------
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-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-90465.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F)))), M:tm-980, 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-90466
in-theory        90466
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 -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-980 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       219
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-90466.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H))), M:tm-980, 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-90467
in-theory        90467
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90467.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-980, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-90468
in-theory        90468
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 -> G)) -> F) -> ((E and (F -> G)) -> G)) or H))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90468.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H)), M:tm-980, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-90469
in-theory        90469
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E)))
theorem-size     47
proof            (modus-ponens tm-980 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       197
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-90469.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E))), M:tm-980, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-90470
in-theory        90470
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 -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G)))
theorem-size     51
proof            (modus-ponens tm-980 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       211
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-90470.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G))), M:tm-980, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-90471
in-theory        90471
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90471.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-980, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-90472
in-theory        90472
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 and G) -> G) -> H)) -> H))
theorem-size     39
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-90472.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and (((F and G) -> G) -> H)) -> H)), M:tm-980, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-90473
in-theory        90473
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) -> G) and H) -> G))
theorem-size     39
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-90473.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E and F) -> F) -> G) and H) -> G)), M:tm-980, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-90474
in-theory        90474
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 -> G)) -> ((E and F) -> G)))
theorem-size     41
proof            (modus-ponens tm-980 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       207
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-90474.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> (F -> G)) -> ((E and F) -> G))), M:tm-980, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-90475
in-theory        90475
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F and G) -> G))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-980 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       169
proof-steps      11
----------------------------------------------------------------
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-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-90475.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F and G) -> G))) -> (not E))), M:tm-980, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-90476
in-theory        90476
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) -> G) -> ((H or ((E and F) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-980 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       183
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-90476.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G))), M:tm-980, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-90477
in-theory        90477
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G and H) -> H))))
theorem-size     37
proof            (modus-ponens tm-980 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90477.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G and H) -> H)))), M:tm-980, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-90478
in-theory        90478
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F and G) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90478.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F and G) -> G)) or H)), M:tm-980, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-90479
in-theory        90479
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 and H) -> H)) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-90479.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> ((G and H) -> H)) and E))), M:tm-980, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-90480
in-theory        90480
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F and G)) -> (E -> G)))
theorem-size     37
proof            (modus-ponens tm-980 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90480.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F and G)) -> (E -> G))), M:tm-980, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-90481
in-theory        90481
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 and H) -> H))))
theorem-size     37
proof            (modus-ponens tm-980 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-90481.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> ((G and H) -> H)))), M:tm-980, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-90482
in-theory        90482
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 (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90482.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (H -> G)))), M:tm-980, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-90483
in-theory        90483
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 ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-90483.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-90484
in-theory        90484
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 ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90484.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G and H) -> G))), M:tm-980, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-90485
in-theory        90485
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 ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90485.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G and H) -> H))), M:tm-980, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-90486
in-theory        90486
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 (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90486.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (G and H))))), M:tm-980, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-90487
in-theory        90487
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 (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90487.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (G or H)))), M:tm-980, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-90488
in-theory        90488
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 (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90488.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (H or G)))), M:tm-980, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-90489
in-theory        90489
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 ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-1.            (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-90489.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-980, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-90490
in-theory        90490
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 ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     45
proof            (modus-ponens tm-980 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       185
proof-steps      11
----------------------------------------------------------------
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-1.            (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-90490.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-980, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-90491
in-theory        90491
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 ((not (not G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90491.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((not (not G)) -> G))), M:tm-980, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-90492
in-theory        90492
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 (G -> (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90492.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (I -> H))))), M:tm-980, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90493
in-theory        90493
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 ((G -> H) -> (G -> G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-90493.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (G -> G)))), M:tm-980, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-90494
in-theory        90494
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 (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     53
proof            (modus-ponens tm-980 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       235
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-90494.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-980, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-90495
in-theory        90495
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 (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-90495.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90496
in-theory        90496
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 ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-90496.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-980, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-90497
in-theory        90497
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 (G -> ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90497.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> ((H and I) -> H)))), M:tm-980, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90498
in-theory        90498
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 (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-90498.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-980, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-90499
in-theory        90499
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 (G -> ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90499.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> ((H and I) -> I)))), M:tm-980, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90500
in-theory        90500
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 (G -> ((H -> (I -> H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90500.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-980, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-90501
in-theory        90501
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90501.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E))), M:tm-980, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-90502
in-theory        90502
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 G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-980 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       195
proof-steps      11
----------------------------------------------------------------
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-1.            (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-90502.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H))), M:tm-980, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-90503
in-theory        90503
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (H -> G)) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90503.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (H -> G)) and F)))), M:tm-980, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-90504
in-theory        90504
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 -> F)) and E)) or H))
theorem-size     39
proof            (modus-ponens tm-980 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90504.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F -> (G -> F)) and E)) or H)), M:tm-980, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-90505
in-theory        90505
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 -> (H -> G)) and F)) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-90505.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> ((G -> (H -> G)) and F)) and E))), M:tm-980, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-90506
in-theory        90506
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 -> (H -> G)) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90506.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> ((G -> (H -> G)) and F)))), M:tm-980, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-90507
in-theory        90507
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 (H -> (I -> H))))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90507.        (((((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 (H -> (I -> H)))), M:tm-980, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-90508
in-theory        90508
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 ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     55
proof            (modus-ponens tm-980 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       223
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90508.        (((((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 ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-980, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-90509
in-theory        90509
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 ((H and I) -> H)))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90509.        (((((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 ((H and I) -> H))), M:tm-980, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-90510
in-theory        90510
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 ((H and I) -> I)))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90510.        (((((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 ((H and I) -> I))), M:tm-980, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-90511
in-theory        90511
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 (H -> (I -> (H and I)))))
theorem-size     49
proof            (modus-ponens tm-980 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       205
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90511.        (((((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 (H -> (I -> (H and I))))), M:tm-980, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-90512
in-theory        90512
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 (H -> (H or I))))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90512.        (((((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 (H -> (H or I)))), M:tm-980, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-90513
in-theory        90513
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 (H -> (I or H))))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90513.        (((((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 (H -> (I or H)))), M:tm-980, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-90514
in-theory        90514
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 ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     55
proof            (modus-ponens tm-980 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       223
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90514.        (((((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 ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-980, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-90515
in-theory        90515
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 ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     53
proof            (modus-ponens tm-980 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       217
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90515.        (((((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 ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-980, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-90516
in-theory        90516
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 ((not (not H)) -> H)))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90516.        (((((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 ((not (not H)) -> H))), M:tm-980, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-90517
in-theory        90517
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 (H -> (I -> (J -> I)))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90517.        (((((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 (H -> (I -> (J -> I))))), M:tm-980, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-90518
in-theory        90518
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 ((H -> I) -> (H -> H))))
theorem-size     49
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90518.        (((((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 ((H -> I) -> (H -> H)))), M:tm-980, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-90519
in-theory        90519
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 (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     61
proof            (modus-ponens tm-980 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       267
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90519.        (((((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 (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-980, 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-90520
in-theory        90520
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 (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     57
proof            (modus-ponens tm-980 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       247
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90520.        (((((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 (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-980, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-90521
in-theory        90521
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 ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     57
proof            (modus-ponens tm-980 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       247
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90521.        (((((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 ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-980, 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-90522
in-theory        90522
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 (H -> ((I and J) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90522.        (((((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 (H -> ((I and J) -> I)))), M:tm-980, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-90523
in-theory        90523
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 (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     57
proof            (modus-ponens tm-980 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       247
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90523.        (((((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 (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-980, 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-90524
in-theory        90524
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 (H -> ((I and J) -> J))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90524.        (((((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 (H -> ((I and J) -> J)))), M:tm-980, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-90525
in-theory        90525
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 (H -> ((I -> (J -> I)) and H))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90525.        (((((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 (H -> ((I -> (J -> I)) and H)))), M:tm-980, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-90526
in-theory        90526
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 (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     59
proof            (modus-ponens tm-980 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       255
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90526.        (((((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 (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-980, 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-90527
in-theory        90527
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 (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-90527.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-980, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-90528
in-theory        90528
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E)))
theorem-size     49
proof            (modus-ponens tm-980 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       209
proof-steps      11
----------------------------------------------------------------
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-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-90528.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E))), M:tm-980, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-90529
in-theory        90529
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 H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I)))
theorem-size     65
proof            (modus-ponens tm-980 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       243
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90529.        (((((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 H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I))), M:tm-980, 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-90530
in-theory        90530
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-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-90530.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-980, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-90531
in-theory        90531
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 -> H)) -> ((F -> G) -> (F -> H))) and E)) or I))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-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-90531.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I)), M:tm-980, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-90532
in-theory        90532
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 -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E)))
theorem-size     49
proof            (modus-ponens tm-980 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       205
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-90532.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E))), M:tm-980, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-90533
in-theory        90533
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 -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-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-90533.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-980, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-90534
in-theory        90534
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 (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90534.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (H -> G)))), M:tm-980, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-90535
in-theory        90535
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 ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-90535.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-90536
in-theory        90536
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 ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> 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-90536.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G and H) -> G))), M:tm-980, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-90537
in-theory        90537
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 ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> 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-90537.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G and H) -> H))), M:tm-980, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-90538
in-theory        90538
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 (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> 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-90538.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (H -> (G and H))))), M:tm-980, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-90539
in-theory        90539
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 (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90539.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (G or H)))), M:tm-980, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-90540
in-theory        90540
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 (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90540.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (H or G)))), M:tm-980, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-90541
in-theory        90541
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 ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-90541.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-980, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-90542
in-theory        90542
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 ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     45
proof            (modus-ponens tm-980 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       185
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-90542.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-980, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-90543
in-theory        90543
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 ((not (not G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> 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-90543.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((not (not G)) -> G))), M:tm-980, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-90544
in-theory        90544
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 (G -> (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90544.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (H -> (I -> H))))), M:tm-980, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90545
in-theory        90545
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 ((G -> H) -> (G -> G))))
theorem-size     41
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-90545.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> H) -> (G -> G)))), M:tm-980, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-90546
in-theory        90546
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 (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     53
proof            (modus-ponens tm-980 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       235
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-90546.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-980, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-90547
in-theory        90547
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 (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90547.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90548
in-theory        90548
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 ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-90548.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-980, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-90549
in-theory        90549
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 (G -> ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90549.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> ((H and I) -> H)))), M:tm-980, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90550
in-theory        90550
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 (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-90550.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-980, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-90551
in-theory        90551
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 (G -> ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90551.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> ((H and I) -> I)))), M:tm-980, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90552
in-theory        90552
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 (G -> ((H -> (I -> H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90552.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G)))), M:tm-980, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-90553
in-theory        90553
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 (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-90553.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-980, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-90554
in-theory        90554
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 (G -> (((H and I) -> H) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-90554.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (((H and I) -> H) and G)))), M:tm-980, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-90555
in-theory        90555
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 (H -> (((I and J) -> I) and H))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90555.        (((((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 (H -> (((I and J) -> I) and H)))), M:tm-980, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-90556
in-theory        90556
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 (G -> (((H and I) -> H) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-1.            (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-90556.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G)))), M:tm-980, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-90557
in-theory        90557
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (((F and G) -> F) and E))) -> (not E)))
theorem-size     41
proof            (modus-ponens tm-980 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       177
proof-steps      11
----------------------------------------------------------------
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-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-90557.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (((F and G) -> F) and E))) -> (not E))), M:tm-980, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-90558
in-theory        90558
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 G) -> H) -> ((G or (((E and F) -> E) and G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-980 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       195
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-90558.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H))), M:tm-980, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-90559
in-theory        90559
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (((G and H) -> G) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90559.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (((G and H) -> G) and F)))), M:tm-980, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-90560
in-theory        90560
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (((F and G) -> F) and E)) or H))
theorem-size     39
proof            (modus-ponens tm-980 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90560.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (((F and G) -> F) and E)) or H)), M:tm-980, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-90561
in-theory        90561
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 and H) -> G) and F)) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-90561.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (((G and H) -> G) and F)) and E))), M:tm-980, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-90562
in-theory        90562
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 and H) -> G) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90562.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (((G and H) -> G) and F)))), M:tm-980, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-90563
in-theory        90563
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 (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90563.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (H -> G)))), M:tm-980, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-90564
in-theory        90564
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 ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-90564.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-90565
in-theory        90565
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 ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> 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-90565.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G and H) -> G))), M:tm-980, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-90566
in-theory        90566
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 ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> 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-90566.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G and H) -> H))), M:tm-980, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-90567
in-theory        90567
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 (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> 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-90567.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (H -> (G and H))))), M:tm-980, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-90568
in-theory        90568
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 (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90568.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (G or H)))), M:tm-980, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-90569
in-theory        90569
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 (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90569.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (H or G)))), M:tm-980, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-90570
in-theory        90570
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 ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-90570.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-980, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-90571
in-theory        90571
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 ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     45
proof            (modus-ponens tm-980 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       185
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-90571.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-980, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-90572
in-theory        90572
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 ((not (not G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> 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-90572.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((not (not G)) -> G))), M:tm-980, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-90573
in-theory        90573
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 (G -> (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90573.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (H -> (I -> H))))), M:tm-980, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90574
in-theory        90574
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 ((G -> H) -> (G -> G))))
theorem-size     41
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-90574.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> H) -> (G -> G)))), M:tm-980, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-90575
in-theory        90575
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 (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     53
proof            (modus-ponens tm-980 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       235
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-90575.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-980, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-90576
in-theory        90576
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 (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90576.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90577
in-theory        90577
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 ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-90577.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-980, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-90578
in-theory        90578
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 (G -> ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90578.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> ((H and I) -> H)))), M:tm-980, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90579
in-theory        90579
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 (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-90579.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-980, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-90580
in-theory        90580
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 (G -> ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90580.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> ((H and I) -> I)))), M:tm-980, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90581
in-theory        90581
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 (G -> ((H -> (I -> H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90581.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G)))), M:tm-980, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-90582
in-theory        90582
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 (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-90582.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-980, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-90583
in-theory        90583
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 (G -> (((H and I) -> H) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-90583.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (((H and I) -> H) and G)))), M:tm-980, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-90584
in-theory        90584
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 (G -> (((H and I) -> I) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-90584.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (((H and I) -> I) and G)))), M:tm-980, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-90585
in-theory        90585
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 (G -> (((H and I) -> I) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-90585.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (((H and I) -> I) and G)))), M:tm-980, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-90586
in-theory        90586
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 (H -> (((I and J) -> J) and H))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90586.        (((((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 (H -> (((I and J) -> J) and H)))), M:tm-980, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-90587
in-theory        90587
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 (G -> (((H and I) -> I) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-1.            (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-90587.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G)))), M:tm-980, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-90588
in-theory        90588
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (((F and G) -> G) and E))) -> (not E)))
theorem-size     41
proof            (modus-ponens tm-980 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       177
proof-steps      11
----------------------------------------------------------------
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-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-90588.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (((F and G) -> G) and E))) -> (not E))), M:tm-980, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-90589
in-theory        90589
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 G) -> H) -> ((G or (((E and F) -> F) and G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-980 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       195
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-90589.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H))), M:tm-980, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-90590
in-theory        90590
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (((G and H) -> H) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90590.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (((G and H) -> H) and F)))), M:tm-980, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-90591
in-theory        90591
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (((F and G) -> G) and E)) or H))
theorem-size     39
proof            (modus-ponens tm-980 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90591.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (((F and G) -> G) and E)) or H)), M:tm-980, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-90592
in-theory        90592
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 and H) -> H) and F)) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-90592.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (((G and H) -> H) and F)) and E))), M:tm-980, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-90593
in-theory        90593
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 and H) -> H) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90593.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (((G and H) -> H) and F)))), M:tm-980, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-90594
in-theory        90594
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 (G -> (H -> G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B 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-90594.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> G)))), M:tm-980, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-90595
in-theory        90595
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 ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     49
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-90595.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-90596
in-theory        90596
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 ((G and H) -> G)))
theorem-size     41
proof            (modus-ponens tm-980 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90596.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G and H) -> G))), M:tm-980, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-90597
in-theory        90597
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 ((G and H) -> H)))
theorem-size     41
proof            (modus-ponens tm-980 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90597.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G and H) -> H))), M:tm-980, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-90598
in-theory        90598
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 (G -> (H -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90598.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H))))), M:tm-980, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-90599
in-theory        90599
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 (G -> (G or H))))
theorem-size     41
proof            (modus-ponens tm-980 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and 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-90599.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (G or H)))), M:tm-980, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-90600
in-theory        90600
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 (G -> (H or G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and 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-90600.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H or G)))), M:tm-980, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-90601
in-theory        90601
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 ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     49
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-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-90601.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-980, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-90602
in-theory        90602
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 ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     47
proof            (modus-ponens tm-980 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       193
proof-steps      11
----------------------------------------------------------------
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-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-90602.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-980, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-90603
in-theory        90603
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 ((not (not G)) -> G)))
theorem-size     41
proof            (modus-ponens tm-980 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90603.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((not (not G)) -> G))), M:tm-980, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-90604
in-theory        90604
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 (G -> (H -> (I -> H)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B 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-90604.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H))))), M:tm-980, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90605
in-theory        90605
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 ((G -> H) -> (G -> G))))
theorem-size     43
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-90605.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G)))), M:tm-980, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-90606
in-theory        90606
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 (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     55
proof            (modus-ponens tm-980 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       243
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-90606.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-980, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-90607
in-theory        90607
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 (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-90607.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90608
in-theory        90608
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 ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-90608.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-980, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-90609
in-theory        90609
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 (G -> ((H and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-90609.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H)))), M:tm-980, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90610
in-theory        90610
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 (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-90610.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-980, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-90611
in-theory        90611
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 (G -> ((H and I) -> I))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-90611.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I)))), M:tm-980, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90612
in-theory        90612
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 (G -> ((H -> (I -> H)) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-90612.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-980, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-90613
in-theory        90613
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 (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     53
proof            (modus-ponens tm-980 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       231
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-90613.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-980, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-90614
in-theory        90614
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 (G -> (((H and I) -> H) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-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-90614.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G)))), M:tm-980, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-90615
in-theory        90615
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 (G -> (((H and I) -> I) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-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-90615.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G)))), M:tm-980, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-90616
in-theory        90616
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 (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     47
proof            (modus-ponens tm-980 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       207
proof-steps      13
----------------------------------------------------------------
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-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-90616.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-980, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-90617
in-theory        90617
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 (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-90617.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-980, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-90618
in-theory        90618
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 (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-90618.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-980, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-90619
in-theory        90619
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 (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     53
proof            (modus-ponens tm-980 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       231
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90619.        (((((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 (H -> ((I -> (J -> (I and J))) and H)))), M:tm-980, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-90620
in-theory        90620
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 (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-1.            (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-90620.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-980, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-90621
in-theory        90621
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E)))
theorem-size     43
proof            (modus-ponens tm-980 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90621.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E))), M:tm-980, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-90622
in-theory        90622
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 G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-980 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       207
proof-steps      11
----------------------------------------------------------------
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-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-90622.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H))), M:tm-980, 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-90623
in-theory        90623
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     41
proof            (modus-ponens tm-980 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90623.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (H -> (G and H))) and F)))), M:tm-980, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-90624
in-theory        90624
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 -> (F and G))) and E)) or H))
theorem-size     41
proof            (modus-ponens tm-980 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90624.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F -> (G -> (F and G))) and E)) or H)), M:tm-980, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-90625
in-theory        90625
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 -> (H -> (G and H))) and F)) and E)))
theorem-size     43
proof            (modus-ponens tm-980 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-90625.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E))), M:tm-980, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-90626
in-theory        90626
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 -> (H -> (G and H))) and F))))
theorem-size     41
proof            (modus-ponens tm-980 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90626.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> ((G -> (H -> (G and H))) and F)))), M:tm-980, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-90627
in-theory        90627
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> E))))
theorem-size     35
proof            (modus-ponens tm-980 tm-305 ((A (-> Am (and Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-90627.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> E)))), M:tm-980, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-90628
in-theory        90628
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 -> G)) and ((E -> F) -> (E -> G)))))
theorem-size     47
proof            (modus-ponens tm-980 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-90628.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G))))), M:tm-980, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-90629
in-theory        90629
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 F) and E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-90629.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and F) -> ((E and F) and E))), M:tm-980, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-90630
in-theory        90630
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 F) and F)))
theorem-size     37
proof            (modus-ponens tm-980 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-90630.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and F) -> ((E and F) and F))), M:tm-980, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-90631
in-theory        90631
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-90631.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (E and F))))), M:tm-980, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-90632
in-theory        90632
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (E or F))))
theorem-size     35
proof            (modus-ponens tm-980 tm-310 ((A (-> Am (and Am (or Am Bm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-90632.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (E or F)))), M:tm-980, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-90633
in-theory        90633
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F or E))))
theorem-size     35
proof            (modus-ponens tm-980 tm-311 ((A (-> Am (and Am (or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-90633.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F or E)))), M:tm-980, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-90634
in-theory        90634
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 -> F) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-980 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-90634.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-90635
in-theory        90635
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 -> F) and ((E -> (not F)) -> (not E)))))
theorem-size     43
proof            (modus-ponens tm-980 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       189
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-90635.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E))))), M:tm-980, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-90636
in-theory        90636
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((not (not E)) -> ((not (not E)) and E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-90636.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((not (not E)) -> ((not (not E)) and E))), M:tm-980, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-90637
in-theory        90637
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (G -> F)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-90637.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (G -> F))))), M:tm-980, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-90638
in-theory        90638
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 -> F) and (E -> E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-90638.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> ((E -> F) and (E -> E)))), M:tm-980, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-90639
in-theory        90639
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 -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-980 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       251
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-90639.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G))))), M:tm-980, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-90640
in-theory        90640
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     45
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-90640.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-980, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-90641
in-theory        90641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F))))
theorem-size     51
proof            (modus-ponens tm-980 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       227
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-90641.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F)))), M:tm-980, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-90642
in-theory        90642
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F and G) -> F))))
theorem-size     37
proof            (modus-ponens tm-980 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-90642.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F and G) -> F)))), M:tm-980, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-90643
in-theory        90643
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 -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G))))
theorem-size     51
proof            (modus-ponens tm-980 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       227
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-90643.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G)))), M:tm-980, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-90644
in-theory        90644
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F and G) -> G))))
theorem-size     37
proof            (modus-ponens tm-980 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-90644.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F and G) -> G)))), M:tm-980, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-90645
in-theory        90645
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (G -> F)) and E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-90645.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (G -> F)) and E)))), M:tm-980, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-90646
in-theory        90646
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     47
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-90646.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-980, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-90647
in-theory        90647
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (((F and G) -> F) and E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-90647.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (((F and G) -> F) and E)))), M:tm-980, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-90648
in-theory        90648
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (((F and G) -> G) and E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-90648.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (((F and G) -> G) and E)))), M:tm-980, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-90649
in-theory        90649
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (G -> (F and G))) and E))))
theorem-size     41
proof            (modus-ponens tm-980 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-90649.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (G -> (F and G))) and E)))), M:tm-980, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-90650
in-theory        90650
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 -> F) and (E -> (E and F)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-90650.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> ((E -> F) and (E -> (E and F))))), M:tm-980, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-90651
in-theory        90651
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 ((G -> H) -> (G -> (G and H)))))
theorem-size     45
proof            (modus-ponens tm-980 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       207
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-90651.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H))))), M:tm-980, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-90652
in-theory        90652
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 ((G -> H) -> (G -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-90652.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H))))), M:tm-980, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-90653
in-theory        90653
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 ((G -> H) -> (G -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-90653.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H))))), M:tm-980, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-90654
in-theory        90654
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 ((H -> I) -> (H -> (H and I)))))
theorem-size     51
proof            (modus-ponens tm-980 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       231
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-90654.        (((((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 ((H -> I) -> (H -> (H and I))))), M:tm-980, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-90655
in-theory        90655
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 ((G -> H) -> (G -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-90655.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H))))), M:tm-980, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-90656
in-theory        90656
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F))))
theorem-size     43
proof            (modus-ponens tm-980 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       189
proof-steps      11
----------------------------------------------------------------
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-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-90656.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F)))), M:tm-980, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-90657
in-theory        90657
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-90657.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G))), M:tm-980, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-90658
in-theory        90658
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> (F -> (F and G)))))
theorem-size     39
proof            (modus-ponens tm-980 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90658.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> (F -> (F and G))))), M:tm-980, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-90659
in-theory        90659
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 -> (E and F))) or G))
theorem-size     39
proof            (modus-ponens tm-980 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90659.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (E -> (E and F))) or G)), M:tm-980, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-90660
in-theory        90660
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) -> (F -> (F and G))) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-90660.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> G) -> (F -> (F and G))) and E))), M:tm-980, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-90661
in-theory        90661
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) -> ((E -> F) -> (E and F))))
theorem-size     41
proof            (modus-ponens tm-980 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-90661.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> E) -> ((E -> F) -> (E and F)))), M:tm-980, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-90662
in-theory        90662
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) -> (F -> (F and G)))))
theorem-size     39
proof            (modus-ponens tm-980 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90662.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> G) -> (F -> (F and G))))), M:tm-980, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-90663
in-theory        90663
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (G -> (F and G))))))
theorem-size     39
proof            (modus-ponens tm-980 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-90663.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (G -> (F and G)))))), M:tm-980, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-90664
in-theory        90664
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 (G -> (H -> (I -> (H and I))))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-90664.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I)))))), M:tm-980, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90665
in-theory        90665
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 (G -> (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90665.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (H -> (I -> (H and I)))))), M:tm-980, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90666
in-theory        90666
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 (G -> (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90666.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (H -> (I -> (H and I)))))), M:tm-980, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90667
in-theory        90667
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 (H -> (I -> (J -> (I and J))))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90667.        (((((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 (H -> (I -> (J -> (I and J)))))), M:tm-980, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-90668
in-theory        90668
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 (G -> (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-90668.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I)))))), M:tm-980, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90669
in-theory        90669
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 -> (G -> (F and G))) -> H)) -> H))
theorem-size     41
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-90669.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and ((F -> (G -> (F and G))) -> H)) -> H)), M:tm-980, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-90670
in-theory        90670
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))) -> G) and H) -> G))
theorem-size     41
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-90670.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F -> (E and F))) -> G) and H) -> G)), M:tm-980, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-90671
in-theory        90671
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)) -> G)) -> (E -> G)))
theorem-size     41
proof            (modus-ponens tm-980 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-90671.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G))), M:tm-980, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-90672
in-theory        90672
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (G -> (F and G))))) -> (not E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90672.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (G -> (F and G))))) -> (not E))), M:tm-980, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-90673
in-theory        90673
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))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G)))
theorem-size     49
proof            (modus-ponens tm-980 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       195
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> 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-90673.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G))), M:tm-980, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-90674
in-theory        90674
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (H -> (G and H))))))
theorem-size     39
proof            (modus-ponens tm-980 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90674.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (H -> (G and H)))))), M:tm-980, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-90675
in-theory        90675
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 -> (F and G)))) or H))
theorem-size     39
proof            (modus-ponens tm-980 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90675.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (G -> (F and G)))) or H)), M:tm-980, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-90676
in-theory        90676
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 -> (H -> (G and H)))) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-90676.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G -> (H -> (G and H)))) and E))), M:tm-980, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-90677
in-theory        90677
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 -> (G -> (F and G)))))
theorem-size     39
proof            (modus-ponens tm-980 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90677.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (E -> (G -> (F and G))))), M:tm-980, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-90678
in-theory        90678
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 -> (H -> (G and H))))))
theorem-size     39
proof            (modus-ponens tm-980 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> 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-90678.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (G -> (H -> (G and H)))))), M:tm-980, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-90679
in-theory        90679
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 ((G -> (H -> G)) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90679.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I))), M:tm-980, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-90680
in-theory        90680
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 ((G -> (H -> G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90680.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> (H -> G)) or I))), M:tm-980, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-90681
in-theory        90681
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 ((G -> (H -> G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90681.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> (H -> G)) or I))), M:tm-980, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-90682
in-theory        90682
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 ((H -> (I -> H)) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90682.        (((((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 ((H -> (I -> H)) or J))), M:tm-980, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-90683
in-theory        90683
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 ((G -> (H -> G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90683.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> (H -> G)) or I))), M:tm-980, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-90684
in-theory        90684
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (G -> F)) or H)))
theorem-size     37
proof            (modus-ponens tm-980 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90684.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (G -> F)) or H))), M:tm-980, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-90685
in-theory        90685
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)) or G) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-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-90685.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> E)) or G) or H)), M:tm-980, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-90686
in-theory        90686
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 -> F)) or H) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-90686.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> (G -> F)) or H) and E))), M:tm-980, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-90687
in-theory        90687
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 -> F)) or H)))
theorem-size     37
proof            (modus-ponens tm-980 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90687.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G -> F)) or H))), M:tm-980, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-90688
in-theory        90688
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 (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90688.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-980, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-90689
in-theory        90689
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 (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90689.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-980, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-90690
in-theory        90690
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 (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90690.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-980, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-90691
in-theory        90691
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 (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     57
proof            (modus-ponens tm-980 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       247
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90691.        (((((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 (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-980, 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-90692
in-theory        90692
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 (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90692.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-980, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-90693
in-theory        90693
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90693.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-980, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-90694
in-theory        90694
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))) or H) or I))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-90694.        (((((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))) or H) or I)), M:tm-980, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-90695
in-theory        90695
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 -> H)) -> ((F -> G) -> (F -> H))) or I) and E)))
theorem-size     47
proof            (modus-ponens tm-980 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       197
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-90695.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E))), M:tm-980, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-90696
in-theory        90696
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 -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90696.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-980, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-90697
in-theory        90697
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 (((G and H) -> G) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90697.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I))), M:tm-980, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-90698
in-theory        90698
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 (((G and H) -> G) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90698.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G and H) -> G) or I))), M:tm-980, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-90699
in-theory        90699
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 (((G and H) -> G) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90699.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G and H) -> G) or I))), M:tm-980, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-90700
in-theory        90700
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 (((H and I) -> H) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90700.        (((((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 (((H and I) -> H) or J))), M:tm-980, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-90701
in-theory        90701
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 (((G and H) -> G) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90701.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G and H) -> G) or I))), M:tm-980, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-90702
in-theory        90702
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F and G) -> F) or H)))
theorem-size     37
proof            (modus-ponens tm-980 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       159
proof-steps      11
----------------------------------------------------------------
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-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-90702.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F and G) -> F) or H))), M:tm-980, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-90703
in-theory        90703
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) or G) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-90703.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and F) -> E) or G) or H)), M:tm-980, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-90704
in-theory        90704
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F and G) -> F) or H) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-90704.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F and G) -> F) or H) and E))), M:tm-980, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-90705
in-theory        90705
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and G) -> F) or H)))
theorem-size     37
proof            (modus-ponens tm-980 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90705.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and G) -> F) or H))), M:tm-980, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-90706
in-theory        90706
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 (((G and H) -> H) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90706.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I))), M:tm-980, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-90707
in-theory        90707
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 (((G and H) -> H) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90707.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G and H) -> H) or I))), M:tm-980, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-90708
in-theory        90708
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 (((G and H) -> H) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90708.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G and H) -> H) or I))), M:tm-980, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-90709
in-theory        90709
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 (((H and I) -> I) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90709.        (((((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 (((H and I) -> I) or J))), M:tm-980, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-90710
in-theory        90710
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 (((G and H) -> H) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90710.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G and H) -> H) or I))), M:tm-980, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-90711
in-theory        90711
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F and G) -> G) or H)))
theorem-size     37
proof            (modus-ponens tm-980 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       159
proof-steps      11
----------------------------------------------------------------
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-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-90711.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F and G) -> G) or H))), M:tm-980, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-90712
in-theory        90712
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) or G) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-90712.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and F) -> F) or G) or H)), M:tm-980, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-90713
in-theory        90713
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F and G) -> G) or H) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-90713.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F and G) -> G) or H) and E))), M:tm-980, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-90714
in-theory        90714
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and G) -> G) or H)))
theorem-size     37
proof            (modus-ponens tm-980 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90714.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F and G) -> G) or H))), M:tm-980, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-90715
in-theory        90715
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 ((G -> (H -> (G and H))) or I)))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90715.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I))), M:tm-980, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-90716
in-theory        90716
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 ((G -> (H -> (G and H))) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90716.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I))), M:tm-980, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-90717
in-theory        90717
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 ((G -> (H -> (G and H))) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90717.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I))), M:tm-980, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-90718
in-theory        90718
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 ((H -> (I -> (H and I))) or J)))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90718.        (((((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 ((H -> (I -> (H and I))) or J))), M:tm-980, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-90719
in-theory        90719
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 ((G -> (H -> (G and H))) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90719.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I))), M:tm-980, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-90720
in-theory        90720
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (G -> (F and G))) or H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90720.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (G -> (F and G))) or H))), M:tm-980, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-90721
in-theory        90721
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))) or G) or H))
theorem-size     39
proof            (modus-ponens tm-980 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), 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-90721.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> (E and F))) or G) or H)), M:tm-980, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-90722
in-theory        90722
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 -> (F and G))) or H) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-90722.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> (G -> (F and G))) or H) and E))), M:tm-980, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-90723
in-theory        90723
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 -> (F and G))) or H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90723.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G -> (F and G))) or H))), M:tm-980, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-90724
in-theory        90724
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 ((G -> (G or H)) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90724.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I))), M:tm-980, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-90725
in-theory        90725
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 ((G -> (G or H)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90725.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> (G or H)) or I))), M:tm-980, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-90726
in-theory        90726
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 ((G -> (G or H)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90726.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> (G or H)) or I))), M:tm-980, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-90727
in-theory        90727
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 ((H -> (H or I)) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90727.        (((((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 ((H -> (H or I)) or J))), M:tm-980, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-90728
in-theory        90728
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 ((G -> (G or H)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90728.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> (G or H)) or I))), M:tm-980, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-90729
in-theory        90729
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (F or G)) or H)))
theorem-size     37
proof            (modus-ponens tm-980 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90729.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (F or G)) or H))), M:tm-980, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-90730
in-theory        90730
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)) or G) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A 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-90730.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (E or F)) or G) or H)), M:tm-980, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-90731
in-theory        90731
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> (F or G)) or H) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-90731.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> (F or G)) or H) and E))), M:tm-980, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-90732
in-theory        90732
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (F or G)) or H)))
theorem-size     37
proof            (modus-ponens tm-980 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90732.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (F or G)) or H))), M:tm-980, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-90733
in-theory        90733
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 (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90733.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (H -> G)))), M:tm-980, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-90734
in-theory        90734
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 ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-90734.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-90735
in-theory        90735
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 ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-90735.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G and H) -> G))), M:tm-980, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-90736
in-theory        90736
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 ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-90736.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G and H) -> H))), M:tm-980, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-90737
in-theory        90737
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 (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-90737.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (H -> (G and H))))), M:tm-980, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-90738
in-theory        90738
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 (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-90738.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (G or H)))), M:tm-980, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-90739
in-theory        90739
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 (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90739.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (H or G)))), M:tm-980, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-90740
in-theory        90740
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 ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-90740.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-980, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-90741
in-theory        90741
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 ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     45
proof            (modus-ponens tm-980 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       185
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-90741.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-980, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-90742
in-theory        90742
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 ((not (not G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-90742.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((not (not G)) -> G))), M:tm-980, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-90743
in-theory        90743
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 (G -> (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90743.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (H -> (I -> H))))), M:tm-980, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90744
in-theory        90744
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 ((G -> H) -> (G -> G))))
theorem-size     41
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-90744.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (G -> G)))), M:tm-980, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-90745
in-theory        90745
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 (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     53
proof            (modus-ponens tm-980 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       235
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-90745.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-980, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-90746
in-theory        90746
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 (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90746.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90747
in-theory        90747
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 ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-90747.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-980, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-90748
in-theory        90748
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 (G -> ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90748.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> ((H and I) -> H)))), M:tm-980, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90749
in-theory        90749
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 (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-90749.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-980, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-90750
in-theory        90750
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 (G -> ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90750.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> ((H and I) -> I)))), M:tm-980, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90751
in-theory        90751
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 (G -> ((H -> (I -> H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90751.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G)))), M:tm-980, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-90752
in-theory        90752
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 (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-90752.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-980, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-90753
in-theory        90753
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 (G -> (((H and I) -> H) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-90753.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G)))), M:tm-980, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-90754
in-theory        90754
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 (G -> (((H and I) -> I) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-90754.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G)))), M:tm-980, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-90755
in-theory        90755
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 (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-90755.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-980, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-90756
in-theory        90756
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 ((G -> H) -> (G -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-90756.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H))))), M:tm-980, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-90757
in-theory        90757
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 (G -> (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90757.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I)))))), M:tm-980, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90758
in-theory        90758
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 ((G -> (H -> G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90758.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> (H -> G)) or I))), M:tm-980, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-90759
in-theory        90759
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 (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-90759.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-980, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-90760
in-theory        90760
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 (((G and H) -> G) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-90760.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G and H) -> G) or I))), M:tm-980, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-90761
in-theory        90761
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 (((G and H) -> H) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-90761.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G and H) -> H) or I))), M:tm-980, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-90762
in-theory        90762
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 ((G -> (H -> (G and H))) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-90762.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I))), M:tm-980, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-90763
in-theory        90763
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 ((G -> (G or H)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-90763.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> (G or H)) or I))), M:tm-980, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-90764
in-theory        90764
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 (G -> ((H -> (H or I)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-90764.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G)))), M:tm-980, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-90765
in-theory        90765
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (F or G)) and E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-90765.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (F or G)) and E)))), M:tm-980, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-90766
in-theory        90766
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 (G -> ((H -> (H or I)) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90766.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G)))), M:tm-980, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-90767
in-theory        90767
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 (G -> ((H -> (H or I)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90767.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G)))), M:tm-980, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-90768
in-theory        90768
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 (G -> ((H -> (H or I)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90768.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G)))), M:tm-980, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-90769
in-theory        90769
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 (H -> ((I -> (I or J)) and H))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90769.        (((((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 (H -> ((I -> (I or J)) and H)))), M:tm-980, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-90770
in-theory        90770
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 (G -> ((H -> (H or I)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90770.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G)))), M:tm-980, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-90771
in-theory        90771
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (F or G)) and E))) -> (not E)))
theorem-size     41
proof            (modus-ponens tm-980 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       177
proof-steps      11
----------------------------------------------------------------
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-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-90771.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (F or G)) and E))) -> (not E))), M:tm-980, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-90772
in-theory        90772
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 G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-980 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       195
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-90772.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H))), M:tm-980, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-90773
in-theory        90773
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (G or H)) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90773.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (G or H)) and F)))), M:tm-980, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-90774
in-theory        90774
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F -> (F or G)) and E)) or H))
theorem-size     39
proof            (modus-ponens tm-980 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-90774.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F -> (F or G)) and E)) or H)), M:tm-980, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-90775
in-theory        90775
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 -> (G or H)) and F)) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-90775.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> ((G -> (G or H)) and F)) and E))), M:tm-980, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-90776
in-theory        90776
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 -> (G or H)) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90776.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> ((G -> (G or H)) and F)))), M:tm-980, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-90777
in-theory        90777
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 (G -> (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90777.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (H -> (H or I))))), M:tm-980, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90778
in-theory        90778
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (F or G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-90778.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (F or G))))), M:tm-980, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-90779
in-theory        90779
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 (G -> (H -> (H or I)))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-90779.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I))))), M:tm-980, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90780
in-theory        90780
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 (G -> (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90780.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (H -> (H or I))))), M:tm-980, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90781
in-theory        90781
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 (G -> (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90781.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (H -> (H or I))))), M:tm-980, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90782
in-theory        90782
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 (H -> (I -> (I or J)))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90782.        (((((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 (H -> (I -> (I or J))))), M:tm-980, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-90783
in-theory        90783
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 (G -> (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90783.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (H or I))))), M:tm-980, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90784
in-theory        90784
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 or G)) -> H)) -> H))
theorem-size     39
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-90784.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and ((F -> (F or G)) -> H)) -> H)), M:tm-980, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-90785
in-theory        90785
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)) -> G) and H) -> G))
theorem-size     39
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-90785.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (E or F)) -> G) and H) -> G)), M:tm-980, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-90786
in-theory        90786
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) -> G)) -> (E -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-90786.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((E or F) -> G)) -> (E -> G))), M:tm-980, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-90787
in-theory        90787
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (F or G)))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-980 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       169
proof-steps      11
----------------------------------------------------------------
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-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-90787.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (F or G)))) -> (not E))), M:tm-980, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-90788
in-theory        90788
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)) -> G) -> ((H or (E -> (E or F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-980 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       183
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-90788.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G))), M:tm-980, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-90789
in-theory        90789
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (G or H)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90789.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (G or H))))), M:tm-980, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-90790
in-theory        90790
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (F or G))) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90790.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (F or G))) or H)), M:tm-980, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-90791
in-theory        90791
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 -> (G or H))) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-90791.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G -> (G or H))) and E))), M:tm-980, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-90792
in-theory        90792
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 -> (F or G))))
theorem-size     37
proof            (modus-ponens tm-980 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-90792.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (E -> (F or G)))), M:tm-980, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-90793
in-theory        90793
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 -> (G or H)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-90793.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (G -> (G or H))))), M:tm-980, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-90794
in-theory        90794
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 (G or (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90794.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G or (H -> (I -> H))))), M:tm-980, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90795
in-theory        90795
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 (G or (H -> (I -> H)))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90795.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H))))), M:tm-980, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90796
in-theory        90796
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 (G or (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90796.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G or (H -> (I -> H))))), M:tm-980, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90797
in-theory        90797
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 (G or (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90797.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G or (H -> (I -> H))))), M:tm-980, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90798
in-theory        90798
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 (H or (I -> (J -> I)))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90798.        (((((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 (H or (I -> (J -> I))))), M:tm-980, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-90799
in-theory        90799
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 (G or (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90799.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G or (H -> (I -> H))))), M:tm-980, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90800
in-theory        90800
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or (G -> (H -> G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-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-90800.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or (G -> (H -> G))))), M:tm-980, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-90801
in-theory        90801
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (G -> F))) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90801.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (G -> F))) or H)), M:tm-980, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-90802
in-theory        90802
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 (G -> (H -> G))) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-90802.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F or (G -> (H -> G))) and E))), M:tm-980, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-90803
in-theory        90803
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 (G -> (H -> G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90803.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or (G -> (H -> G))))), M:tm-980, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-90804
in-theory        90804
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 (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90804.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90805
in-theory        90805
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 (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90805.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90806
in-theory        90806
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 (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90806.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90807
in-theory        90807
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 (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90807.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90808
in-theory        90808
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 (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     57
proof            (modus-ponens tm-980 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       247
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90808.        (((((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 (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-980, 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-90809
in-theory        90809
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 (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90809.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90810
in-theory        90810
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-90810.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-980, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-90811
in-theory        90811
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90811.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-980, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-90812
in-theory        90812
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 ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     47
proof            (modus-ponens tm-980 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       197
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-90812.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-980, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-90813
in-theory        90813
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 ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     45
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-90813.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-980, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-90814
in-theory        90814
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 (G or ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90814.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G or ((H and I) -> H)))), M:tm-980, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90815
in-theory        90815
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 (G or ((H and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90815.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H)))), M:tm-980, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90816
in-theory        90816
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 (G or ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90816.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G or ((H and I) -> H)))), M:tm-980, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90817
in-theory        90817
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 (G or ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90817.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G or ((H and I) -> H)))), M:tm-980, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90818
in-theory        90818
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 (H or ((I and J) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90818.        (((((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 (H or ((I and J) -> I)))), M:tm-980, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-90819
in-theory        90819
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 (G or ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90819.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G or ((H and I) -> H)))), M:tm-980, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90820
in-theory        90820
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or ((G and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-980 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-90820.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or ((G and H) -> G)))), M:tm-980, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-90821
in-theory        90821
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F and G) -> F)) or H))
theorem-size     37
proof            (modus-ponens tm-980 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       159
proof-steps      11
----------------------------------------------------------------
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-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-90821.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F and G) -> F)) or H)), M:tm-980, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-90822
in-theory        90822
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 ((G and H) -> G)) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-90822.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F or ((G and H) -> G)) and E))), M:tm-980, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-90823
in-theory        90823
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 ((G and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-980 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90823.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or ((G and H) -> G)))), M:tm-980, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-90824
in-theory        90824
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 (G or ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90824.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G or ((H and I) -> I)))), M:tm-980, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90825
in-theory        90825
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 (G or ((H and I) -> I))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90825.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I)))), M:tm-980, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90826
in-theory        90826
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 (G or ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90826.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G or ((H and I) -> I)))), M:tm-980, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90827
in-theory        90827
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 (G or ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90827.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G or ((H and I) -> I)))), M:tm-980, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90828
in-theory        90828
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 (H or ((I and J) -> J))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90828.        (((((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 (H or ((I and J) -> J)))), M:tm-980, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-90829
in-theory        90829
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 (G or ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90829.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G or ((H and I) -> I)))), M:tm-980, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90830
in-theory        90830
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or ((G and H) -> H))))
theorem-size     37
proof            (modus-ponens tm-980 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-90830.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or ((G and H) -> H)))), M:tm-980, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-90831
in-theory        90831
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F and G) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-980 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       159
proof-steps      11
----------------------------------------------------------------
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-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-90831.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F and G) -> G)) or H)), M:tm-980, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-90832
in-theory        90832
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 ((G and H) -> H)) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-90832.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F or ((G and H) -> H)) and E))), M:tm-980, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-90833
in-theory        90833
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 ((G and H) -> H))))
theorem-size     37
proof            (modus-ponens tm-980 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90833.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or ((G and H) -> H)))), M:tm-980, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-90834
in-theory        90834
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 (G or (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90834.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G or (H -> (I -> (H and I)))))), M:tm-980, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90835
in-theory        90835
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 (G or (H -> (I -> (H and I))))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90835.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I)))))), M:tm-980, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90836
in-theory        90836
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 (G or (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90836.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G or (H -> (I -> (H and I)))))), M:tm-980, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90837
in-theory        90837
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 (G or (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90837.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G or (H -> (I -> (H and I)))))), M:tm-980, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90838
in-theory        90838
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 (H or (I -> (J -> (I and J))))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90838.        (((((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 (H or (I -> (J -> (I and J)))))), M:tm-980, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-90839
in-theory        90839
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 (G or (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90839.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I)))))), M:tm-980, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90840
in-theory        90840
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or (G -> (H -> (G and H))))))
theorem-size     39
proof            (modus-ponens tm-980 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), 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-90840.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or (G -> (H -> (G and H)))))), M:tm-980, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-90841
in-theory        90841
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (G -> (F and G)))) or H))
theorem-size     39
proof            (modus-ponens tm-980 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90841.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (G -> (F and G)))) or H)), M:tm-980, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-90842
in-theory        90842
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 (G -> (H -> (G and H)))) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-90842.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F or (G -> (H -> (G and H)))) and E))), M:tm-980, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-90843
in-theory        90843
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 (G -> (H -> (G and H))))))
theorem-size     39
proof            (modus-ponens tm-980 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90843.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or (G -> (H -> (G and H)))))), M:tm-980, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-90844
in-theory        90844
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 (G or (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90844.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G or (H -> (H or I))))), M:tm-980, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90845
in-theory        90845
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 (G or (H -> (H or I)))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90845.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (H or I))))), M:tm-980, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90846
in-theory        90846
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 (G or (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90846.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G or (H -> (H or I))))), M:tm-980, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90847
in-theory        90847
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 (G or (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90847.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G or (H -> (H or I))))), M:tm-980, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90848
in-theory        90848
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 (H or (I -> (I or J)))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90848.        (((((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 (H or (I -> (I or J))))), M:tm-980, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-90849
in-theory        90849
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 (G or (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90849.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G or (H -> (H or I))))), M:tm-980, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90850
in-theory        90850
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or (G -> (G or H)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A 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-90850.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or (G -> (G or H))))), M:tm-980, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-90851
in-theory        90851
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (F or G))) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90851.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (F or G))) or H)), M:tm-980, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-90852
in-theory        90852
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 (G -> (G or H))) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-90852.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F or (G -> (G or H))) and E))), M:tm-980, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-90853
in-theory        90853
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 (G -> (G or H)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90853.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or (G -> (G or H))))), M:tm-980, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-90854
in-theory        90854
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 (G or (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90854.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G or (H -> (I or H))))), M:tm-980, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90855
in-theory        90855
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 (G or (H -> (I or H)))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90855.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (I or H))))), M:tm-980, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90856
in-theory        90856
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 (G or (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90856.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G or (H -> (I or H))))), M:tm-980, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90857
in-theory        90857
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 (G or (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90857.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G or (H -> (I or H))))), M:tm-980, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90858
in-theory        90858
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 (H or (I -> (J or I)))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90858.        (((((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 (H or (I -> (J or I))))), M:tm-980, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-90859
in-theory        90859
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 (G or (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90859.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G or (H -> (I or H))))), M:tm-980, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90860
in-theory        90860
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or (G -> (H or G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B 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-90860.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or (G -> (H or G))))), M:tm-980, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-90861
in-theory        90861
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (G or F))) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90861.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (G or F))) or H)), M:tm-980, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-90862
in-theory        90862
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 (G -> (H or G))) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-90862.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F or (G -> (H or G))) and E))), M:tm-980, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-90863
in-theory        90863
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 (G -> (H or G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90863.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or (G -> (H or G))))), M:tm-980, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-90864
in-theory        90864
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 ((G -> (H or G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90864.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> (H or G)) or I))), M:tm-980, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-90865
in-theory        90865
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 ((G -> (H or G)) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90865.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I))), M:tm-980, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-90866
in-theory        90866
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 ((G -> (H or G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90866.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> (H or G)) or I))), M:tm-980, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-90867
in-theory        90867
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 ((G -> (H or G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90867.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> (H or G)) or I))), M:tm-980, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-90868
in-theory        90868
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 ((H -> (I or H)) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90868.        (((((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 ((H -> (I or H)) or J))), M:tm-980, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-90869
in-theory        90869
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 ((G -> (H or G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90869.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> (H or G)) or I))), M:tm-980, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-90870
in-theory        90870
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (G or F)) or H)))
theorem-size     37
proof            (modus-ponens tm-980 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90870.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> (G or F)) or H))), M:tm-980, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-90871
in-theory        90871
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)) or G) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B 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-90871.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F or E)) or G) or H)), M:tm-980, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-90872
in-theory        90872
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 or F)) or H) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-90872.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> (G or F)) or H) and E))), M:tm-980, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-90873
in-theory        90873
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 or F)) or H)))
theorem-size     37
proof            (modus-ponens tm-980 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90873.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G or F)) or H))), M:tm-980, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-90874
in-theory        90874
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 (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90874.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (H -> G)))), M:tm-980, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-90875
in-theory        90875
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 ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-90875.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-90876
in-theory        90876
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 ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or 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-90876.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G and H) -> G))), M:tm-980, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-90877
in-theory        90877
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 ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or 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-90877.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G and H) -> H))), M:tm-980, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-90878
in-theory        90878
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 (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or 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-90878.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (H -> (G and H))))), M:tm-980, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-90879
in-theory        90879
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 (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90879.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (G or H)))), M:tm-980, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-90880
in-theory        90880
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 (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or 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-90880.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (H or G)))), M:tm-980, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-90881
in-theory        90881
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 ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-90881.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-980, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-90882
in-theory        90882
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 ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     45
proof            (modus-ponens tm-980 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       185
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-90882.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-980, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-90883
in-theory        90883
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 ((not (not G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or 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-90883.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((not (not G)) -> G))), M:tm-980, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-90884
in-theory        90884
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 (G -> (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90884.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (H -> (I -> H))))), M:tm-980, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90885
in-theory        90885
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 ((G -> H) -> (G -> G))))
theorem-size     41
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-90885.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (G -> G)))), M:tm-980, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-90886
in-theory        90886
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 (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     53
proof            (modus-ponens tm-980 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       235
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-90886.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-980, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-90887
in-theory        90887
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 (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90887.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90888
in-theory        90888
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 ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-90888.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-980, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-90889
in-theory        90889
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 (G -> ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90889.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> ((H and I) -> H)))), M:tm-980, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90890
in-theory        90890
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 (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-90890.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-980, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-90891
in-theory        90891
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 (G -> ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90891.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> ((H and I) -> I)))), M:tm-980, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90892
in-theory        90892
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 (G -> ((H -> (I -> H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90892.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-980, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-90893
in-theory        90893
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 (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-90893.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-980, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-90894
in-theory        90894
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 (G -> (((H and I) -> H) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-90894.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G)))), M:tm-980, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-90895
in-theory        90895
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 (G -> (((H and I) -> I) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-90895.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G)))), M:tm-980, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-90896
in-theory        90896
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 (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-90896.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-980, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-90897
in-theory        90897
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 ((G -> H) -> (G -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-90897.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H))))), M:tm-980, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-90898
in-theory        90898
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 (G -> (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90898.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I)))))), M:tm-980, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90899
in-theory        90899
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 ((G -> (H -> G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90899.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> (H -> G)) or I))), M:tm-980, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-90900
in-theory        90900
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 (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90900.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-980, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-90901
in-theory        90901
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 (((G and H) -> G) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90901.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G and H) -> G) or I))), M:tm-980, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-90902
in-theory        90902
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 (((G and H) -> H) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90902.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G and H) -> H) or I))), M:tm-980, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-90903
in-theory        90903
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 ((G -> (H -> (G and H))) or I)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90903.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I))), M:tm-980, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-90904
in-theory        90904
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 ((G -> (G or H)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90904.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> (G or H)) or I))), M:tm-980, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-90905
in-theory        90905
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 (G -> ((H -> (H or I)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90905.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G)))), M:tm-980, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-90906
in-theory        90906
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 (G -> (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90906.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (H -> (H or I))))), M:tm-980, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90907
in-theory        90907
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 (G or (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90907.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G or (H -> (I -> H))))), M:tm-980, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-90908
in-theory        90908
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 (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-90908.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-980, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-90909
in-theory        90909
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 (G or ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-90909.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G or ((H and I) -> H)))), M:tm-980, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-90910
in-theory        90910
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 (G or ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-90910.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G or ((H and I) -> I)))), M:tm-980, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-90911
in-theory        90911
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 (G or (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-90911.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G or (H -> (I -> (H and I)))))), M:tm-980, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-90912
in-theory        90912
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 (G or (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90912.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G or (H -> (H or I))))), M:tm-980, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-90913
in-theory        90913
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 (G or (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or 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-90913.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G or (H -> (I or H))))), M:tm-980, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90914
in-theory        90914
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 ((G -> (H or G)) or I)))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-90914.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> (H or G)) or I))), M:tm-980, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-90915
in-theory        90915
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 (G -> ((H -> (I or H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-90915.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G)))), M:tm-980, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-90916
in-theory        90916
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 (G -> ((H -> (I or H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-90916.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G)))), M:tm-980, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-90917
in-theory        90917
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (G or F)) and E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-90917.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and ((F -> (G or F)) and E)))), M:tm-980, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-90918
in-theory        90918
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 (G -> ((H -> (I or H)) and G))))
theorem-size     45
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-90918.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G)))), M:tm-980, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-90919
in-theory        90919
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 (G -> ((H -> (I or H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-90919.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G)))), M:tm-980, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-90920
in-theory        90920
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 (G -> ((H -> (I or H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-90920.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G)))), M:tm-980, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-90921
in-theory        90921
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 (H -> ((I -> (J or I)) and H))))
theorem-size     51
proof            (modus-ponens tm-980 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       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-90921.        (((((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 (H -> ((I -> (J or I)) and H)))), M:tm-980, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-90922
in-theory        90922
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 (G -> ((H -> (I or H)) and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90922.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G)))), M:tm-980, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-90923
in-theory        90923
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (G or F)) and E))) -> (not E)))
theorem-size     41
proof            (modus-ponens tm-980 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       177
proof-steps      11
----------------------------------------------------------------
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-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-90923.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not ((F -> (G or F)) and E))) -> (not E))), M:tm-980, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-90924
in-theory        90924
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 G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-980 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       195
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-90924.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H))), M:tm-980, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-90925
in-theory        90925
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (H or G)) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or 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-90925.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> ((G -> (H or G)) and F)))), M:tm-980, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-90926
in-theory        90926
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 or F)) and E)) or H))
theorem-size     39
proof            (modus-ponens tm-980 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90926.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F -> (G or F)) and E)) or H)), M:tm-980, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-90927
in-theory        90927
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 -> (H or G)) and F)) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-90927.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> ((G -> (H or G)) and F)) and E))), M:tm-980, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-90928
in-theory        90928
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 -> (H or G)) and F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90928.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> ((G -> (H or G)) and F)))), M:tm-980, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-90929
in-theory        90929
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 (G -> (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90929.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G -> (H -> (I or H))))), M:tm-980, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90930
in-theory        90930
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 (G -> (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90930.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G -> (H -> (I or H))))), M:tm-980, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90931
in-theory        90931
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (G or F)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-90931.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E and (F -> (G or F))))), M:tm-980, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-90932
in-theory        90932
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 (G -> (H -> (I or H)))))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-90932.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H))))), M:tm-980, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90933
in-theory        90933
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 (G -> (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90933.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G -> (H -> (I or H))))), M:tm-980, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90934
in-theory        90934
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 (G -> (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90934.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G -> (H -> (I or H))))), M:tm-980, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90935
in-theory        90935
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 (H -> (I -> (J or I)))))
theorem-size     49
proof            (modus-ponens tm-980 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       215
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90935.        (((((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 (H -> (I -> (J or I))))), M:tm-980, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-90936
in-theory        90936
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 (G -> (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-90936.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (I or H))))), M:tm-980, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-90937
in-theory        90937
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 -> (G or F)) -> H)) -> H))
theorem-size     39
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-90937.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and ((F -> (G or F)) -> H)) -> H)), M:tm-980, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-90938
in-theory        90938
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)) -> G) and H) -> G))
theorem-size     39
proof            (modus-ponens tm-980 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       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-90938.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F or E)) -> G) and H) -> G)), M:tm-980, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-90939
in-theory        90939
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) -> G)) -> (E -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-90939.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> ((F or E) -> G)) -> (E -> G))), M:tm-980, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-90940
in-theory        90940
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (G or F)))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-980 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       169
proof-steps      11
----------------------------------------------------------------
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-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-90940.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (not (F -> (G or F)))) -> (not E))), M:tm-980, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-90941
in-theory        90941
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)) -> G) -> ((H or (E -> (F or E))) -> G)))
theorem-size     45
proof            (modus-ponens tm-980 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       183
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-90941.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G))), M:tm-980, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-90942
in-theory        90942
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (H or G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90942.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F -> (G -> (H or G))))), M:tm-980, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-90943
in-theory        90943
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 or F))) or H))
theorem-size     37
proof            (modus-ponens tm-980 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-90943.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (G or F))) or H)), M:tm-980, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-90944
in-theory        90944
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 -> (H or G))) and E)))
theorem-size     39
proof            (modus-ponens tm-980 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-90944.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> (G -> (H or G))) and E))), M:tm-980, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-90945
in-theory        90945
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 -> (G or F))))
theorem-size     37
proof            (modus-ponens tm-980 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-90945.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> (E -> (G or F)))), M:tm-980, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-90946
in-theory        90946
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 -> (H or G)))))
theorem-size     37
proof            (modus-ponens tm-980 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-90946.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (G -> (H or G))))), M:tm-980, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-90947
in-theory        90947
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (F -> E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90947.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (F -> E)))), M:tm-980, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-90948
in-theory        90948
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 (G -> (E -> F))) -> ((G -> E) -> (G -> F))))
theorem-size     45
proof            (modus-ponens tm-980 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       197
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-90948.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F)))), M:tm-980, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-90949
in-theory        90949
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> ((F -> E) and G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90949.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> ((F -> E) and G)))), M:tm-980, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-90950
in-theory        90950
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((F -> E) or G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90950.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((F -> E) or G))), M:tm-980, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-90951
in-theory        90951
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G or (F -> E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90951.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G or (F -> E)))), M:tm-980, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-90952
in-theory        90952
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G))))
theorem-size     43
proof            (modus-ponens tm-980 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90952.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G)))), M:tm-980, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-90953
in-theory        90953
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F))))
theorem-size     41
proof            (modus-ponens tm-980 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90953.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F)))), M:tm-980, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-90954
in-theory        90954
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90954.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (H -> G)))), M:tm-980, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-90955
in-theory        90955
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (F -> F)))
theorem-size     37
proof            (modus-ponens tm-980 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-90955.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (F -> F))), M:tm-980, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-90956
in-theory        90956
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 -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     51
proof            (modus-ponens tm-980 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       241
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-90956.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-980, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-90957
in-theory        90957
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       221
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-90957.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-90958
in-theory        90958
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     45
proof            (modus-ponens tm-980 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       217
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-90958.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-980, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-90959
in-theory        90959
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90959.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G and H) -> G))), M:tm-980, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-90960
in-theory        90960
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G)))
theorem-size     45
proof            (modus-ponens tm-980 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       217
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-90960.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G))), M:tm-980, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-90961
in-theory        90961
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90961.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G and H) -> H))), M:tm-980, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-90962
in-theory        90962
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E))))
theorem-size     43
proof            (modus-ponens tm-980 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90962.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E)))), M:tm-980, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-90963
in-theory        90963
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E))))
theorem-size     51
proof            (modus-ponens tm-980 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       233
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-90963.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E)))), M:tm-980, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-90964
in-theory        90964
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E))))
theorem-size     43
proof            (modus-ponens tm-980 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       201
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-90964.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E)))), M:tm-980, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-90965
in-theory        90965
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E))))
theorem-size     43
proof            (modus-ponens tm-980 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       201
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-90965.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E)))), M:tm-980, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-90966
in-theory        90966
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E))))
theorem-size     45
proof            (modus-ponens tm-980 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       209
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-90966.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E)))), M:tm-980, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-90967
in-theory        90967
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (F -> (F and E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-90967.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (F -> (F and E)))), M:tm-980, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-90968
in-theory        90968
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90968.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (H -> (G and H))))), M:tm-980, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-90969
in-theory        90969
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E))))
theorem-size     43
proof            (modus-ponens tm-980 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       201
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-90969.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E)))), M:tm-980, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-90970
in-theory        90970
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90970.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (G or H)))), M:tm-980, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-90971
in-theory        90971
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E))))
theorem-size     43
proof            (modus-ponens tm-980 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       201
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-90971.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E)))), M:tm-980, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-90972
in-theory        90972
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90972.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (G -> (H or G)))), M:tm-980, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-90973
in-theory        90973
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E)))
theorem-size     43
proof            (modus-ponens tm-980 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90973.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E))), M:tm-980, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-90974
in-theory        90974
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 (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 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       209
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-90974.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-980, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-90975
in-theory        90975
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 (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 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       209
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-90975.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-980, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-90976
in-theory        90976
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) -> G) and ((F or (E -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-980 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       217
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-90976.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G)))), M:tm-980, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-90977
in-theory        90977
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 (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 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       217
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-90977.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-980, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-90978
in-theory        90978
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 (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 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       209
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-90978.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-980, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-90979
in-theory        90979
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 (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 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       209
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-90979.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-980, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-90980
in-theory        90980
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 (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     55
proof            (modus-ponens tm-980 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       241
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-90980.        (((((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 (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-980, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-90981
in-theory        90981
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 (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 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       209
proof-steps      13
----------------------------------------------------------------
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-1.            (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-90981.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-980, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-90982
in-theory        90982
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) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-90982.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> G) -> ((E -> F) -> G))), M:tm-980, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-90983
in-theory        90983
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) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G))))
theorem-size     49
proof            (modus-ponens tm-980 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       203
proof-steps      11
----------------------------------------------------------------
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-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-90983.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G)))), M:tm-980, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-90984
in-theory        90984
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-980 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       213
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-90984.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H))), M:tm-980, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-90985
in-theory        90985
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     43
proof            (modus-ponens tm-980 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       185
proof-steps      11
----------------------------------------------------------------
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-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-90985.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-980, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-90986
in-theory        90986
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) -> ((F or (E -> F)) -> G)) or H))
theorem-size     43
proof            (modus-ponens tm-980 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       185
proof-steps      11
----------------------------------------------------------------
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-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-90986.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H)), M:tm-980, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-90987
in-theory        90987
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) -> H) -> ((G or (F -> G)) -> H)) and E)))
theorem-size     45
proof            (modus-ponens tm-980 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-90987.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E))), M:tm-980, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-90988
in-theory        90988
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) -> (F or (E -> F))) -> (((E -> F) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-980 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       201
proof-steps      11
----------------------------------------------------------------
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-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-90988.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G))), M:tm-980, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-90989
in-theory        90989
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) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     43
proof            (modus-ponens tm-980 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-90989.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-980, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-90990
in-theory        90990
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)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G)))))
theorem-size     51
proof            (modus-ponens tm-980 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       221
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-90990.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G))))), M:tm-980, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-90991
in-theory        90991
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)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G))))
theorem-size     53
proof            (modus-ponens tm-980 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       233
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-90991.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G)))), M:tm-980, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-90992
in-theory        90992
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)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H))))
theorem-size     53
proof            (modus-ponens tm-980 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       227
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-90992.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H)))), M:tm-980, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-90993
in-theory        90993
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)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H)))
theorem-size     51
proof            (modus-ponens tm-980 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       221
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-90993.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H))), M:tm-980, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-90994
in-theory        90994
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)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G)))))
theorem-size     51
proof            (modus-ponens tm-980 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       221
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-90994.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G))))), M:tm-980, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-90995
in-theory        90995
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)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H))))
theorem-size     57
proof            (modus-ponens tm-980 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       241
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-90995.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H)))), M:tm-980, 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-90996
in-theory        90996
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)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F)))))
theorem-size     55
proof            (modus-ponens tm-980 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       235
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-90996.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F))))), M:tm-980, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-90997
in-theory        90997
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)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H))))
theorem-size     47
proof            (modus-ponens tm-980 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       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-90997.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H)))), M:tm-980, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-90998
in-theory        90998
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)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F))))
theorem-size     49
proof            (modus-ponens tm-980 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       237
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-90998.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F)))), M:tm-980, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-90999
in-theory        90999
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) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     55
proof            (modus-ponens tm-980 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       269
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-90999.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-980, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-91000
in-theory        91000
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)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     55
proof            (modus-ponens tm-980 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       257
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-91000.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-980, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-91001
in-theory        91001
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)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H)))
theorem-size     47
proof            (modus-ponens tm-980 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       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-91001.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H))), M:tm-980, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-91002
in-theory        91002
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)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I)))
theorem-size     47
proof            (modus-ponens tm-980 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       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-91002.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I))), M:tm-980, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-91003
in-theory        91003
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)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-980 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       245
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-91003.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G))))), M:tm-980, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-91004
in-theory        91004
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)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G)))))
theorem-size     63
proof            (modus-ponens tm-980 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       277
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91004.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> 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-980, 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-91005
in-theory        91005
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)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-980 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       245
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91005.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G))))), M:tm-980, 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-91006
in-theory        91006
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)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-980 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       245
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91006.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G))))), M:tm-980, 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-91007
in-theory        91007
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)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G)))))
theorem-size     57
proof            (modus-ponens tm-980 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       253
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91007.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G))))), M:tm-980, 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-91008
in-theory        91008
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)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G)))))
theorem-size     53
proof            (modus-ponens tm-980 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       249
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91008.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G))))), M:tm-980, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-91009
in-theory        91009
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)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I)))))
theorem-size     49
proof            (modus-ponens tm-980 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       233
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-91009.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I))))), M:tm-980, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-91010
in-theory        91010
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)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-980 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       245
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91010.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G))))), M:tm-980, 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-91011
in-theory        91011
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)) or ((E -> F) -> (E -> G))) -> (H -> (H or I))))
theorem-size     47
proof            (modus-ponens tm-980 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       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-91011.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I)))), M:tm-980, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-91012
in-theory        91012
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)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-980 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       245
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91012.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G))))), M:tm-980, 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-91013
in-theory        91013
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)) or ((E -> F) -> (E -> G))) -> (H -> (I or H))))
theorem-size     47
proof            (modus-ponens tm-980 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       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-91013.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H)))), M:tm-980, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-91014
in-theory        91014
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)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G))))
theorem-size     51
proof            (modus-ponens tm-980 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       247
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-91014.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G)))), M:tm-980, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-91015
in-theory        91015
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 -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H))))
theorem-size     71
proof            (modus-ponens tm-980 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       307
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91015.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> 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-980, 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-91016
in-theory        91016
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E)))
theorem-size     55
proof            (modus-ponens tm-980 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       255
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-91016.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E))), M:tm-980, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-91017
in-theory        91017
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 ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     59
proof            (modus-ponens tm-980 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       253
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-91017.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-980, 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-91018
in-theory        91018
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 ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     59
proof            (modus-ponens tm-980 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       253
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-91018.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-980, 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-91019
in-theory        91019
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 -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     63
proof            (modus-ponens tm-980 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       269
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-91019.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> 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-980, 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-91020
in-theory        91020
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 ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     61
proof            (modus-ponens tm-980 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       261
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-91020.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> 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-980, 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-91021
in-theory        91021
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 ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     59
proof            (modus-ponens tm-980 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       253
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-91021.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-980, 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-91022
in-theory        91022
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 ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     59
proof            (modus-ponens tm-980 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       253
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-91022.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-980, 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-91023
in-theory        91023
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 ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     67
proof            (modus-ponens tm-980 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       285
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-91023.        (((((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 ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-980, 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-91024
in-theory        91024
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 ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     59
proof            (modus-ponens tm-980 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       253
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-91024.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-980, 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-91025
in-theory        91025
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 -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-980 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       233
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-91025.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H))), M:tm-980, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-91026
in-theory        91026
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 -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H))))
theorem-size     65
proof            (modus-ponens tm-980 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       255
proof-steps      11
----------------------------------------------------------------
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-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-91026.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> 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-980, 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-91027
in-theory        91027
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)) 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     73
proof            (modus-ponens tm-980 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       273
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-91027.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> 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-980, 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-91028
in-theory        91028
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     55
proof            (modus-ponens tm-980 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       229
proof-steps      11
----------------------------------------------------------------
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-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-91028.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-980, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-91029
in-theory        91029
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 -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I))
theorem-size     55
proof            (modus-ponens tm-980 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       229
proof-steps      11
----------------------------------------------------------------
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-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-91029.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I)), M:tm-980, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-91030
in-theory        91030
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) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E)))
theorem-size     57
proof            (modus-ponens tm-980 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       235
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-91030.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E))), M:tm-980, 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-91031
in-theory        91031
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 -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H)))
theorem-size     63
proof            (modus-ponens tm-980 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       253
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91031.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H))), M:tm-980, 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-91032
in-theory        91032
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) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     55
proof            (modus-ponens tm-980 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       229
proof-steps      11
----------------------------------------------------------------
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-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-91032.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-980, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-91033
in-theory        91033
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) or E) -> (G -> E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91033.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (G -> E))), M:tm-980, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-91034
in-theory        91034
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)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     49
proof            (modus-ponens tm-980 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       203
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-91034.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-980, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-91035
in-theory        91035
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) and G) or (E and F)) -> E))
theorem-size     39
proof            (modus-ponens tm-980 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
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-91035.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and F) and G) or (E and F)) -> E)), M:tm-980, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-91036
in-theory        91036
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) and G) or (E and F)) -> F))
theorem-size     39
proof            (modus-ponens tm-980 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       175
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91036.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E and F) and G) or (E and F)) -> F)), M:tm-980, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-91037
in-theory        91037
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) or E) -> (G -> (E and G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
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-91037.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (G -> (E and G)))), M:tm-980, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-91038
in-theory        91038
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) or E) -> (E or G)))
theorem-size     37
proof            (modus-ponens tm-980 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
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-91038.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (E or G))), M:tm-980, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-91039
in-theory        91039
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) or E) -> (G or E)))
theorem-size     37
proof            (modus-ponens tm-980 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
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-91039.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (G or E))), M:tm-980, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-91040
in-theory        91040
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H))))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91040.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H)))), M:tm-980, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-91041
in-theory        91041
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     45
proof            (modus-ponens tm-980 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       193
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91041.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-980, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-91042
in-theory        91042
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((not (not E)) and F) or (not (not E))) -> E))
theorem-size     39
proof            (modus-ponens tm-980 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       175
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91042.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((not (not E)) and F) or (not (not E))) -> E)), M:tm-980, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-91043
in-theory        91043
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) or E) -> (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91043.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (G -> (H -> G)))), M:tm-980, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-91044
in-theory        91044
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (E -> E)))
theorem-size     41
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-91044.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (E -> E))), M:tm-980, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-91045
in-theory        91045
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)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     59
proof            (modus-ponens tm-980 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       255
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-91045.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-980, 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-91046
in-theory        91046
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) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       219
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91046.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-91047
in-theory        91047
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     53
proof            (modus-ponens tm-980 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       231
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-91047.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-980, 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-91048
in-theory        91048
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) or E) -> ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91048.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> ((G and H) -> G))), M:tm-980, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-91049
in-theory        91049
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 -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     53
proof            (modus-ponens tm-980 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       231
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-91049.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-980, 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-91050
in-theory        91050
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) or E) -> ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 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       187
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91050.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> ((G and H) -> H))), M:tm-980, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-91051
in-theory        91051
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) or E) -> ((G -> (H -> G)) and E)))
theorem-size     41
proof            (modus-ponens tm-980 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       195
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91051.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> ((G -> (H -> G)) and E))), M:tm-980, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-91052
in-theory        91052
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) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E)))
theorem-size     49
proof            (modus-ponens tm-980 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       227
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-91052.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E))), M:tm-980, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-91053
in-theory        91053
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) or E) -> (((G and H) -> G) and E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
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-91053.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (((G and H) -> G) and E))), M:tm-980, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-91054
in-theory        91054
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) or E) -> (((G and H) -> H) and E)))
theorem-size     41
proof            (modus-ponens tm-980 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       195
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91054.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (((G and H) -> H) and E))), M:tm-980, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-91055
in-theory        91055
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) or E) -> ((G -> (H -> (G and H))) and E)))
theorem-size     43
proof            (modus-ponens tm-980 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       203
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91055.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E))), M:tm-980, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-91056
in-theory        91056
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F))))
theorem-size     43
proof            (modus-ponens tm-980 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       207
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-91056.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F)))), M:tm-980, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-91057
in-theory        91057
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) or E) -> (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 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       195
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91057.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (G -> (H -> (G and H))))), M:tm-980, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-91058
in-theory        91058
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) or E) -> ((G -> (G or H)) and E)))
theorem-size     41
proof            (modus-ponens tm-980 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       195
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91058.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> ((G -> (G or H)) and E))), M:tm-980, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-91059
in-theory        91059
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) or E) -> (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 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       187
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91059.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (G -> (G or H)))), M:tm-980, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-91060
in-theory        91060
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) or E) -> ((G -> (H or G)) and E)))
theorem-size     41
proof            (modus-ponens tm-980 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       195
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91060.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> ((G -> (H or G)) and E))), M:tm-980, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-91061
in-theory        91061
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) or E) -> (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 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       187
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91061.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or E) -> (G -> (H or G)))), M:tm-980, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-91062
in-theory        91062
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) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     49
proof            (modus-ponens tm-980 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       221
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-91062.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-980, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-91063
in-theory        91063
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 -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     65
proof            (modus-ponens tm-980 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       273
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-91063.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> 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-980, 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-91064
in-theory        91064
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F)))
theorem-size     45
proof            (modus-ponens tm-980 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       211
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91064.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F))), M:tm-980, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-91065
in-theory        91065
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)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G))))
theorem-size     55
proof            (modus-ponens tm-980 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       253
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91065.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G)))), M:tm-980, 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-91066
in-theory        91066
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((F and G) or F) -> E)))
theorem-size     41
proof            (modus-ponens tm-980 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       205
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-91066.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((F and G) or F) -> E))), M:tm-980, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-91067
in-theory        91067
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 ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 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       203
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-91067.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-980, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-91068
in-theory        91068
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 ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 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       203
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-91068.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-980, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-91069
in-theory        91069
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 -> F) and (((E and G) or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-980 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       207
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-91069.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F)))), M:tm-980, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-91070
in-theory        91070
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 ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     47
proof            (modus-ponens tm-980 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       211
proof-steps      13
----------------------------------------------------------------
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-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-91070.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-980, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-91071
in-theory        91071
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 ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 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       203
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-91071.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-980, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-91072
in-theory        91072
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 ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 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       203
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-91072.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-980, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-91073
in-theory        91073
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 ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     53
proof            (modus-ponens tm-980 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       235
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-91073.        (((((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 ((H -> I) -> (((H and J) or H) -> I)))), M:tm-980, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-91074
in-theory        91074
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 ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 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       203
proof-steps      13
----------------------------------------------------------------
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-1.            (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-91074.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-980, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-91075
in-theory        91075
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F))))
theorem-size     45
proof            (modus-ponens tm-980 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       193
proof-steps      11
----------------------------------------------------------------
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-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-91075.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F)))), M:tm-980, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-91076
in-theory        91076
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) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-980 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       207
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-91076.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H))), M:tm-980, 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-91077
in-theory        91077
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-980 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       179
proof-steps      11
----------------------------------------------------------------
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-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-91077.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> (((F and H) or F) -> G)))), M:tm-980, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-91078
in-theory        91078
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 G) or E) -> F)) or H))
theorem-size     41
proof            (modus-ponens tm-980 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       179
proof-steps      11
----------------------------------------------------------------
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-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-91078.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (((E and G) or E) -> F)) or H)), M:tm-980, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-91079
in-theory        91079
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) -> (((F and H) or F) -> G)) and E)))
theorem-size     43
proof            (modus-ponens tm-980 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-91079.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E))), M:tm-980, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-91080
in-theory        91080
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 G) or E)) -> ((E -> F) -> F)))
theorem-size     43
proof            (modus-ponens tm-980 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       191
proof-steps      11
----------------------------------------------------------------
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-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-91080.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F))), M:tm-980, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-91081
in-theory        91081
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) -> (((F and H) or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91081.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> G) -> (((F and H) or F) -> G)))), M:tm-980, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-91082
in-theory        91082
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) or F) -> (G -> F)))
theorem-size     37
proof            (modus-ponens tm-980 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-91082.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (G -> F))), M:tm-980, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-91083
in-theory        91083
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 -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H))))
theorem-size     49
proof            (modus-ponens tm-980 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       203
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-91083.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H)))), M:tm-980, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-91084
in-theory        91084
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 and G)) or (F and G)) -> F))
theorem-size     39
proof            (modus-ponens tm-980 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       175
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-91084.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F and G)) or (F and G)) -> F)), M:tm-980, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-91085
in-theory        91085
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 and G)) or (F and G)) -> G))
theorem-size     39
proof            (modus-ponens tm-980 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91085.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F and G)) or (F and G)) -> G)), M:tm-980, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-91086
in-theory        91086
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) or F) -> (G -> (F and G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91086.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (G -> (F and G)))), M:tm-980, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-91087
in-theory        91087
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) or F) -> (F or G)))
theorem-size     37
proof            (modus-ponens tm-980 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91087.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (F or G))), M:tm-980, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-91088
in-theory        91088
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) or F) -> (G or F)))
theorem-size     37
proof            (modus-ponens tm-980 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91088.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (G or F))), M:tm-980, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-91089
in-theory        91089
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 -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H))))
theorem-size     47
proof            (modus-ponens tm-980 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       199
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-91089.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H)))), M:tm-980, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-91090
in-theory        91090
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 -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F))))
theorem-size     45
proof            (modus-ponens tm-980 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       193
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-91090.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F)))), M:tm-980, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-91091
in-theory        91091
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (not (not F))) or (not (not F))) -> F))
theorem-size     39
proof            (modus-ponens tm-980 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       175
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-91091.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (not (not F))) or (not (not F))) -> F)), M:tm-980, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-91092
in-theory        91092
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) or F) -> (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-91092.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (G -> (H -> G)))), M:tm-980, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-91093
in-theory        91093
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 -> G)) or (F -> G)) -> (F -> F)))
theorem-size     41
proof            (modus-ponens tm-980 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       199
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-91093.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (F -> F))), M:tm-980, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-91094
in-theory        91094
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 -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H))))
theorem-size     59
proof            (modus-ponens tm-980 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       255
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-91094.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H)))), M:tm-980, 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-91095
in-theory        91095
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) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 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       219
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-91095.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-91096
in-theory        91096
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 -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G)))
theorem-size     53
proof            (modus-ponens tm-980 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       231
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-91096.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G))), M:tm-980, 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-91097
in-theory        91097
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) or F) -> ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 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       187
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-91097.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> ((G and H) -> G))), M:tm-980, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-91098
in-theory        91098
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 and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H)))
theorem-size     53
proof            (modus-ponens tm-980 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       231
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-91098.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H))), M:tm-980, 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-91099
in-theory        91099
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) or F) -> ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-91099.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> ((G and H) -> H))), M:tm-980, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-91100
in-theory        91100
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) or F) -> ((G -> (H -> G)) and F)))
theorem-size     41
proof            (modus-ponens tm-980 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       195
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-91100.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> ((G -> (H -> G)) and F))), M:tm-980, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-91101
in-theory        91101
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) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))
theorem-size     49
proof            (modus-ponens tm-980 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       227
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-91101.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))), M:tm-980, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-91102
in-theory        91102
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) or F) -> (((G and H) -> G) and F)))
theorem-size     41
proof            (modus-ponens tm-980 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       195
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-91102.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (((G and H) -> G) and F))), M:tm-980, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-91103
in-theory        91103
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) or F) -> (((G and H) -> H) and F)))
theorem-size     41
proof            (modus-ponens tm-980 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91103.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (((G and H) -> H) and F))), M:tm-980, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-91104
in-theory        91104
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) or F) -> ((G -> (H -> (G and H))) and F)))
theorem-size     43
proof            (modus-ponens tm-980 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       203
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-91104.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F))), M:tm-980, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-91105
in-theory        91105
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 -> G)) or (F -> G)) -> (F -> (F and G))))
theorem-size     43
proof            (modus-ponens tm-980 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       207
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-91105.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G)))), M:tm-980, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-91106
in-theory        91106
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) or F) -> (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), 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-91106.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (G -> (H -> (G and H))))), M:tm-980, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-91107
in-theory        91107
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) or F) -> ((G -> (G or H)) and F)))
theorem-size     41
proof            (modus-ponens tm-980 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-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-91107.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> ((G -> (G or H)) and F))), M:tm-980, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-91108
in-theory        91108
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) or F) -> (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-91108.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (G -> (G or H)))), M:tm-980, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-91109
in-theory        91109
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) or F) -> ((G -> (H or G)) and F)))
theorem-size     41
proof            (modus-ponens tm-980 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-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-91109.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> ((G -> (H or G)) and F))), M:tm-980, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-91110
in-theory        91110
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) or F) -> (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-91110.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) or F) -> (G -> (H or G)))), M:tm-980, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-91111
in-theory        91111
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 -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-980 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-91111.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H))), M:tm-980, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-91112
in-theory        91112
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 -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))
theorem-size     65
proof            (modus-ponens tm-980 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       273
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-91112.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))), M:tm-980, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-91113
in-theory        91113
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 -> G)) or (F -> G)) -> (((F and H) or F) -> G)))
theorem-size     45
proof            (modus-ponens tm-980 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91113.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G))), M:tm-980, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-91114
in-theory        91114
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 -> G)) or (F -> G)) -> (((H and F) or F) -> G)))
theorem-size     45
proof            (modus-ponens tm-980 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91114.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G))), M:tm-980, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-91115
in-theory        91115
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F)))
theorem-size     45
proof            (modus-ponens tm-980 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
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-91115.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F))), M:tm-980, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-91116
in-theory        91116
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)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G))))
theorem-size     55
proof            (modus-ponens tm-980 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       253
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91116.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G)))), M:tm-980, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-91117
in-theory        91117
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((G and F) or F) -> E)))
theorem-size     41
proof            (modus-ponens tm-980 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-91117.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> E)) -> (((G and F) or F) -> E))), M:tm-980, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-91118
in-theory        91118
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 ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or 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-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-91118.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-980, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-91119
in-theory        91119
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 ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-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-91119.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-980, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-91120
in-theory        91120
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 -> F) and (((G and E) or E) -> F))))
theorem-size     43
proof            (modus-ponens tm-980 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-91120.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F)))), M:tm-980, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-91121
in-theory        91121
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 ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     47
proof            (modus-ponens tm-980 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-91121.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-980, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-91122
in-theory        91122
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 ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-91122.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-980, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-91123
in-theory        91123
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 ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> 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-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-91123.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-980, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-91124
in-theory        91124
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 ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     53
proof            (modus-ponens tm-980 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-91124.        (((((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 ((H -> I) -> (((J and H) or H) -> I)))), M:tm-980, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-91125
in-theory        91125
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 ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-980 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-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-91125.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-980, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-91126
in-theory        91126
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F))))
theorem-size     45
proof            (modus-ponens tm-980 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
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-91126.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F)))), M:tm-980, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-91127
in-theory        91127
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) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-980 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91127.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H))), M:tm-980, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-91128
in-theory        91128
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
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-91128.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((F -> G) -> (((H and F) or F) -> G)))), M:tm-980, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-91129
in-theory        91129
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 and E) or E) -> F)) or H))
theorem-size     41
proof            (modus-ponens tm-980 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
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-91129.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> (((G and E) or E) -> F)) or H)), M:tm-980, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-91130
in-theory        91130
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) -> (((H and F) or F) -> G)) and E)))
theorem-size     43
proof            (modus-ponens tm-980 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91130.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E))), M:tm-980, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-91131
in-theory        91131
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 and E) or E)) -> ((E -> F) -> F)))
theorem-size     43
proof            (modus-ponens tm-980 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-91131.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F))), M:tm-980, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-91132
in-theory        91132
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) -> (((H and F) or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-91132.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F -> G) -> (((H and F) or F) -> G)))), M:tm-980, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-91133
in-theory        91133
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91133.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F))))), M:tm-980, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-91134
in-theory        91134
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G))))
theorem-size     45
proof            (modus-ponens tm-980 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91134.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G)))), M:tm-980, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-91135
in-theory        91135
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G)))
theorem-size     43
proof            (modus-ponens tm-980 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91135.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G))), M:tm-980, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-91136
in-theory        91136
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G or (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91136.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G or (F -> (E and F))))), M:tm-980, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-91137
in-theory        91137
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G))))
theorem-size     49
proof            (modus-ponens tm-980 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91137.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G)))), M:tm-980, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-91138
in-theory        91138
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F))))
theorem-size     45
proof            (modus-ponens tm-980 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91138.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F)))), M:tm-980, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-91139
in-theory        91139
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H -> G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91139.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H -> G)))), M:tm-980, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-91140
in-theory        91140
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (F -> F)))
theorem-size     39
proof            (modus-ponens tm-980 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91140.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (F -> F))), M:tm-980, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-91141
in-theory        91141
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91141.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-91142
in-theory        91142
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G and H) -> G)))
theorem-size     41
proof            (modus-ponens tm-980 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91142.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G and H) -> G))), M:tm-980, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-91143
in-theory        91143
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G and H) -> H)))
theorem-size     41
proof            (modus-ponens tm-980 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91143.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G and H) -> H))), M:tm-980, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-91144
in-theory        91144
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F)))))
theorem-size     47
proof            (modus-ponens tm-980 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91144.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F))))), M:tm-980, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-91145
in-theory        91145
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F)))))
theorem-size     55
proof            (modus-ponens tm-980 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91145.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F))))), M:tm-980, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-91146
in-theory        91146
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F)))))
theorem-size     47
proof            (modus-ponens tm-980 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91146.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F))))), M:tm-980, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-91147
in-theory        91147
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F)))))
theorem-size     47
proof            (modus-ponens tm-980 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91147.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F))))), M:tm-980, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-91148
in-theory        91148
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91148.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F))))), M:tm-980, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-91149
in-theory        91149
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (F -> (F and (E and F)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91149.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (F -> (F and (E and F))))), M:tm-980, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-91150
in-theory        91150
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-980 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91150.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H))))), M:tm-980, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-91151
in-theory        91151
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F)))))
theorem-size     47
proof            (modus-ponens tm-980 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91151.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F))))), M:tm-980, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-91152
in-theory        91152
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (G or H))))
theorem-size     41
proof            (modus-ponens tm-980 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91152.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (G or H)))), M:tm-980, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-91153
in-theory        91153
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F)))))
theorem-size     47
proof            (modus-ponens tm-980 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91153.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F))))), M:tm-980, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-91154
in-theory        91154
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H or G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91154.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (G -> (H or G)))), M:tm-980, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-91155
in-theory        91155
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G)))))
theorem-size     51
proof            (modus-ponens tm-980 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91155.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G))))), M:tm-980, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-91156
in-theory        91156
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H))))))
theorem-size     71
proof            (modus-ponens tm-980 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       293
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-91156.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H)))))), M:tm-980, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-91157
in-theory        91157
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F))))
theorem-size     45
proof            (modus-ponens tm-980 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91157.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F)))), M:tm-980, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-91158
in-theory        91158
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F))))
theorem-size     45
proof            (modus-ponens tm-980 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91158.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F)))), M:tm-980, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-91159
in-theory        91159
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F))))))
theorem-size     59
proof            (modus-ponens tm-980 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91159.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F)))))), M:tm-980, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-91160
in-theory        91160
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 -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H)))
theorem-size     55
proof            (modus-ponens tm-980 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-91160.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H))), M:tm-980, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-91161
in-theory        91161
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     55
proof            (modus-ponens tm-980 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-91161.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-980, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-91162
in-theory        91162
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G))))
theorem-size     57
proof            (modus-ponens tm-980 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       265
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-91162.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G)))), M:tm-980, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-91163
in-theory        91163
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E)))
theorem-size     47
proof            (modus-ponens tm-980 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-91163.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E))), M:tm-980, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-91164
in-theory        91164
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 (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-980 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48.           (((A -> (B and 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-91164.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-980, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-91165
in-theory        91165
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 (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-980 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-91165.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-980, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-91166
in-theory        91166
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G))))
theorem-size     53
proof            (modus-ponens tm-980 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-91166.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G)))), M:tm-980, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-91167
in-theory        91167
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 (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     53
proof            (modus-ponens tm-980 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (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-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-91167.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-980, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-91168
in-theory        91168
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 (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-980 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91168.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-980, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-91169
in-theory        91169
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 (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-980 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48.           (((A -> (B and 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-91169.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-980, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-91170
in-theory        91170
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 (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     59
proof            (modus-ponens tm-980 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-91170.        (((((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 (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-980, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-91171
in-theory        91171
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 (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-980 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48.           (((A -> (B and 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-91171.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-980, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-91172
in-theory        91172
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G)))
theorem-size     43
proof            (modus-ponens tm-980 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-91172.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G))), M:tm-980, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-91173
in-theory        91173
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G))))
theorem-size     55
proof            (modus-ponens tm-980 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-91173.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G)))), M:tm-980, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-91174
in-theory        91174
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H)))
theorem-size     59
proof            (modus-ponens tm-980 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91174.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H))), M:tm-980, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-91175
in-theory        91175
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     47
proof            (modus-ponens tm-980 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), 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-91175.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-980, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-91176
in-theory        91176
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H))
theorem-size     47
proof            (modus-ponens tm-980 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-91176.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H)), M:tm-980, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-91177
in-theory        91177
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 and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E)))
theorem-size     49
proof            (modus-ponens tm-980 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91177.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E))), M:tm-980, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-91178
in-theory        91178
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G)))
theorem-size     53
proof            (modus-ponens tm-980 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       219
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-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-91178.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G))), M:tm-980, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-91179
in-theory        91179
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 and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     47
proof            (modus-ponens tm-980 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-91179.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-980, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-91180
in-theory        91180
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (E or F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91180.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (E or F)))), M:tm-980, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-91181
in-theory        91181
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> ((E or F) and G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-91181.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> ((E or F) and G)))), M:tm-980, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-91182
in-theory        91182
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((E or F) or G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91182.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((E or F) or G))), M:tm-980, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-91183
in-theory        91183
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G or (E or F))))
theorem-size     39
proof            (modus-ponens tm-980 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91183.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G or (E or F)))), M:tm-980, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-91184
in-theory        91184
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91184.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (H -> G)))), M:tm-980, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-91185
in-theory        91185
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91185.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-91186
in-theory        91186
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91186.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G and H) -> G))), M:tm-980, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-91187
in-theory        91187
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91187.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G and H) -> H))), M:tm-980, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-91188
in-theory        91188
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F))))
theorem-size     43
proof            (modus-ponens tm-980 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-91188.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F)))), M:tm-980, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-91189
in-theory        91189
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F))))
theorem-size     51
proof            (modus-ponens tm-980 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-91189.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F)))), M:tm-980, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-91190
in-theory        91190
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (((G and H) -> G) and (E or F))))
theorem-size     43
proof            (modus-ponens tm-980 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-91190.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (((G and H) -> G) and (E or F)))), M:tm-980, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-91191
in-theory        91191
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (((G and H) -> H) and (E or F))))
theorem-size     43
proof            (modus-ponens tm-980 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-91191.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (((G and H) -> H) and (E or F)))), M:tm-980, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-91192
in-theory        91192
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F))))
theorem-size     45
proof            (modus-ponens tm-980 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-91192.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F)))), M:tm-980, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-91193
in-theory        91193
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-91193.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (H -> (G and H))))), M:tm-980, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-91194
in-theory        91194
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F))))
theorem-size     43
proof            (modus-ponens tm-980 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-91194.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F)))), M:tm-980, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-91195
in-theory        91195
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91195.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (G or H)))), M:tm-980, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-91196
in-theory        91196
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F))))
theorem-size     43
proof            (modus-ponens tm-980 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-91196.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F)))), M:tm-980, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-91197
in-theory        91197
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91197.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (G -> (H or G)))), M:tm-980, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-91198
in-theory        91198
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G)))))
theorem-size     51
proof            (modus-ponens tm-980 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91198.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G))))), M:tm-980, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-91199
in-theory        91199
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 or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-980 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91199.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H))), M:tm-980, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-91200
in-theory        91200
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     49
proof            (modus-ponens tm-980 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
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-91200.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-980, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-91201
in-theory        91201
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E)))
theorem-size     43
proof            (modus-ponens tm-980 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-91201.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E))), M:tm-980, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-91202
in-theory        91202
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 (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-91202.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-980, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91203
in-theory        91203
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 (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-49.           (((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-91203.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-980, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91204
in-theory        91204
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-980 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-91204.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G)))), M:tm-980, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-91205
in-theory        91205
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 (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-91205.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-980, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91206
in-theory        91206
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 (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91206.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-980, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91207
in-theory        91207
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 (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-91207.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-980, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91208
in-theory        91208
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 (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     55
proof            (modus-ponens tm-980 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-91208.        (((((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 (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-980, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-91209
in-theory        91209
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 (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-91209.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-980, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91210
in-theory        91210
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> ((E or F) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-91210.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> ((E or F) -> G))), M:tm-980, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-91211
in-theory        91211
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     49
proof            (modus-ponens tm-980 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-91211.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-980, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-91212
in-theory        91212
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-980 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91212.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H))), M:tm-980, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-91213
in-theory        91213
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     43
proof            (modus-ponens tm-980 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-91213.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-980, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-91214
in-theory        91214
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H))
theorem-size     43
proof            (modus-ponens tm-980 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91214.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H)), M:tm-980, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-91215
in-theory        91215
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 G) -> H) -> ((F or (F or G)) -> H)) and E)))
theorem-size     45
proof            (modus-ponens tm-980 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-91215.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E))), M:tm-980, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-91216
in-theory        91216
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-980 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-91216.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G))), M:tm-980, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-91217
in-theory        91217
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 G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     43
proof            (modus-ponens tm-980 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-91217.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-980, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-91218
in-theory        91218
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (F or E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91218.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (F or E)))), M:tm-980, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-91219
in-theory        91219
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> ((F or E) and G))))
theorem-size     41
proof            (modus-ponens tm-980 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-91219.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> ((F or E) and G)))), M:tm-980, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-91220
in-theory        91220
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((F or E) or G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91220.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((F or E) or G))), M:tm-980, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-91221
in-theory        91221
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G or (F or E))))
theorem-size     39
proof            (modus-ponens tm-980 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91221.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G or (F or E)))), M:tm-980, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-91222
in-theory        91222
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91222.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (H -> G)))), M:tm-980, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-91223
in-theory        91223
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-980 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91223.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-980, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-91224
in-theory        91224
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-980 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91224.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G and H) -> G))), M:tm-980, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-91225
in-theory        91225
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-980 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91225.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G and H) -> H))), M:tm-980, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-91226
in-theory        91226
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E))))
theorem-size     43
proof            (modus-ponens tm-980 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-91226.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E)))), M:tm-980, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-91227
in-theory        91227
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E))))
theorem-size     51
proof            (modus-ponens tm-980 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-91227.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E)))), M:tm-980, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-91228
in-theory        91228
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (((G and H) -> G) and (F or E))))
theorem-size     43
proof            (modus-ponens tm-980 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-91228.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (((G and H) -> G) and (F or E)))), M:tm-980, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-91229
in-theory        91229
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (((G and H) -> H) and (F or E))))
theorem-size     43
proof            (modus-ponens tm-980 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-91229.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (((G and H) -> H) and (F or E)))), M:tm-980, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-91230
in-theory        91230
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E))))
theorem-size     45
proof            (modus-ponens tm-980 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-91230.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E)))), M:tm-980, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-91231
in-theory        91231
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-980 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-91231.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (H -> (G and H))))), M:tm-980, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-91232
in-theory        91232
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E))))
theorem-size     43
proof            (modus-ponens tm-980 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-91232.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E)))), M:tm-980, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-91233
in-theory        91233
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-980 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91233.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (G or H)))), M:tm-980, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-91234
in-theory        91234
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E))))
theorem-size     43
proof            (modus-ponens tm-980 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-91234.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E)))), M:tm-980, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-91235
in-theory        91235
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-980 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91235.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (G -> (H or G)))), M:tm-980, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-91236
in-theory        91236
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G)))))
theorem-size     51
proof            (modus-ponens tm-980 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-91236.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G))))), M:tm-980, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-91237
in-theory        91237
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 or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-980 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
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-91237.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H))), M:tm-980, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-91238
in-theory        91238
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     49
proof            (modus-ponens tm-980 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
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-91238.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-980, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-91239
in-theory        91239
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E)))
theorem-size     43
proof            (modus-ponens tm-980 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-91239.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E))), M:tm-980, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-91240
in-theory        91240
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 (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-50.           (((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-91240.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-980, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91241
in-theory        91241
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 (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-91241.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-980, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91242
in-theory        91242
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-980 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-91242.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G)))), M:tm-980, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-91243
in-theory        91243
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 (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-91243.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-980, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91244
in-theory        91244
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 (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91244.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-980, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91245
in-theory        91245
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 (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-91245.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-980, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91246
in-theory        91246
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 (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     55
proof            (modus-ponens tm-980 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-91246.        (((((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 (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-980, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-91247
in-theory        91247
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 (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-91247.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-980, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-91248
in-theory        91248
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     49
proof            (modus-ponens tm-980 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-91248.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-980, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-91249
in-theory        91249
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-980 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91249.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H))), M:tm-980, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-91250
in-theory        91250
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     43
proof            (modus-ponens tm-980 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91250.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-980, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-91251
in-theory        91251
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H))
theorem-size     43
proof            (modus-ponens tm-980 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-91251.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H)), M:tm-980, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-91252
in-theory        91252
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 G) -> H) -> ((G or (F or G)) -> H)) and E)))
theorem-size     45
proof            (modus-ponens tm-980 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-91252.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E))), M:tm-980, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-91253
in-theory        91253
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-980 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-91253.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G))), M:tm-980, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-91254
in-theory        91254
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 G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     43
proof            (modus-ponens tm-980 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-91254.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-980, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-91255
in-theory        91255
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 ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-980 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91255.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91256
in-theory        91256
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 ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G))))
theorem-size     55
proof            (modus-ponens tm-980 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91256.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G)))), M:tm-980, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-91257
in-theory        91257
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 ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H))))
theorem-size     55
proof            (modus-ponens tm-980 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
proof-size       233
proof-steps      11
----------------------------------------------------------------
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-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-91257.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H)))), M:tm-980, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-91258
in-theory        91258
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 ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H)))
theorem-size     53
proof            (modus-ponens tm-980 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91258.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H))), M:tm-980, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-91259
in-theory        91259
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 ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-980 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91259.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91260
in-theory        91260
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 ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H))))
theorem-size     61
proof            (modus-ponens tm-980 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-8)
proof-size       251
proof-steps      11
----------------------------------------------------------------
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-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-91260.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H)))), M:tm-980, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-91261
in-theory        91261
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 ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G)))))
theorem-size     57
proof            (modus-ponens tm-980 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       241
proof-steps      11
----------------------------------------------------------------
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-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-91261.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G))))), M:tm-980, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-91262
in-theory        91262
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 ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H))))
theorem-size     47
proof            (modus-ponens tm-980 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91262.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H)))), M:tm-980, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-91263
in-theory        91263
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 ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G))))
theorem-size     49
proof            (modus-ponens tm-980 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-91263.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G)))), M:tm-980, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-91264
in-theory        91264
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 ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     55
proof            (modus-ponens tm-980 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       259
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-91264.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-980, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-91265
in-theory        91265
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 ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H)))
theorem-size     47
proof            (modus-ponens tm-980 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-91265.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H))), M:tm-980, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-91266
in-theory        91266
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 ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I)))
theorem-size     47
proof            (modus-ponens tm-980 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-91266.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I))), M:tm-980, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-91267
in-theory        91267
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 ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     57
proof            (modus-ponens tm-980 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (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-91267.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91268
in-theory        91268
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 ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     65
proof            (modus-ponens tm-980 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       283
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-91268.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91269
in-theory        91269
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 ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     57
proof            (modus-ponens tm-980 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> 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-91269.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91270
in-theory        91270
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 ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     57
proof            (modus-ponens tm-980 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> 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-91270.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91271
in-theory        91271
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 ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     59
proof            (modus-ponens tm-980 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       259
proof-steps      13
----------------------------------------------------------------
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-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-91271.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91272
in-theory        91272
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 ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G)))))
theorem-size     55
proof            (modus-ponens tm-980 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-91272.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G))))), M:tm-980, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91273
in-theory        91273
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 ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), 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-91273.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I))))), M:tm-980, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-91274
in-theory        91274
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 ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     57
proof            (modus-ponens tm-980 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or 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-91274.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91275
in-theory        91275
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 ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-91275.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I)))), M:tm-980, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-91276
in-theory        91276
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 ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     57
proof            (modus-ponens tm-980 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or 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-91276.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-91277
in-theory        91277
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 ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H))))
theorem-size     47
proof            (modus-ponens tm-980 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-91277.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H)))), M:tm-980, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-91278
in-theory        91278
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 ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G))))
theorem-size     53
proof            (modus-ponens tm-980 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       253
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-91278.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G)))), M:tm-980, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-91279
in-theory        91279
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)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H)))))
theorem-size     75
proof            (modus-ponens tm-980 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       317
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-91279.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H))))), M:tm-980, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-91280
in-theory        91280
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 ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G))))
theorem-size     57
proof            (modus-ponens tm-980 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       259
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-91280.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G)))), M:tm-980, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-91281
in-theory        91281
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 ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G))))
theorem-size     57
proof            (modus-ponens tm-980 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       259
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-91281.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G)))), M:tm-980, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-91282
in-theory        91282
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 ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F)))))
theorem-size     61
proof            (modus-ponens tm-980 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-8)
proof-size       275
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-91282.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F))))), M:tm-980, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-91283
in-theory        91283
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)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G)))))
theorem-size     81
proof            (modus-ponens tm-980 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       331
proof-steps      13
----------------------------------------------------------------
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-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-91283.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G))))), M:tm-980, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-91284
in-theory        91284
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G))))))
theorem-size     77
proof            (modus-ponens tm-980 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-8)
proof-size       307
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-91284.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G)))))), M:tm-980, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-91285
in-theory        91285
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 -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))
theorem-size     69
proof            (modus-ponens tm-980 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       283
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-91285.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))), M:tm-980, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91286
in-theory        91286
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 or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     69
proof            (modus-ponens tm-980 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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       283
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
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-91286.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-980, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-91287
in-theory        91287
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 or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H))))
theorem-size     75
proof            (modus-ponens tm-980 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       317
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-91287.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H)))), M:tm-980, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-91288
in-theory        91288
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E)))
theorem-size     57
proof            (modus-ponens tm-980 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
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-91288.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E))), M:tm-980, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-91289
in-theory        91289
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 ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     61
proof            (modus-ponens tm-980 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       259
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-91289.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-980, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-91290
in-theory        91290
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 ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     61
proof            (modus-ponens tm-980 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       259
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-91290.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-980, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-91291
in-theory        91291
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 or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     67
proof            (modus-ponens tm-980 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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       279
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
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-91291.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-980, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-91292
in-theory        91292
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 ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     63
proof            (modus-ponens tm-980 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
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-91292.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-980, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-91293
in-theory        91293
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 ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     61
proof            (modus-ponens tm-980 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       259
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-91293.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-980, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-91294
in-theory        91294
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 ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     61
proof            (modus-ponens tm-980 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       259
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-91294.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-980, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-91295
in-theory        91295
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 ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     69
proof            (modus-ponens tm-980 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       291
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-91295.        (((((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 ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-980, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-91296
in-theory        91296
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 ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     61
proof            (modus-ponens tm-980 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       259
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-91296.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-980, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-91297
in-theory        91297
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 or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H)))
theorem-size     51
proof            (modus-ponens tm-980 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
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-91297.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H))), M:tm-980, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-91298
in-theory        91298
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 or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H))))
theorem-size     69
proof            (modus-ponens tm-980 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       265
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
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-91298.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H)))), M:tm-980, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-91299
in-theory        91299
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 ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I)))
theorem-size     75
proof            (modus-ponens tm-980 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8)
proof-size       279
proof-steps      11
----------------------------------------------------------------
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-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-91299.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I))), M:tm-980, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-91300
in-theory        91300
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     57
proof            (modus-ponens tm-980 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
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-91300.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-980, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91301
in-theory        91301
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 or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) or I))
theorem-size     57
proof            (modus-ponens tm-980 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
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-91301.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) or I)), M:tm-980, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-91302
in-theory        91302
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) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E)))
theorem-size     59
proof            (modus-ponens tm-980 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-8)
proof-size       241
proof-steps      11
----------------------------------------------------------------
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-91302.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E))), M:tm-980, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91303
in-theory        91303
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     71
proof            (modus-ponens tm-977 tm-980 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5)
proof-size       275
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-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-5.            (A -> (B -> (A and B))), axiom
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-91303.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-980, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-91304
in-theory        91304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> ((C or A) -> B))))
theorem-size     47
proof            (modus-ponens tm-975 tm-980 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-5.            (A -> (B -> (A and B))), axiom
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-91304.        (((A -> B) -> ((C or A) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, m:tm-980, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-91305
in-theory        91305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     99
proof            (modus-ponens tm-969 tm-980 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       311
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-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-91305.        ((((A -> B) -> ((C or A) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, m:tm-980, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-91306
in-theory        91306
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     45
proof            (modus-ponens tm-930 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91306.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-930, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91307
in-theory        91307
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B or (A or B)) -> C)))
theorem-size     49
proof            (modus-ponens tm-927 tm-980 ((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       209
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-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-5.            (A -> (B -> (A and B))), 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-91307.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B or (A or B)) -> C))), M:tm-927, m:tm-980, u:((Am (-> (or A (or B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-91308
in-theory        91308
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B))) and ((B or (A or B)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B))))
theorem-size     73
proof            (modus-ponens tm-920 tm-980 ((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (or A B)))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91308.        (((A or B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B))) and ((B or (A or B)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B)))), M:tm-920, m:tm-980, u:((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (or A B))))
================================================================
tm-name          tm-91309
in-theory        91309
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     45
proof            (modus-ponens tm-893 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91309.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-893, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91310
in-theory        91310
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A or (A or B)) -> C)))
theorem-size     49
proof            (modus-ponens tm-890 tm-980 ((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       209
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-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-5.            (A -> (B -> (A and B))), 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-91310.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A or (A or B)) -> C))), M:tm-890, m:tm-980, u:((Am (-> (or A (or A B)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-91311
in-theory        91311
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B)))
theorem-size     35
proof            (modus-ponens tm-888 tm-980 ((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), 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-91311.        ((A or B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B))), M:tm-888, m:tm-980, u:((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (or A B))))
================================================================
tm-name          tm-91312
in-theory        91312
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B))) and ((A or (A or B)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B))))
theorem-size     73
proof            (modus-ponens tm-882 tm-980 ((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91312.        (((A or B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B))) and ((A or (A or B)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A or B)))), M:tm-882, m:tm-980, u:((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (or A B))))
================================================================
tm-name          tm-91313
in-theory        91313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     49
proof            (modus-ponens tm-855 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91313.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-855, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91314
in-theory        91314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B or (A -> (B and A))) -> C)))
theorem-size     55
proof            (modus-ponens tm-852 tm-980 ((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
proof-size       227
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91314.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-980, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-91315
in-theory        91315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> (B and A))))
theorem-size     39
proof            (modus-ponens tm-850 tm-980 ((Am (-> A (and B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91315.        ((A -> (B and A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> (B and A)))), M:tm-850, m:tm-980, u:((Am (-> A (and B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (and B A)))))
================================================================
tm-name          tm-91316
in-theory        91316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> (B and A)))))
theorem-size     81
proof            (modus-ponens tm-844 tm-980 ((Am (-> A (and B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91316.        (((A -> (B and A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> (B and A))))), M:tm-844, m:tm-980, u:((Am (-> A (and B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (and B A)))))
================================================================
tm-name          tm-91317
in-theory        91317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     43
proof            (modus-ponens tm-808 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91317.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-808, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91318
in-theory        91318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((C and A) or A) -> B)))
theorem-size     47
proof            (modus-ponens tm-805 tm-980 ((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 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-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-5.            (A -> (B -> (A and B))), 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-91318.        (((A -> B) or (((C and A) or A) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((C and A) or A) -> B))), M:tm-805, m:tm-980, u:((Am (-> (or (and A B) B) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-91319
in-theory        91319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((F and A) or A) -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))
theorem-size     67
proof            (modus-ponens tm-798 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91319.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((F and A) or A) -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))), M:tm-798, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91320
in-theory        91320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     43
proof            (modus-ponens tm-757 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-91320.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-757, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91321
in-theory        91321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((A and C) or A) -> B)))
theorem-size     47
proof            (modus-ponens tm-754 tm-980 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 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-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91321.        (((A -> B) or (((A and C) or A) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((A and C) or A) -> B))), M:tm-754, m:tm-980, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-91322
in-theory        91322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((A and F) or A) -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))
theorem-size     67
proof            (modus-ponens tm-747 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-91322.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((A and F) or A) -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))), M:tm-747, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91323
in-theory        91323
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E)))
theorem-size     57
proof            (modus-ponens tm-708 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91323.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E))), M:tm-708, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91324
in-theory        91324
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     69
proof            (modus-ponens tm-705 tm-980 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       269
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91324.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-980, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-91325
in-theory        91325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-703 tm-980 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91325.        (((A -> B) -> (A -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-980, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-91326
in-theory        91326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> (A -> C)))))
theorem-size     93
proof            (modus-ponens tm-697 tm-980 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A B) (-> A C))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-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-91326.        ((((A -> B) -> (A -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-980, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-91327
in-theory        91327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     45
proof            (modus-ponens tm-665 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-91327.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-665, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91328
in-theory        91328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B or (A -> B)) -> C)))
theorem-size     49
proof            (modus-ponens tm-662 tm-980 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91328.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-980, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-91329
in-theory        91329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> B)))
theorem-size     35
proof            (modus-ponens tm-660 tm-980 ((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A B)))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91329.        ((A -> B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> B))), M:tm-660, m:tm-980, u:((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A B))))
================================================================
tm-name          tm-91330
in-theory        91330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> B))) and ((B or (A -> B)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> B))))
theorem-size     73
proof            (modus-ponens tm-654 tm-980 ((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A B)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91330.        (((A -> B) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> B))) and ((B or (A -> B)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> B)))), M:tm-654, m:tm-980, u:((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A B))))
================================================================
tm-name          tm-91331
in-theory        91331
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A)))
theorem-size     33
proof            (modus-ponens tm-623 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91331.        (A -> (B or (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A))), M:tm-623, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91332
in-theory        91332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-622 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91332.        ((A -> (B -> (C or B))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-622, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91333
in-theory        91333
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (B -> (C or B))))
theorem-size     41
proof            (modus-ponens tm-619 tm-980 ((Am (-> A (or B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91333.        ((A or (B -> (C or B))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (B -> (C or B)))), M:tm-619, m:tm-980, u:((Am (-> A (or B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (or B A)))))
================================================================
tm-name          tm-91334
in-theory        91334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (G or F)))
theorem-size     37
proof            (modus-ponens tm-609 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91334.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (G or F))), M:tm-609, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91335
in-theory        91335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-605 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91335.        ((A -> ((B -> (C or B)) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-605, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91336
in-theory        91336
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> (C or B)) and A)))
theorem-size     45
proof            (modus-ponens tm-602 tm-980 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91336.        ((A or ((B -> (C or B)) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-980, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-91337
in-theory        91337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (G or F)) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     69
proof            (modus-ponens tm-595 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-91337.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (G or F)) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-595, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91338
in-theory        91338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-550 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91338.        (((A -> (B or A)) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-550, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91339
in-theory        91339
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-540 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91339.        ((A or (B -> (C or B))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-540, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91340
in-theory        91340
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-530 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91340.        ((A or (B -> (B or C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-530, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91341
in-theory        91341
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-520 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91341.        ((A or (B -> (C -> (B and C)))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-520, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91342
in-theory        91342
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-510 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91342.        ((A or ((B and C) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-510, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91343
in-theory        91343
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-500 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91343.        ((A or ((B and C) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-500, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91344
in-theory        91344
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E)))
theorem-size     47
proof            (modus-ponens tm-490 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91344.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E))), M:tm-490, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91345
in-theory        91345
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-480 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91345.        ((A or (B -> (C -> B))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-480, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91346
in-theory        91346
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A) or F))
theorem-size     33
proof            (modus-ponens tm-470 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91346.        (A -> ((((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A) or F)), M:tm-470, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91347
in-theory        91347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-469 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91347.        ((A -> (B -> (B or C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-469, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91348
in-theory        91348
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (B -> (B or C))))
theorem-size     41
proof            (modus-ponens tm-466 tm-980 ((Am (-> A (or A B))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91348.        ((A or (B -> (B or C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (B -> (B or C)))), M:tm-466, m:tm-980, u:((Am (-> A (or A B))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (or A B)))))
================================================================
tm-name          tm-91349
in-theory        91349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (F or G)))
theorem-size     37
proof            (modus-ponens tm-456 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91349.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (F or G))), M:tm-456, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91350
in-theory        91350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-453 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91350.        ((A -> ((B -> (B or C)) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-453, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91351
in-theory        91351
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> (B or C)) and A)))
theorem-size     45
proof            (modus-ponens tm-450 tm-980 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91351.        ((A or ((B -> (B or C)) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-980, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-91352
in-theory        91352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (F or G)) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     69
proof            (modus-ponens tm-443 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-91352.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (F or G)) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-443, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91353
in-theory        91353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-409 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91353.        (((A -> (A or B)) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-409, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91354
in-theory        91354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-400 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91354.        (((A -> (B -> (A and B))) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-400, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91355
in-theory        91355
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-391 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91355.        ((((A and B) -> B) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-391, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91356
in-theory        91356
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-382 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91356.        ((((A and B) -> A) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-382, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91357
in-theory        91357
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E)))
theorem-size     47
proof            (modus-ponens tm-373 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91357.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E))), M:tm-373, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91358
in-theory        91358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-364 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91358.        (((A -> (B -> A)) or C) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-364, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91359
in-theory        91359
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A) and B)))
theorem-size     35
proof            (modus-ponens tm-355 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91359.        (A -> (B -> ((((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A) and B))), M:tm-355, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91360
in-theory        91360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-354 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91360.        ((A -> (B -> (C -> (B and C)))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-354, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91361
in-theory        91361
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (B -> (C -> (B and C)))))
theorem-size     45
proof            (modus-ponens tm-351 tm-980 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 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-5.            (A -> (B -> (A and 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-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-91361.        ((A or (B -> (C -> (B and C)))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-980, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-91362
in-theory        91362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (G -> (F and G))))
theorem-size     39
proof            (modus-ponens tm-341 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91362.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91363
in-theory        91363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C)))
theorem-size     41
proof            (modus-ponens tm-338 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91363.        (((A -> B) -> (A -> (A and B))) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C))), M:tm-338, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91364
in-theory        91364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> (A and B))))
theorem-size     43
proof            (modus-ponens tm-335 tm-980 ((Am (-> A (and A B))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 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-5.            (A -> (B -> (A and B))), axiom
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-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-91364.        (((A -> B) or (A -> (A and B))) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> (A and B)))), M:tm-335, m:tm-980, u:((Am (-> A (and A B))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (and A B)))))
================================================================
tm-name          tm-91365
in-theory        91365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (A -> (A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     65
proof            (modus-ponens tm-328 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
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-328.          ((A -> 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-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-91365.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (A -> (A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-328, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91366
in-theory        91366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (G -> (F and G))) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     71
proof            (modus-ponens tm-327 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-91366.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (G -> (F and G))) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-327, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91367
in-theory        91367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((F and G) -> G) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     69
proof            (modus-ponens tm-326 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-91367.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((F and G) -> G) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-326, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91368
in-theory        91368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((F and G) -> F) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     69
proof            (modus-ponens tm-325 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-91368.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((F and G) -> F) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-325, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91369
in-theory        91369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     77
proof            (modus-ponens tm-324 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-91369.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-324, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91370
in-theory        91370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (G -> F)) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     69
proof            (modus-ponens tm-323 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-91370.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (G -> F)) and (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-323, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91371
in-theory        91371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F and G) -> G))
theorem-size     37
proof            (modus-ponens tm-322 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91371.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F and G) -> G)), M:tm-322, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91372
in-theory        91372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F and G) -> F))
theorem-size     37
proof            (modus-ponens tm-320 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91372.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F and G) -> F)), M:tm-320, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91373
in-theory        91373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     45
proof            (modus-ponens tm-318 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91373.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91374
in-theory        91374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (A -> A))
theorem-size     35
proof            (modus-ponens tm-316 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-91374.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (A -> A)), M:tm-316, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91375
in-theory        91375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (G -> F)))
theorem-size     37
proof            (modus-ponens tm-315 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91375.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (G -> F))), M:tm-315, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91376
in-theory        91376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((A -> (not (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))) -> (not A)))
theorem-size     67
proof            (modus-ponens tm-313 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-91376.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((A -> (not (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))) -> (not A))), M:tm-313, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91377
in-theory        91377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A) -> F) -> ((A or (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) -> F)))
theorem-size     97
proof            (modus-ponens tm-312 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       247
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-91377.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (((((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A) -> F) -> ((A or (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) -> F))), M:tm-312, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91378
in-theory        91378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F or (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     65
proof            (modus-ponens tm-311 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-91378.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F or (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-311, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91379
in-theory        91379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) or F))
theorem-size     65
proof            (modus-ponens tm-310 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-91379.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) or F)), M:tm-310, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91380
in-theory        91380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and F)))
theorem-size     67
proof            (modus-ponens tm-309 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-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-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-91380.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and F))), M:tm-309, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91381
in-theory        91381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))))
theorem-size     65
proof            (modus-ponens tm-305 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 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-1.            (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-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-91381.        ((A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)) and (F -> (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)))), M:tm-305, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91382
in-theory        91382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     43
proof            (modus-ponens tm-303 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91382.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-303, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91383
in-theory        91383
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> (C -> (B and C))) and A)))
theorem-size     49
proof            (modus-ponens tm-300 tm-980 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91383.        ((A or ((B -> (C -> (B and C))) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-980, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-91384
in-theory        91384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-270 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91384.        ((A -> (((B and C) -> C) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-270, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91385
in-theory        91385
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((B and C) -> C) and A)))
theorem-size     45
proof            (modus-ponens tm-267 tm-980 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91385.        ((A or (((B and C) -> C) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((B and C) -> C) and A))), M:tm-267, m:tm-980, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-91386
in-theory        91386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-239 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91386.        ((A -> (((B and C) -> B) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-239, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91387
in-theory        91387
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((B and C) -> B) and A)))
theorem-size     45
proof            (modus-ponens tm-236 tm-980 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91387.        ((A or (((B and C) -> B) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((B and C) -> B) and A))), M:tm-236, m:tm-980, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-91388
in-theory        91388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E)))
theorem-size     49
proof            (modus-ponens tm-210 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91388.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E))), M:tm-210, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91389
in-theory        91389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     61
proof            (modus-ponens tm-207 tm-980 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       239
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91389.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-980, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-91390
in-theory        91390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-183 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91390.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-183, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91391
in-theory        91391
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> (C -> B)) and A)))
theorem-size     45
proof            (modus-ponens tm-180 tm-980 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91391.        ((A or ((B -> (C -> B)) and A)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-980, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-91392
in-theory        91392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-157 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91392.        ((A -> ((B and C) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-157, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91393
in-theory        91393
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B and C) -> C)))
theorem-size     41
proof            (modus-ponens tm-154 tm-980 ((Am (-> (and A B) B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91393.        ((A or ((B and C) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B and C) -> C))), M:tm-154, m:tm-980, u:((Am (-> (and A B) B)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (and A B) B))))
================================================================
tm-name          tm-91394
in-theory        91394
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     47
proof            (modus-ponens tm-147 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91394.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-147, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91395
in-theory        91395
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A and (B -> C)) -> C)))
theorem-size     51
proof            (modus-ponens tm-144 tm-980 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91395.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-980, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-91396
in-theory        91396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-134 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91396.        ((A -> ((B and C) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-134, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91397
in-theory        91397
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B and C) -> B)))
theorem-size     41
proof            (modus-ponens tm-131 tm-980 ((Am (-> (and A B) A)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91397.        ((A or ((B and C) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((B and C) -> B))), M:tm-131, m:tm-980, u:((Am (-> (and A B) A)) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (and A B) A))))
================================================================
tm-name          tm-91398
in-theory        91398
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     47
proof            (modus-ponens tm-125 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91398.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-125, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91399
in-theory        91399
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((A -> B) and C) -> B)))
theorem-size     51
proof            (modus-ponens tm-122 tm-980 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91399.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-980, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-91400
in-theory        91400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E)))
theorem-size     47
proof            (modus-ponens tm-113 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91400.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E))), M:tm-113, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91401
in-theory        91401
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     57
proof            (modus-ponens tm-110 tm-980 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
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-5.            (A -> (B -> (A and B))), 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-91401.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-980, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-91402
in-theory        91402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     51
proof            (modus-ponens tm-105 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91402.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-105, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91403
in-theory        91403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     57
proof            (modus-ponens tm-102 tm-980 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
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-5.            (A -> (B -> (A and B))), 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-91403.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-980, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-91404
in-theory        91404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C)))
theorem-size     39
proof            (modus-ponens tm-95 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91404.        (((A -> B) -> (A -> A)) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C))), M:tm-95, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91405
in-theory        91405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> A)))
theorem-size     39
proof            (modus-ponens tm-92 tm-980 ((Am (-> A A)) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91405.        (((A -> B) or (A -> A)) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and (A -> A))), M:tm-92, m:tm-980, u:((Am (-> A A)) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A A))))
================================================================
tm-name          tm-91406
in-theory        91406
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A)))
theorem-size     33
proof            (modus-ponens tm-84 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91406.        (A -> (B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and A))), M:tm-84, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91407
in-theory        91407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-83 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91407.        ((A -> (B -> (C -> B))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-83, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91408
in-theory        91408
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (B -> (C -> B))))
theorem-size     41
proof            (modus-ponens tm-80 tm-980 ((Am (-> A (-> B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91408.        ((A or (B -> (C -> B))) -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and (B -> (C -> B)))), M:tm-80, m:tm-980, u:((Am (-> A (-> B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> A (-> B A)))))
================================================================
tm-name          tm-91409
in-theory        91409
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B)))
theorem-size     37
proof            (modus-ponens tm-76 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-10 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91409.        (((not (not A)) -> A) and (B -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and B))), M:tm-76, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91410
in-theory        91410
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))
theorem-size     35
proof            (modus-ponens tm-73 tm-980 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       155
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91410.        (((not (not A)) or A) -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)), M:tm-73, m:tm-980, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))
================================================================
tm-name          tm-91411
in-theory        91411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C)))
theorem-size     43
proof            (modus-ponens tm-69 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-9 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91411.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)) and C))), M:tm-69, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91412
in-theory        91412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and ((A -> (not B)) -> (not A))))
theorem-size     47
proof            (modus-ponens tm-66 tm-980 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       185
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91412.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-980, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-91413
in-theory        91413
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D)))
theorem-size     45
proof            (modus-ponens tm-54 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91413.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) and D))), M:tm-54, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-91414
in-theory        91414
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) -> D)
theorem-size     17
proof            (modus-ponens tm-981 tm-365 ((Am (-> (-> (-> (-> Cm Bm) B) (-> (or Bm (-> Cm Bm)) B)) D)) (C Bm) (A (-> Cm Bm)) (Dm (-> (-> (-> Cm Bm) B) (-> (or Bm (-> Cm Bm)) B)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       153
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91414.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) -> D), M:tm-981, m:tm-365, u:((Am (-> (-> (-> (-> Cm Bm) B) (-> (or Bm (-> Cm Bm)) B)) D)) (C Bm) (A (-> Cm Bm)) (Dm (-> (-> (-> Cm Bm) B) (-> (or Bm (-> Cm Bm)) B))))
================================================================
tm-name          tm-91415
in-theory        91415
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> E)
theorem-size     29
proof            (modus-ponens tm-981 tm-374 ((Am (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) B) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)) D)) (C (-> Bm (-> Cm Dm))) (A (-> (-> Bm Cm) (-> Bm Dm))) (Em (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) B) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       189
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91415.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> E), M:tm-981, m:tm-374, u:((Am (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) B) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)) D)) (C (-> Bm (-> Cm Dm))) (A (-> (-> Bm Cm) (-> Bm Dm))) (Em (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) B) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B))))
================================================================
tm-name          tm-91416
in-theory        91416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) -> D) -> D)
theorem-size     15
proof            (modus-ponens tm-981 tm-383 ((Am (-> (-> (-> Bm B) (-> (or (and Bm Cm) Bm) B)) D)) (C (and Bm Cm)) (A Bm) (Dm (-> (-> Bm B) (-> (or (and Bm Cm) Bm) B)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91416.        ((((A -> B) -> (((A and C) or A) -> B)) -> D) -> D), M:tm-981, m:tm-383, u:((Am (-> (-> (-> Bm B) (-> (or (and Bm Cm) Bm) B)) D)) (C (and Bm Cm)) (A Bm) (Dm (-> (-> Bm B) (-> (or (and Bm Cm) Bm) B))))
================================================================
tm-name          tm-91417
in-theory        91417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C and A) or A) -> B)) -> D) -> D)
theorem-size     15
proof            (modus-ponens tm-981 tm-392 ((Am (-> (-> (-> Cm B) (-> (or (and Bm Cm) Cm) B)) D)) (C (and Bm Cm)) (A Cm) (Dm (-> (-> Cm B) (-> (or (and Bm Cm) Cm) B)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91417.        ((((A -> B) -> (((C and A) or A) -> B)) -> D) -> D), M:tm-981, m:tm-392, u:((Am (-> (-> (-> Cm B) (-> (or (and Bm Cm) Cm) B)) D)) (C (and Bm Cm)) (A Cm) (Dm (-> (-> Cm B) (-> (or (and Bm Cm) Cm) B))))
================================================================
tm-name          tm-91418
in-theory        91418
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) -> D)
theorem-size     21
proof            (modus-ponens tm-981 tm-401 ((Am (-> (-> (-> (-> Cm (and Bm Cm)) B) (-> (or Bm (-> Cm (and Bm Cm))) B)) D)) (C Bm) (A (-> Cm (and Bm Cm))) (Dm (-> (-> (-> Cm (and Bm Cm)) B) (-> (or Bm (-> Cm (and Bm Cm))) B)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-5)
proof-size       163
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91418.        (((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) -> D) -> D), M:tm-981, m:tm-401, u:((Am (-> (-> (-> (-> Cm (and Bm Cm)) B) (-> (or Bm (-> Cm (and Bm Cm))) B)) D)) (C Bm) (A (-> Cm (and Bm Cm))) (Dm (-> (-> (-> Cm (and Bm Cm)) B) (-> (or Bm (-> Cm (and Bm Cm))) B))))
================================================================
tm-name          tm-91419
in-theory        91419
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) -> D)
theorem-size     17
proof            (modus-ponens tm-981 tm-410 ((Am (-> (-> (-> (or Bm Cm) B) (-> (or Bm (or Bm Cm)) B)) D)) (C Bm) (A (or Bm Cm)) (Dm (-> (-> (or Bm Cm) B) (-> (or Bm (or Bm Cm)) B)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       153
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91419.        (((((A or B) -> C) -> ((A or (A or B)) -> C)) -> D) -> D), M:tm-981, m:tm-410, u:((Am (-> (-> (-> (or Bm Cm) B) (-> (or Bm (or Bm Cm)) B)) D)) (C Bm) (A (or Bm Cm)) (Dm (-> (-> (or Bm Cm) B) (-> (or Bm (or Bm Cm)) B))))
================================================================
tm-name          tm-91420
in-theory        91420
times-derived    1
----------------------------------------------------------------
theorem          (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) -> D)
theorem-size     17
proof            (modus-ponens tm-981 tm-551 ((Am (-> (-> (-> (or Cm Bm) B) (-> (or Bm (or Cm Bm)) B)) D)) (C Bm) (A (or Cm Bm)) (Dm (-> (-> (or Cm Bm) B) (-> (or Bm (or Cm Bm)) B)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-7)
proof-size       153
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-91420.        (((((A or B) -> C) -> ((B or (A or B)) -> C)) -> D) -> D), M:tm-981, m:tm-551, u:((Am (-> (-> (-> (or Cm Bm) B) (-> (or Bm (or Cm Bm)) B)) D)) (C Bm) (A (or Cm Bm)) (Dm (-> (-> (or Cm Bm) B) (-> (or Bm (or Cm Bm)) B))))
================================================================
tm-name          tm-91421
in-theory        91421
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 or E) -> F)) -> H) -> ((G -> E) or ((E -> F) -> ((G or E) -> F)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H)))
theorem-size     67
proof            (modus-ponens tm-980 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       263
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-91421.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((E -> F) -> ((G or E) -> F)) -> H) -> ((G -> E) or ((E -> F) -> ((G or E) -> F)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H))), M:tm-980, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91422
in-theory        91422
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     53
proof            (modus-ponens tm-930 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-91422.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-930, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91423
in-theory        91423
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     53
proof            (modus-ponens tm-893 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-91423.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-893, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91424
in-theory        91424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     57
proof            (modus-ponens tm-855 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-91424.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-855, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91425
in-theory        91425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     51
proof            (modus-ponens tm-808 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-91425.        (((A -> B) -> (((C and A) or A) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-808, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91426
in-theory        91426
times-derived    1
----------------------------------------------------------------
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)) and (((E and ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))) or ((((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     107
proof            (modus-ponens tm-798 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       285
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91426.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (((E and ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))) or ((((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-798, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91427
in-theory        91427
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     51
proof            (modus-ponens tm-757 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91427.        (((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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-757, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91428
in-theory        91428
times-derived    1
----------------------------------------------------------------
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)) and (((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) and E) or ((((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     107
proof            (modus-ponens tm-747 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       285
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-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-91428.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) and E) or ((((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-747, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91429
in-theory        91429
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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H)))
theorem-size     65
proof            (modus-ponens tm-708 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       257
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-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-91429.        (((((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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H))), M:tm-708, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91430
in-theory        91430
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     53
proof            (modus-ponens tm-665 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91430.        ((((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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-665, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91431
in-theory        91431
times-derived    1
----------------------------------------------------------------
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)) and ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or ((((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     93
proof            (modus-ponens tm-654 tm-981 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) 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-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-91431.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((((C -> A) or ((A -> B) -> ((C or A) -> B))) or ((((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-654, m:tm-981, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91432
in-theory        91432
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (E or ((((A -> B) -> ((C or A) -> B)) -> D) -> D)))
theorem-size     41
proof            (modus-ponens tm-623 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-91432.        (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (E or ((((A -> B) -> ((C or A) -> B)) -> D) -> D))), M:tm-623, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91433
in-theory        91433
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-622 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91433.        ((A -> (B -> (C or B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-622, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91434
in-theory        91434
times-derived    1
----------------------------------------------------------------
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)) and (E -> (F or E)))
theorem-size     45
proof            (modus-ponens tm-609 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-91434.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91435
in-theory        91435
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-605 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91435.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-605, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91436
in-theory        91436
times-derived    1
----------------------------------------------------------------
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)) and ((E -> (F or E)) 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     85
proof            (modus-ponens tm-595 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-91436.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((E -> (F or E)) 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-595, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91437
in-theory        91437
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-550 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91437.        (((A -> (B or A)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-550, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91438
in-theory        91438
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-540 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91438.        ((A or (B -> (C or B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-540, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91439
in-theory        91439
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-530 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91439.        ((A or (B -> (B or C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-530, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91440
in-theory        91440
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-520 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91440.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-520, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91441
in-theory        91441
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-510 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91441.        ((A or ((B and C) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-510, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91442
in-theory        91442
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-500 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91442.        ((A or ((B and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-500, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91443
in-theory        91443
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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H)))
theorem-size     55
proof            (modus-ponens tm-490 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-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-91443.        ((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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H))), M:tm-490, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91444
in-theory        91444
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-480 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91444.        ((A or (B -> (C -> B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-480, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91445
in-theory        91445
times-derived    1
----------------------------------------------------------------
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) or E))
theorem-size     41
proof            (modus-ponens tm-470 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-91445.        (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> D) or E)), M:tm-470, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91446
in-theory        91446
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-469 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91446.        ((A -> (B -> (B or C))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-469, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91447
in-theory        91447
times-derived    1
----------------------------------------------------------------
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)) and (E -> (E or F)))
theorem-size     45
proof            (modus-ponens tm-456 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-91447.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91448
in-theory        91448
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-453 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91448.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-453, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91449
in-theory        91449
times-derived    1
----------------------------------------------------------------
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)) and ((E -> (E or F)) 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     85
proof            (modus-ponens tm-443 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-91449.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((E -> (E or F)) 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-443, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91450
in-theory        91450
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-409 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91450.        (((A -> (A or B)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-409, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91451
in-theory        91451
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-400 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91451.        (((A -> (B -> (A and B))) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-400, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91452
in-theory        91452
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-391 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91452.        ((((A and B) -> B) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-391, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91453
in-theory        91453
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-382 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91453.        ((((A and B) -> A) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-382, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91454
in-theory        91454
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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H)))
theorem-size     55
proof            (modus-ponens tm-373 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-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-91454.        ((((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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H))), M:tm-373, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91455
in-theory        91455
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-364 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91455.        (((A -> (B -> A)) or C) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-364, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91456
in-theory        91456
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (E -> (((((A -> B) -> ((C or A) -> B)) -> D) -> D) and E)))
theorem-size     43
proof            (modus-ponens tm-355 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91456.        (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (E -> (((((A -> B) -> ((C or A) -> B)) -> D) -> D) and E))), M:tm-355, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91457
in-theory        91457
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-354 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91457.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-354, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91458
in-theory        91458
times-derived    1
----------------------------------------------------------------
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)) and (E -> (F -> (E and F))))
theorem-size     47
proof            (modus-ponens tm-341 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-91458.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91459
in-theory        91459
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)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F)))
theorem-size     49
proof            (modus-ponens tm-338 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-91459.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F))), M:tm-338, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91460
in-theory        91460
times-derived    1
----------------------------------------------------------------
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)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> D))))
theorem-size     105
proof            (modus-ponens tm-328 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) 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-328.          ((A -> 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-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-91460.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> 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) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> D)))), M:tm-328, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91461
in-theory        91461
times-derived    1
----------------------------------------------------------------
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)) and ((E -> (F -> (E and F))) 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     87
proof            (modus-ponens tm-327 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       259
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-91461.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((E -> (F -> (E and F))) 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-327, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91462
in-theory        91462
times-derived    1
----------------------------------------------------------------
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)) and (((E and F) -> F) 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     85
proof            (modus-ponens tm-326 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-91462.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (((E and F) -> F) 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-326, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91463
in-theory        91463
times-derived    1
----------------------------------------------------------------
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)) and (((E and F) -> E) 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     85
proof            (modus-ponens tm-325 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-91463.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (((E and F) -> E) 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-325, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91464
in-theory        91464
times-derived    1
----------------------------------------------------------------
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)) 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)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D))))
theorem-size     93
proof            (modus-ponens tm-324 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       283
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-91464.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> 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)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)))), M:tm-324, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91465
in-theory        91465
times-derived    1
----------------------------------------------------------------
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)) and ((E -> (F -> E)) 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     85
proof            (modus-ponens tm-323 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-91465.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((E -> (F -> E)) 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-323, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91466
in-theory        91466
times-derived    1
----------------------------------------------------------------
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)) and ((E and F) -> F))
theorem-size     45
proof            (modus-ponens tm-322 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-91466.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91467
in-theory        91467
times-derived    1
----------------------------------------------------------------
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)) and ((E and F) -> E))
theorem-size     45
proof            (modus-ponens tm-320 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91467.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91468
in-theory        91468
times-derived    1
----------------------------------------------------------------
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)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     53
proof            (modus-ponens tm-318 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-91468.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91469
in-theory        91469
times-derived    1
----------------------------------------------------------------
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)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))))
theorem-size     91
proof            (modus-ponens tm-316 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-91469.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> 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) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))), M:tm-316, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91470
in-theory        91470
times-derived    1
----------------------------------------------------------------
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)) and (E -> (F -> E)))
theorem-size     45
proof            (modus-ponens tm-315 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-91470.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91471
in-theory        91471
times-derived    1
----------------------------------------------------------------
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)) and ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> D))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))))
theorem-size     107
proof            (modus-ponens tm-313 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       267
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-91471.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> D))) -> (not ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))))), M:tm-313, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91472
in-theory        91472
times-derived    1
----------------------------------------------------------------
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)) and ((((((A -> B) -> ((C or A) -> B)) -> D) -> D) -> E) -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) or ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) -> E)))
theorem-size     97
proof            (modus-ponens tm-312 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       261
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-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-91472.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and ((((((A -> B) -> ((C or A) -> B)) -> D) -> D) -> E) -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) or ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) -> E))), M:tm-312, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91473
in-theory        91473
times-derived    1
----------------------------------------------------------------
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)) and (E or (((((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     81
proof            (modus-ponens tm-311 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-91473.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (E or (((((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-311, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91474
in-theory        91474
times-derived    1
----------------------------------------------------------------
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)) 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)) or E))
theorem-size     81
proof            (modus-ponens tm-310 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-91474.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> 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)) or E)), M:tm-310, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91475
in-theory        91475
times-derived    1
----------------------------------------------------------------
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)) and (E -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and E)))
theorem-size     83
proof            (modus-ponens tm-309 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
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-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-91475.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (E -> ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and E))), M:tm-309, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91476
in-theory        91476
times-derived    1
----------------------------------------------------------------
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)) and ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((A -> B) -> ((C or A) -> B)) -> D)) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D)))
theorem-size     105
proof            (modus-ponens tm-306 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       271
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (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-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-91476.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> 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)) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> D))), M:tm-306, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (C Dm))
================================================================
tm-name          tm-91477
in-theory        91477
times-derived    1
----------------------------------------------------------------
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)) and (E -> (((((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     81
proof            (modus-ponens tm-305 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-91477.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)) and (E -> (((((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-305, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91478
in-theory        91478
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     51
proof            (modus-ponens tm-303 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91478.        ((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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-303, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91479
in-theory        91479
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-270 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91479.        ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-270, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91480
in-theory        91480
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-239 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91480.        ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-239, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91481
in-theory        91481
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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H)))
theorem-size     57
proof            (modus-ponens tm-210 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-91481.        ((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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H))), M:tm-210, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91482
in-theory        91482
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-183 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91482.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-183, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91483
in-theory        91483
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-157 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91483.        ((A -> ((B and C) -> C)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-157, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91484
in-theory        91484
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     55
proof            (modus-ponens tm-147 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-91484.        ((((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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-147, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91485
in-theory        91485
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-134 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91485.        ((A -> ((B and C) -> B)) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-134, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91486
in-theory        91486
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     55
proof            (modus-ponens tm-125 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-91486.        (((((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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-125, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91487
in-theory        91487
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> E)))
theorem-size     59
proof            (modus-ponens tm-114 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D)) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       227
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91487.        (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> E))), M:tm-114, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D)) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D))) (Dm (-> C D)))
================================================================
tm-name          tm-91488
in-theory        91488
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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H)))
theorem-size     55
proof            (modus-ponens tm-113 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-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-91488.        ((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)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H))), M:tm-113, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91489
in-theory        91489
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     59
proof            (modus-ponens tm-105 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-91489.        ((((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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-105, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91490
in-theory        91490
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)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F)))
theorem-size     47
proof            (modus-ponens tm-95 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-91490.        (((A -> B) -> (A -> A)) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F))), M:tm-95, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91491
in-theory        91491
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (E -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)))
theorem-size     41
proof            (modus-ponens tm-84 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-91491.        (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (E -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D))), M:tm-84, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91492
in-theory        91492
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-83 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91492.        ((A -> (B -> (C -> B))) and (((((D -> E) -> ((F or D) -> E)) -> G) -> ((F -> D) or ((D -> E) -> ((F or D) -> E)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-83, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91493
in-theory        91493
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)))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E)))
theorem-size     45
proof            (modus-ponens tm-76 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91493.        (((not (not A)) -> A) and (((((B -> C) -> ((D or B) -> C)) -> E) -> ((D -> B) or ((B -> C) -> ((D or B) -> C)))) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> E))), M:tm-76, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91494
in-theory        91494
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or ((((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-73 tm-981 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       201
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91494.        (((not (not ((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))) or ((((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-73, m:tm-981, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))) (B (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))
================================================================
tm-name          tm-91495
in-theory        91495
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (not (((A -> B) -> ((C or A) -> B)) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B)))))))
theorem-size     64
proof            (modus-ponens tm-70 tm-981 ((B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (not (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))))) (Dm (not (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-2 tm-9 tm-8)
proof-size       208
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91495.        (((((A -> B) -> ((C or A) -> B)) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (not (((A -> B) -> ((C or A) -> B)) -> (not ((C -> A) or ((A -> B) -> ((C or A) -> B))))))), M:tm-70, m:tm-981, u:((B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (not (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))))) (Dm (not (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-91496
in-theory        91496
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)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F)))
theorem-size     51
proof            (modus-ponens tm-69 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91496.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> ((E or C) -> D)) -> F) -> ((E -> C) or ((C -> D) -> ((E or C) -> D)))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> F))), M:tm-69, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91497
in-theory        91497
times-derived    1
----------------------------------------------------------------
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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G)))
theorem-size     53
proof            (modus-ponens tm-54 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       195
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91497.        (((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)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> G))), M:tm-54, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-91498
in-theory        91498
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) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     57
proof            (modus-ponens tm-980 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
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-91498.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-980, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91499
in-theory        91499
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     55
proof            (modus-ponens tm-977 tm-982 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-1)
proof-size       255
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-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-1.            (A -> (B -> A)), axiom
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-91499.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-977, m:tm-982, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91500
in-theory        91500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-975 tm-982 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-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-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-91500.        (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-975, m:tm-982, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91501
in-theory        91501
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     79
proof            (modus-ponens tm-969 tm-982 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       287
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, 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-1.            (A -> (B -> A)), axiom
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-91501.        ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-969, m:tm-982, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91502
in-theory        91502
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-930 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-91502.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-930, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91503
in-theory        91503
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-927 tm-982 ((Am (-> (or A (or B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-7 tm-1)
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-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-1.            (A -> (B -> A)), 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-91503.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-927, m:tm-982, u:((Am (-> (or A (or B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91504
in-theory        91504
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((B or (A or B)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     65
proof            (modus-ponens tm-920 tm-982 ((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), 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-91504.        (((A or B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((B or (A or B)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-920, m:tm-982, u:((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91505
in-theory        91505
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-893 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-91505.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-893, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91506
in-theory        91506
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-890 tm-982 ((Am (-> (or A (or A B)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-6 tm-1)
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-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-1.            (A -> (B -> A)), 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-91506.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-890, m:tm-982, u:((Am (-> (or A (or A B)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91507
in-theory        91507
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-888 tm-982 ((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-1 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91507.        ((A or B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-888, m:tm-982, u:((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91508
in-theory        91508
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((A or (A or B)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     65
proof            (modus-ponens tm-882 tm-982 ((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-91508.        (((A or B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((A or (A or B)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-882, m:tm-982, u:((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91509
in-theory        91509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     47
proof            (modus-ponens tm-855 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-91509.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-855, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91510
in-theory        91510
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     45
proof            (modus-ponens tm-852 tm-982 ((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-5 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-91510.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-852, m:tm-982, u:((Am (-> (or A (-> B (and A B))) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91511
in-theory        91511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-850 tm-982 ((Am (-> A (and B A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91511.        ((A -> (B and A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-850, m:tm-982, u:((Am (-> A (and B A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91512
in-theory        91512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((B or (A -> (B and A))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     69
proof            (modus-ponens tm-844 tm-982 ((Am (-> A (and B A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), 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-91512.        (((A -> (B and A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((B or (A -> (B and A))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-844, m:tm-982, u:((Am (-> A (and B A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91513
in-theory        91513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-808 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-91513.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-808, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91514
in-theory        91514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-805 tm-982 ((Am (-> (or (and A B) B) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-4 tm-1)
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-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-1.            (A -> (B -> A)), 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-91514.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-805, m:tm-982, u:((Am (-> (or (and A B) B) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91515
in-theory        91515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and A) or A) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))
theorem-size     63
proof            (modus-ponens tm-798 tm-982 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), 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-91515.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and A) or A) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))), M:tm-798, m:tm-982, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91516
in-theory        91516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-757 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91516.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-757, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91517
in-theory        91517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-754 tm-982 ((Am (-> (or (and A B) A) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-3 tm-1)
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-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91517.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-754, m:tm-982, u:((Am (-> (or (and A B) A) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91518
in-theory        91518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((A and F) or A) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))
theorem-size     63
proof            (modus-ponens tm-747 tm-982 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91518.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((A and F) or A) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))), M:tm-747, m:tm-982, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91519
in-theory        91519
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     55
proof            (modus-ponens tm-708 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-1.            (A -> (B -> A)), 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-91519.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-708, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91520
in-theory        91520
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     53
proof            (modus-ponens tm-705 tm-982 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-2 tm-1)
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-1.            (A -> (B -> A)), 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-91520.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-705, m:tm-982, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91521
in-theory        91521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-703 tm-982 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M: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-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-91521.        (((A -> B) -> (A -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-703, m:tm-982, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91522
in-theory        91522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     77
proof            (modus-ponens tm-697 tm-982 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91522.        ((((A -> B) -> (A -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-697, m:tm-982, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91523
in-theory        91523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-665 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-91523.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-665, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91524
in-theory        91524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-662 tm-982 ((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-1)
proof-size       197
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91524.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-662, m:tm-982, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91525
in-theory        91525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-660 tm-982 ((Am (-> A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
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-12.           ((A -> B) -> (A -> A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91525.        ((A -> B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-660, m:tm-982, u:((Am (-> A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91526
in-theory        91526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((B or (A -> B)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     65
proof            (modus-ponens tm-654 tm-982 ((Am (-> A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91526.        (((A -> B) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))) and ((B or (A -> B)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-654, m:tm-982, u:((Am (-> A B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91527
in-theory        91527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-622 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91527.        ((A -> (B -> (C or B))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-622, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91528
in-theory        91528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-619 tm-982 ((Am (-> A (or B A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       169
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91528.        ((A or (B -> (C or B))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-619, m:tm-982, u:((Am (-> A (or B A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91529
in-theory        91529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91529.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91530
in-theory        91530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-605 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-91530.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-605, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91531
in-theory        91531
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-602 tm-982 ((Am (and (-> A (or B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91531.        ((A or ((B -> (C or B)) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-602, m:tm-982, u:((Am (and (-> A (or B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91532
in-theory        91532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G or F)) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91532.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G or F)) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-595, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91533
in-theory        91533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-550 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8)
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-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-91533.        (((A -> (B or A)) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-550, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91534
in-theory        91534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-540 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-91534.        ((A or (B -> (C or B))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-540, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91535
in-theory        91535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-530 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8)
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-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-91535.        ((A or (B -> (B or C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-530, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91536
in-theory        91536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-520 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-91536.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-520, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91537
in-theory        91537
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-510 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8)
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-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-91537.        ((A or ((B and C) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-510, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91538
in-theory        91538
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-500 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
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-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-91538.        ((A or ((B and C) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-500, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91539
in-theory        91539
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-490 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 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-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-91539.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-490, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91540
in-theory        91540
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-480 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91540.        ((A or (B -> (C -> B))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-480, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91541
in-theory        91541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-469 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91541.        ((A -> (B -> (B or C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-469, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91542
in-theory        91542
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-466 tm-982 ((Am (-> A (or A B))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       169
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91542.        ((A or (B -> (B or C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-466, m:tm-982, u:((Am (-> A (or A B))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91543
in-theory        91543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91543.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91544
in-theory        91544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-453 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-91544.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-453, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91545
in-theory        91545
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-450 tm-982 ((Am (and (-> A (or A B)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91545.        ((A or ((B -> (B or C)) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-450, m:tm-982, u:((Am (and (-> A (or A B)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91546
in-theory        91546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (F or G)) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91546.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (F or G)) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-443, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91547
in-theory        91547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-409 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-91547.        (((A -> (A or B)) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-409, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91548
in-theory        91548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-400 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-91548.        (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-400, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91549
in-theory        91549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-391 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8)
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-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-91549.        ((((A and B) -> B) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-391, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91550
in-theory        91550
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-382 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
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-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-91550.        ((((A and B) -> A) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-382, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91551
in-theory        91551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-373 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 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-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-91551.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-373, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91552
in-theory        91552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-364 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91552.        (((A -> (B -> A)) or C) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-364, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91553
in-theory        91553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-354 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91553.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-354, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91554
in-theory        91554
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-351 tm-982 ((Am (-> A (-> B (and A B)))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       179
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91554.        ((A or (B -> (C -> (B and C)))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-351, m:tm-982, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91555
in-theory        91555
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (A and ((C -> D) -> ((B or C) -> D)))))
theorem-size     27
proof            (modus-ponens tm-349 tm-982 ((A Am) (B (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (Em (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
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-5.            (A -> (B -> (A and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91555.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (A and ((C -> D) -> ((B or C) -> D))))), M:tm-349, m:tm-982, u:((A Am) (B (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (Em (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-91556
in-theory        91556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-91556.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91557
in-theory        91557
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> 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-339 tm-982 ((Am (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B)) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91557.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and E)), M:tm-339, m:tm-982, u:((Am (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B)) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91558
in-theory        91558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     39
proof            (modus-ponens tm-338 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91558.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-338, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91559
in-theory        91559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-335 tm-982 ((Am (-> A (and A B))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       185
proof-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91559.        (((A -> B) or (A -> (A and B))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-335, m:tm-982, u:((Am (-> A (and A B))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91560
in-theory        91560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (A -> (A and ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-328 tm-982 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
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-328.          ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91560.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (A -> (A and ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-328, m:tm-982, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91561
in-theory        91561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> (F and G))) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91561.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> (F and G))) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-327, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91562
in-theory        91562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and G) -> G) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91562.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and G) -> G) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-326, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91563
in-theory        91563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and G) -> F) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91563.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F and G) -> F) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-325, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91564
in-theory        91564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-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-91564.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-324, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91565
in-theory        91565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> F)) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-91565.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> F)) and (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-323, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91566
in-theory        91566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91566.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91567
in-theory        91567
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F)) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F)) -> F))
theorem-size     93
proof            (modus-ponens tm-321 tm-982 ((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) C))) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91567.        (((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F)) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F)) -> F)), M:tm-321, m:tm-982, u:((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) C))) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91568
in-theory        91568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91568.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91569
in-theory        91569
times-derived    1
----------------------------------------------------------------
theorem          ((((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) and F) -> ((((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)) -> E) and F) -> E))
theorem-size     93
proof            (modus-ponens tm-319 tm-982 ((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B) C)) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91569.        ((((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) and F) -> ((((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)) -> E) and F) -> E)), M:tm-319, m:tm-982, u:((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B) C)) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91570
in-theory        91570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91570.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91571
in-theory        91571
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> E)) -> ((((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) -> E)) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> E)))
theorem-size     101
proof            (modus-ponens tm-317 tm-982 ((Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em) C))) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 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-13.           (((A -> (B -> C)) -> (A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91571.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> E)) -> ((((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) -> E)) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> E))), M:tm-317, m:tm-982, u:((Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em) C))) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-91572
in-theory        91572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (A -> A))
theorem-size     33
proof            (modus-ponens tm-316 tm-982 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-91572.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (A -> A)), M:tm-316, m:tm-982, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91573
in-theory        91573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91573.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91574
in-theory        91574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A -> (not ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))) -> (not A)))
theorem-size     63
proof            (modus-ponens tm-313 tm-982 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91574.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A -> (not ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))) -> (not A))), M:tm-313, m:tm-982, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91575
in-theory        91575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F) -> ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> F)))
theorem-size     91
proof            (modus-ponens tm-312 tm-982 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), 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-91575.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F) -> ((A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) -> F))), M:tm-312, m:tm-982, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91576
in-theory        91576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F or (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91576.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F or (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-311, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91577
in-theory        91577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91577.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) or F)), M:tm-310, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91578
in-theory        91578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91578.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and F))), M:tm-309, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91579
in-theory        91579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A -> (((B -> C) -> ((D or B) -> C)) -> E)) -> (A -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))
theorem-size     61
proof            (modus-ponens tm-306 tm-982 ((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 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-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-91579.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and ((A -> (((B -> C) -> ((D or B) -> C)) -> E)) -> (A -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))), M:tm-306, m:tm-982, u:((A Am) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-91580
in-theory        91580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91580.        ((A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))) and (F -> (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))))), M:tm-305, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91581
in-theory        91581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-303 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-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-91581.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-303, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91582
in-theory        91582
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-300 tm-982 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-5 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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91582.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-300, m:tm-982, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91583
in-theory        91583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-270 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
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-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-91583.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-270, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91584
in-theory        91584
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-267 tm-982 ((Am (and (-> (and A B) B) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-5 tm-4 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-4.            ((A and B) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91584.        ((A or (((B and C) -> C) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-267, m:tm-982, u:((Am (and (-> (and A B) B) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91585
in-theory        91585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-239 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
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-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-91585.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-239, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91586
in-theory        91586
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-236 tm-982 ((Am (and (-> (and A B) A) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-5 tm-3 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-3.            ((A and B) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91586.        ((A or (((B and C) -> B) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-236, m:tm-982, u:((Am (and (-> (and A B) A) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91587
in-theory        91587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-210 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-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-91587.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-210, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91588
in-theory        91588
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     45
proof            (modus-ponens tm-207 tm-982 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       219
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91588.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-207, m:tm-982, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91589
in-theory        91589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-183 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91589.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-183, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91590
in-theory        91590
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-180 tm-982 ((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-5 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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91590.        ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-180, m:tm-982, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91591
in-theory        91591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-157 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91591.        ((A -> ((B and C) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-157, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91592
in-theory        91592
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-154 tm-982 ((Am (-> (and A B) B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       169
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91592.        ((A or ((B and C) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-154, m:tm-982, u:((Am (-> (and A B) B)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91593
in-theory        91593
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))
theorem-size     29
proof            (modus-ponens tm-152 tm-982 ((Am (and A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-1 tm-4 tm-8)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91593.        ((A and (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)), M:tm-152, m:tm-982, u:((Am (and A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-91594
in-theory        91594
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     45
proof            (modus-ponens tm-147 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 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-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-91594.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-147, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91595
in-theory        91595
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-144 tm-982 ((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91595.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-144, m:tm-982, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91596
in-theory        91596
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F)) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     59
proof            (modus-ponens tm-142 tm-982 ((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) C))) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91596.        ((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> F)) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-142, m:tm-982, u:((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) C))) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91597
in-theory        91597
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> (((B -> C) -> ((D or B) -> C)) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))
theorem-size     57
proof            (modus-ponens tm-141 tm-982 ((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-4 tm-1 tm-8)
proof-size       243
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91597.        ((A and (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) -> (((B -> C) -> ((D or B) -> C)) -> E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)), M:tm-141, m:tm-982, u:((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-91598
in-theory        91598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-134 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91598.        ((A -> ((B and C) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-134, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91599
in-theory        91599
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-131 tm-982 ((Am (-> (and A B) A)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       169
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91599.        ((A or ((B and C) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-131, m:tm-982, u:((Am (-> (and A B) A)) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91600
in-theory        91600
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) and E) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     29
proof            (modus-ponens tm-129 tm-982 ((Am (and (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) B)) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91600.        (((((A -> B) -> ((C or A) -> B)) -> D) and E) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-129, m:tm-982, u:((Am (and (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) B)) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-91601
in-theory        91601
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     45
proof            (modus-ponens tm-125 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 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-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-91601.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-125, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91602
in-theory        91602
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-122 tm-982 ((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91602.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-122, m:tm-982, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91603
in-theory        91603
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) and F) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     59
proof            (modus-ponens tm-120 tm-982 ((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B) C)) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91603.        (((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) and F) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-120, m:tm-982, u:((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B) C)) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91604
in-theory        91604
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D)) and E) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     57
proof            (modus-ponens tm-119 tm-982 ((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) C)) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-3 tm-1 tm-8)
proof-size       243
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91604.        (((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((A -> B) -> ((C or A) -> B)) -> D)) and E) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-119, m:tm-982, u:((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) C)) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-91605
in-theory        91605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-113 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91605.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-113, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91606
in-theory        91606
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     43
proof            (modus-ponens tm-110 tm-982 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91606.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-110, m:tm-982, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91607
in-theory        91607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C or A) -> B) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))
theorem-size     31
proof            (modus-ponens tm-108 tm-982 ((Am (-> (-> Bm Cm) (-> (-> (or Dm Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or Dm Bm) Cm)) (Em (-> (-> Bm Cm) C)) (D (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (-> 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91607.        (((A -> B) -> (((C or A) -> B) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))), M:tm-108, m:tm-982, u:((Am (-> (-> Bm Cm) (-> (-> (or Dm Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or Dm Bm) Cm)) (Em (-> (-> Bm Cm) C)) (D (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (-> Bm Cm) C))))
================================================================
tm-name          tm-91608
in-theory        91608
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((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-106 tm-982 ((Am (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Em)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       241
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91608.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((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-106, m:tm-982, u:((Am (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (B (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))) (C Em))
================================================================
tm-name          tm-91609
in-theory        91609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     49
proof            (modus-ponens tm-105 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-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-91609.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-105, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91610
in-theory        91610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     47
proof            (modus-ponens tm-102 tm-982 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91610.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-102, m:tm-982, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91611
in-theory        91611
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> 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-100 tm-982 ((Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em) C))) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91611.        (((((A -> B) -> ((C or A) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> E)) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-100, m:tm-982, u:((Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em) C))) (A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (B (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-91612
in-theory        91612
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> A))
theorem-size     17
proof            (modus-ponens tm-98 tm-982 ((Em Am) (B (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (A Am) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91612.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> A)), M:tm-98, m:tm-982, u:((Em Am) (B (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (A Am) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))
================================================================
tm-name          tm-91613
in-theory        91613
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> 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-96 tm-982 ((Am (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B)) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       193
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91613.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-96, m:tm-982, u:((Am (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B)) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91614
in-theory        91614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     37
proof            (modus-ponens tm-95 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-91614.        (((A -> B) -> (A -> A)) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-95, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91615
in-theory        91615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-92 tm-982 ((Am (-> A A)) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
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-1.            (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-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-91615.        (((A -> B) or (A -> A)) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-92, m:tm-982, u:((Am (-> A A)) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91616
in-theory        91616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-83 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91616.        ((A -> (B -> (C -> B))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-83, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91617
in-theory        91617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-80 tm-982 ((Am (-> A (-> B A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-1)
proof-size       169
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91617.        ((A or (B -> (C -> B))) -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-80, m:tm-982, u:((Am (-> A (-> B A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91618
in-theory        91618
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E))) -> E)
theorem-size     33
proof            (modus-ponens tm-77 tm-982 ((Am (not (not (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B)))) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-2 tm-10 tm-1 tm-8)
proof-size       153
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91618.        ((not (not (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E))) -> E), M:tm-77, m:tm-982, u:((Am (not (not (-> (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) B)))) (A (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91619
in-theory        91619
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))))
theorem-size     35
proof            (modus-ponens tm-76 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8)
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-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-91619.        (((not (not A)) -> A) and (B -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))), M:tm-76, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91620
in-theory        91620
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-73 tm-982 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-10 tm-1)
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-1.            (A -> (B -> A)), 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-91620.        (((not (not A)) or A) -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-73, m:tm-982, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91621
in-theory        91621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))))
theorem-size     41
proof            (modus-ponens tm-69 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8)
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-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-91621.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))), M:tm-69, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91622
in-theory        91622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     39
proof            (modus-ponens tm-66 tm-982 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-8 tm-9 tm-1)
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-1.            (A -> (B -> A)), 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-91622.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-66, m:tm-982, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-91623
in-theory        91623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((D or B) -> C)) -> E)) -> ((A or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     43
proof            (modus-ponens tm-55 tm-982 ((Am (-> A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       173
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-91623.        ((A -> (((B -> C) -> ((D or B) -> C)) -> E)) -> ((A or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-55, m:tm-982, u:((Am (-> A (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em))) (B (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (C (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))
================================================================
tm-name          tm-91624
in-theory        91624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-54 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), 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-91624.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-54, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-91625
in-theory        91625
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 (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-91625.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-980, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91626
in-theory        91626
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-930 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-91626.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-930, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91627
in-theory        91627
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-893 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-91627.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-893, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91628
in-theory        91628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-91628.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-855, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91629
in-theory        91629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-91629.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-808, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91630
in-theory        91630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-91630.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-757, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91631
in-theory        91631
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-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-91631.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-708, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91632
in-theory        91632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-91632.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-665, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91633
in-theory        91633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-91633.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-622, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91634
in-theory        91634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-91634.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G))), M:tm-609, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91635
in-theory        91635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91635.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-605, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91636
in-theory        91636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-91636.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-595, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91637
in-theory        91637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91637.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-550, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91638
in-theory        91638
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91638.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-540, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91639
in-theory        91639
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-91639.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-530, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91640
in-theory        91640
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91640.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-520, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91641
in-theory        91641
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-91641.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-510, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91642
in-theory        91642
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-91642.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-500, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91643
in-theory        91643
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-91643.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-490, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91644
in-theory        91644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-91644.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-480, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91645
in-theory        91645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-91645.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-469, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91646
in-theory        91646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-91646.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H))), M:tm-456, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91647
in-theory        91647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91647.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-453, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91648
in-theory        91648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-91648.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-443, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91649
in-theory        91649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91649.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-409, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91650
in-theory        91650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91650.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-400, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91651
in-theory        91651
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-91651.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-391, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91652
in-theory        91652
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-91652.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-382, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91653
in-theory        91653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-91653.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-373, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91654
in-theory        91654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-91654.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-364, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91655
in-theory        91655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-91655.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-354, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91656
in-theory        91656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-983 ((A (and (-> Am (or Bm Am)) (or 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      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-91656.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91657
in-theory        91657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-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-91657.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-338, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91658
in-theory        91658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-91658.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-327, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91659
in-theory        91659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-91659.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-326, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91660
in-theory        91660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-91660.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-325, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91661
in-theory        91661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-91661.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-324, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91662
in-theory        91662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-91662.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-323, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91663
in-theory        91663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-91663.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91664
in-theory        91664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91664.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91665
in-theory        91665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-91665.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91666
in-theory        91666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-91666.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91667
in-theory        91667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-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-91667.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-311, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91668
in-theory        91668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-91668.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)), M:tm-310, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91669
in-theory        91669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-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-91669.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G))), M:tm-309, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91670
in-theory        91670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-983 ((A (-> Am (or Bm Am))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-91670.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-308, m:tm-983, u:((A (-> Am (or Bm Am))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91671
in-theory        91671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (A -> (B or A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-983 ((A (-> Am (or Bm Am))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
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-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-91671.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (A -> (B or A))), M:tm-307, m:tm-983, u:((A (-> Am (or Bm Am))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91672
in-theory        91672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-91672.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-305, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91673
in-theory        91673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91673.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-303, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91674
in-theory        91674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-91674.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-270, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91675
in-theory        91675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-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-91675.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-239, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91676
in-theory        91676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-91676.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-210, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91677
in-theory        91677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-91677.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-183, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91678
in-theory        91678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-91678.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-157, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91679
in-theory        91679
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8)
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-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-91679.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-147, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91680
in-theory        91680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-91680.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-134, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91681
in-theory        91681
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
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-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-91681.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-125, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91682
in-theory        91682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
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-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-91682.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-113, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91683
in-theory        91683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-91683.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-105, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91684
in-theory        91684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
proof-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-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-91684.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-95, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91685
in-theory        91685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-91685.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-83, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91686
in-theory        91686
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8)
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-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-91686.        (((not (not A)) -> A) and ((B -> (C or B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-76, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91687
in-theory        91687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8)
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-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-91687.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-69, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91688
in-theory        91688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-91688.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-54, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91689
in-theory        91689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-91689.        ((A -> (B or A)) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-42, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91690
in-theory        91690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-91690.        ((A -> (A or B)) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-32, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91691
in-theory        91691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91691.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-23, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91692
in-theory        91692
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-91692.        (((A and B) -> B) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-22, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91693
in-theory        91693
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-91693.        (((A and B) -> A) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-21, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91694
in-theory        91694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-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-91694.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-20, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91695
in-theory        91695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-91695.        ((A -> (B -> A)) and ((C -> (D or C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-19, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91696
in-theory        91696
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-7 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-7 tm-5 tm-8)
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-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-91696.        (A or ((B -> (C or B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-7, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91697
in-theory        91697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8)
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-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-91697.        (((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G), M:tm-6, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91698
in-theory        91698
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-91698.        (A -> (((B -> (C or B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A)), M:tm-5, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91699
in-theory        91699
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-1 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8)
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-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-91699.        (A -> ((B -> (C or B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-1, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91700
in-theory        91700
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 (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-91700.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-980, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91701
in-theory        91701
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-930 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-91701.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-930, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91702
in-theory        91702
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-893 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-91702.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-893, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91703
in-theory        91703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-91703.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-855, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91704
in-theory        91704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-91704.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-808, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91705
in-theory        91705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-91705.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-757, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91706
in-theory        91706
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-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-91706.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-708, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91707
in-theory        91707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-91707.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-665, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91708
in-theory        91708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-91708.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-622, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91709
in-theory        91709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-91709.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G))), M:tm-609, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91710
in-theory        91710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-91710.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-605, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91711
in-theory        91711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-91711.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-595, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91712
in-theory        91712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91712.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-550, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91713
in-theory        91713
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-91713.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-540, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91714
in-theory        91714
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-91714.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-530, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91715
in-theory        91715
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-91715.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-520, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91716
in-theory        91716
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-91716.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-510, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91717
in-theory        91717
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-91717.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-500, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91718
in-theory        91718
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-91718.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-490, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91719
in-theory        91719
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-91719.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-480, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91720
in-theory        91720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-91720.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-469, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91721
in-theory        91721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-91721.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H))), M:tm-456, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91722
in-theory        91722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91722.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-453, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91723
in-theory        91723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-91723.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-443, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91724
in-theory        91724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91724.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-409, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91725
in-theory        91725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91725.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-400, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91726
in-theory        91726
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-91726.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-391, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91727
in-theory        91727
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-91727.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-382, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91728
in-theory        91728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-91728.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-373, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91729
in-theory        91729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-91729.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-364, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91730
in-theory        91730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-91730.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-354, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91731
in-theory        91731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-91731.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91732
in-theory        91732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-8)
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-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-91732.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-338, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91733
in-theory        91733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-91733.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-327, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91734
in-theory        91734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-91734.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-326, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91735
in-theory        91735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-91735.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-325, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91736
in-theory        91736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-91736.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-324, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91737
in-theory        91737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-91737.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-323, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91738
in-theory        91738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-91738.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91739
in-theory        91739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91739.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91740
in-theory        91740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-91740.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91741
in-theory        91741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-91741.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91742
in-theory        91742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-91742.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-311, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91743
in-theory        91743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-91743.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)), M:tm-310, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91744
in-theory        91744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-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-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-91744.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G))), M:tm-309, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91745
in-theory        91745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-984 ((A (-> Am (or Am Bm))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-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-91745.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-308, m:tm-984, u:((A (-> Am (or Am Bm))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91746
in-theory        91746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (A -> (A or B)))
theorem-size     27
proof            (modus-ponens tm-307 tm-984 ((A (-> Am (or Am Bm))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7 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-3.            ((A and B) -> A), axiom
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-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-91746.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (A -> (A or B))), M:tm-307, m:tm-984, u:((A (-> Am (or Am Bm))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91747
in-theory        91747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (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-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-91747.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-305, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91748
in-theory        91748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91748.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-303, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91749
in-theory        91749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-8)
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-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-91749.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-270, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91750
in-theory        91750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-8)
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-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-91750.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-239, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91751
in-theory        91751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-91751.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-210, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91752
in-theory        91752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-91752.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-183, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91753
in-theory        91753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7 tm-8)
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-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-91753.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-157, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91754
in-theory        91754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7 tm-8)
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-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-91754.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-147, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91755
in-theory        91755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7 tm-8)
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-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-91755.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-134, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91756
in-theory        91756
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7 tm-8)
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-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-91756.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-125, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91757
in-theory        91757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7 tm-8)
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-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-91757.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-113, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91758
in-theory        91758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-91758.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-105, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91759
in-theory        91759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7 tm-8)
proof-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-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-91759.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-95, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91760
in-theory        91760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-91760.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-83, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91761
in-theory        91761
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7 tm-8)
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-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-91761.        (((not (not A)) -> A) and ((B -> (B or C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-76, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91762
in-theory        91762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7 tm-8)
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-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-91762.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-69, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91763
in-theory        91763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-91763.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-54, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91764
in-theory        91764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-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-91764.        ((A -> (B or A)) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-42, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91765
in-theory        91765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-91765.        ((A -> (A or B)) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-32, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91766
in-theory        91766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91766.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-23, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91767
in-theory        91767
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-91767.        (((A and B) -> B) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-22, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91768
in-theory        91768
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-91768.        (((A and B) -> A) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-21, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91769
in-theory        91769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-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-91769.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-20, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91770
in-theory        91770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B 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-91770.        ((A -> (B -> A)) and ((C -> (C or D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-19, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91771
in-theory        91771
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-7 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8)
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-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-91771.        (A or ((B -> (B or C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-7, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91772
in-theory        91772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8)
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-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-91772.        (((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G), M:tm-6, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91773
in-theory        91773
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 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-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-91773.        (A -> (((B -> (B or C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A)), M:tm-5, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91774
in-theory        91774
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-1 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7 tm-8)
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-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-91774.        (A -> ((B -> (B or C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-1, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91775
in-theory        91775
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 (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     51
proof            (modus-ponens tm-980 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-91775.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-980, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91776
in-theory        91776
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-930 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
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-91776.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-930, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91777
in-theory        91777
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-893 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-91777.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-893, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91778
in-theory        91778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     41
proof            (modus-ponens tm-855 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-91778.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-855, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91779
in-theory        91779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-808 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-91779.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-808, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91780
in-theory        91780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-757 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-91780.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-757, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91781
in-theory        91781
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     49
proof            (modus-ponens tm-708 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-91781.        (((((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) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-708, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91782
in-theory        91782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-665 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-91782.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-665, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91783
in-theory        91783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-622 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-91783.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-622, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91784
in-theory        91784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or 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      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-91784.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G))), M:tm-609, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91785
in-theory        91785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-605 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91785.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-605, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91786
in-theory        91786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-91786.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-595, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91787
in-theory        91787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-550 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91787.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-550, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91788
in-theory        91788
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-540 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91788.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-540, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91789
in-theory        91789
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-530 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-91789.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-530, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91790
in-theory        91790
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-520 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91790.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-520, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91791
in-theory        91791
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-510 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-91791.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-510, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91792
in-theory        91792
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-500 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-91792.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-500, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91793
in-theory        91793
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-490 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-91793.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-490, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91794
in-theory        91794
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-480 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-91794.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-480, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91795
in-theory        91795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-469 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-91795.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-469, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91796
in-theory        91796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-91796.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H))), M:tm-456, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91797
in-theory        91797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-453 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91797.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-453, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91798
in-theory        91798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-91798.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-443, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91799
in-theory        91799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-409 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91799.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-409, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91800
in-theory        91800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-400 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-91800.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-400, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91801
in-theory        91801
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-391 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-91801.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-391, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91802
in-theory        91802
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-382 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-91802.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-382, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91803
in-theory        91803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-373 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-91803.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-373, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91804
in-theory        91804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-364 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-91804.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-364, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91805
in-theory        91805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-354 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-91805.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-354, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91806
in-theory        91806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-91806.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91807
in-theory        91807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-338 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-91807.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-338, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91808
in-theory        91808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-91808.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-327, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91809
in-theory        91809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-91809.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-326, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91810
in-theory        91810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-91810.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-325, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91811
in-theory        91811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-91811.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-324, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91812
in-theory        91812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-91812.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-323, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91813
in-theory        91813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-91813.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91814
in-theory        91814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91814.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91815
in-theory        91815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-91815.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91816
in-theory        91816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or 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      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-91816.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91817
in-theory        91817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-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-91817.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-311, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91818
in-theory        91818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-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-91818.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)), M:tm-310, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91819
in-theory        91819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 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-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-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-91819.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G))), M:tm-309, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91820
in-theory        91820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     39
proof            (modus-ponens tm-308 tm-985 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-91820.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-308, m:tm-985, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91821
in-theory        91821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (A -> (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-307 tm-985 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-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-91821.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-985, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91822
in-theory        91822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-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-91822.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-305, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91823
in-theory        91823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-303 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91823.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-303, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91824
in-theory        91824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-270 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-91824.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-270, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91825
in-theory        91825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-239 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-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-91825.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-239, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91826
in-theory        91826
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     41
proof            (modus-ponens tm-210 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-91826.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-210, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91827
in-theory        91827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-183 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-91827.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-183, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91828
in-theory        91828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-157 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-91828.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-157, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91829
in-theory        91829
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) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     39
proof            (modus-ponens tm-147 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-91829.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-147, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91830
in-theory        91830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-134 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-91830.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-134, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91831
in-theory        91831
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) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     39
proof            (modus-ponens tm-125 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-91831.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-125, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91832
in-theory        91832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-113 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
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-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-91832.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-113, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91833
in-theory        91833
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) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     43
proof            (modus-ponens tm-105 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-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-91833.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-105, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91834
in-theory        91834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-95 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
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-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-91834.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-95, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91835
in-theory        91835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-83 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-91835.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-83, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91836
in-theory        91836
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     29
proof            (modus-ponens tm-76 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8)
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-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-91836.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-76, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91837
in-theory        91837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     35
proof            (modus-ponens tm-69 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8)
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-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-91837.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-69, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91838
in-theory        91838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-54 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-91838.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-54, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91839
in-theory        91839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-42 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am 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-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-91839.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-42, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91840
in-theory        91840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-32 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-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-91840.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-32, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91841
in-theory        91841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-23 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91841.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-23, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91842
in-theory        91842
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-22 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 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-23.           (A -> ((B -> (C -> (B and 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-91842.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-22, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91843
in-theory        91843
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-21 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 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-23.           (A -> ((B -> (C -> (B and 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-91843.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-21, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91844
in-theory        91844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-20 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-23.           (A -> ((B -> (C -> (B and 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-91844.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-20, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91845
in-theory        91845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-19 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-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-91845.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-19, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91846
in-theory        91846
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-7 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-7 tm-5 tm-8)
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-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-91846.        (A or ((B -> (C -> (B and C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-7, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91847
in-theory        91847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8)
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-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-91847.        (((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G), M:tm-6, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91848
in-theory        91848
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-91848.        (A -> (((B -> (C -> (B and C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A)), M:tm-5, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91849
in-theory        91849
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-1 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8)
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-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-91849.        (A -> ((B -> (C -> (B and C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-1, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91850
in-theory        91850
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 (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91850.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-980, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91851
in-theory        91851
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-930 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-91851.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-930, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91852
in-theory        91852
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-893 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91852.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-893, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91853
in-theory        91853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91853.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-855, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91854
in-theory        91854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91854.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-808, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91855
in-theory        91855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91855.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-757, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91856
in-theory        91856
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-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-91856.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-708, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91857
in-theory        91857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91857.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-665, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91858
in-theory        91858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-8)
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-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-91858.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-622, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91859
in-theory        91859
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-91859.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G))), M:tm-609, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91860
in-theory        91860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-91860.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-605, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91861
in-theory        91861
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-91861.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-595, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91862
in-theory        91862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-8)
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-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-91862.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-550, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91863
in-theory        91863
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-91863.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-540, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91864
in-theory        91864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-8)
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-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-91864.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-530, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91865
in-theory        91865
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-91865.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-520, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91866
in-theory        91866
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-91866.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-510, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91867
in-theory        91867
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-8)
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-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-91867.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-500, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91868
in-theory        91868
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-8)
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-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-91868.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-490, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91869
in-theory        91869
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-8)
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-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-91869.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-480, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91870
in-theory        91870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7 tm-8)
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-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-91870.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-469, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91871
in-theory        91871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-91871.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H))), M:tm-456, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91872
in-theory        91872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-91872.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-453, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91873
in-theory        91873
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-91873.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-443, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91874
in-theory        91874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-91874.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-409, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91875
in-theory        91875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-91875.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-400, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91876
in-theory        91876
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-91876.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-391, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91877
in-theory        91877
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7 tm-8)
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-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-91877.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-382, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91878
in-theory        91878
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7 tm-8)
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-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-91878.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-373, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91879
in-theory        91879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7 tm-8)
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-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-91879.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-364, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91880
in-theory        91880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-91880.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-354, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91881
in-theory        91881
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-91881.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91882
in-theory        91882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8)
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-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-91882.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-338, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91883
in-theory        91883
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-91883.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-327, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91884
in-theory        91884
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-91884.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-326, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91885
in-theory        91885
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-91885.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-325, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91886
in-theory        91886
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-91886.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-324, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91887
in-theory        91887
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-91887.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-323, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91888
in-theory        91888
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-91888.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91889
in-theory        91889
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91889.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91890
in-theory        91890
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-91890.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91891
in-theory        91891
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-91891.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91892
in-theory        91892
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-91892.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-311, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91893
in-theory        91893
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 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-6.            (A -> (A or 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-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-91893.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)), M:tm-310, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91894
in-theory        91894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 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-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-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-91894.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G))), M:tm-309, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91895
in-theory        91895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-986 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-91895.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-308, m:tm-986, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91896
in-theory        91896
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((A and B) -> B))
theorem-size     27
proof            (modus-ponens tm-307 tm-986 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7 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-3.            ((A and B) -> A), axiom
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-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-91896.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((A and B) -> B)), M:tm-307, m:tm-986, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91897
in-theory        91897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (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-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-91897.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-305, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91898
in-theory        91898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-91898.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-303, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91899
in-theory        91899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-91899.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-270, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91900
in-theory        91900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7 tm-8)
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-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-91900.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-239, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91901
in-theory        91901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-91901.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-210, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91902
in-theory        91902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-91902.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-183, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91903
in-theory        91903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-91903.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-157, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91904
in-theory        91904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8)
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-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-91904.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-147, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91905
in-theory        91905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7 tm-8)
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-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-91905.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-134, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91906
in-theory        91906
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7 tm-8)
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-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-91906.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-125, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91907
in-theory        91907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7 tm-8)
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-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-91907.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-113, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91908
in-theory        91908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-91908.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-105, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91909
in-theory        91909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7 tm-8)
proof-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-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-91909.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-95, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91910
in-theory        91910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-91910.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-83, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91911
in-theory        91911
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7 tm-8)
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-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-91911.        (((not (not A)) -> A) and (((B and C) -> C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-76, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91912
in-theory        91912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7 tm-8)
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-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-91912.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-69, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91913
in-theory        91913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91913.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-54, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91914
in-theory        91914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-91914.        ((A -> (B or A)) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-42, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91915
in-theory        91915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-91915.        ((A -> (A or B)) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-32, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91916
in-theory        91916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-91916.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-23, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91917
in-theory        91917
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-91917.        (((A and B) -> B) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-22, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91918
in-theory        91918
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-91918.        (((A and B) -> A) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-21, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91919
in-theory        91919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-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-91919.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-20, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91920
in-theory        91920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-91920.        ((A -> (B -> A)) and (((C and D) -> D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-19, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91921
in-theory        91921
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-7 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8)
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-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-91921.        (A or (((B and C) -> C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-7, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91922
in-theory        91922
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7 tm-8)
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-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-91922.        ((((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G), M:tm-6, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91923
in-theory        91923
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 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-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-91923.        (A -> ((((B and C) -> C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A)), M:tm-5, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91924
in-theory        91924
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-1 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7 tm-8)
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-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-91924.        (A -> (((B and C) -> C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-1, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91925
in-theory        91925
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 (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91925.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-980, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91926
in-theory        91926
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-930 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-91926.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-930, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91927
in-theory        91927
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-893 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91927.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-893, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91928
in-theory        91928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91928.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-855, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91929
in-theory        91929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91929.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-808, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91930
in-theory        91930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91930.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-757, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91931
in-theory        91931
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-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-91931.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-708, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91932
in-theory        91932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91932.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-665, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91933
in-theory        91933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-8)
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-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-91933.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-622, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91934
in-theory        91934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-91934.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G))), M:tm-609, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91935
in-theory        91935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-91935.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-605, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91936
in-theory        91936
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-91936.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-595, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91937
in-theory        91937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-8)
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-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-91937.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-550, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91938
in-theory        91938
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-91938.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-540, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91939
in-theory        91939
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-8)
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-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-91939.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-530, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91940
in-theory        91940
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-91940.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-520, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91941
in-theory        91941
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-8)
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-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-91941.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-510, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91942
in-theory        91942
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-91942.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-500, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91943
in-theory        91943
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-8)
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-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-91943.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-490, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91944
in-theory        91944
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-8)
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-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-91944.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-480, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91945
in-theory        91945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7 tm-8)
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-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-91945.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-469, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91946
in-theory        91946
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-91946.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H))), M:tm-456, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91947
in-theory        91947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-91947.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-453, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91948
in-theory        91948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-91948.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-443, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91949
in-theory        91949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-91949.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-409, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91950
in-theory        91950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-91950.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-400, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91951
in-theory        91951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7 tm-8)
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-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-91951.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-391, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91952
in-theory        91952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-91952.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-382, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91953
in-theory        91953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7 tm-8)
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-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-91953.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-373, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91954
in-theory        91954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7 tm-8)
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-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-91954.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-364, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91955
in-theory        91955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-91955.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-354, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91956
in-theory        91956
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-91956.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91957
in-theory        91957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
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-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-91957.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-338, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91958
in-theory        91958
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-91958.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-327, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91959
in-theory        91959
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-91959.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-326, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91960
in-theory        91960
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-91960.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-325, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91961
in-theory        91961
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-91961.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-324, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91962
in-theory        91962
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-91962.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-323, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91963
in-theory        91963
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-91963.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91964
in-theory        91964
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91964.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91965
in-theory        91965
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-91965.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91966
in-theory        91966
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-91966.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91967
in-theory        91967
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-91967.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-311, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91968
in-theory        91968
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 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-6.            (A -> (A or 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-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-91968.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)), M:tm-310, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91969
in-theory        91969
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 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-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-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-91969.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G))), M:tm-309, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91970
in-theory        91970
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-987 ((A (-> (and Am Bm) Am)) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
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-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-91970.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-308, m:tm-987, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91971
in-theory        91971
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((A and B) -> A))
theorem-size     27
proof            (modus-ponens tm-307 tm-987 ((A (-> (and Am Bm) Am)) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
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-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-91971.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((A and B) -> A)), M:tm-307, m:tm-987, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-91972
in-theory        91972
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-1.            (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-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-91972.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-305, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91973
in-theory        91973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-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-91973.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-303, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91974
in-theory        91974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7 tm-8)
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-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-91974.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-270, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91975
in-theory        91975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-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-91975.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-239, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91976
in-theory        91976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-91976.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-210, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91977
in-theory        91977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-91977.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-183, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91978
in-theory        91978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7 tm-8)
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-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-91978.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-157, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91979
in-theory        91979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7 tm-8)
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-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-91979.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-147, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91980
in-theory        91980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-91980.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-134, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91981
in-theory        91981
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
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-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-91981.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-125, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91982
in-theory        91982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7 tm-8)
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-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-91982.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-113, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91983
in-theory        91983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-91983.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-105, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91984
in-theory        91984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7 tm-8)
proof-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-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-91984.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-95, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91985
in-theory        91985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-91985.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-83, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91986
in-theory        91986
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7 tm-8)
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-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-91986.        (((not (not A)) -> A) and (((B and C) -> B) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-76, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91987
in-theory        91987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7 tm-8)
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-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-91987.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-69, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91988
in-theory        91988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-91988.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-54, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91989
in-theory        91989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-91989.        ((A -> (B or A)) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-42, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91990
in-theory        91990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-91990.        ((A -> (A or B)) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-32, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91991
in-theory        91991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-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-91991.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-23, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91992
in-theory        91992
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-91992.        (((A and B) -> B) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-22, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91993
in-theory        91993
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-91993.        (((A and B) -> A) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-21, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91994
in-theory        91994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-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-91994.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-20, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91995
in-theory        91995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-91995.        ((A -> (B -> A)) and (((C and D) -> C) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-19, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91996
in-theory        91996
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-7 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8)
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-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-91996.        (A or (((B and C) -> B) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-7, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91997
in-theory        91997
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7 tm-8)
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-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-91997.        ((((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G), M:tm-6, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91998
in-theory        91998
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 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-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-91998.        (A -> ((((B and C) -> B) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A)), M:tm-5, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-91999
in-theory        91999
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-1 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7 tm-8)
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-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-91999.        (A -> (((B and C) -> B) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-1, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92000
in-theory        92000
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 (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     57
proof            (modus-ponens tm-980 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-92000.        (((((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 (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-980, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92001
in-theory        92001
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-930 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
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-92001.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-930, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92002
in-theory        92002
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-893 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-92002.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-893, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92003
in-theory        92003
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 (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     47
proof            (modus-ponens tm-855 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-92003.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-855, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92004
in-theory        92004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     41
proof            (modus-ponens tm-808 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-92004.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-808, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92005
in-theory        92005
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     41
proof            (modus-ponens tm-757 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) 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-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-92005.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-757, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92006
in-theory        92006
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) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     55
proof            (modus-ponens tm-708 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) 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-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-92006.        (((((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) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-708, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92007
in-theory        92007
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-665 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) 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-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-92007.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-665, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92008
in-theory        92008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-622 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
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-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-92008.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-622, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92009
in-theory        92009
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I or H)))
theorem-size     35
proof            (modus-ponens tm-609 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am 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-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-92009.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I or H))), M:tm-609, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92010
in-theory        92010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-605 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-92010.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-605, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92011
in-theory        92011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-92011.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-595, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92012
in-theory        92012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-550 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
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-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-92012.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-550, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92013
in-theory        92013
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-540 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-92013.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-540, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92014
in-theory        92014
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-530 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
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-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-92014.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-530, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92015
in-theory        92015
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-520 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-92015.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-520, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92016
in-theory        92016
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-510 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
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-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-92016.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-510, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92017
in-theory        92017
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-500 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
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-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-92017.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-500, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92018
in-theory        92018
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) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-490 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-92018.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-490, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92019
in-theory        92019
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-480 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
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-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-92019.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-480, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92020
in-theory        92020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-469 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7 tm-8)
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-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-92020.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-469, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92021
in-theory        92021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (H or I)))
theorem-size     35
proof            (modus-ponens tm-456 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-92021.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (H or I))), M:tm-456, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92022
in-theory        92022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-453 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-92022.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-453, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92023
in-theory        92023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-92023.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-443, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92024
in-theory        92024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-409 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-92024.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-409, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92025
in-theory        92025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-400 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-92025.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-400, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92026
in-theory        92026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-391 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7 tm-8)
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-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-92026.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-391, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92027
in-theory        92027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-382 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7 tm-8)
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-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-92027.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-382, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92028
in-theory        92028
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) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-373 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-92028.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-373, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92029
in-theory        92029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-364 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7 tm-8)
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-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-92029.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-364, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92030
in-theory        92030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-354 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
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-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-92030.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-354, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92031
in-theory        92031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I -> (H and I))))
theorem-size     37
proof            (modus-ponens tm-341 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-92031.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92032
in-theory        92032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     39
proof            (modus-ponens tm-338 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-7 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-92032.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-338, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92033
in-theory        92033
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-92033.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-327, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92034
in-theory        92034
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-92034.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-326, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92035
in-theory        92035
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-92035.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-325, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92036
in-theory        92036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-92036.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-324, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92037
in-theory        92037
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-92037.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-323, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92038
in-theory        92038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H and I) -> I))
theorem-size     35
proof            (modus-ponens tm-322 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-92038.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H and I) -> I)), M:tm-322, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92039
in-theory        92039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H and I) -> H))
theorem-size     35
proof            (modus-ponens tm-320 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-92039.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H and I) -> H)), M:tm-320, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92040
in-theory        92040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     43
proof            (modus-ponens tm-318 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-92040.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92041
in-theory        92041
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-92041.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I -> H))), M:tm-315, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92042
in-theory        92042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-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-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-92042.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-311, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92043
in-theory        92043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-92043.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) or H)), M:tm-310, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92044
in-theory        92044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-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-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-92044.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and H))), M:tm-309, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92045
in-theory        92045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-308 tm-988 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-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-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-92045.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-308, m:tm-988, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))
================================================================
tm-name          tm-92046
in-theory        92046
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-988 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-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-92046.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-988, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))
================================================================
tm-name          tm-92047
in-theory        92047
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-92047.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-305, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92048
in-theory        92048
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     41
proof            (modus-ponens tm-303 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-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-92048.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-303, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92049
in-theory        92049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-270 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7 tm-8)
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-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-92049.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-270, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92050
in-theory        92050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-239 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7 tm-8)
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-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-92050.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-239, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92051
in-theory        92051
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) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     47
proof            (modus-ponens tm-210 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-92051.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-210, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92052
in-theory        92052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-183 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
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-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-92052.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-183, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92053
in-theory        92053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-157 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7 tm-8)
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-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-92053.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-157, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92054
in-theory        92054
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     45
proof            (modus-ponens tm-147 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8)
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-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-92054.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-147, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92055
in-theory        92055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-134 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7 tm-8)
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-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-92055.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-134, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92056
in-theory        92056
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     45
proof            (modus-ponens tm-125 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
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-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-92056.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-125, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92057
in-theory        92057
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) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-113 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92057.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-113, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92058
in-theory        92058
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     49
proof            (modus-ponens tm-105 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-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-92058.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-105, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92059
in-theory        92059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-95 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92059.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-95, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92060
in-theory        92060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-83 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
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-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-92060.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-83, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92061
in-theory        92061
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     35
proof            (modus-ponens tm-76 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7 tm-8)
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-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-92061.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-76, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92062
in-theory        92062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     41
proof            (modus-ponens tm-69 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7 tm-8)
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-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-92062.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-69, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92063
in-theory        92063
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-54 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) 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-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-92063.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-54, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92064
in-theory        92064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-42 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am 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-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-92064.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-42, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92065
in-theory        92065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-32 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92065.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-32, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92066
in-theory        92066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-23 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-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-92066.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-23, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92067
in-theory        92067
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-22 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92067.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-22, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92068
in-theory        92068
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-21 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92068.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-21, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92069
in-theory        92069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-20 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92069.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-20, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92070
in-theory        92070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-19 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92070.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-19, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92071
in-theory        92071
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-7 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8)
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-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-92071.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-7, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92072
in-theory        92072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) or H)
theorem-size     31
proof            (modus-ponens tm-6 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7 tm-8)
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-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-92072.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) or H), M:tm-6, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92073
in-theory        92073
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-7 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-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-92073.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))) and A)), M:tm-5, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92074
in-theory        92074
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-1 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7 tm-8)
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-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-92074.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-1, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-92075
in-theory        92075
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 (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     49
proof            (modus-ponens tm-980 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-92075.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-980, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92076
in-theory        92076
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-930 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-92076.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-930, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92077
in-theory        92077
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-893 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-92077.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-893, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92078
in-theory        92078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     39
proof            (modus-ponens tm-855 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-92078.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-855, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92079
in-theory        92079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-808 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-92079.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-808, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92080
in-theory        92080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-92080.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-757, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92081
in-theory        92081
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) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-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-92081.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-708, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92082
in-theory        92082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-92082.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-665, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92083
in-theory        92083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-92083.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-622, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92084
in-theory        92084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-92084.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H or G))), M:tm-609, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92085
in-theory        92085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-92085.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-605, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92086
in-theory        92086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-92086.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H or G)) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-595, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92087
in-theory        92087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8)
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-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-92087.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-550, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92088
in-theory        92088
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-92088.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-540, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92089
in-theory        92089
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8)
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-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-92089.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-530, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92090
in-theory        92090
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-92090.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-520, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92091
in-theory        92091
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8)
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-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-92091.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-510, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92092
in-theory        92092
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
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-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-92092.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-500, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92093
in-theory        92093
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
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-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-92093.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-490, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92094
in-theory        92094
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-92094.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-480, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92095
in-theory        92095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-92095.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-469, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92096
in-theory        92096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-92096.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (G or H))), M:tm-456, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92097
in-theory        92097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-92097.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-453, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92098
in-theory        92098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-92098.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (G or H)) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-443, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92099
in-theory        92099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-92099.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-409, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92100
in-theory        92100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-92100.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-400, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92101
in-theory        92101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7 tm-8)
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-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-92101.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-391, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92102
in-theory        92102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7 tm-8)
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-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-92102.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-382, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92103
in-theory        92103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7 tm-8)
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-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-92103.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-373, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92104
in-theory        92104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-92104.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-364, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92105
in-theory        92105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-92105.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-354, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92106
in-theory        92106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-989 ((A (and (-> Am (-> Bm Am)) (or 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      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-92106.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92107
in-theory        92107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
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-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-92107.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-338, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92108
in-theory        92108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-92108.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-327, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92109
in-theory        92109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-92109.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> H) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-326, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92110
in-theory        92110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-92110.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G and H) -> G) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-325, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92111
in-theory        92111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-92111.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-324, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92112
in-theory        92112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-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-92112.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> G)) and ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-323, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92113
in-theory        92113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-92113.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92114
in-theory        92114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-92114.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92115
in-theory        92115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-92115.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92116
in-theory        92116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-92116.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92117
in-theory        92117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-92117.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G or ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-311, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92118
in-theory        92118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 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-6.            (A -> (A or 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-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-92118.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)), M:tm-310, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92119
in-theory        92119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-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-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-92119.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and G))), M:tm-309, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92120
in-theory        92120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-989 ((A (-> Am (-> Bm Am))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-92120.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-308, m:tm-989, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-92121
in-theory        92121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (A -> (B -> A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-989 ((A (-> Am (-> Bm Am))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 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-3.            ((A and B) -> A), axiom
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-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-92121.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (A -> (B -> A))), M:tm-307, m:tm-989, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-92122
in-theory        92122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-92122.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and (G -> ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))), M:tm-305, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92123
in-theory        92123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-92123.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-303, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92124
in-theory        92124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-8)
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-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-92124.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-270, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92125
in-theory        92125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-8)
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-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-92125.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-239, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92126
in-theory        92126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-92126.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-210, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92127
in-theory        92127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-92127.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-183, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92128
in-theory        92128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-92128.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-157, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92129
in-theory        92129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7 tm-8)
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-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-92129.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-147, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92130
in-theory        92130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-92130.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-134, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92131
in-theory        92131
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7 tm-8)
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-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-92131.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-125, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92132
in-theory        92132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
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-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-92132.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-113, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92133
in-theory        92133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-92133.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-105, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92134
in-theory        92134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
proof-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-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-92134.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-95, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92135
in-theory        92135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-92135.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-83, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92136
in-theory        92136
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7 tm-8)
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-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-92136.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-76, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92137
in-theory        92137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7 tm-8)
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-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-92137.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-69, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92138
in-theory        92138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-92138.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-54, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92139
in-theory        92139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-92139.        ((A -> (B or A)) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-42, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92140
in-theory        92140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92140.        ((A -> (A or B)) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-32, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92141
in-theory        92141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-92141.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-23, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92142
in-theory        92142
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92142.        (((A and B) -> B) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-22, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92143
in-theory        92143
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92143.        (((A and B) -> A) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-21, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92144
in-theory        92144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-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-92144.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-20, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92145
in-theory        92145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
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-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-92145.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-19, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92146
in-theory        92146
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-7 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-7 tm-5 tm-1 tm-8)
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-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-92146.        (A or ((B -> (C -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-7, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92147
in-theory        92147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7 tm-8)
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-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-92147.        (((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) or G), M:tm-6, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92148
in-theory        92148
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 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-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-92148.        (A -> (((B -> (C -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and A)), M:tm-5, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92149
in-theory        92149
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-1 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8)
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-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-92149.        (A -> ((B -> (C -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-1, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-92150
in-theory        92150
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     45
proof            (modus-ponens tm-980 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-92150.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-980, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92151
in-theory        92151
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-930 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-92151.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-930, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92152
in-theory        92152
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-893 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-92152.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-893, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92153
in-theory        92153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     35
proof            (modus-ponens tm-855 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-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-92153.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-855, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92154
in-theory        92154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-808 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-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-92154.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-808, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92155
in-theory        92155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-757 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92155.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-757, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92156
in-theory        92156
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) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     43
proof            (modus-ponens tm-708 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92156.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-708, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92157
in-theory        92157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-665 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92157.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-665, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92158
in-theory        92158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-622 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92158.        ((A -> (B -> (C or B))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-622, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92159
in-theory        92159
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92159.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G or F))), M:tm-609, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92160
in-theory        92160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-605 tm-990 ((A (or Am (or 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-92160.        ((A -> ((B -> (C or B)) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-605, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92161
in-theory        92161
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G or F)) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-92161.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G or F)) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-595, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92162
in-theory        92162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-550 tm-990 ((A (or Am (or 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-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-92162.        (((A -> (B or A)) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-550, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92163
in-theory        92163
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-540 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92163.        ((A or (B -> (C or B))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-540, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92164
in-theory        92164
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-530 tm-990 ((A (or Am (or 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-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-92164.        ((A or (B -> (B or C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-530, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92165
in-theory        92165
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-520 tm-990 ((A (or Am (or 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-92165.        ((A or (B -> (C -> (B and C)))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-520, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92166
in-theory        92166
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-510 tm-990 ((A (or Am (or 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-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-92166.        ((A or ((B and C) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-510, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92167
in-theory        92167
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-500 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92167.        ((A or ((B and C) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-500, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92168
in-theory        92168
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-490 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92168.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-490, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92169
in-theory        92169
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-480 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92169.        ((A or (B -> (C -> B))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-480, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92170
in-theory        92170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-469 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92170.        ((A -> (B -> (B or C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-469, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92171
in-theory        92171
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92171.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (F or G))), M:tm-456, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92172
in-theory        92172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-453 tm-990 ((A (or Am (or 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-92172.        ((A -> ((B -> (B or C)) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-453, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92173
in-theory        92173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (F or G)) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-92173.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (F or G)) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-443, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92174
in-theory        92174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-409 tm-990 ((A (or Am (or 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-92174.        (((A -> (A or B)) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-409, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92175
in-theory        92175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-400 tm-990 ((A (or Am (or 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-92175.        (((A -> (B -> (A and B))) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-400, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92176
in-theory        92176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-391 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92176.        ((((A and B) -> B) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-391, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92177
in-theory        92177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-382 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92177.        ((((A and B) -> A) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-382, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92178
in-theory        92178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-373 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92178.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-373, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92179
in-theory        92179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-364 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92179.        (((A -> (B -> A)) or C) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-364, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92180
in-theory        92180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-354 tm-990 ((A (or Am (or 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-92180.        ((A -> (B -> (C -> (B and C)))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-354, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92181
in-theory        92181
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-990 ((A (or Am (or 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-92181.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92182
in-theory        92182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     27
proof            (modus-ponens tm-338 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92182.        (((A -> B) -> (A -> (A and B))) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-338, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92183
in-theory        92183
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> (F and G))) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-92183.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> (F and G))) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-327, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92184
in-theory        92184
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and G) -> G) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-92184.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and G) -> G) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-326, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92185
in-theory        92185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and G) -> F) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-92185.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and G) -> F) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-325, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92186
in-theory        92186
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-92186.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-324, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92187
in-theory        92187
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> F)) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-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-92187.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> F)) and (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-323, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92188
in-theory        92188
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92188.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F and G) -> G)), M:tm-322, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92189
in-theory        92189
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92189.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F and G) -> F)), M:tm-320, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92190
in-theory        92190
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92190.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92191
in-theory        92191
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92191.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G -> F))), M:tm-315, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92192
in-theory        92192
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F or (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-92192.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F or (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-311, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92193
in-theory        92193
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or 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-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-92193.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) or F)), M:tm-310, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92194
in-theory        92194
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
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-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-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-92194.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and F))), M:tm-309, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92195
in-theory        92195
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-990 ((A (or Am (or Bm (-> (-> 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      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-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-92195.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-305, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92196
in-theory        92196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-303 tm-990 ((A (or Am (or 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-92196.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-303, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92197
in-theory        92197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-270 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92197.        ((A -> (((B and C) -> C) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-270, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92198
in-theory        92198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-239 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92198.        ((A -> (((B and C) -> B) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-239, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92199
in-theory        92199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-210 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92199.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-210, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92200
in-theory        92200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-183 tm-990 ((A (or Am (or 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-92200.        ((A -> ((B -> (C -> B)) and A)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-183, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92201
in-theory        92201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-157 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92201.        ((A -> ((B and C) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-157, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92202
in-theory        92202
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-147 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92202.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-147, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92203
in-theory        92203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-134 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92203.        ((A -> ((B and C) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-134, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92204
in-theory        92204
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-125 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92204.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-125, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92205
in-theory        92205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-113 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92205.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-113, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92206
in-theory        92206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     37
proof            (modus-ponens tm-105 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92206.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-105, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92207
in-theory        92207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     25
proof            (modus-ponens tm-95 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92207.        (((A -> B) -> (A -> A)) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-95, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92208
in-theory        92208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-83 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92208.        ((A -> (B -> (C -> B))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-83, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92209
in-theory        92209
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     23
proof            (modus-ponens tm-76 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92209.        (((not (not A)) -> A) and (B or (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-76, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92210
in-theory        92210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     29
proof            (modus-ponens tm-69 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92210.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-69, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92211
in-theory        92211
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-54 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92211.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-54, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92212
in-theory        92212
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-42 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92212.        ((A -> (B or A)) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-42, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92213
in-theory        92213
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-32 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92213.        ((A -> (A or B)) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-32, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92214
in-theory        92214
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     25
proof            (modus-ponens tm-23 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92214.        ((A -> (B -> (A and B))) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-23, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92215
in-theory        92215
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-22 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92215.        (((A and B) -> B) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-22, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92216
in-theory        92216
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-21 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92216.        (((A and B) -> A) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-21, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92217
in-theory        92217
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-20 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92217.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-20, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92218
in-theory        92218
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-19 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92218.        ((A -> (B -> A)) and (C or (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-19, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92219
in-theory        92219
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     19
proof            (modus-ponens tm-7 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-7 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
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-92219.        (A or (B or (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-7, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92220
in-theory        92220
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-6 tm-7 tm-8)
proof-size       79
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-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-92220.        ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) or F), M:tm-6, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92221
in-theory        92221
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-990 ((A (or Am (or Bm (-> (-> 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-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-92221.        (A -> ((B or (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and A)), M:tm-5, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92222
in-theory        92222
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     19
proof            (modus-ponens tm-1 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-1 tm-7 tm-8)
proof-size       79
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-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-92222.        (A -> (B or (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-1, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-92223
in-theory        92223
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I))
theorem-size     45
proof            (modus-ponens tm-980 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
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-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-92223.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I)), M:tm-980, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92224
in-theory        92224
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-966 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> (-> B C) (-> (or D B) C)) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
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-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-92224.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-966, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> (-> B C) (-> (or D B) C)) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92225
in-theory        92225
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-962 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> (-> B C) (-> (or D B) C)) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (-> (-> B C) (-> (or D B) C)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       233
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-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-92225.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> C) -> ((A or B) -> C)))), M:tm-962, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> (-> B C) (-> (or D B) C)) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (-> (-> B C) (-> (or D B) C))))))
================================================================
tm-name          tm-92226
in-theory        92226
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-930 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), 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-92226.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-930, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92227
in-theory        92227
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-917 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (or B C) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       153
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), 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-92227.        ((A or (B or A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-917, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (or B C) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92228
in-theory        92228
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-914 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (or B C) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (or B C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-92228.        ((A or (B or A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (B or A))), M:tm-914, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (or B C) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (or B C)))))
================================================================
tm-name          tm-92229
in-theory        92229
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-893 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-92229.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-893, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92230
in-theory        92230
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-879 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (or B C) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       153
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-92230.        ((A or (A or B)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-879, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (or B C) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92231
in-theory        92231
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-876 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (or B C) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (or B C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-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-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-92231.        ((A or (A or B)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B))), M:tm-876, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (or B C) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (or B C)))))
================================================================
tm-name          tm-92232
in-theory        92232
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-874 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-92232.        ((A -> (B or A)) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-874, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92233
in-theory        92233
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-872 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-92233.        ((A -> (A or B)) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-872, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92234
in-theory        92234
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     25
proof            (modus-ponens tm-870 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-92234.        ((A -> (B -> (A and B))) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-870, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92235
in-theory        92235
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-869 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-4 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-92235.        (((A and B) -> B) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-869, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92236
in-theory        92236
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-868 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-3 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-92236.        (((A and B) -> A) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-868, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92237
in-theory        92237
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-867 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-2 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-92237.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-867, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92238
in-theory        92238
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-866 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-92238.        ((A -> (B -> A)) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-866, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92239
in-theory        92239
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F))
theorem-size     19
proof            (modus-ponens tm-861 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-7)
proof-size       121
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-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-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-92239.        (A or ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)), M:tm-861, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92240
in-theory        92240
times-derived    2
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) or F)
theorem-size     19
proof            (modus-ponens tm-860 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-7)
proof-size       121
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-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-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-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-92240.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) or F), M:tm-860, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92241
in-theory        92241
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F) and A))
theorem-size     21
proof            (modus-ponens tm-859 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       127
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-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-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-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-92241.        (A -> (((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F) and A)), M:tm-859, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92242
in-theory        92242
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F))
theorem-size     19
proof            (modus-ponens tm-858 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       121
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-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-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-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-92242.        (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)), M:tm-858, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))
================================================================
tm-name          tm-92243
in-theory        92243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     35
proof            (modus-ponens tm-855 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-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-92243.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-855, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92244
in-theory        92244
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     23
proof            (modus-ponens tm-841 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> B (and C B)) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 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-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-6.            (A -> (A or B)), axiom
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-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-92244.        ((A or (B -> (A and B))) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-841, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> B (and C B)) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92245
in-theory        92245
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-837 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> B (and C B)) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (-> B (and C B)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-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-92245.        ((A or (B -> (A and B))) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (B -> (A and B)))), M:tm-837, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> B (and C B)) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (-> B (and C B))))))
================================================================
tm-name          tm-92246
in-theory        92246
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B))
theorem-size     23
proof            (modus-ponens tm-836 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-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-92246.        (((A and B) or B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B)), M:tm-836, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92247
in-theory        92247
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-835 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-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-92247.        (((A and B) or A) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A)), M:tm-835, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92248
in-theory        92248
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-834 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> (-> B C) (-> B D)) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-7)
proof-size       223
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-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-92248.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> (A -> C)))), M:tm-834, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> (-> B C) (-> B D)) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-92249
in-theory        92249
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-833 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> B C) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (-> B C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-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-92249.        ((A or (B -> A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (B -> A))), M:tm-833, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> B C) (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (-> B C)))))
================================================================
tm-name          tm-92250
in-theory        92250
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-831 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-92250.        ((A -> (B or A)) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C))), M:tm-831, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92251
in-theory        92251
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-829 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-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-92251.        ((A -> (A or B)) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C))), M:tm-829, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92252
in-theory        92252
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))
theorem-size     21
proof            (modus-ponens tm-827 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-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-92252.        (A -> (A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))), M:tm-827, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92253
in-theory        92253
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C)))
theorem-size     27
proof            (modus-ponens tm-826 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-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-92253.        ((A -> (B -> (A and B))) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C))), M:tm-826, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92254
in-theory        92254
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-825 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-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-92254.        (((A and B) -> B) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C))), M:tm-825, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92255
in-theory        92255
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-824 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-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-92255.        (((A and B) -> A) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C))), M:tm-824, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92256
in-theory        92256
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-823 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-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-92256.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-823, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92257
in-theory        92257
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-822 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-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-92257.        ((A -> (B -> A)) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C))), M:tm-822, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92258
in-theory        92258
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-816 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-9 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-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-92258.        ((A -> (not ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))) -> (not A)), M:tm-816, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92259
in-theory        92259
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E) -> F) -> ((E or ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E)) -> F))
theorem-size     41
proof            (modus-ponens tm-815 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-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-92259.        ((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E) -> F) -> ((E or ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E)) -> F)), M:tm-815, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92260
in-theory        92260
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B)))
theorem-size     21
proof            (modus-ponens tm-814 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
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-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-6.            (A -> (A or B)), 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-92260.        (A or (B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B))), M:tm-814, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92261
in-theory        92261
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) or F)
theorem-size     21
proof            (modus-ponens tm-813 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-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-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-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-92261.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) or F), M:tm-813, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92262
in-theory        92262
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B)) and A))
theorem-size     23
proof            (modus-ponens tm-812 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
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-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-92262.        (A -> ((B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B)) and A)), M:tm-812, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92263
in-theory        92263
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B)))
theorem-size     21
proof            (modus-ponens tm-811 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-7)
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-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-6.            (A -> (A or B)), axiom
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-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-92263.        (A -> (B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B))), M:tm-811, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (and (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B))))
================================================================
tm-name          tm-92264
in-theory        92264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     29
proof            (modus-ponens tm-808 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
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-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-92264.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-808, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92265
in-theory        92265
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-795 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-4 tm-6 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-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-6.            (A -> (A or B)), axiom
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-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-92265.        (((A and B) or B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-795, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92266
in-theory        92266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     29
proof            (modus-ponens tm-757 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-6.            (A -> (A or B)), axiom
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-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-92266.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-757, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92267
in-theory        92267
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-744 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-3 tm-6 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-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-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-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-92267.        (((A and B) or A) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-744, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92268
in-theory        92268
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)))) or I))
theorem-size     43
proof            (modus-ponens tm-708 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-92268.        (((((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)))) or I)), M:tm-708, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92269
in-theory        92269
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-694 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> (-> B C) (-> B D)) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-7)
proof-size       193
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-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-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-92269.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-694, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> (-> B C) (-> B D)) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92270
in-theory        92270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-665 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
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-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-92270.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-665, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92271
in-theory        92271
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-651 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> B C) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       153
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-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-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-92271.        ((A or (B -> A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-651, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (-> B C) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92272
in-theory        92272
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-649 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-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-92272.        ((A -> (B or A)) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-649, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92273
in-theory        92273
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-647 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-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-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-92273.        ((A -> (A or B)) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-647, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92274
in-theory        92274
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     19
proof            (modus-ponens tm-645 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6 tm-7)
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-5.            (A -> (B -> (A and B))), axiom
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-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-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-92274.        (A -> (A and (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-645, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92275
in-theory        92275
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     25
proof            (modus-ponens tm-644 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
proof-size       153
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-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-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-92275.        ((A -> (B -> (A and B))) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-644, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92276
in-theory        92276
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-643 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4 tm-6 tm-7)
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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-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-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-92276.        (((A and B) -> B) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-643, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92277
in-theory        92277
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-642 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3 tm-6 tm-7)
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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-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-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-92277.        (((A and B) -> A) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-642, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92278
in-theory        92278
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-641 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6 tm-7)
proof-size       177
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-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-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-92278.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-641, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92279
in-theory        92279
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     23
proof            (modus-ponens tm-640 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
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-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-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-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-92279.        ((A -> (B -> A)) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-640, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92280
in-theory        92280
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F)) -> F)
theorem-size     21
proof            (modus-ponens tm-638 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (and B (-> (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) C)) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4 tm-6 tm-7)
proof-size       157
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-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-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-92280.        ((A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F)) -> F), M:tm-638, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (and B (-> (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) C)) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92281
in-theory        92281
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) and F) -> E)
theorem-size     21
proof            (modus-ponens tm-636 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (and (-> (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B) C) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3 tm-6 tm-7)
proof-size       157
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-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-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-92281.        ((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) and F) -> E), M:tm-636, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> (and (-> (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) B) C) (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92282
in-theory        92282
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-631 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-9 tm-6 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-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-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-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-92282.        ((A -> (not (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))) -> (not A)), M:tm-631, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92283
in-theory        92283
times-derived    2
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> ((F or (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))) -> E))
theorem-size     37
proof            (modus-ponens tm-630 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 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-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-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-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-92283.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> ((F or (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))) -> E)), M:tm-630, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92284
in-theory        92284
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     19
proof            (modus-ponens tm-629 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-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-92284.        (A or (B -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-629, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92285
in-theory        92285
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) or F)
theorem-size     19
proof            (modus-ponens tm-628 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-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-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-92285.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) or F), M:tm-628, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92286
in-theory        92286
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and A))
theorem-size     21
proof            (modus-ponens tm-627 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
proof-size       127
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-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-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-92286.        (A -> ((B -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and A)), M:tm-627, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92287
in-theory        92287
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     19
proof            (modus-ponens tm-625 tm-991 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-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-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-92287.        (A -> (B -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-625, m:tm-991, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))) (Em (-> B (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
================================================================
tm-name          tm-92288
in-theory        92288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-622 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92288.        ((A -> (B -> (C or B))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-622, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92289
in-theory        92289
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92289.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (G or F))), M:tm-609, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92290
in-theory        92290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-605 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92290.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-605, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92291
in-theory        92291
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (G or F)) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-595 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-92291.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (G or F)) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))), M:tm-595, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92292
in-theory        92292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-550 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92292.        (((A -> (B or A)) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-550, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92293
in-theory        92293
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-540 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92293.        ((A or (B -> (C or B))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-540, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92294
in-theory        92294
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-530 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92294.        ((A or (B -> (B or C))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-530, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92295
in-theory        92295
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-520 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92295.        ((A or (B -> (C -> (B and C)))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-520, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92296
in-theory        92296
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-510 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92296.        ((A or ((B and C) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-510, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92297
in-theory        92297
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-500 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92297.        ((A or ((B and C) -> B)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-500, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92298
in-theory        92298
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-490 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92298.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I)), M:tm-490, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92299
in-theory        92299
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-480 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92299.        ((A or (B -> (C -> B))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-480, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92300
in-theory        92300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-469 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92300.        ((A -> (B -> (B or C))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-469, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92301
in-theory        92301
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92301.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (F or G))), M:tm-456, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92302
in-theory        92302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-453 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92302.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-453, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92303
in-theory        92303
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (F or G)) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-443 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-92303.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (F or G)) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))), M:tm-443, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92304
in-theory        92304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-409 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92304.        (((A -> (A or B)) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-409, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92305
in-theory        92305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-400 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92305.        (((A -> (B -> (A and B))) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-400, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92306
in-theory        92306
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-391 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92306.        ((((A and B) -> B) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-391, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92307
in-theory        92307
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-382 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92307.        ((((A and B) -> A) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-382, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92308
in-theory        92308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-373 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92308.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I)), M:tm-373, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92309
in-theory        92309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-364 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-92309.        (((A -> (B -> A)) or C) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-364, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92310
in-theory        92310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-354 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 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-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-92310.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-354, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92311
in-theory        92311
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-92311.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (G -> (F and G)))), M:tm-341, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92312
in-theory        92312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     27
proof            (modus-ponens tm-338 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 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-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-92312.        (((A -> B) -> (A -> (A and B))) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-338, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92313
in-theory        92313
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (G -> (F and G))) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)))
theorem-size     43
proof            (modus-ponens tm-327 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-92313.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (G -> (F and G))) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))), M:tm-327, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92314
in-theory        92314
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (((F and G) -> G) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-326 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-92314.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (((F and G) -> G) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))), M:tm-326, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92315
in-theory        92315
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (((F and G) -> F) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-325 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-92315.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (((F and G) -> F) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))), M:tm-325, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92316
in-theory        92316
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)))
theorem-size     49
proof            (modus-ponens tm-324 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-92316.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))), M:tm-324, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92317
in-theory        92317
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (G -> F)) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-323 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-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-92317.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (G -> F)) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))), M:tm-323, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92318
in-theory        92318
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-92318.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F and G) -> G)), M:tm-322, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92319
in-theory        92319
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-92319.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F and G) -> F)), M:tm-320, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92320
in-theory        92320
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-92320.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92321
in-theory        92321
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-92321.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (G -> F))), M:tm-315, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92322
in-theory        92322
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F or ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)))
theorem-size     37
proof            (modus-ponens tm-311 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or 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-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-92322.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F or ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))), M:tm-311, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92323
in-theory        92323
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or 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-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-92323.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) or F)), M:tm-310, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92324
in-theory        92324
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 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-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-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-92324.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and F))), M:tm-309, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92325
in-theory        92325
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)))
theorem-size     37
proof            (modus-ponens tm-305 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-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-92325.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E) and (F -> ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))), M:tm-305, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92326
in-theory        92326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     29
proof            (modus-ponens tm-303 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-92326.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-303, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92327
in-theory        92327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-270 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-4 tm-6 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-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-92327.        ((A -> (((B and C) -> C) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-270, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92328
in-theory        92328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-239 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-3 tm-6 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-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-92328.        ((A -> (((B and C) -> B) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-239, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92329
in-theory        92329
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)))) or I))
theorem-size     35
proof            (modus-ponens tm-210 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 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-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-92329.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I)), M:tm-210, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92330
in-theory        92330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-183 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 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-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-92330.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-183, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92331
in-theory        92331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-157 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-92331.        ((A -> ((B and C) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-157, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92332
in-theory        92332
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)))) or H))
theorem-size     33
proof            (modus-ponens tm-147 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 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-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-92332.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-147, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92333
in-theory        92333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-134 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-92333.        ((A -> ((B and C) -> B)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-134, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92334
in-theory        92334
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)))) or H))
theorem-size     33
proof            (modus-ponens tm-125 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-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-92334.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-125, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92335
in-theory        92335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-113 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 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-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-92335.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I)), M:tm-113, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92336
in-theory        92336
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)))) or H))
theorem-size     37
proof            (modus-ponens tm-105 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 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-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-92336.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-105, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92337
in-theory        92337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     25
proof            (modus-ponens tm-95 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 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-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-92337.        (((A -> B) -> (A -> A)) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-95, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92338
in-theory        92338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-83 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-92338.        ((A -> (B -> (C -> B))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-83, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92339
in-theory        92339
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F))
theorem-size     23
proof            (modus-ponens tm-76 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-10 tm-6 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-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-92339.        (((not (not A)) -> A) and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)), M:tm-76, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92340
in-theory        92340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     29
proof            (modus-ponens tm-69 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-9 tm-6 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-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-92340.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-69, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92341
in-theory        92341
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-54 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
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-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-92341.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) or H)), M:tm-54, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-92342
in-theory        92342
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       101
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-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-92342.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-992, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-92343
in-theory        92343
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-92343.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-992, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-92344
in-theory        92344
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((not (not E)) -> E))
theorem-size     21
proof            (modus-ponens tm-992 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       85
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-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-10.           ((not (not A)) -> A), axiom
tm-92344.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((not (not E)) -> E)), M:tm-992, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-92345
in-theory        92345
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-992 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-92345.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> F)))), M:tm-992, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-92346
in-theory        92346
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-992 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92346.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> E))), M:tm-992, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-92347
in-theory        92347
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-992 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-92347.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-992, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-92348
in-theory        92348
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-92348.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-992, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-92349
in-theory        92349
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-992 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-92349.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-992, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-92350
in-theory        92350
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-992 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-92350.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F and G) -> F))), M:tm-992, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-92351
in-theory        92351
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-992 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-92351.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-992, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-92352
in-theory        92352
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-992 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-92352.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F and G) -> G))), M:tm-992, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-92353
in-theory        92353
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> F)) and E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-92353.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> F)) and E))), M:tm-992, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-92354
in-theory        92354
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-992 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-92354.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-992, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-92355
in-theory        92355
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and G) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-92355.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and G) -> F) and E))), M:tm-992, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-92356
in-theory        92356
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and G) -> G) and E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-92356.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and G) -> G) and E))), M:tm-992, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-92357
in-theory        92357
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-92357.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (F and G))) and E))), M:tm-992, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-92358
in-theory        92358
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-992 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-92358.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (E and F)))), M:tm-992, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-92359
in-theory        92359
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-92359.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (F and G))))), M:tm-992, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-92360
in-theory        92360
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-992 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-92360.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) or G)), M:tm-992, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-92361
in-theory        92361
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-992 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-92361.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-992, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-92362
in-theory        92362
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) or G))
theorem-size     23
proof            (modus-ponens tm-992 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-92362.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) or G)), M:tm-992, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-92363
in-theory        92363
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) or G))
theorem-size     23
proof            (modus-ponens tm-992 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-92363.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) or G)), M:tm-992, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-92364
in-theory        92364
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) or G))
theorem-size     25
proof            (modus-ponens tm-992 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-92364.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) or G)), M:tm-992, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-92365
in-theory        92365
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) or G))
theorem-size     23
proof            (modus-ponens tm-992 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-92365.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) or G)), M:tm-992, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-92366
in-theory        92366
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (F or G)) and E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-92366.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (F or G)) and E))), M:tm-992, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-92367
in-theory        92367
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-992 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-92367.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (F or G)))), M:tm-992, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-92368
in-theory        92368
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-992 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-92368.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> F)))), M:tm-992, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-92369
in-theory        92369
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-92369.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-992, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-92370
in-theory        92370
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-992 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-92370.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F and G) -> F))), M:tm-992, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-92371
in-theory        92371
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-992 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-92371.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F and G) -> G))), M:tm-992, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-92372
in-theory        92372
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm 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-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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-92372.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (F and G))))), M:tm-992, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-92373
in-theory        92373
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-992 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-92373.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (F or G)))), M:tm-992, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-92374
in-theory        92374
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-992 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
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-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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-92374.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G or F)))), M:tm-992, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-92375
in-theory        92375
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) or G))
theorem-size     23
proof            (modus-ponens tm-992 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-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-92375.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) or G)), M:tm-992, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-92376
in-theory        92376
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G or F)) and E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) 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-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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-92376.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G or F)) and E))), M:tm-992, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-92377
in-theory        92377
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-992 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-92377.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G or F)))), M:tm-992, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-92378
in-theory        92378
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-992 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-92378.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-992, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-92379
in-theory        92379
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     41
proof            (modus-ponens tm-992 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       151
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-92379.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-992, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-92380
in-theory        92380
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-992 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-92380.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (((E and G) or E) -> F))), M:tm-992, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-92381
in-theory        92381
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-992 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-92381.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (((G and E) or E) -> F))), M:tm-992, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-92382
in-theory        92382
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-992 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       129
proof-steps      9
----------------------------------------------------------------
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-92382.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-992, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-92383
in-theory        92383
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-992 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       119
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-92383.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-992, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-92384
in-theory        92384
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-992 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-92384.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-992, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-92385
in-theory        92385
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       155
proof-steps      9
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-92385.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-992, 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-92386
in-theory        92386
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-92386.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-992, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-92387
in-theory        92387
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-992 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-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-92387.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-992, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-92388
in-theory        92388
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-992 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-92388.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))), M:tm-992, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-92389
in-theory        92389
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
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-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-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-92389.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G)))), M:tm-992, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-92390
in-theory        92390
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-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-92390.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-992, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-92391
in-theory        92391
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92391.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> E))) -> (not E))), M:tm-992, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-92392
in-theory        92392
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
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-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-92392.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G))))), M:tm-992, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-92393
in-theory        92393
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> (not E)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92393.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> (not E)) -> (not (E and F)))), M:tm-992, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-92394
in-theory        92394
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> (not F)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92394.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> (not F)) -> (not (E and F)))), M:tm-992, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-92395
in-theory        92395
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (E and F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
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-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-92395.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (E and F)))) -> (not E))), M:tm-992, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-92396
in-theory        92396
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (E or F))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92396.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (E or F))) -> (not E))), M:tm-992, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-92397
in-theory        92397
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F or E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
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-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-92397.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F or E))) -> (not E))), M:tm-992, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-92398
in-theory        92398
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F))))
theorem-size     35
proof            (modus-ponens tm-992 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
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-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-92398.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F)))), M:tm-992, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-92399
in-theory        92399
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-992 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
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-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-92399.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F)))), M:tm-992, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-92400
in-theory        92400
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-992 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       145
proof-steps      9
----------------------------------------------------------------
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-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-92400.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G))), M:tm-992, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-92401
in-theory        92401
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
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-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-92401.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-992, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-92402
in-theory        92402
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G))
theorem-size     29
proof            (modus-ponens tm-992 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92402.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G)), M:tm-992, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-92403
in-theory        92403
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E)))
theorem-size     31
proof            (modus-ponens tm-992 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-92403.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E))), M:tm-992, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-92404
in-theory        92404
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-992 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92404.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E)))), M:tm-992, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-92405
in-theory        92405
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92405.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-992, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-92406
in-theory        92406
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((not (not E)) -> (not E)) -> (not (not (not E)))))
theorem-size     27
proof            (modus-ponens tm-992 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92406.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((not (not E)) -> (not E)) -> (not (not (not E))))), M:tm-992, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-92407
in-theory        92407
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (((not (not E)) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-992 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 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-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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-92407.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (((not (not E)) or E) -> F))), M:tm-992, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-92408
in-theory        92408
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-992 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-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-92408.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((not (not F)) -> F))), M:tm-992, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-92409
in-theory        92409
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((not (not E)) -> E) or F))
theorem-size     23
proof            (modus-ponens tm-992 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92409.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((not (not E)) -> E) or F)), M:tm-992, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-92410
in-theory        92410
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((not (not F)) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-92410.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((not (not F)) -> F) and E))), M:tm-992, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-92411
in-theory        92411
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F)))
theorem-size     31
proof            (modus-ponens tm-992 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92411.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F))), M:tm-992, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-92412
in-theory        92412
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-992 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92412.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((not (not F)) -> F))), M:tm-992, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-92413
in-theory        92413
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (G -> F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92413.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (G -> F)))) -> (not E))), M:tm-992, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-92414
in-theory        92414
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-992 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       139
proof-steps      11
----------------------------------------------------------------
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-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-92414.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G))), M:tm-992, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-92415
in-theory        92415
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm 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-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-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-92415.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (H -> G))))), M:tm-992, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-92416
in-theory        92416
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92416.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (G -> F))) or H)), M:tm-992, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-92417
in-theory        92417
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-92417.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (H -> G))) and E))), M:tm-992, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-92418
in-theory        92418
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-992 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-92418.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (G -> F)))), M:tm-992, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-92419
in-theory        92419
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm 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-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-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-92419.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (H -> G))))), M:tm-992, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-92420
in-theory        92420
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> E))
theorem-size     19
proof            (modus-ponens tm-992 tm-86 ((A (-> Am Am))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92420.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> E)), M:tm-992, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-92421
in-theory        92421
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> G)) -> (E -> (F -> G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92421.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> G)) -> (E -> (F -> G)))), M:tm-992, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-92422
in-theory        92422
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> (E and F)))
theorem-size     23
proof            (modus-ponens tm-992 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92422.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> (E and F))), M:tm-992, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-92423
in-theory        92423
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> F)))
theorem-size     23
proof            (modus-ponens tm-992 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92423.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> F))), M:tm-992, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-92424
in-theory        92424
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((not (not E)) -> (not (not E))))
theorem-size     23
proof            (modus-ponens tm-992 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92424.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((not (not E)) -> (not (not E)))), M:tm-992, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-92425
in-theory        92425
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not (E -> E))) -> (not (E -> F))))
theorem-size     29
proof            (modus-ponens tm-992 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
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-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-92425.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not (E -> E))) -> (not (E -> F)))), M:tm-992, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-92426
in-theory        92426
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-992 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       143
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92426.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F))), M:tm-992, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-92427
in-theory        92427
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-992 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92427.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> (F -> F)))), M:tm-992, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-92428
in-theory        92428
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (E -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-992 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92428.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (E -> E)) or G)), M:tm-992, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-92429
in-theory        92429
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> (F -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-92429.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> (F -> F)) and E))), M:tm-992, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-92430
in-theory        92430
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> E) -> ((E -> F) -> E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92430.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> E) -> ((E -> F) -> E))), M:tm-992, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-92431
in-theory        92431
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-992 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92431.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> (F -> F)))), M:tm-992, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-92432
in-theory        92432
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-92432.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> E) -> G)) -> (E -> G))), M:tm-992, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-92433
in-theory        92433
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E -> F)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-992 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-92433.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E -> F)) -> (E -> F))), M:tm-992, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-92434
in-theory        92434
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-992 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92434.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F)))), M:tm-992, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-92435
in-theory        92435
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-9 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
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-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-92435.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F))))), M:tm-992, 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-92436
in-theory        92436
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-92436.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H))), M:tm-992, 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-92437
in-theory        92437
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-92437.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-992, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-92438
in-theory        92438
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H))
theorem-size     37
proof            (modus-ponens tm-992 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
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-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-92438.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H)), M:tm-992, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-92439
in-theory        92439
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E)))
theorem-size     39
proof            (modus-ponens tm-992 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-92439.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E))), M:tm-992, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-92440
in-theory        92440
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-992 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-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-92440.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G)))), M:tm-992, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-92441
in-theory        92441
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
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-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-92441.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-992, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-92442
in-theory        92442
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-992 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-92442.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H))), M:tm-992, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-92443
in-theory        92443
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E)))
theorem-size     35
proof            (modus-ponens tm-992 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9 tm-1 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
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-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-92443.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E))), M:tm-992, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-92444
in-theory        92444
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       187
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-92444.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H))), M:tm-992, 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-92445
in-theory        92445
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-992 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-92445.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-992, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-92446
in-theory        92446
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-992 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-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-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-92446.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-992, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-92447
in-theory        92447
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-992 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-92447.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-992, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-92448
in-theory        92448
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-992 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
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-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-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-92448.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H))))), M:tm-992, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-92449
in-theory        92449
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-992 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-92449.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-992, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-92450
in-theory        92450
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) and E) -> F))
theorem-size     23
proof            (modus-ponens tm-992 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-92450.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) and E) -> F)), M:tm-992, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-92451
in-theory        92451
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-992 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-92451.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> E)) -> G) and H) -> G)), M:tm-992, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-92452
in-theory        92452
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H))
theorem-size     35
proof            (modus-ponens tm-992 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-92452.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H)), M:tm-992, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-92453
in-theory        92453
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F)))
theorem-size     37
proof            (modus-ponens tm-992 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-92453.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F))), M:tm-992, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-92454
in-theory        92454
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E)))
theorem-size     31
proof            (modus-ponens tm-992 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92454.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E))), M:tm-992, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-92455
in-theory        92455
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-9 tm-2 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
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-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-92455.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E)))), M:tm-992, 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-92456
in-theory        92456
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       175
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-92456.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H))), M:tm-992, 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-92457
in-theory        92457
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-92457.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-992, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-92458
in-theory        92458
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H))
theorem-size     33
proof            (modus-ponens tm-992 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-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-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-92458.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H)), M:tm-992, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-92459
in-theory        92459
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E)))
theorem-size     35
proof            (modus-ponens tm-992 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-92459.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E))), M:tm-992, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-92460
in-theory        92460
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F)))
theorem-size     39
proof            (modus-ponens tm-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-92460.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F))), M:tm-992, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-92461
in-theory        92461
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-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-92461.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-992, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-92462
in-theory        92462
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and F) -> E) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-992 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-92462.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and F) -> E) -> G) and H) -> G)), M:tm-992, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-92463
in-theory        92463
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> (E -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-992 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-92463.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> (E -> G)) -> ((E and F) -> G))), M:tm-992, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-92464
in-theory        92464
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F and G) -> F))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92464.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F and G) -> F))) -> (not E))), M:tm-992, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-92465
in-theory        92465
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-992 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       139
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-92465.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G))), M:tm-992, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-92466
in-theory        92466
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-992 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-92466.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G and H) -> G)))), M:tm-992, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-92467
in-theory        92467
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92467.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F and G) -> F)) or H)), M:tm-992, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-92468
in-theory        92468
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-92468.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G and H) -> G)) and E))), M:tm-992, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-92469
in-theory        92469
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F and G)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-992 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92469.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F and G)) -> (E -> F))), M:tm-992, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-92470
in-theory        92470
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-992 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-92470.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G and H) -> G)))), M:tm-992, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-92471
in-theory        92471
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and (E -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-992 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-92471.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and (E -> F)) -> F)), M:tm-992, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-92472
in-theory        92472
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and ((F -> (G -> F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-992 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-92472.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and ((F -> (G -> F)) -> H)) -> H)), M:tm-992, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-92473
in-theory        92473
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I))
theorem-size     35
proof            (modus-ponens tm-992 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-92473.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I)), M:tm-992, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-92474
in-theory        92474
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and (((F and G) -> F) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-992 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-92474.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and (((F and G) -> F) -> H)) -> H)), M:tm-992, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-92475
in-theory        92475
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-992 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-92475.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G))), M:tm-992, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-92476
in-theory        92476
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F)))
theorem-size     31
proof            (modus-ponens tm-992 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92476.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F))), M:tm-992, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-92477
in-theory        92477
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-9 tm-2 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
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-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-92477.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F)))), M:tm-992, 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-92478
in-theory        92478
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       175
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-92478.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H))), M:tm-992, 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-92479
in-theory        92479
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-92479.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-992, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-92480
in-theory        92480
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H))
theorem-size     33
proof            (modus-ponens tm-992 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-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-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-92480.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H)), M:tm-992, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-92481
in-theory        92481
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E)))
theorem-size     35
proof            (modus-ponens tm-992 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-92481.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E))), M:tm-992, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-92482
in-theory        92482
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G)))
theorem-size     39
proof            (modus-ponens tm-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-92482.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G))), M:tm-992, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-92483
in-theory        92483
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-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-92483.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-992, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-92484
in-theory        92484
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and (((F and G) -> G) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-992 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-92484.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and (((F and G) -> G) -> H)) -> H)), M:tm-992, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-92485
in-theory        92485
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and F) -> F) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-992 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-92485.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and F) -> F) -> G) and H) -> G)), M:tm-992, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-92486
in-theory        92486
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> (F -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-992 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-92486.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> (F -> G)) -> ((E and F) -> G))), M:tm-992, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-92487
in-theory        92487
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F and G) -> G))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92487.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F and G) -> G))) -> (not E))), M:tm-992, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-92488
in-theory        92488
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-992 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       139
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-92488.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G))), M:tm-992, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-92489
in-theory        92489
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-992 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-92489.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G and H) -> H)))), M:tm-992, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-92490
in-theory        92490
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92490.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F and G) -> G)) or H)), M:tm-992, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-92491
in-theory        92491
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-92491.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G and H) -> H)) and E))), M:tm-992, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-92492
in-theory        92492
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F and G)) -> (E -> G)))
theorem-size     25
proof            (modus-ponens tm-992 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92492.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F and G)) -> (E -> G))), M:tm-992, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-92493
in-theory        92493
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-992 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-92493.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G and H) -> H)))), M:tm-992, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-92494
in-theory        92494
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
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-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-1.            (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-92494.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> G)))), M:tm-992, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-92495
in-theory        92495
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-92495.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-92496
in-theory        92496
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92496.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G and H) -> G))), M:tm-992, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-92497
in-theory        92497
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92497.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G and H) -> H))), M:tm-992, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-92498
in-theory        92498
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-1.            (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-92498.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (G and H))))), M:tm-992, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-92499
in-theory        92499
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92499.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (G or H)))), M:tm-992, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-92500
in-theory        92500
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
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-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-1.            (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-92500.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H or G)))), M:tm-992, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-92501
in-theory        92501
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 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-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-1.            (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-92501.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-992, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-92502
in-theory        92502
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-992 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92502.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-992, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-92503
in-theory        92503
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92503.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((not (not G)) -> G))), M:tm-992, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-92504
in-theory        92504
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-1.            (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-92504.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> H))))), M:tm-992, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92505
in-theory        92505
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-92505.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> G)))), M:tm-992, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-92506
in-theory        92506
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-992 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-92506.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-992, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-92507
in-theory        92507
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-92507.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92508
in-theory        92508
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-992 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-92508.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-992, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-92509
in-theory        92509
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92509.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> H)))), M:tm-992, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92510
in-theory        92510
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-92510.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-992, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-92511
in-theory        92511
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92511.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> I)))), M:tm-992, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92512
in-theory        92512
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-1.            (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-92512.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-992, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-92513
in-theory        92513
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92513.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E))), M:tm-992, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-92514
in-theory        92514
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-992 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       151
proof-steps      11
----------------------------------------------------------------
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-1.            (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-92514.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H))), M:tm-992, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-92515
in-theory        92515
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
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-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-1.            (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-92515.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (H -> G)) and F)))), M:tm-992, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-92516
in-theory        92516
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (G -> F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-992 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92516.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (G -> F)) and E)) or H)), M:tm-992, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-92517
in-theory        92517
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (H -> G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-92517.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (H -> G)) and F)) and E))), M:tm-992, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-92518
in-theory        92518
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
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-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-1.            (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-92518.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (H -> G)) and F)))), M:tm-992, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-92519
in-theory        92519
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-992 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92519.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H)))), M:tm-992, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-92520
in-theory        92520
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-992 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-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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92520.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-992, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-92521
in-theory        92521
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-992 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92521.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H))), M:tm-992, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-92522
in-theory        92522
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-992 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92522.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I))), M:tm-992, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-92523
in-theory        92523
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92523.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I))))), M:tm-992, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-92524
in-theory        92524
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92524.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I)))), M:tm-992, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-92525
in-theory        92525
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-992 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92525.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H)))), M:tm-992, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-92526
in-theory        92526
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92526.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-992, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-92527
in-theory        92527
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     41
proof            (modus-ponens tm-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92527.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-992, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-92528
in-theory        92528
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-992 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92528.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H))), M:tm-992, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-92529
in-theory        92529
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92529.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I))))), M:tm-992, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-92530
in-theory        92530
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-992 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92530.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H)))), M:tm-992, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-92531
in-theory        92531
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-2)
proof-size       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92531.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-992, 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-92532
in-theory        92532
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92532.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-992, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-92533
in-theory        92533
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92533.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-992, 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-92534
in-theory        92534
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92534.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I)))), M:tm-992, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-92535
in-theory        92535
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92535.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-992, 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-92536
in-theory        92536
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-992 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92536.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J)))), M:tm-992, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-92537
in-theory        92537
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     39
proof            (modus-ponens tm-992 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92537.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-992, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-92538
in-theory        92538
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92538.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-992, 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-92539
in-theory        92539
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-992 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-92539.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-992, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-92540
in-theory        92540
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-992 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
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-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-92540.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E))), M:tm-992, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-92541
in-theory        92541
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or 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     53
proof            (modus-ponens tm-992 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92541.        ((A or ((B -> C) -> ((C -> D) -> ((B or 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-992, 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-92542
in-theory        92542
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-992 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92542.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-992, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-92543
in-theory        92543
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I))
theorem-size     35
proof            (modus-ponens tm-992 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-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-92543.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I)), M:tm-992, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-92544
in-theory        92544
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E)))
theorem-size     37
proof            (modus-ponens tm-992 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-92544.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E))), M:tm-992, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-92545
in-theory        92545
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-992 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
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-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-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-92545.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-992, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-92546
in-theory        92546
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92546.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> G)))), M:tm-992, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-92547
in-theory        92547
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-92547.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-92548
in-theory        92548
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
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-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-3.            ((A and B) -> 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-92548.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G and H) -> G))), M:tm-992, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-92549
in-theory        92549
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> 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-92549.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G and H) -> H))), M:tm-992, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-92550
in-theory        92550
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-92550.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (G and H))))), M:tm-992, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-92551
in-theory        92551
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92551.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (G or H)))), M:tm-992, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-92552
in-theory        92552
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
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-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-3.            ((A and B) -> 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-92552.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H or G)))), M:tm-992, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-92553
in-theory        92553
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 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-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-3.            ((A and B) -> 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-92553.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-992, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-92554
in-theory        92554
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-992 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> 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-92554.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-992, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-92555
in-theory        92555
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> 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-92555.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((not (not G)) -> G))), M:tm-992, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-92556
in-theory        92556
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92556.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> H))))), M:tm-992, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92557
in-theory        92557
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-92557.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> G)))), M:tm-992, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-92558
in-theory        92558
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-992 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-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-92558.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-992, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-92559
in-theory        92559
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92559.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92560
in-theory        92560
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-992 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-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-92560.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-992, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-92561
in-theory        92561
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92561.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> H)))), M:tm-992, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92562
in-theory        92562
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 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-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-92562.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-992, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-92563
in-theory        92563
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92563.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> I)))), M:tm-992, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92564
in-theory        92564
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92564.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G)))), M:tm-992, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-92565
in-theory        92565
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-992 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-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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-92565.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-992, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-92566
in-theory        92566
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-92566.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> H) and G)))), M:tm-992, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-92567
in-theory        92567
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     39
proof            (modus-ponens tm-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92567.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-992, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-92568
in-theory        92568
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92568.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G)))), M:tm-992, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-92569
in-theory        92569
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (((F and G) -> F) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92569.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (((F and G) -> F) and E))) -> (not E))), M:tm-992, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-92570
in-theory        92570
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       151
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-92570.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H))), M:tm-992, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-92571
in-theory        92571
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
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-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-3.            ((A and B) -> 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-92571.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (((G and H) -> G) and F)))), M:tm-992, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-92572
in-theory        92572
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (((F and G) -> F) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-992 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92572.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (((F and G) -> F) and E)) or H)), M:tm-992, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-92573
in-theory        92573
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (((G and H) -> G) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-92573.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (((G and H) -> G) and F)) and E))), M:tm-992, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-92574
in-theory        92574
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92574.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (((G and H) -> G) and F)))), M:tm-992, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-92575
in-theory        92575
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92575.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> G)))), M:tm-992, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-92576
in-theory        92576
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-92576.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-92577
in-theory        92577
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> 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-92577.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G and H) -> G))), M:tm-992, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-92578
in-theory        92578
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) 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-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-4.            ((A and B) -> 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-92578.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G and H) -> H))), M:tm-992, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-92579
in-theory        92579
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-92579.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (G and H))))), M:tm-992, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-92580
in-theory        92580
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92580.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (G or H)))), M:tm-992, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-92581
in-theory        92581
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
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-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-4.            ((A and B) -> 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-92581.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H or G)))), M:tm-992, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-92582
in-theory        92582
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-92582.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-992, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-92583
in-theory        92583
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-992 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> 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-92583.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-992, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-92584
in-theory        92584
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> 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-92584.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((not (not G)) -> G))), M:tm-992, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-92585
in-theory        92585
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92585.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> H))))), M:tm-992, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92586
in-theory        92586
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-92586.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> G)))), M:tm-992, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-92587
in-theory        92587
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-992 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-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-92587.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-992, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-92588
in-theory        92588
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92588.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92589
in-theory        92589
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-992 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-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-92589.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-992, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-92590
in-theory        92590
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92590.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> H)))), M:tm-992, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92591
in-theory        92591
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 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-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-92591.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-992, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-92592
in-theory        92592
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92592.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> I)))), M:tm-992, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92593
in-theory        92593
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92593.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G)))), M:tm-992, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-92594
in-theory        92594
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-992 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-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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-92594.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-992, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-92595
in-theory        92595
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> 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-92595.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> H) and G)))), M:tm-992, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-92596
in-theory        92596
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-92596.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> I) and G)))), M:tm-992, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-92597
in-theory        92597
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> 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-92597.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> I) and G)))), M:tm-992, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-92598
in-theory        92598
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     39
proof            (modus-ponens tm-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92598.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-992, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-92599
in-theory        92599
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92599.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G)))), M:tm-992, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-92600
in-theory        92600
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (((F and G) -> G) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92600.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (((F and G) -> G) and E))) -> (not E))), M:tm-992, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-92601
in-theory        92601
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       151
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-92601.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H))), M:tm-992, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-92602
in-theory        92602
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
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-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-4.            ((A and B) -> 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-92602.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (((G and H) -> H) and F)))), M:tm-992, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-92603
in-theory        92603
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (((F and G) -> G) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-992 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92603.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (((F and G) -> G) and E)) or H)), M:tm-992, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-92604
in-theory        92604
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (((G and H) -> H) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-92604.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (((G and H) -> H) and F)) and E))), M:tm-992, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-92605
in-theory        92605
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92605.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (((G and H) -> H) and F)))), M:tm-992, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-92606
in-theory        92606
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-92606.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> G)))), M:tm-992, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-92607
in-theory        92607
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-92607.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-92608
in-theory        92608
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-992 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-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-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-92608.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> G))), M:tm-992, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-92609
in-theory        92609
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-992 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) 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-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-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-92609.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> H))), M:tm-992, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-92610
in-theory        92610
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
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-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-92610.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H))))), M:tm-992, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-92611
in-theory        92611
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-92611.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (G or H)))), M:tm-992, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-92612
in-theory        92612
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
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-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-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-92612.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H or G)))), M:tm-992, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-92613
in-theory        92613
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-992 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       155
proof-steps      11
----------------------------------------------------------------
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-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-92613.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-992, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-92614
in-theory        92614
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
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-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-92614.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-992, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-92615
in-theory        92615
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-992 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-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-92615.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((not (not G)) -> G))), M:tm-992, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-92616
in-theory        92616
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-92616.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H))))), M:tm-992, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92617
in-theory        92617
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-92617.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G)))), M:tm-992, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-92618
in-theory        92618
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-92618.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-992, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-92619
in-theory        92619
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-992 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
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-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-23.           (A -> ((B -> (C -> (B 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-92619.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92620
in-theory        92620
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-92620.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-992, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-92621
in-theory        92621
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-992 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-23.           (A -> ((B -> (C -> (B 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-92621.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H)))), M:tm-992, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92622
in-theory        92622
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-92622.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-992, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-92623
in-theory        92623
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-992 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-23.           (A -> ((B -> (C -> (B 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-92623.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I)))), M:tm-992, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92624
in-theory        92624
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-92624.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-992, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-92625
in-theory        92625
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-92625.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-992, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-92626
in-theory        92626
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-92626.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G)))), M:tm-992, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-92627
in-theory        92627
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-92627.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G)))), M:tm-992, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-92628
in-theory        92628
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-992 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
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-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-92628.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-992, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-92629
in-theory        92629
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-92629.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-992, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-92630
in-theory        92630
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-92630.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-992, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-92631
in-theory        92631
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92631.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-992, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-92632
in-theory        92632
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-1.            (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-92632.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-992, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-92633
in-theory        92633
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-992 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-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-92633.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E))), M:tm-992, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-92634
in-theory        92634
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       163
proof-steps      11
----------------------------------------------------------------
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-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-92634.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H))), M:tm-992, 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-92635
in-theory        92635
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-992 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
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-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-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-92635.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (H -> (G and H))) and F)))), M:tm-992, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-92636
in-theory        92636
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (G -> (F and G))) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-992 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-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-92636.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (G -> (F and G))) and E)) or H)), M:tm-992, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-92637
in-theory        92637
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-992 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-92637.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E))), M:tm-992, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-92638
in-theory        92638
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-992 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-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-92638.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (H -> (G and H))) and F)))), M:tm-992, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-92639
in-theory        92639
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> E))))
theorem-size     23
proof            (modus-ponens tm-992 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-92639.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> E)))), M:tm-992, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-92640
in-theory        92640
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-92640.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G))))), M:tm-992, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-92641
in-theory        92641
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> ((E and F) and E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-92641.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> ((E and F) and E))), M:tm-992, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-92642
in-theory        92642
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> ((E and F) and F)))
theorem-size     25
proof            (modus-ponens tm-992 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-92642.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> ((E and F) and F))), M:tm-992, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-92643
in-theory        92643
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-92643.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (E and F))))), M:tm-992, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-92644
in-theory        92644
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (E or F))))
theorem-size     23
proof            (modus-ponens tm-992 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-92644.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (E or F)))), M:tm-992, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-92645
in-theory        92645
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F or E))))
theorem-size     23
proof            (modus-ponens tm-992 tm-311 ((A (-> Am (and Am (or Bm Am))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-92645.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F or E)))), M:tm-992, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-92646
in-theory        92646
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-992 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-92646.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-92647
in-theory        92647
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-92647.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E))))), M:tm-992, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-92648
in-theory        92648
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((not (not E)) -> ((not (not E)) and E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-92648.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((not (not E)) -> ((not (not E)) and E))), M:tm-992, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-92649
in-theory        92649
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-92649.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (G -> F))))), M:tm-992, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-92650
in-theory        92650
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and (E -> E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-92650.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and (E -> E)))), M:tm-992, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-92651
in-theory        92651
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-92651.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G))))), M:tm-992, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-92652
in-theory        92652
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-992 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-92652.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-992, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-92653
in-theory        92653
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-92653.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F)))), M:tm-992, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-92654
in-theory        92654
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-992 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-92654.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F and G) -> F)))), M:tm-992, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-92655
in-theory        92655
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-92655.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G)))), M:tm-992, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-92656
in-theory        92656
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-992 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-92656.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F and G) -> G)))), M:tm-992, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-92657
in-theory        92657
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-92657.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (G -> F)) and E)))), M:tm-992, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-92658
in-theory        92658
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-992 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-92658.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-992, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-92659
in-theory        92659
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-92659.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (((F and G) -> F) and E)))), M:tm-992, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-92660
in-theory        92660
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-92660.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (((F and G) -> G) and E)))), M:tm-992, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-92661
in-theory        92661
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-992 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-92661.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (G -> (F and G))) and E)))), M:tm-992, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-92662
in-theory        92662
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-92662.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and (E -> (E and F))))), M:tm-992, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-92663
in-theory        92663
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-992 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-92663.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H))))), M:tm-992, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-92664
in-theory        92664
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-92664.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H))))), M:tm-992, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-92665
in-theory        92665
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-92665.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H))))), M:tm-992, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-92666
in-theory        92666
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-992 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92666.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-992, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-92667
in-theory        92667
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-92667.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H))))), M:tm-992, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-92668
in-theory        92668
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F))))
theorem-size     31
proof            (modus-ponens tm-992 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
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-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-92668.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F)))), M:tm-992, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-92669
in-theory        92669
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-992 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       155
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-92669.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G))), M:tm-992, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-92670
in-theory        92670
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-992 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-92670.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> (F -> (F and G))))), M:tm-992, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-92671
in-theory        92671
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (E -> (E and F))) or G))
theorem-size     27
proof            (modus-ponens tm-992 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92671.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (E -> (E and F))) or G)), M:tm-992, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-92672
in-theory        92672
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> (F -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-92672.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> (F -> (F and G))) and E))), M:tm-992, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-92673
in-theory        92673
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> E) -> ((E -> F) -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-992 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-92673.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> E) -> ((E -> F) -> (E and F)))), M:tm-992, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-92674
in-theory        92674
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-992 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92674.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> (F -> (F and G))))), M:tm-992, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-92675
in-theory        92675
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-992 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-92675.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (G -> (F and G)))))), M:tm-992, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-92676
in-theory        92676
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-992 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-92676.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I)))))), M:tm-992, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92677
in-theory        92677
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92677.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> (H and I)))))), M:tm-992, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92678
in-theory        92678
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92678.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> (H and I)))))), M:tm-992, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92679
in-theory        92679
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-992 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92679.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-992, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-92680
in-theory        92680
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-1.            (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-92680.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I)))))), M:tm-992, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92681
in-theory        92681
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and ((F -> (G -> (F and G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-992 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-92681.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and ((F -> (G -> (F and G))) -> H)) -> H)), M:tm-992, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-92682
in-theory        92682
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> (E and F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-992 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-92682.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> (E and F))) -> G) and H) -> G)), M:tm-992, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-92683
in-theory        92683
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G)))
theorem-size     29
proof            (modus-ponens tm-992 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-92683.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G))), M:tm-992, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-92684
in-theory        92684
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (G -> (F and G))))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92684.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (G -> (F and G))))) -> (not E))), M:tm-992, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-92685
in-theory        92685
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G)))
theorem-size     37
proof            (modus-ponens tm-992 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       151
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> 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-92685.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G))), M:tm-992, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-92686
in-theory        92686
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-992 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
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-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-1.            (A -> (B -> 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-92686.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (H -> (G and H)))))), M:tm-992, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-92687
in-theory        92687
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-992 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92687.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (G -> (F and G)))) or H)), M:tm-992, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-92688
in-theory        92688
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-92688.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (H -> (G and H)))) and E))), M:tm-992, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-92689
in-theory        92689
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-992 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92689.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (G -> (F and G))))), M:tm-992, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-92690
in-theory        92690
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-992 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
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-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-1.            (A -> (B -> 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-92690.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (H -> (G and H)))))), M:tm-992, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-92691
in-theory        92691
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-23.           (A -> ((B -> (C -> (B and 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-92691.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I))), M:tm-992, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-92692
in-theory        92692
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92692.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (H -> G)) or I))), M:tm-992, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-92693
in-theory        92693
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92693.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (H -> G)) or I))), M:tm-992, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-92694
in-theory        92694
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92694.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J))), M:tm-992, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-92695
in-theory        92695
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92695.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (H -> G)) or I))), M:tm-992, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-92696
in-theory        92696
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-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-92696.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (G -> F)) or H))), M:tm-992, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-92697
in-theory        92697
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-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-92697.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> E)) or G) or H)), M:tm-992, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-92698
in-theory        92698
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-92698.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> F)) or H) and E))), M:tm-992, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-92699
in-theory        92699
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
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-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-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-92699.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> F)) or H))), M:tm-992, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-92700
in-theory        92700
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-992 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-8 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-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-23.           (A -> ((B -> (C -> (B and 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-92700.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-992, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-92701
in-theory        92701
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92701.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-992, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-92702
in-theory        92702
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92702.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-992, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-92703
in-theory        92703
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92703.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-992, 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-92704
in-theory        92704
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92704.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-992, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-92705
in-theory        92705
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-992 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-92705.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-992, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-92706
in-theory        92706
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-992 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-92706.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I)), M:tm-992, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-92707
in-theory        92707
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-992 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-92707.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E))), M:tm-992, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-92708
in-theory        92708
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-992 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 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-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-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-92708.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-992, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-92709
in-theory        92709
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-23.           (A -> ((B -> (C -> (B and 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-92709.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I))), M:tm-992, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-92710
in-theory        92710
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92710.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G and H) -> G) or I))), M:tm-992, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-92711
in-theory        92711
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92711.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G and H) -> G) or I))), M:tm-992, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-92712
in-theory        92712
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92712.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J))), M:tm-992, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-92713
in-theory        92713
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92713.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G and H) -> G) or I))), M:tm-992, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-92714
in-theory        92714
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-92714.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F and G) -> F) or H))), M:tm-992, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-92715
in-theory        92715
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) -> E) or G) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-92715.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) -> E) or G) or H)), M:tm-992, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-92716
in-theory        92716
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F and G) -> F) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-92716.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F and G) -> F) or H) and E))), M:tm-992, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-92717
in-theory        92717
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92717.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and G) -> F) or H))), M:tm-992, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-92718
in-theory        92718
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-23.           (A -> ((B -> (C -> (B and 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-92718.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I))), M:tm-992, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-92719
in-theory        92719
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92719.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G and H) -> H) or I))), M:tm-992, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-92720
in-theory        92720
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92720.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G and H) -> H) or I))), M:tm-992, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-92721
in-theory        92721
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92721.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J))), M:tm-992, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-92722
in-theory        92722
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92722.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G and H) -> H) or I))), M:tm-992, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-92723
in-theory        92723
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-92723.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F and G) -> G) or H))), M:tm-992, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-92724
in-theory        92724
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) -> F) or G) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-92724.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) -> F) or G) or H)), M:tm-992, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-92725
in-theory        92725
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F and G) -> G) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-92725.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F and G) -> G) or H) and E))), M:tm-992, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-92726
in-theory        92726
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92726.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F and G) -> G) or H))), M:tm-992, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-92727
in-theory        92727
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-992 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-92727.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I))), M:tm-992, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-92728
in-theory        92728
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92728.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I))), M:tm-992, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-92729
in-theory        92729
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92729.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I))), M:tm-992, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-92730
in-theory        92730
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     39
proof            (modus-ponens tm-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92730.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-992, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-92731
in-theory        92731
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92731.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I))), M:tm-992, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-92732
in-theory        92732
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-992 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-92732.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (G -> (F and G))) or H))), M:tm-992, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-92733
in-theory        92733
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> (E and F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-992 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-92733.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> (E and F))) or G) or H)), M:tm-992, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-92734
in-theory        92734
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> (F and G))) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-92734.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G -> (F and G))) or H) and E))), M:tm-992, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-92735
in-theory        92735
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-992 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92735.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (F and G))) or H))), M:tm-992, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-92736
in-theory        92736
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-92736.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I))), M:tm-992, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-92737
in-theory        92737
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92737.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (G or H)) or I))), M:tm-992, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-92738
in-theory        92738
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92738.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (G or H)) or I))), M:tm-992, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-92739
in-theory        92739
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92739.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J))), M:tm-992, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-92740
in-theory        92740
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92740.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (G or H)) or I))), M:tm-992, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-92741
in-theory        92741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A 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-92741.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (F or G)) or H))), M:tm-992, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-92742
in-theory        92742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (E or F)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A 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-92742.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (E or F)) or G) or H)), M:tm-992, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-92743
in-theory        92743
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (F or G)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-92743.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (F or G)) or H) and E))), M:tm-992, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-92744
in-theory        92744
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
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-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-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-92744.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (F or G)) or H))), M:tm-992, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-92745
in-theory        92745
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92745.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> G)))), M:tm-992, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-92746
in-theory        92746
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-92746.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-92747
in-theory        92747
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92747.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G and H) -> G))), M:tm-992, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-92748
in-theory        92748
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92748.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G and H) -> H))), M:tm-992, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-92749
in-theory        92749
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-92749.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (G and H))))), M:tm-992, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-92750
in-theory        92750
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-92750.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (G or H)))), M:tm-992, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-92751
in-theory        92751
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-92751.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H or G)))), M:tm-992, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-92752
in-theory        92752
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-92752.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-992, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-92753
in-theory        92753
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-992 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92753.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-992, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-92754
in-theory        92754
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92754.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((not (not G)) -> G))), M:tm-992, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-92755
in-theory        92755
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92755.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> H))))), M:tm-992, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92756
in-theory        92756
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-92756.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> G)))), M:tm-992, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-92757
in-theory        92757
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-992 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-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-92757.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-992, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-92758
in-theory        92758
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92758.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92759
in-theory        92759
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-992 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-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-92759.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-992, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-92760
in-theory        92760
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92760.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> H)))), M:tm-992, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92761
in-theory        92761
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 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-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-92761.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-992, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-92762
in-theory        92762
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92762.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> I)))), M:tm-992, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92763
in-theory        92763
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92763.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G)))), M:tm-992, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-92764
in-theory        92764
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-992 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-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-92764.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-992, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-92765
in-theory        92765
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92765.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G)))), M:tm-992, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-92766
in-theory        92766
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92766.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G)))), M:tm-992, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-92767
in-theory        92767
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-92767.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-992, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-92768
in-theory        92768
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-92768.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H))))), M:tm-992, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-92769
in-theory        92769
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92769.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I)))))), M:tm-992, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92770
in-theory        92770
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92770.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (H -> G)) or I))), M:tm-992, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-92771
in-theory        92771
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-92771.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-992, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-92772
in-theory        92772
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92772.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G and H) -> G) or I))), M:tm-992, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-92773
in-theory        92773
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92773.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G and H) -> H) or I))), M:tm-992, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-92774
in-theory        92774
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-92774.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I))), M:tm-992, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-92775
in-theory        92775
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-92775.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (G or H)) or I))), M:tm-992, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-92776
in-theory        92776
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-92776.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G)))), M:tm-992, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-92777
in-theory        92777
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-92777.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (F or G)) and E)))), M:tm-992, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-92778
in-theory        92778
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-92778.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G)))), M:tm-992, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-92779
in-theory        92779
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92779.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G)))), M:tm-992, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-92780
in-theory        92780
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92780.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G)))), M:tm-992, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-92781
in-theory        92781
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     39
proof            (modus-ponens tm-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92781.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-992, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-92782
in-theory        92782
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92782.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G)))), M:tm-992, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-92783
in-theory        92783
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (F or G)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92783.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (F or G)) and E))) -> (not E))), M:tm-992, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-92784
in-theory        92784
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       151
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-92784.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H))), M:tm-992, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-92785
in-theory        92785
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-92785.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (G or H)) and F)))), M:tm-992, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-92786
in-theory        92786
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (F or G)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-992 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-92786.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (F or G)) and E)) or H)), M:tm-992, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-92787
in-theory        92787
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (G or H)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-92787.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (G or H)) and F)) and E))), M:tm-992, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-92788
in-theory        92788
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92788.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (G or H)) and F)))), M:tm-992, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-92789
in-theory        92789
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92789.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (H or I))))), M:tm-992, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92790
in-theory        92790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-92790.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (F or G))))), M:tm-992, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-92791
in-theory        92791
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-23.           (A -> ((B -> (C -> (B 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-92791.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I))))), M:tm-992, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92792
in-theory        92792
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92792.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (H or I))))), M:tm-992, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92793
in-theory        92793
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92793.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (H or I))))), M:tm-992, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92794
in-theory        92794
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92794.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J))))), M:tm-992, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-92795
in-theory        92795
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92795.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (H or I))))), M:tm-992, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92796
in-theory        92796
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and ((F -> (F or G)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-992 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-92796.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and ((F -> (F or G)) -> H)) -> H)), M:tm-992, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-92797
in-theory        92797
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (E or F)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-992 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-92797.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (E or F)) -> G) and H) -> G)), M:tm-992, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-92798
in-theory        92798
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((E or F) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-92798.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((E or F) -> G)) -> (E -> G))), M:tm-992, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-92799
in-theory        92799
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (F or G)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92799.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (F or G)))) -> (not E))), M:tm-992, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-92800
in-theory        92800
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-992 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       139
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-92800.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G))), M:tm-992, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-92801
in-theory        92801
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-92801.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (G or H))))), M:tm-992, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-92802
in-theory        92802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92802.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (F or G))) or H)), M:tm-992, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-92803
in-theory        92803
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-92803.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (G or H))) and E))), M:tm-992, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-92804
in-theory        92804
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-992 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-92804.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (F or G)))), M:tm-992, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-92805
in-theory        92805
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
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-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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-92805.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (G or H))))), M:tm-992, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-92806
in-theory        92806
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92806.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> H))))), M:tm-992, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92807
in-theory        92807
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-92807.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H))))), M:tm-992, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92808
in-theory        92808
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92808.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or (H -> (I -> H))))), M:tm-992, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92809
in-theory        92809
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92809.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or (H -> (I -> H))))), M:tm-992, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92810
in-theory        92810
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92810.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I))))), M:tm-992, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-92811
in-theory        92811
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-1.            (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-92811.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> H))))), M:tm-992, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92812
in-theory        92812
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm 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-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-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-92812.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or (G -> (H -> G))))), M:tm-992, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-92813
in-theory        92813
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92813.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (G -> F))) or H)), M:tm-992, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-92814
in-theory        92814
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-92814.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or (G -> (H -> G))) and E))), M:tm-992, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-92815
in-theory        92815
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm 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-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-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-92815.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or (G -> (H -> G))))), M:tm-992, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-92816
in-theory        92816
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-92816.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92817
in-theory        92817
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-992 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-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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-92817.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92818
in-theory        92818
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-92818.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92819
in-theory        92819
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-92819.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92820
in-theory        92820
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92820.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-992, 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-92821
in-theory        92821
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-92821.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92822
in-theory        92822
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-992 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-92822.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-992, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-92823
in-theory        92823
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-992 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92823.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-992, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-92824
in-theory        92824
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-992 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-92824.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-992, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-92825
in-theory        92825
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-992 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92825.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-992, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-92826
in-theory        92826
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92826.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> H)))), M:tm-992, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92827
in-theory        92827
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-992 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-92827.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H)))), M:tm-992, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92828
in-theory        92828
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> 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-92828.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or ((H and I) -> H)))), M:tm-992, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92829
in-theory        92829
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 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-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-3.            ((A and B) -> 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-92829.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or ((H and I) -> H)))), M:tm-992, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92830
in-theory        92830
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92830.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I)))), M:tm-992, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-92831
in-theory        92831
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92831.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> H)))), M:tm-992, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92832
in-theory        92832
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-992 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 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-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-3.            ((A and 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-92832.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or ((G and H) -> G)))), M:tm-992, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-92833
in-theory        92833
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92833.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F and G) -> F)) or H)), M:tm-992, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-92834
in-theory        92834
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-92834.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or ((G and H) -> G)) and E))), M:tm-992, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-92835
in-theory        92835
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-992 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) 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-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-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-92835.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or ((G and H) -> G)))), M:tm-992, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-92836
in-theory        92836
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or 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-92836.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> I)))), M:tm-992, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92837
in-theory        92837
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-992 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-92837.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I)))), M:tm-992, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92838
in-theory        92838
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-92838.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or ((H and I) -> I)))), M:tm-992, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92839
in-theory        92839
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> 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-92839.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or ((H and I) -> I)))), M:tm-992, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92840
in-theory        92840
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-992 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92840.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J)))), M:tm-992, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-92841
in-theory        92841
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (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-92841.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> I)))), M:tm-992, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92842
in-theory        92842
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-992 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and 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-92842.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or ((G and H) -> H)))), M:tm-992, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-92843
in-theory        92843
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92843.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F and G) -> G)) or H)), M:tm-992, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-92844
in-theory        92844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-92844.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or ((G and H) -> H)) and E))), M:tm-992, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-92845
in-theory        92845
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-992 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
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-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-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-92845.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or ((G and H) -> H)))), M:tm-992, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-92846
in-theory        92846
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-92846.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> (H and I)))))), M:tm-992, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92847
in-theory        92847
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-992 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-92847.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I)))))), M:tm-992, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92848
in-theory        92848
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-92848.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or (H -> (I -> (H and I)))))), M:tm-992, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92849
in-theory        92849
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-92849.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or (H -> (I -> (H and I)))))), M:tm-992, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92850
in-theory        92850
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-992 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-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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92850.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-992, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-92851
in-theory        92851
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-1.            (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-92851.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I)))))), M:tm-992, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92852
in-theory        92852
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-992 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
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-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-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-92852.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or (G -> (H -> (G and H)))))), M:tm-992, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-92853
in-theory        92853
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-992 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-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-92853.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (G -> (F and G)))) or H)), M:tm-992, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-92854
in-theory        92854
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-92854.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or (G -> (H -> (G and H)))) and E))), M:tm-992, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-92855
in-theory        92855
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-992 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
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-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-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-92855.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or (G -> (H -> (G and H)))))), M:tm-992, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-92856
in-theory        92856
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-92856.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or (H -> (H or I))))), M:tm-992, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92857
in-theory        92857
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-92857.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (H or I))))), M:tm-992, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92858
in-theory        92858
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92858.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or (H -> (H or I))))), M:tm-992, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92859
in-theory        92859
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92859.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or (H -> (H or I))))), M:tm-992, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92860
in-theory        92860
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92860.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J))))), M:tm-992, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-92861
in-theory        92861
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92861.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or (H -> (H or I))))), M:tm-992, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92862
in-theory        92862
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A 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-92862.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or (G -> (G or H))))), M:tm-992, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-92863
in-theory        92863
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A 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-92863.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (F or G))) or H)), M:tm-992, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-92864
in-theory        92864
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-92864.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or (G -> (G or H))) and E))), M:tm-992, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-92865
in-theory        92865
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
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-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-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-92865.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or (G -> (G or H))))), M:tm-992, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-92866
in-theory        92866
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-92866.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or (H -> (I or H))))), M:tm-992, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92867
in-theory        92867
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-92867.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I or H))))), M:tm-992, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92868
in-theory        92868
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-92868.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or (H -> (I or H))))), M:tm-992, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92869
in-theory        92869
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 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-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-3.            ((A and B) -> 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-92869.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or (H -> (I or H))))), M:tm-992, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92870
in-theory        92870
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92870.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I))))), M:tm-992, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-92871
in-theory        92871
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-1.            (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-92871.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or (H -> (I or H))))), M:tm-992, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92872
in-theory        92872
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
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-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-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-92872.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or (G -> (H or G))))), M:tm-992, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-92873
in-theory        92873
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-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-92873.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (G or F))) or H)), M:tm-992, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-92874
in-theory        92874
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-92874.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or (G -> (H or G))) and E))), M:tm-992, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-92875
in-theory        92875
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm 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-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-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-92875.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or (G -> (H or G))))), M:tm-992, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-92876
in-theory        92876
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-92876.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> (H or G)) or I))), M:tm-992, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-92877
in-theory        92877
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-92877.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I))), M:tm-992, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-92878
in-theory        92878
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-92878.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> (H or G)) or I))), M:tm-992, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-92879
in-theory        92879
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-92879.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> (H or G)) or I))), M:tm-992, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-92880
in-theory        92880
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-92880.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J))), M:tm-992, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-92881
in-theory        92881
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-92881.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> (H or G)) or I))), M:tm-992, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-92882
in-theory        92882
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-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-92882.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> (G or F)) or H))), M:tm-992, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-92883
in-theory        92883
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F or E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-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-92883.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F or E)) or G) or H)), M:tm-992, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-92884
in-theory        92884
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G or F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-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-92884.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G or F)) or H) and E))), M:tm-992, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-92885
in-theory        92885
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-992 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
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-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-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-92885.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G or F)) or H))), M:tm-992, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-92886
in-theory        92886
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
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-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-42.           (A -> ((B -> (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-92886.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> G)))), M:tm-992, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-92887
in-theory        92887
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-92887.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-92888
in-theory        92888
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
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-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-42.           (A -> ((B -> (C 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-92888.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G and H) -> G))), M:tm-992, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-92889
in-theory        92889
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) 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-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-42.           (A -> ((B -> (C 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-92889.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G and H) -> H))), M:tm-992, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-92890
in-theory        92890
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-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-92890.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (G and H))))), M:tm-992, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-92891
in-theory        92891
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-92891.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (G or H)))), M:tm-992, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-92892
in-theory        92892
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
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-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-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-92892.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H or G)))), M:tm-992, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-92893
in-theory        92893
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 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       147
proof-steps      11
----------------------------------------------------------------
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-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-92893.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-992, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-92894
in-theory        92894
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-992 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-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-92894.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-992, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-92895
in-theory        92895
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-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-92895.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((not (not G)) -> G))), M:tm-992, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-92896
in-theory        92896
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-92896.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> H))))), M:tm-992, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92897
in-theory        92897
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-42.           (A -> ((B -> (C or B)) and 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-92897.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> G)))), M:tm-992, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-92898
in-theory        92898
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-992 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-8 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-92898.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-992, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-92899
in-theory        92899
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-42.           (A -> ((B -> (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-92899.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92900
in-theory        92900
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-992 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-8 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-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-42.           (A -> ((B -> (C or B)) and 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-92900.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-992, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-92901
in-theory        92901
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-42.           (A -> ((B -> (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-92901.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> H)))), M:tm-992, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92902
in-theory        92902
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 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-8 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-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-42.           (A -> ((B -> (C or B)) and 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-92902.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-992, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-92903
in-theory        92903
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-42.           (A -> ((B -> (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-92903.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> I)))), M:tm-992, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92904
in-theory        92904
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-92904.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-992, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-92905
in-theory        92905
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-992 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-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-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-42.           (A -> ((B -> (C or B)) and 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-92905.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-992, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-92906
in-theory        92906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-92906.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G)))), M:tm-992, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-92907
in-theory        92907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-92907.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G)))), M:tm-992, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-92908
in-theory        92908
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-92908.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-992, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-92909
in-theory        92909
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 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-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-42.           (A -> ((B -> (C or B)) and 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-92909.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H))))), M:tm-992, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-92910
in-theory        92910
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-92910.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I)))))), M:tm-992, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92911
in-theory        92911
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-42.           (A -> ((B -> (C 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-92911.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (H -> G)) or I))), M:tm-992, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-92912
in-theory        92912
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-42.           (A -> ((B -> (C 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-92912.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-992, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-92913
in-theory        92913
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-42.           (A -> ((B -> (C 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-92913.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G and H) -> G) or I))), M:tm-992, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-92914
in-theory        92914
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-42.           (A -> ((B -> (C 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-92914.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G and H) -> H) or I))), M:tm-992, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-92915
in-theory        92915
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-992 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-92915.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I))), M:tm-992, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-92916
in-theory        92916
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-92916.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (G or H)) or I))), M:tm-992, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-92917
in-theory        92917
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-92917.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G)))), M:tm-992, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-92918
in-theory        92918
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-42.           (A -> ((B -> (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-92918.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (H or I))))), M:tm-992, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92919
in-theory        92919
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-92919.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> H))))), M:tm-992, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-92920
in-theory        92920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 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-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-42.           (A -> ((B -> (C or B)) and 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-92920.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-992, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-92921
in-theory        92921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 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-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-42.           (A -> ((B -> (C 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-92921.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> H)))), M:tm-992, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-92922
in-theory        92922
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-992 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-92922.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> I)))), M:tm-992, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-92923
in-theory        92923
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-992 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-92923.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> (H and I)))))), M:tm-992, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-92924
in-theory        92924
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-92924.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or (H -> (H or I))))), M:tm-992, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-92925
in-theory        92925
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-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-92925.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or (H -> (I or H))))), M:tm-992, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92926
in-theory        92926
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-992 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-92926.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> (H or G)) or I))), M:tm-992, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-92927
in-theory        92927
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-92927.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G)))), M:tm-992, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-92928
in-theory        92928
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-92928.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G)))), M:tm-992, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-92929
in-theory        92929
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-92929.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and ((F -> (G or F)) and E)))), M:tm-992, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-92930
in-theory        92930
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-92930.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G)))), M:tm-992, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-92931
in-theory        92931
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-92931.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G)))), M:tm-992, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-92932
in-theory        92932
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-92932.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G)))), M:tm-992, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-92933
in-theory        92933
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     39
proof            (modus-ponens tm-992 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-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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-92933.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-992, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-92934
in-theory        92934
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-992 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-1.            (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-92934.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G)))), M:tm-992, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-92935
in-theory        92935
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (G or F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-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-92935.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not ((F -> (G or F)) and E))) -> (not E))), M:tm-992, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-92936
in-theory        92936
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       151
proof-steps      11
----------------------------------------------------------------
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-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-92936.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H))), M:tm-992, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-92937
in-theory        92937
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
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-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-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-92937.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> ((G -> (H or G)) and F)))), M:tm-992, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-92938
in-theory        92938
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (G or F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-992 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-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-92938.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F -> (G or F)) and E)) or H)), M:tm-992, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-92939
in-theory        92939
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (H or G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-92939.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> ((G -> (H or G)) and F)) and E))), M:tm-992, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-92940
in-theory        92940
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
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-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-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-92940.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> ((G -> (H or G)) and F)))), M:tm-992, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-92941
in-theory        92941
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-92941.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G -> (H -> (I or H))))), M:tm-992, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92942
in-theory        92942
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92942.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G -> (H -> (I or H))))), M:tm-992, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92943
in-theory        92943
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-92943.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E and (F -> (G or F))))), M:tm-992, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-92944
in-theory        92944
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-92944.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H))))), M:tm-992, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92945
in-theory        92945
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92945.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G -> (H -> (I or H))))), M:tm-992, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92946
in-theory        92946
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92946.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G -> (H -> (I or H))))), M:tm-992, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92947
in-theory        92947
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92947.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I))))), M:tm-992, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-92948
in-theory        92948
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-1.            (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-92948.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I or H))))), M:tm-992, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-92949
in-theory        92949
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and ((F -> (G or F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-992 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-92949.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and ((F -> (G or F)) -> H)) -> H)), M:tm-992, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-92950
in-theory        92950
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F or E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-992 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-92950.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F or E)) -> G) and H) -> G)), M:tm-992, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-92951
in-theory        92951
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F or E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-92951.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> ((F or E) -> G)) -> (E -> G))), M:tm-992, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-92952
in-theory        92952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (G or F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92952.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (not (F -> (G or F)))) -> (not E))), M:tm-992, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-92953
in-theory        92953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-992 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       139
proof-steps      11
----------------------------------------------------------------
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-1.            (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-92953.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G))), M:tm-992, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-92954
in-theory        92954
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm 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-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-1.            (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-92954.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F -> (G -> (H or G))))), M:tm-992, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-92955
in-theory        92955
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-992 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92955.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (G or F))) or H)), M:tm-992, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-92956
in-theory        92956
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-992 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-1.            (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-92956.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> (G -> (H or G))) and E))), M:tm-992, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-92957
in-theory        92957
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-992 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-92957.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> (E -> (G or F)))), M:tm-992, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-92958
in-theory        92958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-992 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm 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-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-1.            (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-92958.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (G -> (H or G))))), M:tm-992, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-92959
in-theory        92959
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), 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-92959.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (F -> E)))), M:tm-992, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-92960
in-theory        92960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-992 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       153
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-92960.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F)))), M:tm-992, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-92961
in-theory        92961
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> ((F -> E) and G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), 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-92961.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> ((F -> E) and G)))), M:tm-992, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-92962
in-theory        92962
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((F -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-992 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       133
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92962.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((F -> E) or G))), M:tm-992, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-92963
in-theory        92963
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G or (F -> E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), 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-92963.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G or (F -> E)))), M:tm-992, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-92964
in-theory        92964
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G))))
theorem-size     31
proof            (modus-ponens tm-992 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       149
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92964.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G)))), M:tm-992, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-92965
in-theory        92965
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F))))
theorem-size     29
proof            (modus-ponens tm-992 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       143
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92965.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F)))), M:tm-992, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-92966
in-theory        92966
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), 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-92966.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (H -> G)))), M:tm-992, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-92967
in-theory        92967
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (F -> F)))
theorem-size     25
proof            (modus-ponens tm-992 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-92967.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (F -> F))), M:tm-992, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-92968
in-theory        92968
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-992 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       197
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-92968.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-992, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-92969
in-theory        92969
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 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       177
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-92969.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-92970
in-theory        92970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-992 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       173
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-92970.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-992, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-92971
in-theory        92971
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 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       145
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92971.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G and H) -> G))), M:tm-992, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-92972
in-theory        92972
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-992 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       173
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-92972.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G))), M:tm-992, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-92973
in-theory        92973
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 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       145
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92973.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G and H) -> H))), M:tm-992, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-92974
in-theory        92974
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-992 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92974.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E)))), M:tm-992, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-92975
in-theory        92975
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E))))
theorem-size     39
proof            (modus-ponens tm-992 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       189
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-92975.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E)))), M:tm-992, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-92976
in-theory        92976
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-992 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92976.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E)))), M:tm-992, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-92977
in-theory        92977
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-992 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92977.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E)))), M:tm-992, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-92978
in-theory        92978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-992 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       165
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92978.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E)))), M:tm-992, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-92979
in-theory        92979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (F -> (F and E))))
theorem-size     27
proof            (modus-ponens tm-992 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-92979.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (F -> (F and E)))), M:tm-992, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-92980
in-theory        92980
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), 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-92980.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (H -> (G and H))))), M:tm-992, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-92981
in-theory        92981
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-992 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92981.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E)))), M:tm-992, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-92982
in-theory        92982
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 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       145
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92982.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (G or H)))), M:tm-992, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-92983
in-theory        92983
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-992 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92983.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E)))), M:tm-992, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-92984
in-theory        92984
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), 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-92984.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (G -> (H or G)))), M:tm-992, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-92985
in-theory        92985
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-992 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       167
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92985.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E))), M:tm-992, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-92986
in-theory        92986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 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       165
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (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-92986.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-992, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-92987
in-theory        92987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (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-92987.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-992, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-92988
in-theory        92988
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-992 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-92988.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G)))), M:tm-992, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-92989
in-theory        92989
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 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       173
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-92989.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-992, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-92990
in-theory        92990
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-92990.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-992, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-92991
in-theory        92991
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-92991.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-992, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-92992
in-theory        92992
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-2 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-92992.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-992, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-92993
in-theory        92993
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-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-1.            (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-92993.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-992, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-92994
in-theory        92994
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> G) -> ((E -> F) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-92994.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> G) -> ((E -> F) -> G))), M:tm-992, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-92995
in-theory        92995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G))))
theorem-size     37
proof            (modus-ponens tm-992 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
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-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-92995.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G)))), M:tm-992, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-92996
in-theory        92996
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       169
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-92996.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H))), M:tm-992, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-92997
in-theory        92997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-992 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       141
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-92997.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-992, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-92998
in-theory        92998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-992 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-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-92998.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H)), M:tm-992, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-92999
in-theory        92999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-992 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       147
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-92999.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E))), M:tm-992, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-93000
in-theory        93000
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-992 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
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-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-93000.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G))), M:tm-992, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-93001
in-theory        93001
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-992 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), 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-93001.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-992, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-93002
in-theory        93002
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-992 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       177
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93002.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G))))), M:tm-992, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-93003
in-theory        93003
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G))))
theorem-size     41
proof            (modus-ponens tm-992 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       189
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93003.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G)))), M:tm-992, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-93004
in-theory        93004
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H))))
theorem-size     41
proof            (modus-ponens tm-992 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       183
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93004.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H)))), M:tm-992, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-93005
in-theory        93005
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H)))
theorem-size     39
proof            (modus-ponens tm-992 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       177
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93005.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H))), M:tm-992, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-93006
in-theory        93006
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-992 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       177
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93006.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G))))), M:tm-992, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-93007
in-theory        93007
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       197
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93007.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H)))), M:tm-992, 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-93008
in-theory        93008
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       191
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93008.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F))))), M:tm-992, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-93009
in-theory        93009
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-992 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93009.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H)))), M:tm-992, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-93010
in-theory        93010
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F))))
theorem-size     37
proof            (modus-ponens tm-992 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       193
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93010.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F)))), M:tm-992, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-93011
in-theory        93011
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-992 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       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93011.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-992, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-93012
in-theory        93012
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-992 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       213
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93012.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-992, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-93013
in-theory        93013
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-992 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93013.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H))), M:tm-992, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-93014
in-theory        93014
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-992 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93014.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I))), M:tm-992, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-93015
in-theory        93015
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93015.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G))))), M:tm-992, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-93016
in-theory        93016
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or 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     51
proof            (modus-ponens tm-992 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       233
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93016.        ((A or ((B -> C) -> ((C -> D) -> ((B or 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-992, 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-93017
in-theory        93017
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93017.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G))))), M:tm-992, 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-93018
in-theory        93018
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93018.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G))))), M:tm-992, 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-93019
in-theory        93019
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93019.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G))))), M:tm-992, 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-93020
in-theory        93020
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G)))))
theorem-size     41
proof            (modus-ponens tm-992 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       205
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93020.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G))))), M:tm-992, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-93021
in-theory        93021
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-992 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       189
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93021.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I))))), M:tm-992, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-93022
in-theory        93022
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93022.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G))))), M:tm-992, 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-93023
in-theory        93023
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-992 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93023.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I)))), M:tm-992, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-93024
in-theory        93024
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93024.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G))))), M:tm-992, 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-93025
in-theory        93025
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-992 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93025.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H)))), M:tm-992, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-93026
in-theory        93026
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-992 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       203
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-93026.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G)))), M:tm-992, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-93027
in-theory        93027
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or 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     59
proof            (modus-ponens tm-992 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       263
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93027.        ((A or ((B -> C) -> ((C -> D) -> ((B or 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-992, 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-93028
in-theory        93028
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       211
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-93028.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E))), M:tm-992, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-93029
in-theory        93029
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       209
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and 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-93029.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-992, 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-93030
in-theory        93030
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-6 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and 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-93030.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-992, 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-93031
in-theory        93031
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or 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     51
proof            (modus-ponens tm-992 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-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-93031.        ((A or ((B -> C) -> ((C -> D) -> ((B or 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-992, 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-93032
in-theory        93032
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or 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     49
proof            (modus-ponens tm-992 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       217
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-93032.        ((A or ((B -> C) -> ((C -> D) -> ((B or 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-992, 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-93033
in-theory        93033
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-4 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-93033.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-992, 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-93034
in-theory        93034
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-3 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-93034.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-992, 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-93035
in-theory        93035
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or 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     55
proof            (modus-ponens tm-992 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-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-93035.        ((A or ((B -> C) -> ((C -> D) -> ((B or 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-992, 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-93036
in-theory        93036
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-1 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-93036.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-992, 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-93037
in-theory        93037
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H)))
theorem-size     35
proof            (modus-ponens tm-992 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-93037.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H))), M:tm-992, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-93038
in-theory        93038
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or 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     53
proof            (modus-ponens tm-992 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-8 tm-9 tm-2)
proof-size       211
proof-steps      11
----------------------------------------------------------------
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-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-93038.        ((A or ((B -> C) -> ((C -> D) -> ((B or 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-992, 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-93039
in-theory        93039
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or 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     61
proof            (modus-ponens tm-992 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       229
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-93039.        ((A or ((B -> C) -> ((C -> D) -> ((B or 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-992, 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-93040
in-theory        93040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       185
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93040.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-992, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-93041
in-theory        93041
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-6 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
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-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-93041.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I)), M:tm-992, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-93042
in-theory        93042
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       191
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-93042.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E))), M:tm-992, 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-93043
in-theory        93043
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 tm-2)
proof-size       209
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93043.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H))), M:tm-992, 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-93044
in-theory        93044
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-992 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-8 tm-1 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
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-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-93044.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-992, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-93045
in-theory        93045
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93045.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> E))), M:tm-992, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-93046
in-theory        93046
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-992 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       159
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-93046.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-992, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-93047
in-theory        93047
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) and G) or (E and F)) -> E))
theorem-size     27
proof            (modus-ponens tm-992 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       131
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93047.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) and G) or (E and F)) -> E)), M:tm-992, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-93048
in-theory        93048
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) and G) or (E and F)) -> F))
theorem-size     27
proof            (modus-ponens tm-992 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       131
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93048.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E and F) and G) or (E and F)) -> F)), M:tm-992, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-93049
in-theory        93049
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (E and G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 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-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-3.            ((A and B) -> A), axiom
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-93049.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (E and G)))), M:tm-992, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-93050
in-theory        93050
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (E or G)))
theorem-size     25
proof            (modus-ponens tm-992 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       127
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93050.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (E or G))), M:tm-992, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-93051
in-theory        93051
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G or E)))
theorem-size     25
proof            (modus-ponens tm-992 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
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-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-3.            ((A and B) -> A), axiom
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-93051.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G or E))), M:tm-992, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-93052
in-theory        93052
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H))))
theorem-size     35
proof            (modus-ponens tm-992 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       155
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93052.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H)))), M:tm-992, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-93053
in-theory        93053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-992 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       149
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93053.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-992, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-93054
in-theory        93054
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((not (not E)) and F) or (not (not E))) -> E))
theorem-size     27
proof            (modus-ponens tm-992 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       131
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93054.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((not (not E)) and F) or (not (not E))) -> E)), M:tm-992, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-93055
in-theory        93055
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93055.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (H -> G)))), M:tm-992, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-93056
in-theory        93056
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> E)))
theorem-size     29
proof            (modus-ponens tm-992 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-93056.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> E))), M:tm-992, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-93057
in-theory        93057
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       211
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-93057.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-992, 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-93058
in-theory        93058
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 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       175
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93058.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-93059
in-theory        93059
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       187
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-93059.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-992, 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-93060
in-theory        93060
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93060.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G and H) -> G))), M:tm-992, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-93061
in-theory        93061
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       187
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-93061.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-992, 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-93062
in-theory        93062
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93062.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G and H) -> H))), M:tm-992, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-93063
in-theory        93063
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (H -> G)) and E)))
theorem-size     29
proof            (modus-ponens tm-992 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93063.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (H -> G)) and E))), M:tm-992, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-93064
in-theory        93064
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E)))
theorem-size     37
proof            (modus-ponens tm-992 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-93064.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E))), M:tm-992, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-93065
in-theory        93065
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (((G and H) -> G) and E)))
theorem-size     29
proof            (modus-ponens tm-992 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93065.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (((G and H) -> G) and E))), M:tm-992, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-93066
in-theory        93066
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (((G and H) -> H) and E)))
theorem-size     29
proof            (modus-ponens tm-992 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93066.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (((G and H) -> H) and E))), M:tm-992, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-93067
in-theory        93067
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E)))
theorem-size     31
proof            (modus-ponens tm-992 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       159
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93067.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E))), M:tm-992, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-93068
in-theory        93068
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-992 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       163
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-93068.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F)))), M:tm-992, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-93069
in-theory        93069
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93069.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (H -> (G and H))))), M:tm-992, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-93070
in-theory        93070
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (G or H)) and E)))
theorem-size     29
proof            (modus-ponens tm-992 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93070.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (G or H)) and E))), M:tm-992, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-93071
in-theory        93071
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93071.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (G or H)))), M:tm-992, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-93072
in-theory        93072
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (H or G)) and E)))
theorem-size     29
proof            (modus-ponens tm-992 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93072.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> ((G -> (H or G)) and E))), M:tm-992, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-93073
in-theory        93073
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93073.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or E) -> (G -> (H or G)))), M:tm-992, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-93074
in-theory        93074
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-992 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       177
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-93074.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-992, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-93075
in-theory        93075
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or 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     53
proof            (modus-ponens tm-992 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       229
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-93075.        ((A or ((B -> C) -> ((C -> D) -> ((B or 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-992, 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-93076
in-theory        93076
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-992 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       167
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93076.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F))), M:tm-992, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-93077
in-theory        93077
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93077.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G)))), M:tm-992, 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-93078
in-theory        93078
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((F and G) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-992 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       161
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-93078.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((F and G) or F) -> E))), M:tm-992, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-93079
in-theory        93079
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 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       159
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C 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-93079.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-992, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-93080
in-theory        93080
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-93080.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-992, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-93081
in-theory        93081
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-992 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-93081.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F)))), M:tm-992, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-93082
in-theory        93082
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-992 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       167
proof-steps      13
----------------------------------------------------------------
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-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-93082.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-992, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-93083
in-theory        93083
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-93083.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-992, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-93084
in-theory        93084
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 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-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-3.            ((A and B) -> 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-93084.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-992, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-93085
in-theory        93085
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-93085.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-992, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-93086
in-theory        93086
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-1.            (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-93086.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-992, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-93087
in-theory        93087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-992 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
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-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-93087.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F)))), M:tm-992, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-93088
in-theory        93088
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       163
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-93088.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H))), M:tm-992, 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-93089
in-theory        93089
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-992 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       135
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93089.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> (((F and H) or F) -> G)))), M:tm-992, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-93090
in-theory        93090
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (((E and G) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-992 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-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-93090.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (((E and G) or E) -> F)) or H)), M:tm-992, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-93091
in-theory        93091
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-992 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       141
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-93091.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E))), M:tm-992, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-93092
in-theory        93092
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-992 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-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-93092.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F))), M:tm-992, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-93093
in-theory        93093
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-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-93093.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> (((F and H) or F) -> G)))), M:tm-992, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-93094
in-theory        93094
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-992 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-93094.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> F))), M:tm-992, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-93095
in-theory        93095
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-992 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       159
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-93095.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H)))), M:tm-992, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-93096
in-theory        93096
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F and G)) or (F and G)) -> F))
theorem-size     27
proof            (modus-ponens tm-992 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       131
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93096.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F and G)) or (F and G)) -> F)), M:tm-992, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-93097
in-theory        93097
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F and G)) or (F and G)) -> G))
theorem-size     27
proof            (modus-ponens tm-992 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       131
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93097.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F and G)) or (F and G)) -> G)), M:tm-992, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-93098
in-theory        93098
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 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-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-4.            ((A and B) -> B), axiom
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-93098.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (F and G)))), M:tm-992, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-93099
in-theory        93099
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-992 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       127
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93099.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (F or G))), M:tm-992, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-93100
in-theory        93100
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-992 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
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-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-4.            ((A and B) -> B), axiom
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-93100.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G or F))), M:tm-992, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-93101
in-theory        93101
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-992 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       155
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93101.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H)))), M:tm-992, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-93102
in-theory        93102
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-992 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       149
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93102.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F)))), M:tm-992, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-93103
in-theory        93103
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (not (not F))) or (not (not F))) -> F))
theorem-size     27
proof            (modus-ponens tm-992 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       131
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93103.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (not (not F))) or (not (not F))) -> F)), M:tm-992, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-93104
in-theory        93104
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 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       143
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-93104.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (H -> G)))), M:tm-992, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-93105
in-theory        93105
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> F)))
theorem-size     29
proof            (modus-ponens tm-992 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-93105.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> F))), M:tm-992, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-93106
in-theory        93106
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       211
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-93106.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H)))), M:tm-992, 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-93107
in-theory        93107
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 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       175
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-93107.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-93108
in-theory        93108
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       187
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-93108.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G))), M:tm-992, 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-93109
in-theory        93109
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 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       143
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-93109.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G and H) -> G))), M:tm-992, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-93110
in-theory        93110
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> 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-992 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       187
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-93110.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H))), M:tm-992, 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-93111
in-theory        93111
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 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       143
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-93111.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G and H) -> H))), M:tm-992, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-93112
in-theory        93112
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (H -> G)) and F)))
theorem-size     29
proof            (modus-ponens tm-992 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       151
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-93112.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (H -> G)) and F))), M:tm-992, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-93113
in-theory        93113
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))
theorem-size     37
proof            (modus-ponens tm-992 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-93113.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))), M:tm-992, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-93114
in-theory        93114
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (((G and H) -> G) and F)))
theorem-size     29
proof            (modus-ponens tm-992 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       151
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93114.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (((G and H) -> G) and F))), M:tm-992, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-93115
in-theory        93115
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (((G and H) -> H) and F)))
theorem-size     29
proof            (modus-ponens tm-992 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       151
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93115.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (((G and H) -> H) and F))), M:tm-992, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-93116
in-theory        93116
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F)))
theorem-size     31
proof            (modus-ponens tm-992 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       159
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93116.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F))), M:tm-992, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-93117
in-theory        93117
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-992 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       163
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-93117.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G)))), M:tm-992, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-93118
in-theory        93118
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), 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-93118.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (H -> (G and H))))), M:tm-992, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-93119
in-theory        93119
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (G or H)) and F)))
theorem-size     29
proof            (modus-ponens tm-992 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-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-93119.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (G or H)) and F))), M:tm-992, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-93120
in-theory        93120
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-93120.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (G or H)))), M:tm-992, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-93121
in-theory        93121
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (H or G)) and F)))
theorem-size     29
proof            (modus-ponens tm-992 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-93121.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> ((G -> (H or G)) and F))), M:tm-992, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-93122
in-theory        93122
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-93122.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) or F) -> (G -> (H or G)))), M:tm-992, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-93123
in-theory        93123
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-992 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-93123.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H))), M:tm-992, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-93124
in-theory        93124
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))
theorem-size     53
proof            (modus-ponens tm-992 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       229
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-93124.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))), M:tm-992, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-93125
in-theory        93125
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-992 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93125.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G))), M:tm-992, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-93126
in-theory        93126
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-992 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93126.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G))), M:tm-992, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-93127
in-theory        93127
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-992 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93127.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F))), M:tm-992, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-93128
in-theory        93128
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-992 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93128.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G)))), M:tm-992, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-93129
in-theory        93129
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((G and F) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-992 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-93129.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> E)) -> (((G and F) or F) -> E))), M:tm-992, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-93130
in-theory        93130
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 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-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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (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-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-93130.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-992, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-93131
in-theory        93131
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or 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-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-93131.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-992, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-93132
in-theory        93132
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-992 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-93132.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F)))), M:tm-992, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-93133
in-theory        93133
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-992 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-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-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-93133.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-992, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-93134
in-theory        93134
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-93134.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-992, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-93135
in-theory        93135
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-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-93135.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-992, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-93136
in-theory        93136
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-992 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-93136.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-992, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-93137
in-theory        93137
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-992 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-1.            (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-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-93137.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-992, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-93138
in-theory        93138
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-992 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
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-93138.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F)))), M:tm-992, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-93139
in-theory        93139
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-992 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93139.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H))), M:tm-992, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-93140
in-theory        93140
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93140.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((F -> G) -> (((H and F) or F) -> G)))), M:tm-992, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-93141
in-theory        93141
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (((G and E) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-992 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
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-93141.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> (((G and E) or E) -> F)) or H)), M:tm-992, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-93142
in-theory        93142
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-992 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93142.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E))), M:tm-992, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-93143
in-theory        93143
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-992 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-93143.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F))), M:tm-992, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-93144
in-theory        93144
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-93144.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F -> G) -> (((H and F) or F) -> G)))), M:tm-992, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-93145
in-theory        93145
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 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-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-48.           (((A -> (B and 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-93145.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F))))), M:tm-992, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-93146
in-theory        93146
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G))))
theorem-size     33
proof            (modus-ponens tm-992 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93146.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G)))), M:tm-992, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-93147
in-theory        93147
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G)))
theorem-size     31
proof            (modus-ponens tm-992 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93147.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G))), M:tm-992, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-93148
in-theory        93148
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G or (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-93148.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G or (F -> (E and F))))), M:tm-992, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-93149
in-theory        93149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-992 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93149.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G)))), M:tm-992, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-93150
in-theory        93150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-992 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93150.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F)))), M:tm-992, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-93151
in-theory        93151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93151.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> G)))), M:tm-992, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-93152
in-theory        93152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (F -> F)))
theorem-size     27
proof            (modus-ponens tm-992 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-48.           (((A -> (B and 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-93152.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (F -> F))), M:tm-992, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-93153
in-theory        93153
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-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-48.           (((A -> (B and 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-93153.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-93154
in-theory        93154
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-992 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93154.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> G))), M:tm-992, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-93155
in-theory        93155
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-992 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93155.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G and H) -> H))), M:tm-992, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-93156
in-theory        93156
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93156.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F))))), M:tm-992, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-93157
in-theory        93157
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-992 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93157.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F))))), M:tm-992, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-93158
in-theory        93158
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93158.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F))))), M:tm-992, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-93159
in-theory        93159
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93159.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F))))), M:tm-992, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-93160
in-theory        93160
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93160.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F))))), M:tm-992, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-93161
in-theory        93161
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (F -> (F and (E and F)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 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-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-48.           (((A -> (B and 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-93161.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (F -> (F and (E and F))))), M:tm-992, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-93162
in-theory        93162
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-992 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93162.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H))))), M:tm-992, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-93163
in-theory        93163
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93163.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F))))), M:tm-992, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-93164
in-theory        93164
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-992 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93164.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (G or H)))), M:tm-992, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-93165
in-theory        93165
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-93165.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F))))), M:tm-992, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-93166
in-theory        93166
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-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-93166.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (G -> (H or G)))), M:tm-992, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-93167
in-theory        93167
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G)))))
theorem-size     39
proof            (modus-ponens tm-992 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 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-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-48.           (((A -> (B and 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-93167.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G))))), M:tm-992, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-93168
in-theory        93168
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H))))))
theorem-size     59
proof            (modus-ponens tm-992 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93168.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H)))))), M:tm-992, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-93169
in-theory        93169
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-992 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93169.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F)))), M:tm-992, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-93170
in-theory        93170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-992 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93170.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F)))), M:tm-992, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-93171
in-theory        93171
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F))))))
theorem-size     47
proof            (modus-ponens tm-992 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93171.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F)))))), M:tm-992, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-93172
in-theory        93172
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H)))
theorem-size     43
proof            (modus-ponens tm-992 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-93172.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H))), M:tm-992, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-93173
in-theory        93173
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-992 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-93173.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-992, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-93174
in-theory        93174
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-992 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       221
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-93174.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G)))), M:tm-992, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-93175
in-theory        93175
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E)))
theorem-size     35
proof            (modus-ponens tm-992 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-93175.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E))), M:tm-992, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-93176
in-theory        93176
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-992 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48.           (((A -> (B and 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-93176.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-992, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-93177
in-theory        93177
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-992 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-93177.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-992, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-93178
in-theory        93178
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G))))
theorem-size     41
proof            (modus-ponens tm-992 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-93178.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G)))), M:tm-992, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-93179
in-theory        93179
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-992 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (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-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-93179.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-992, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-93180
in-theory        93180
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-992 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93180.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-992, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-93181
in-theory        93181
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-992 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48.           (((A -> (B and 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-93181.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-992, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-93182
in-theory        93182
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-992 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-93182.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-992, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-93183
in-theory        93183
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-992 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48.           (((A -> (B and 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-93183.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-992, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-93184
in-theory        93184
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-992 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-93184.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G))), M:tm-992, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-93185
in-theory        93185
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G))))
theorem-size     43
proof            (modus-ponens tm-992 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       177
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-93185.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G)))), M:tm-992, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-93186
in-theory        93186
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-992 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93186.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H))), M:tm-992, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-93187
in-theory        93187
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-992 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93187.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-992, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-93188
in-theory        93188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-992 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or 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-93188.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H)), M:tm-992, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-93189
in-theory        93189
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E)))
theorem-size     37
proof            (modus-ponens tm-992 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93189.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E))), M:tm-992, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-93190
in-theory        93190
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G)))
theorem-size     41
proof            (modus-ponens tm-992 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-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-93190.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G))), M:tm-992, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-93191
in-theory        93191
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-992 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-93191.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-992, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-93192
in-theory        93192
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93192.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (E or F)))), M:tm-992, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-93193
in-theory        93193
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> ((E or F) and G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-93193.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> ((E or F) and G)))), M:tm-992, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-93194
in-theory        93194
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((E or F) or G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93194.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((E or F) or G))), M:tm-992, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-93195
in-theory        93195
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G or (E or F))))
theorem-size     27
proof            (modus-ponens tm-992 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-93195.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G or (E or F)))), M:tm-992, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-93196
in-theory        93196
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93196.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (H -> G)))), M:tm-992, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-93197
in-theory        93197
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-1 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93197.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-93198
in-theory        93198
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93198.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G and H) -> G))), M:tm-992, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-93199
in-theory        93199
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93199.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G and H) -> H))), M:tm-992, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-93200
in-theory        93200
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-992 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-93200.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F)))), M:tm-992, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-93201
in-theory        93201
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-992 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-20.           (A -> (((B -> (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-93201.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F)))), M:tm-992, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-93202
in-theory        93202
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (((G and H) -> G) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-992 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-93202.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (((G and H) -> G) and (E or F)))), M:tm-992, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-93203
in-theory        93203
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (((G and H) -> H) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-992 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-93203.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (((G and H) -> H) and (E or F)))), M:tm-992, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-93204
in-theory        93204
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-992 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-93204.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F)))), M:tm-992, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-93205
in-theory        93205
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-93205.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (H -> (G and H))))), M:tm-992, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-93206
in-theory        93206
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-992 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-93206.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F)))), M:tm-992, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-93207
in-theory        93207
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93207.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (G or H)))), M:tm-992, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-93208
in-theory        93208
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-992 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (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-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-93208.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F)))), M:tm-992, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-93209
in-theory        93209
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-93209.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (G -> (H or G)))), M:tm-992, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-93210
in-theory        93210
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-992 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93210.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G))))), M:tm-992, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-93211
in-theory        93211
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-992 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93211.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H))), M:tm-992, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-93212
in-theory        93212
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-992 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93212.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-992, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-93213
in-theory        93213
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-992 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-93213.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E))), M:tm-992, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-93214
in-theory        93214
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-93214.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-992, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93215
in-theory        93215
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-49.           (((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-93215.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-992, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93216
in-theory        93216
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-992 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-93216.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G)))), M:tm-992, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-93217
in-theory        93217
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-93217.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-992, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93218
in-theory        93218
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93218.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-992, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93219
in-theory        93219
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-93219.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-992, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93220
in-theory        93220
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-992 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-93220.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-992, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-93221
in-theory        93221
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-93221.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-992, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93222
in-theory        93222
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> ((E or F) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-93222.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> ((E or F) -> G))), M:tm-992, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-93223
in-theory        93223
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-992 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-93223.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-992, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-93224
in-theory        93224
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-992 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       169
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93224.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H))), M:tm-992, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-93225
in-theory        93225
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-992 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93225.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-992, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-93226
in-theory        93226
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-992 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93226.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H)), M:tm-992, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-93227
in-theory        93227
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-992 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-93227.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E))), M:tm-992, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-93228
in-theory        93228
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-992 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-93228.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G))), M:tm-992, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-93229
in-theory        93229
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-992 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-93229.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-992, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-93230
in-theory        93230
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-93230.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (F or E)))), M:tm-992, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-93231
in-theory        93231
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> ((F or E) and G))))
theorem-size     29
proof            (modus-ponens tm-992 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
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-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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-93231.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> ((F or E) and G)))), M:tm-992, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-93232
in-theory        93232
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((F or E) or G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-50.           (((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-93232.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((F or E) or G))), M:tm-992, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-93233
in-theory        93233
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G or (F or E))))
theorem-size     27
proof            (modus-ponens tm-992 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-50.           (((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-93233.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G or (F or E)))), M:tm-992, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-93234
in-theory        93234
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-93234.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (H -> G)))), M:tm-992, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-93235
in-theory        93235
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-992 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-50.           (((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-93235.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-992, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-93236
in-theory        93236
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-992 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-93236.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G and H) -> G))), M:tm-992, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-93237
in-theory        93237
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-992 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-93237.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G and H) -> H))), M:tm-992, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-93238
in-theory        93238
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-992 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-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-93238.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E)))), M:tm-992, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-93239
in-theory        93239
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-992 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-50.           (((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-20.           (A -> (((B -> (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-93239.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E)))), M:tm-992, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-93240
in-theory        93240
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (((G and H) -> G) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-992 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-50.           (((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-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-93240.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (((G and H) -> G) and (F or E)))), M:tm-992, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-93241
in-theory        93241
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (((G and H) -> H) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-992 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-50.           (((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-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-93241.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (((G and H) -> H) and (F or E)))), M:tm-992, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-93242
in-theory        93242
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-992 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-93242.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E)))), M:tm-992, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-93243
in-theory        93243
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-992 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-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-93243.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (H -> (G and H))))), M:tm-992, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-93244
in-theory        93244
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-992 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-50.           (((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-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-93244.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E)))), M:tm-992, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-93245
in-theory        93245
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-992 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-93245.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (G or H)))), M:tm-992, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-93246
in-theory        93246
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-992 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-93246.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E)))), M:tm-992, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-93247
in-theory        93247
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-992 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 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-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-50.           (((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-93247.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (G -> (H or G)))), M:tm-992, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-93248
in-theory        93248
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-992 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am 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-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-93248.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G))))), M:tm-992, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-93249
in-theory        93249
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-992 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-93249.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H))), M:tm-992, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-93250
in-theory        93250
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-992 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-50.           (((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-93250.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-992, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-93251
in-theory        93251
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-992 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-50.           (((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-93251.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E))), M:tm-992, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-93252
in-theory        93252
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-50.           (((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-93252.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-992, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93253
in-theory        93253
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am 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-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-93253.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-992, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93254
in-theory        93254
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-992 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am 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-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-93254.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G)))), M:tm-992, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-93255
in-theory        93255
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am 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-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-93255.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-992, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93256
in-theory        93256
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93256.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-992, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93257
in-theory        93257
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-50.           (((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-93257.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-992, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93258
in-theory        93258
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-992 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-50.           (((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-93258.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-992, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-93259
in-theory        93259
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-50.           (((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-93259.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-992, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-93260
in-theory        93260
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-992 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-50.           (((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-93260.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-992, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-93261
in-theory        93261
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-992 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
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-50.           (((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-93261.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H))), M:tm-992, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-93262
in-theory        93262
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-992 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-50.           (((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-93262.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-992, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-93263
in-theory        93263
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-992 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-50.           (((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-93263.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H)), M:tm-992, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-93264
in-theory        93264
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-992 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-50.           (((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-93264.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E))), M:tm-992, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-93265
in-theory        93265
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-992 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-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-93265.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G))), M:tm-992, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-93266
in-theory        93266
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-992 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), axiom
tm-50.           (((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-93266.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-992, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-93267
in-theory        93267
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-992 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93267.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93268
in-theory        93268
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G))))
theorem-size     43
proof            (modus-ponens tm-992 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       195
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93268.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G)))), M:tm-992, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-93269
in-theory        93269
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H))))
theorem-size     43
proof            (modus-ponens tm-992 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-93269.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H)))), M:tm-992, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-93270
in-theory        93270
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H)))
theorem-size     41
proof            (modus-ponens tm-992 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       183
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93270.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H))), M:tm-992, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-93271
in-theory        93271
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-992 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-93271.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93272
in-theory        93272
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H))))
theorem-size     49
proof            (modus-ponens tm-992 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93272.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H)))), M:tm-992, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-93273
in-theory        93273
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G)))))
theorem-size     45
proof            (modus-ponens tm-992 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       197
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93273.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G))))), M:tm-992, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-93274
in-theory        93274
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-992 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93274.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H)))), M:tm-992, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-93275
in-theory        93275
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G))))
theorem-size     37
proof            (modus-ponens tm-992 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93275.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G)))), M:tm-992, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-93276
in-theory        93276
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-992 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93276.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-992, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-93277
in-theory        93277
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-992 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93277.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H))), M:tm-992, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-93278
in-theory        93278
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-992 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93278.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I))), M:tm-992, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-93279
in-theory        93279
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-992 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-93279.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93280
in-theory        93280
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-992 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-20.           (A -> (((B -> (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-93280.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93281
in-theory        93281
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-992 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-93281.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93282
in-theory        93282
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-992 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-93282.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93283
in-theory        93283
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-992 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-93283.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93284
in-theory        93284
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G)))))
theorem-size     43
proof            (modus-ponens tm-992 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-93284.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G))))), M:tm-992, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93285
in-theory        93285
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-93285.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I))))), M:tm-992, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-93286
in-theory        93286
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-992 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-93286.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93287
in-theory        93287
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93287.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I)))), M:tm-992, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-93288
in-theory        93288
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-992 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-93288.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-93289
in-theory        93289
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-992 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-93289.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H)))), M:tm-992, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-93290
in-theory        93290
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-992 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93290.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G)))), M:tm-992, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-93291
in-theory        93291
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H)))))
theorem-size     63
proof            (modus-ponens tm-992 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       273
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93291.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H))))), M:tm-992, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-93292
in-theory        93292
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-992 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93292.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G)))), M:tm-992, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-93293
in-theory        93293
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-992 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93293.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G)))), M:tm-992, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-93294
in-theory        93294
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F)))))
theorem-size     49
proof            (modus-ponens tm-992 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-93294.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F))))), M:tm-992, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-93295
in-theory        93295
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G)))))
theorem-size     69
proof            (modus-ponens tm-992 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93295.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G))))), M:tm-992, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-93296
in-theory        93296
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G))))))
theorem-size     65
proof            (modus-ponens tm-992 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-93296.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G)))))), M:tm-992, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-93297
in-theory        93297
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))
theorem-size     57
proof            (modus-ponens tm-992 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-93297.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))), M:tm-992, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-93298
in-theory        93298
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     57
proof            (modus-ponens tm-992 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-93298.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-992, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-93299
in-theory        93299
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H))))
theorem-size     63
proof            (modus-ponens tm-992 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       273
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-93299.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H)))), M:tm-992, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-93300
in-theory        93300
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E)))
theorem-size     45
proof            (modus-ponens tm-992 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-93300.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E))), M:tm-992, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-93301
in-theory        93301
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-992 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-93301.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-992, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-93302
in-theory        93302
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-992 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-93302.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-992, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-93303
in-theory        93303
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     55
proof            (modus-ponens tm-992 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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 tm-2)
proof-size       235
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-93303.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-992, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-93304
in-theory        93304
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-992 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-93304.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-992, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-93305
in-theory        93305
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-992 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93305.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-992, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-93306
in-theory        93306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-992 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-93306.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-992, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-93307
in-theory        93307
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-992 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       247
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-93307.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-992, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-93308
in-theory        93308
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-992 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-93308.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-992, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-93309
in-theory        93309
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H)))
theorem-size     39
proof            (modus-ponens tm-992 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-93309.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H))), M:tm-992, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-93310
in-theory        93310
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H))))
theorem-size     57
proof            (modus-ponens tm-992 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       221
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-93310.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H)))), M:tm-992, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-93311
in-theory        93311
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I)))
theorem-size     63
proof            (modus-ponens tm-992 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       235
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93311.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I))), M:tm-992, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-93312
in-theory        93312
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-992 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93312.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-992, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-93313
in-theory        93313
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) or I))
theorem-size     45
proof            (modus-ponens tm-992 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       191
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-93313.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) or I)), M:tm-992, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-93314
in-theory        93314
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E)))
theorem-size     47
proof            (modus-ponens tm-992 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-93314.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E))), M:tm-992, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-93315
in-theory        93315
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> ((G -> E) or ((E -> F) -> ((G or E) -> F)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H)))
theorem-size     55
proof            (modus-ponens tm-992 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       219
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-93315.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((((E -> F) -> ((G or E) -> F)) -> H) -> ((G -> E) or ((E -> F) -> ((G or E) -> F)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H))), M:tm-992, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-93316
in-theory        93316
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-992 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       191
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-93316.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-992, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-93317
in-theory        93317
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-93317.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-992, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-93318
in-theory        93318
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93318.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-992, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-93319
in-theory        93319
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-992 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
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-93319.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-992, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-93320
in-theory        93320
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-93320.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-992, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-93321
in-theory        93321
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-93321.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-992, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-93322
in-theory        93322
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-992 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-93322.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-992, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-93323
in-theory        93323
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-992 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-93323.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-992, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-93324
in-theory        93324
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-992 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-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-93324.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-992, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93325
in-theory        93325
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-992 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
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-93325.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I)), M:tm-992, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-93326
in-theory        93326
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-992 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-93326.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E))), M:tm-992, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93327
in-theory        93327
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 ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E)))
theorem-size     47
proof            (modus-ponens tm-980 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-93327.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E))), M:tm-980, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93328
in-theory        93328
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     59
proof            (modus-ponens tm-977 tm-992 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       231
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-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-5.            (A -> (B -> (A and B))), axiom
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-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-93328.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-992, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-93329
in-theory        93329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-975 tm-992 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
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-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-93329.        (((A -> B) -> ((C or A) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, m:tm-992, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-93330
in-theory        93330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-969 tm-992 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-93330.        ((((A -> B) -> ((C or A) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, m:tm-992, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-93331
in-theory        93331
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-930 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-93331.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-930, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93332
in-theory        93332
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-927 tm-992 ((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 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-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-5.            (A -> (B -> (A and B))), 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-93332.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B or (A or B)) -> C))), M:tm-927, m:tm-992, u:((Am (-> (or A (or B A)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-93333
in-theory        93333
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B))) and ((B or (A or B)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-920 tm-992 ((Am (or A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-93333.        (((A or B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B))) and ((B or (A or B)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B)))), M:tm-920, m:tm-992, u:((Am (or A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (or A B))))
================================================================
tm-name          tm-93334
in-theory        93334
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-893 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-93334.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-893, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93335
in-theory        93335
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-890 tm-992 ((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
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-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-93335.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A or (A or B)) -> C))), M:tm-890, m:tm-992, u:((Am (-> (or A (or A B)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-93336
in-theory        93336
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-888 tm-992 ((Am (or A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (or A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and B))), axiom
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-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-93336.        ((A or B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B))), M:tm-888, m:tm-992, u:((Am (or A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (or A B))))
================================================================
tm-name          tm-93337
in-theory        93337
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B))) and ((A or (A or B)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-992 ((Am (or A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-93337.        (((A or B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B))) and ((A or (A or B)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A or B)))), M:tm-882, m:tm-992, u:((Am (or A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (or A B))))
================================================================
tm-name          tm-93338
in-theory        93338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     37
proof            (modus-ponens tm-855 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-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-93338.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-855, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93339
in-theory        93339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B or (A -> (B and A))) -> C)))
theorem-size     43
proof            (modus-ponens tm-852 tm-992 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-48.           (((A -> (B and 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-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-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-93339.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-992, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-93340
in-theory        93340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-850 tm-992 ((Am (-> A (and B A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-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-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-93340.        ((A -> (B and A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> (B and A)))), M:tm-850, m:tm-992, u:((Am (-> A (and B A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (and B A)))))
================================================================
tm-name          tm-93341
in-theory        93341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> (B and A)))))
theorem-size     57
proof            (modus-ponens tm-844 tm-992 ((Am (-> A (and B A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-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-93341.        (((A -> (B and A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> (B and A))))), M:tm-844, m:tm-992, u:((Am (-> A (and B A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (and B A)))))
================================================================
tm-name          tm-93342
in-theory        93342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     31
proof            (modus-ponens tm-808 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-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-93342.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-808, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93343
in-theory        93343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((C and A) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-805 tm-992 ((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
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-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-5.            (A -> (B -> (A and B))), axiom
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-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-93343.        (((A -> B) or (((C and A) or A) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((C and A) or A) -> B))), M:tm-805, m:tm-992, u:((Am (-> (or (and A B) B) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-93344
in-theory        93344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((F and A) or A) -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))
theorem-size     43
proof            (modus-ponens tm-798 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-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-93344.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((F and A) or A) -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))), M:tm-798, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93345
in-theory        93345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     31
proof            (modus-ponens tm-757 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-93345.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-757, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93346
in-theory        93346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((A and C) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-754 tm-992 ((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
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-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-93346.        (((A -> B) or (((A and C) or A) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((A and C) or A) -> B))), M:tm-754, m:tm-992, u:((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-93347
in-theory        93347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((A and F) or A) -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))
theorem-size     43
proof            (modus-ponens tm-747 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93347.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((A and F) or A) -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))), M:tm-747, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93348
in-theory        93348
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E)))
theorem-size     45
proof            (modus-ponens tm-708 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93348.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E))), M:tm-708, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93349
in-theory        93349
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-705 tm-992 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93349.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-992, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-93350
in-theory        93350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-703 tm-992 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93350.        (((A -> B) -> (A -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-992, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-93351
in-theory        93351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-697 tm-992 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93351.        ((((A -> B) -> (A -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-992, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-93352
in-theory        93352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-665 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-93352.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-665, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93353
in-theory        93353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B or (A -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-662 tm-992 ((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((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-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-93353.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-992, u:((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-93354
in-theory        93354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> B)))
theorem-size     23
proof            (modus-ponens tm-660 tm-992 ((Am (-> A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93354.        ((A -> B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> B))), M:tm-660, m:tm-992, u:((Am (-> A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A B))))
================================================================
tm-name          tm-93355
in-theory        93355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> B))) and ((B or (A -> B)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> B))))
theorem-size     49
proof            (modus-ponens tm-654 tm-992 ((Am (-> A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93355.        (((A -> B) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> B))) and ((B or (A -> B)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> B)))), M:tm-654, m:tm-992, u:((Am (-> A B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A B))))
================================================================
tm-name          tm-93356
in-theory        93356
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A)))
theorem-size     21
proof            (modus-ponens tm-623 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 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-5.            (A -> (B -> (A and B))), 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-93356.        (A -> (B or ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A))), M:tm-623, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93357
in-theory        93357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-622 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-93357.        ((A -> (B -> (C or B))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-622, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93358
in-theory        93358
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (B -> (C or B))))
theorem-size     29
proof            (modus-ponens tm-619 tm-992 ((Am (-> A (or B A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
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-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-93358.        ((A or (B -> (C or B))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (B -> (C or B)))), M:tm-619, m:tm-992, u:((Am (-> A (or B A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (or B A)))))
================================================================
tm-name          tm-93359
in-theory        93359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
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-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-93359.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (G or F))), M:tm-609, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93360
in-theory        93360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-605 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-93360.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-605, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93361
in-theory        93361
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> (C or B)) and A)))
theorem-size     33
proof            (modus-ponens tm-602 tm-992 ((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-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-93361.        ((A or ((B -> (C or B)) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-992, u:((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-93362
in-theory        93362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (G or F)) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-595 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
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-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-93362.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (G or F)) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-595, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93363
in-theory        93363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-550 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93363.        (((A -> (B or A)) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-550, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93364
in-theory        93364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-540 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-93364.        ((A or (B -> (C or B))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-540, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93365
in-theory        93365
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-530 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93365.        ((A or (B -> (B or C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-530, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93366
in-theory        93366
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-520 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-93366.        ((A or (B -> (C -> (B and C)))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-520, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93367
in-theory        93367
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-510 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-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-93367.        ((A or ((B and C) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-510, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93368
in-theory        93368
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-500 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-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-93368.        ((A or ((B and C) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-500, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93369
in-theory        93369
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-490 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-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-93369.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E))), M:tm-490, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93370
in-theory        93370
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-480 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-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-93370.        ((A or (B -> (C -> B))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-480, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93371
in-theory        93371
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A) or F))
theorem-size     21
proof            (modus-ponens tm-470 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-93371.        (A -> (((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A) or F)), M:tm-470, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93372
in-theory        93372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-469 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-93372.        ((A -> (B -> (B or C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-469, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93373
in-theory        93373
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (B -> (B or C))))
theorem-size     29
proof            (modus-ponens tm-466 tm-992 ((Am (-> A (or A B))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
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-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-93373.        ((A or (B -> (B or C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (B -> (B or C)))), M:tm-466, m:tm-992, u:((Am (-> A (or A B))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (or A B)))))
================================================================
tm-name          tm-93374
in-theory        93374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-93374.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (F or G))), M:tm-456, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93375
in-theory        93375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-453 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93375.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-453, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93376
in-theory        93376
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> (B or C)) and A)))
theorem-size     33
proof            (modus-ponens tm-450 tm-992 ((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
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-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-93376.        ((A or ((B -> (B or C)) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-992, u:((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-93377
in-theory        93377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (F or G)) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-443 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-93377.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (F or G)) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-443, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93378
in-theory        93378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-409 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93378.        (((A -> (A or B)) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-409, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93379
in-theory        93379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-400 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93379.        (((A -> (B -> (A and B))) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-400, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93380
in-theory        93380
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-391 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-93380.        ((((A and B) -> B) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-391, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93381
in-theory        93381
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-382 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-93381.        ((((A and B) -> A) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-382, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93382
in-theory        93382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-373 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-93382.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E))), M:tm-373, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93383
in-theory        93383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-364 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-93383.        (((A -> (B -> A)) or C) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-364, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93384
in-theory        93384
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A) and B)))
theorem-size     23
proof            (modus-ponens tm-355 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7 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-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-93384.        (A -> (B -> (((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A) and B))), M:tm-355, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93385
in-theory        93385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-354 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-93385.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-354, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93386
in-theory        93386
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (B -> (C -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-351 tm-992 ((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
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-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-93386.        ((A or (B -> (C -> (B and C)))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-992, u:((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-93387
in-theory        93387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-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-93387.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93388
in-theory        93388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C)))
theorem-size     29
proof            (modus-ponens tm-338 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
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-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-93388.        (((A -> B) -> (A -> (A and B))) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C))), M:tm-338, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93389
in-theory        93389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-335 tm-992 ((Am (-> A (and A B))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93389.        (((A -> B) or (A -> (A and B))) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> (A and B)))), M:tm-335, m:tm-992, u:((Am (-> A (and A B))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (and A B)))))
================================================================
tm-name          tm-93390
in-theory        93390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (A -> (A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     41
proof            (modus-ponens tm-328 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-93390.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (A -> (A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-328, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93391
in-theory        93391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (G -> (F and G))) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     47
proof            (modus-ponens tm-327 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-93391.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (G -> (F and G))) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-327, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93392
in-theory        93392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((F and G) -> G) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-326 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-93392.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((F and G) -> G) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-326, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93393
in-theory        93393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((F and G) -> F) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-325 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-93393.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((F and G) -> F) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-325, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93394
in-theory        93394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     53
proof            (modus-ponens tm-324 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-93394.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-324, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93395
in-theory        93395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (G -> F)) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-323 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-93395.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (G -> F)) and (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-323, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93396
in-theory        93396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-93396.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F and G) -> G)), M:tm-322, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93397
in-theory        93397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93397.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F and G) -> F)), M:tm-320, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93398
in-theory        93398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-93398.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93399
in-theory        93399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-93399.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (A -> A)), M:tm-316, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93400
in-theory        93400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-93400.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (G -> F))), M:tm-315, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93401
in-theory        93401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((A -> (not ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-93401.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((A -> (not ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))) -> (not A))), M:tm-313, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93402
in-theory        93402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A) -> F) -> ((A or ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) -> F)))
theorem-size     61
proof            (modus-ponens tm-312 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93402.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A) -> F) -> ((A or ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) -> F))), M:tm-312, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93403
in-theory        93403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F or (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     41
proof            (modus-ponens tm-311 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
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-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-93403.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F or (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-311, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93404
in-theory        93404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-93404.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) or F)), M:tm-310, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93405
in-theory        93405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-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-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-93405.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and F))), M:tm-309, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93406
in-theory        93406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))))
theorem-size     41
proof            (modus-ponens tm-305 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
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-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-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-93406.        ((A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)) and (F -> (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)))), M:tm-305, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93407
in-theory        93407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     31
proof            (modus-ponens tm-303 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
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-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-93407.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-303, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93408
in-theory        93408
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> (C -> (B and C))) and A)))
theorem-size     37
proof            (modus-ponens tm-300 tm-992 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
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-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-93408.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-992, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-93409
in-theory        93409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-270 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
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-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-93409.        ((A -> (((B and C) -> C) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-270, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93410
in-theory        93410
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((B and C) -> C) and A)))
theorem-size     33
proof            (modus-ponens tm-267 tm-992 ((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7)
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-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-93410.        ((A or (((B and C) -> C) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((B and C) -> C) and A))), M:tm-267, m:tm-992, u:((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-93411
in-theory        93411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-239 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
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-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-93411.        ((A -> (((B and C) -> B) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-239, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93412
in-theory        93412
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((B and C) -> B) and A)))
theorem-size     33
proof            (modus-ponens tm-236 tm-992 ((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7)
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-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-93412.        ((A or (((B and C) -> B) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((B and C) -> B) and A))), M:tm-236, m:tm-992, u:((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-93413
in-theory        93413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E)))
theorem-size     37
proof            (modus-ponens tm-210 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-93413.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E))), M:tm-210, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93414
in-theory        93414
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     49
proof            (modus-ponens tm-207 tm-992 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93414.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-992, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-93415
in-theory        93415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-183 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-93415.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-183, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93416
in-theory        93416
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> (C -> B)) and A)))
theorem-size     33
proof            (modus-ponens tm-180 tm-992 ((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
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-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-93416.        ((A or ((B -> (C -> B)) and A)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-992, u:((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-93417
in-theory        93417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-157 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
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-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-93417.        ((A -> ((B and C) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-157, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93418
in-theory        93418
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B and C) -> C)))
theorem-size     29
proof            (modus-ponens tm-154 tm-992 ((Am (-> (and A B) B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
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-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-93418.        ((A or ((B and C) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B and C) -> C))), M:tm-154, m:tm-992, u:((Am (-> (and A B) B)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (and A B) B))))
================================================================
tm-name          tm-93419
in-theory        93419
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     35
proof            (modus-ponens tm-147 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-93419.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-147, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93420
in-theory        93420
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A and (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-144 tm-992 ((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93420.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-992, u:((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-93421
in-theory        93421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-134 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
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-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-93421.        ((A -> ((B and C) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-134, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93422
in-theory        93422
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-131 tm-992 ((Am (-> (and A B) A)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
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-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-93422.        ((A or ((B and C) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((B and C) -> B))), M:tm-131, m:tm-992, u:((Am (-> (and A B) A)) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (and A B) A))))
================================================================
tm-name          tm-93423
in-theory        93423
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     35
proof            (modus-ponens tm-125 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-93423.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-125, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93424
in-theory        93424
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((A -> B) and C) -> B)))
theorem-size     39
proof            (modus-ponens tm-122 tm-992 ((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93424.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-992, u:((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-93425
in-theory        93425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-113 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 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-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-93425.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E))), M:tm-113, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93426
in-theory        93426
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-110 tm-992 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93426.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-992, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-93427
in-theory        93427
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     39
proof            (modus-ponens tm-105 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-93427.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-105, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93428
in-theory        93428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-102 tm-992 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93428.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-992, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-93429
in-theory        93429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C)))
theorem-size     27
proof            (modus-ponens tm-95 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 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-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-93429.        (((A -> B) -> (A -> A)) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C))), M:tm-95, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93430
in-theory        93430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> A)))
theorem-size     27
proof            (modus-ponens tm-92 tm-992 ((Am (-> A A)) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93430.        (((A -> B) or (A -> A)) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (A -> A))), M:tm-92, m:tm-992, u:((Am (-> A A)) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A A))))
================================================================
tm-name          tm-93431
in-theory        93431
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A)))
theorem-size     21
proof            (modus-ponens tm-84 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-5 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-93431.        (A -> (B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A))), M:tm-84, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93432
in-theory        93432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-83 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-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-93432.        ((A -> (B -> (C -> B))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-83, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93433
in-theory        93433
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (B -> (C -> B))))
theorem-size     29
proof            (modus-ponens tm-80 tm-992 ((Am (-> A (-> B A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
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-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-93433.        ((A or (B -> (C -> B))) -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and (B -> (C -> B)))), M:tm-80, m:tm-992, u:((Am (-> A (-> B A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> A (-> B A)))))
================================================================
tm-name          tm-93434
in-theory        93434
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B)))
theorem-size     25
proof            (modus-ponens tm-76 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-10 tm-7 tm-8)
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-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-93434.        (((not (not A)) -> A) and (B -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and B))), M:tm-76, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93435
in-theory        93435
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))
theorem-size     23
proof            (modus-ponens tm-73 tm-992 ((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
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-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-93435.        (((not (not A)) or A) -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)), M:tm-73, m:tm-992, u:((A Am) (B (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))
================================================================
tm-name          tm-93436
in-theory        93436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C)))
theorem-size     31
proof            (modus-ponens tm-69 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-9 tm-7 tm-8)
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-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-93436.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and C))), M:tm-69, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93437
in-theory        93437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((A -> (not B)) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-66 tm-992 ((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7)
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-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-93437.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-992, u:((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-93438
in-theory        93438
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-54 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
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-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-93438.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) and D))), M:tm-54, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-93439
in-theory        93439
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-992 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-7 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-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-1.            (A -> (B -> A)), axiom
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-93439.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-992, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93440
in-theory        93440
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 ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     45
proof            (modus-ponens tm-980 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
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-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-93440.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-980, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93441
in-theory        93441
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     43
proof            (modus-ponens tm-977 tm-993 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       211
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-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-1.            (A -> (B -> A)), axiom
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-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-93441.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-977, m:tm-993, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93442
in-theory        93442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-975 tm-993 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-93442.        (((A -> B) -> ((C or A) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-975, m:tm-993, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93443
in-theory        93443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     55
proof            (modus-ponens tm-969 tm-993 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
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-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-93443.        ((((A -> B) -> ((C or A) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-969, m:tm-993, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93444
in-theory        93444
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-930 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> 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-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-93444.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-930, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93445
in-theory        93445
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-927 tm-993 ((Am (-> (or A (or B A)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-7 tm-1)
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-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-1.            (A -> (B -> 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-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-93445.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-927, m:tm-993, u:((Am (-> (or A (or B A)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93446
in-theory        93446
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((B or (A or B)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     41
proof            (modus-ponens tm-920 tm-993 ((Am (or A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> 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-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-93446.        (((A or B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((B or (A or B)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-920, m:tm-993, u:((Am (or A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93447
in-theory        93447
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-893 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
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-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-93447.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-893, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93448
in-theory        93448
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-890 tm-993 ((Am (-> (or A (or A B)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
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-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-1.            (A -> (B -> A)), axiom
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-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-93448.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-890, m:tm-993, u:((Am (-> (or A (or A B)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93449
in-theory        93449
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     19
proof            (modus-ponens tm-888 tm-993 ((Am (or A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-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-93449.        ((A or B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-888, m:tm-993, u:((Am (or A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93450
in-theory        93450
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((A or (A or B)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     41
proof            (modus-ponens tm-882 tm-993 ((Am (or A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
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-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-93450.        (((A or B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((A or (A or B)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-882, m:tm-993, u:((Am (or A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93451
in-theory        93451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     35
proof            (modus-ponens tm-855 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
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-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-93451.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-855, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93452
in-theory        93452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-852 tm-993 ((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
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-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-1.            (A -> (B -> A)), axiom
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-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-93452.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-852, m:tm-993, u:((Am (-> (or A (-> B (and A B))) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93453
in-theory        93453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-850 tm-993 ((Am (-> A (and B A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
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-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-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-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-93453.        ((A -> (B and A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-850, m:tm-993, u:((Am (-> A (and B A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93454
in-theory        93454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((B or (A -> (B and A))) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     45
proof            (modus-ponens tm-844 tm-993 ((Am (-> A (and B A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
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-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-93454.        (((A -> (B and A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((B or (A -> (B and A))) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-844, m:tm-993, u:((Am (-> A (and B A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93455
in-theory        93455
times-derived    3
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) -> D)
theorem-size     17
proof            (modus-ponens tm-809 tm-993 ((Am (-> (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) B)) (Bm (and C (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))) (A (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-8 tm-4 tm-1 tm-7)
proof-size       129
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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
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-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-93455.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) -> D), M:tm-809, m:tm-993, u:((Am (-> (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) B)) (Bm (and C (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))) (A (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-93456
in-theory        93456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-808 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
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-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-93456.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-808, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93457
in-theory        93457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-805 tm-993 ((Am (-> (or (and A B) B) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
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-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-1.            (A -> (B -> A)), axiom
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-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-93457.        (((A -> B) or (((C and A) or A) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-805, m:tm-993, u:((Am (-> (or (and A B) B) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93458
in-theory        93458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and A) or A) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     39
proof            (modus-ponens tm-798 tm-993 ((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
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-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-93458.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and A) or A) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-798, m:tm-993, u:((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93459
in-theory        93459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-757 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-93459.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-757, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93460
in-theory        93460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-754 tm-993 ((Am (-> (or (and A B) A) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
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-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-93460.        (((A -> B) or (((A and C) or A) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-754, m:tm-993, u:((Am (-> (or (and A B) A) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93461
in-theory        93461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((A and F) or A) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     39
proof            (modus-ponens tm-747 tm-993 ((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93461.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((A and F) or A) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-747, m:tm-993, u:((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93462
in-theory        93462
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) -> ((A -> B) -> (((A -> B) or A) -> B))) -> C) -> C)
theorem-size     21
proof            (modus-ponens tm-709 tm-993 ((Am (-> (-> (-> (-> Dm Em) Dm) (-> (-> Dm Em) (-> (or (-> Dm Em) Dm) Em))) D)) (Bm (-> (-> Dm Em) (-> Dm (-> (or (-> Dm Em) Dm) Em)))) (Cm (-> Dm Em)) (B Dm) (A (-> Dm Em)) (C (-> (or (-> Dm Em) Dm) Em))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       175
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-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-93462.        (((((A -> B) -> A) -> ((A -> B) -> (((A -> B) or A) -> B))) -> C) -> C), M:tm-709, m:tm-993, u:((Am (-> (-> (-> (-> Dm Em) Dm) (-> (-> Dm Em) (-> (or (-> Dm Em) Dm) Em))) D)) (Bm (-> (-> Dm Em) (-> Dm (-> (or (-> Dm Em) Dm) Em)))) (Cm (-> Dm Em)) (B Dm) (A (-> Dm Em)) (C (-> (or (-> Dm Em) Dm) Em)))
================================================================
tm-name          tm-93463
in-theory        93463
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     43
proof            (modus-ponens tm-708 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93463.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-708, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93464
in-theory        93464
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     41
proof            (modus-ponens tm-705 tm-993 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93464.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-705, m:tm-993, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93465
in-theory        93465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-703 tm-993 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93465.        (((A -> B) -> (A -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-703, m:tm-993, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93466
in-theory        93466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     53
proof            (modus-ponens tm-697 tm-993 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93466.        ((((A -> B) -> (A -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-697, m:tm-993, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93467
in-theory        93467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-665 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93467.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-665, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93468
in-theory        93468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-662 tm-993 ((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-1 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((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-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-93468.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-662, m:tm-993, u:((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93469
in-theory        93469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     19
proof            (modus-ponens tm-660 tm-993 ((Am (-> A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93469.        ((A -> B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-660, m:tm-993, u:((Am (-> A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93470
in-theory        93470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((B or (A -> B)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     41
proof            (modus-ponens tm-654 tm-993 ((Am (-> A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93470.        (((A -> B) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))) and ((B or (A -> B)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-654, m:tm-993, u:((Am (-> A B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93471
in-theory        93471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-622 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93471.        ((A -> (B -> (C or B))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-622, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93472
in-theory        93472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-619 tm-993 ((Am (-> A (or B A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
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-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-93472.        ((A or (B -> (C or B))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-619, m:tm-993, u:((Am (-> A (or B A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93473
in-theory        93473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93473.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G or F))), M:tm-609, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93474
in-theory        93474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-605 tm-993 ((A (-> Am (or 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-93474.        ((A -> ((B -> (C or B)) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-605, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93475
in-theory        93475
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-602 tm-993 ((Am (and (-> A (or B A)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-5 tm-7 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-7.            (A -> (B or 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-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-93475.        ((A or ((B -> (C or B)) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-602, m:tm-993, u:((Am (and (-> A (or B A)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93476
in-theory        93476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G or F)) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-93476.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G or F)) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-595, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93477
in-theory        93477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-550 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93477.        (((A -> (B or A)) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-550, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93478
in-theory        93478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-540 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93478.        ((A or (B -> (C or B))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-540, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93479
in-theory        93479
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-530 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93479.        ((A or (B -> (B or C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-530, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93480
in-theory        93480
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-520 tm-993 ((A (-> Am (or 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-93480.        ((A or (B -> (C -> (B and C)))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-520, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93481
in-theory        93481
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-510 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93481.        ((A or ((B and C) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-510, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93482
in-theory        93482
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-500 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93482.        ((A or ((B and C) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-500, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93483
in-theory        93483
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-490 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93483.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-490, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93484
in-theory        93484
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-480 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93484.        ((A or (B -> (C -> B))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-480, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93485
in-theory        93485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-469 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93485.        ((A -> (B -> (B or C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-469, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93486
in-theory        93486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-466 tm-993 ((Am (-> A (or A B))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
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-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-93486.        ((A or (B -> (B or C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-466, m:tm-993, u:((Am (-> A (or A B))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93487
in-theory        93487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93487.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (F or G))), M:tm-456, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93488
in-theory        93488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-453 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-6 tm-1 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-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-93488.        ((A -> ((B -> (B or C)) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-453, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93489
in-theory        93489
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-450 tm-993 ((Am (and (-> A (or A B)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 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-6.            (A -> (A or 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-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-93489.        ((A or ((B -> (B or C)) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-450, m:tm-993, u:((Am (and (-> A (or A B)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93490
in-theory        93490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (F or G)) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-93490.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (F or G)) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-443, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93491
in-theory        93491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-409 tm-993 ((A (-> Am (or Bm (-> (-> 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-93491.        (((A -> (A or B)) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-409, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93492
in-theory        93492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-400 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-6 tm-1 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-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-93492.        (((A -> (B -> (A and B))) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-400, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93493
in-theory        93493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-391 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-93493.        ((((A and B) -> B) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-391, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93494
in-theory        93494
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-382 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-93494.        ((((A and B) -> A) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-382, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93495
in-theory        93495
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-373 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 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-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-93495.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-373, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93496
in-theory        93496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-364 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93496.        (((A -> (B -> A)) or C) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-364, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93497
in-theory        93497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-354 tm-993 ((A (-> Am (or 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-93497.        ((A -> (B -> (C -> (B and C)))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-354, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93498
in-theory        93498
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-993 ((Am (-> A (-> B (and A B)))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
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-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-93498.        ((A or (B -> (C -> (B and C)))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-351, m:tm-993, u:((Am (-> A (-> B (and A B)))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93499
in-theory        93499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-993 ((A (-> Am (or 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-93499.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93500
in-theory        93500
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E))
theorem-size     35
proof            (modus-ponens tm-339 tm-993 ((Am (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B)) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-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-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-93500.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E)), M:tm-339, m:tm-993, u:((Am (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B)) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93501
in-theory        93501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     27
proof            (modus-ponens tm-338 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-2 tm-1 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-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-93501.        (((A -> B) -> (A -> (A and B))) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-338, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93502
in-theory        93502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-335 tm-993 ((Am (-> A (and A B))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93502.        (((A -> B) or (A -> (A and B))) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-335, m:tm-993, u:((Am (-> A (and A B))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93503
in-theory        93503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (A -> (A and (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     37
proof            (modus-ponens tm-328 tm-993 ((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
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-328.          ((A -> 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-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-93503.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (A -> (A and (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-328, m:tm-993, u:((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93504
in-theory        93504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> (F and G))) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-993 ((A (-> Am (or Bm (-> (-> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-93504.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> (F and G))) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-327, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93505
in-theory        93505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and G) -> G) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-93505.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and G) -> G) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-326, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93506
in-theory        93506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and G) -> F) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-93506.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F and G) -> F) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-325, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93507
in-theory        93507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-93507.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-324, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93508
in-theory        93508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> F)) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-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-93508.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> F)) and (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-323, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93509
in-theory        93509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93509.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F and G) -> G)), M:tm-322, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93510
in-theory        93510
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F)) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F)) -> F))
theorem-size     57
proof            (modus-ponens tm-321 tm-993 ((Am (and A (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) C))) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-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-93510.        (((A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F)) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F)) -> F)), M:tm-321, m:tm-993, u:((Am (and A (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) C))) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93511
in-theory        93511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93511.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F and G) -> F)), M:tm-320, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93512
in-theory        93512
times-derived    1
----------------------------------------------------------------
theorem          (((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) and F) -> (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))) and ((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) and F) -> E))
theorem-size     57
proof            (modus-ponens tm-319 tm-993 ((Am (and (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B) C)) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-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-93512.        (((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) and F) -> (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))) and ((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) and F) -> E)), M:tm-319, m:tm-993, u:((Am (and (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B) C)) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93513
in-theory        93513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93513.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93514
in-theory        93514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-993 ((A Am) (B (or 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-93514.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (A -> A)), M:tm-316, m:tm-993, u:((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93515
in-theory        93515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93515.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (G -> F))), M:tm-315, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93516
in-theory        93516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((A -> (not (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-993 ((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-93516.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((A -> (not (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))) -> (not A))), M:tm-313, m:tm-993, u:((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93517
in-theory        93517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F) -> ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) -> F)))
theorem-size     55
proof            (modus-ponens tm-312 tm-993 ((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93517.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F) -> ((A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) -> F))), M:tm-312, m:tm-993, u:((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93518
in-theory        93518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F or (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-93518.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F or (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-311, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93519
in-theory        93519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 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-6.            (A -> (A or 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-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-93519.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) or F)), M:tm-310, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93520
in-theory        93520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-2 tm-5 tm-1 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-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-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-93520.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and F))), M:tm-309, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93521
in-theory        93521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-993 ((A (-> Am (or Bm (-> (-> 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      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (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-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-93521.        ((A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))) and (F -> (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))), M:tm-305, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93522
in-theory        93522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     29
proof            (modus-ponens tm-303 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-93522.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-303, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93523
in-theory        93523
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-300 tm-993 ((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
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-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-93523.        ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-300, m:tm-993, u:((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93524
in-theory        93524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-270 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-4 tm-1 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-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-93524.        ((A -> (((B and C) -> C) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-270, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93525
in-theory        93525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-267 tm-993 ((Am (and (-> (and A B) B) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 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-4.            ((A and B) -> 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-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-93525.        ((A or (((B and C) -> C) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-267, m:tm-993, u:((Am (and (-> (and A B) B) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93526
in-theory        93526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-239 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-3 tm-1 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-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-93526.        ((A -> (((B and C) -> B) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-239, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93527
in-theory        93527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-236 tm-993 ((Am (and (-> (and A B) A) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 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-3.            ((A and B) -> 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-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-93527.        ((A or (((B and C) -> B) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-236, m:tm-993, u:((Am (and (-> (and A B) A) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93528
in-theory        93528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-210 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-2 tm-1 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-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-93528.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-210, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93529
in-theory        93529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-207 tm-993 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93529.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-207, m:tm-993, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93530
in-theory        93530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     27
proof            (modus-ponens tm-183 tm-993 ((A (-> Am (or 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-93530.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-183, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93531
in-theory        93531
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-180 tm-993 ((Am (and (-> A (-> B A)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-5 tm-1 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-1.            (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-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-93531.        ((A or ((B -> (C -> B)) and A)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-180, m:tm-993, u:((Am (and (-> A (-> B A)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93532
in-theory        93532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-157 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93532.        ((A -> ((B and C) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-157, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93533
in-theory        93533
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-154 tm-993 ((Am (-> (and A B) B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-1 tm-4 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-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-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-93533.        ((A or ((B and C) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-154, m:tm-993, u:((Am (-> (and A B) B)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93534
in-theory        93534
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-147 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 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-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-93534.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-147, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93535
in-theory        93535
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-144 tm-993 ((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93535.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-144, m:tm-993, u:((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93536
in-theory        93536
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F)) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     35
proof            (modus-ponens tm-142 tm-993 ((Am (and A (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) C))) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-1 tm-4 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-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-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-93536.        ((A and ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) -> F)) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-142, m:tm-993, u:((Am (and A (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) C))) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93537
in-theory        93537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-134 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93537.        ((A -> ((B and C) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-134, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93538
in-theory        93538
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-131 tm-993 ((Am (-> (and A B) A)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-1 tm-3 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-3.            ((A 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-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-93538.        ((A or ((B and C) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-131, m:tm-993, u:((Am (-> (and A B) A)) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93539
in-theory        93539
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     33
proof            (modus-ponens tm-125 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 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-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-93539.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-125, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93540
in-theory        93540
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-122 tm-993 ((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93540.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-122, m:tm-993, u:((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93541
in-theory        93541
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) and F) -> (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     35
proof            (modus-ponens tm-120 tm-993 ((Am (and (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B) C)) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-1 tm-3 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-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-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-93541.        ((((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) and F) -> (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))), M:tm-120, m:tm-993, u:((Am (and (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B) C)) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93542
in-theory        93542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-113 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93542.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-113, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93543
in-theory        93543
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-110 tm-993 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93543.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-110, m:tm-993, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93544
in-theory        93544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     37
proof            (modus-ponens tm-105 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-2 tm-1 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-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-93544.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-105, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93545
in-theory        93545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     35
proof            (modus-ponens tm-102 tm-993 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93545.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-102, m:tm-993, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93546
in-theory        93546
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     33
proof            (modus-ponens tm-96 tm-993 ((Am (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B)) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-1 tm-7 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-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-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-93546.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))), M:tm-96, m:tm-993, u:((Am (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B)) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93547
in-theory        93547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     25
proof            (modus-ponens tm-95 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93547.        (((A -> B) -> (A -> A)) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-95, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93548
in-theory        93548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     23
proof            (modus-ponens tm-92 tm-993 ((Am (-> A A)) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93548.        (((A -> B) or (A -> A)) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-92, m:tm-993, u:((Am (-> A A)) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93549
in-theory        93549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     25
proof            (modus-ponens tm-83 tm-993 ((A (-> Am (or Bm (-> (-> 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-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-93549.        ((A -> (B -> (C -> B))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-83, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93550
in-theory        93550
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-80 tm-993 ((Am (-> A (-> B A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
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-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-93550.        ((A or (B -> (C -> B))) -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-80, m:tm-993, u:((Am (-> A (-> B A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93551
in-theory        93551
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E))) -> E)
theorem-size     21
proof            (modus-ponens tm-77 tm-993 ((Am (not (not (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B)))) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-10 tm-1 tm-7 tm-8)
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-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-93551.        ((not (not ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E))) -> E), M:tm-77, m:tm-993, u:((Am (not (not (-> (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) B)))) (A (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93552
in-theory        93552
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     23
proof            (modus-ponens tm-76 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-10 tm-1 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-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-93552.        (((not (not A)) -> A) and (B -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-76, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93553
in-theory        93553
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     21
proof            (modus-ponens tm-73 tm-993 ((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
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-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-93553.        (((not (not A)) or A) -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-73, m:tm-993, u:((A Am) (B (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93554
in-theory        93554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))
theorem-size     29
proof            (modus-ponens tm-69 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-9 tm-1 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-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-93554.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))), M:tm-69, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93555
in-theory        93555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-66 tm-993 ((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-7)
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-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-93555.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-66, m:tm-993, u:((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-93556
in-theory        93556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-54 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
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-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-93556.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-54, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-93557
in-theory        93557
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93557.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-992, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93558
in-theory        93558
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 (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93558.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-980, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93559
in-theory        93559
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93559.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-930, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93560
in-theory        93560
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-93560.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-893, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93561
in-theory        93561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93561.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-855, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93562
in-theory        93562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93562.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-808, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93563
in-theory        93563
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93563.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-757, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93564
in-theory        93564
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))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93564.        (((((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))) or J))), M:tm-708, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93565
in-theory        93565
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93565.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-665, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93566
in-theory        93566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-93566.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-622, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93567
in-theory        93567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93567.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93568
in-theory        93568
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93568.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-605, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93569
in-theory        93569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-93569.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-595, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93570
in-theory        93570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93570.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-550, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93571
in-theory        93571
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93571.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-540, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93572
in-theory        93572
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93572.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-530, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93573
in-theory        93573
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93573.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-520, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93574
in-theory        93574
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-93574.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-510, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93575
in-theory        93575
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-93575.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-500, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93576
in-theory        93576
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-93576.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-490, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93577
in-theory        93577
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-93577.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-480, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93578
in-theory        93578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
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-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-93578.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-469, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93579
in-theory        93579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-93579.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93580
in-theory        93580
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93580.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-453, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93581
in-theory        93581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-93581.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-443, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93582
in-theory        93582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93582.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-409, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93583
in-theory        93583
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93583.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-400, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93584
in-theory        93584
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
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-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-93584.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-391, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93585
in-theory        93585
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
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-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-93585.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-382, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93586
in-theory        93586
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
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-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-93586.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-373, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93587
in-theory        93587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
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-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-93587.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-364, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93588
in-theory        93588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-93588.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-354, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93589
in-theory        93589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-93589.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93590
in-theory        93590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-8)
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-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-93590.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-338, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93591
in-theory        93591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-93591.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-327, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93592
in-theory        93592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-93592.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-326, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93593
in-theory        93593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-93593.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-325, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93594
in-theory        93594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-93594.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-324, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93595
in-theory        93595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-93595.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-323, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93596
in-theory        93596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-93596.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93597
in-theory        93597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93597.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93598
in-theory        93598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-93598.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93599
in-theory        93599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-93599.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93600
in-theory        93600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-93600.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-311, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93601
in-theory        93601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-93601.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)), M:tm-310, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93602
in-theory        93602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 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-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-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-93602.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G))), M:tm-309, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93603
in-theory        93603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-994 ((A (-> Am (or Bm Am))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-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-93603.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-308, m:tm-994, u:((A (-> Am (or Bm Am))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93604
in-theory        93604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (A -> (B or A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-994 ((A (-> Am (or Bm Am))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6 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-3.            ((A and B) -> A), axiom
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-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-93604.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (A -> (B or A))), M:tm-307, m:tm-994, u:((A (-> Am (or Bm Am))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93605
in-theory        93605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (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-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-93605.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-305, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93606
in-theory        93606
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93606.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-303, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93607
in-theory        93607
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-8)
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-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-93607.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-270, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93608
in-theory        93608
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-8)
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-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-93608.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-239, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93609
in-theory        93609
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-93609.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-210, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93610
in-theory        93610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-93610.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-183, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93611
in-theory        93611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6 tm-8)
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-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-93611.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-157, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93612
in-theory        93612
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6 tm-8)
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-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-93612.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-147, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93613
in-theory        93613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6 tm-8)
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-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-93613.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-134, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93614
in-theory        93614
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6 tm-8)
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-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-93614.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-125, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93615
in-theory        93615
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6 tm-8)
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-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-93615.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-113, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93616
in-theory        93616
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))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-93616.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-105, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93617
in-theory        93617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6 tm-8)
proof-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-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-93617.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-95, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93618
in-theory        93618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-93618.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-83, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93619
in-theory        93619
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6 tm-8)
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-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-93619.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-76, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93620
in-theory        93620
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))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6 tm-8)
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-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-93620.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-69, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93621
in-theory        93621
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93621.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-54, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93622
in-theory        93622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-93622.        ((A -> (B or A)) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-42, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93623
in-theory        93623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm 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-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-93623.        ((A -> (A or B)) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-32, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93624
in-theory        93624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93624.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-23, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93625
in-theory        93625
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-93625.        (((A and B) -> B) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-22, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93626
in-theory        93626
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-93626.        (((A and B) -> A) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-21, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93627
in-theory        93627
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-7 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-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-93627.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-20, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93628
in-theory        93628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C 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-93628.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-19, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93629
in-theory        93629
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-7 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-6 tm-8)
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-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-93629.        (A or ((B -> (C or B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-7, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93630
in-theory        93630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-7 tm-8)
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-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-93630.        (((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G), M:tm-6, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93631
in-theory        93631
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 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-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-93631.        (A -> (((B -> (C or B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A)), M:tm-5, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93632
in-theory        93632
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-1 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-7 tm-6 tm-8)
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-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-93632.        (A -> ((B -> (C or B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-1, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93633
in-theory        93633
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93633.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-992, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93634
in-theory        93634
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 (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93634.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-980, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93635
in-theory        93635
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93635.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-930, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93636
in-theory        93636
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93636.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-893, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93637
in-theory        93637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93637.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-855, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93638
in-theory        93638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93638.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-808, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93639
in-theory        93639
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93639.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-757, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93640
in-theory        93640
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))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93640.        (((((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))) or J))), M:tm-708, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93641
in-theory        93641
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93641.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-665, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93642
in-theory        93642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-93642.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-622, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93643
in-theory        93643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93643.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93644
in-theory        93644
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93644.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-605, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93645
in-theory        93645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-93645.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-595, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93646
in-theory        93646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93646.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-550, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93647
in-theory        93647
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93647.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-540, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93648
in-theory        93648
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93648.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-530, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93649
in-theory        93649
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93649.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-520, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93650
in-theory        93650
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-93650.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-510, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93651
in-theory        93651
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-93651.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-500, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93652
in-theory        93652
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-93652.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-490, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93653
in-theory        93653
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-93653.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-480, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93654
in-theory        93654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-93654.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-469, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93655
in-theory        93655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-93655.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93656
in-theory        93656
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93656.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-453, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93657
in-theory        93657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-93657.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-443, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93658
in-theory        93658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93658.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-409, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93659
in-theory        93659
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93659.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-400, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93660
in-theory        93660
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-93660.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-391, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93661
in-theory        93661
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-93661.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-382, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93662
in-theory        93662
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-93662.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-373, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93663
in-theory        93663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-93663.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-364, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93664
in-theory        93664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-93664.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-354, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93665
in-theory        93665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-93665.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93666
in-theory        93666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
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-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-93666.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-338, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93667
in-theory        93667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-93667.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-327, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93668
in-theory        93668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-93668.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-326, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93669
in-theory        93669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-93669.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-325, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93670
in-theory        93670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-93670.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-324, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93671
in-theory        93671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-93671.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-323, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93672
in-theory        93672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-93672.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93673
in-theory        93673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93673.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93674
in-theory        93674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-93674.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93675
in-theory        93675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-93675.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93676
in-theory        93676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-93676.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-311, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93677
in-theory        93677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-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-93677.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)), M:tm-310, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93678
in-theory        93678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-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-93678.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G))), M:tm-309, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93679
in-theory        93679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-995 ((A (-> Am (or Am Bm))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-93679.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-308, m:tm-995, u:((A (-> Am (or Am Bm))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93680
in-theory        93680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (A -> (A or B)))
theorem-size     27
proof            (modus-ponens tm-307 tm-995 ((A (-> Am (or Am Bm))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
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-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-93680.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (A -> (A or B))), M:tm-307, m:tm-995, u:((A (-> Am (or Am Bm))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93681
in-theory        93681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-93681.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-305, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93682
in-theory        93682
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93682.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-303, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93683
in-theory        93683
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-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-93683.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-270, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93684
in-theory        93684
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
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-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-93684.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-239, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93685
in-theory        93685
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-93685.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-210, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93686
in-theory        93686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-93686.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-183, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93687
in-theory        93687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-93687.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-157, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93688
in-theory        93688
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8)
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-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-93688.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-147, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93689
in-theory        93689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-93689.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-134, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93690
in-theory        93690
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
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-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-93690.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-125, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93691
in-theory        93691
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
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-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-93691.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-113, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93692
in-theory        93692
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))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-93692.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-105, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93693
in-theory        93693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
proof-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-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-93693.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-95, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93694
in-theory        93694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-93694.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-83, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93695
in-theory        93695
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-6 tm-8)
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-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-93695.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-76, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93696
in-theory        93696
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))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-6 tm-8)
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-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-93696.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-69, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93697
in-theory        93697
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-93697.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-54, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93698
in-theory        93698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-93698.        ((A -> (B or A)) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-42, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93699
in-theory        93699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-93699.        ((A -> (A or B)) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-32, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93700
in-theory        93700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93700.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-23, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93701
in-theory        93701
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-93701.        (((A and B) -> B) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-22, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93702
in-theory        93702
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-93702.        (((A and B) -> A) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-21, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93703
in-theory        93703
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-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-93703.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-20, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93704
in-theory        93704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-93704.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-19, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93705
in-theory        93705
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-7 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-6 tm-8)
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-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-93705.        (A or ((B -> (B or C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-7, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93706
in-theory        93706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-8)
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-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-93706.        (((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G), M:tm-6, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93707
in-theory        93707
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-93707.        (A -> (((B -> (B or C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A)), M:tm-5, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93708
in-theory        93708
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-1 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-6 tm-8)
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-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-93708.        (A -> ((B -> (B or C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-1, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93709
in-theory        93709
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-992 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93709.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-992, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93710
in-theory        93710
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 (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     51
proof            (modus-ponens tm-980 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93710.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-980, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93711
in-theory        93711
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-930 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93711.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-930, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93712
in-theory        93712
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-893 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
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-93712.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-893, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93713
in-theory        93713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-855 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93713.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-855, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93714
in-theory        93714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-808 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93714.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-808, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93715
in-theory        93715
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-757 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93715.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-757, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93716
in-theory        93716
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))) or J)))
theorem-size     49
proof            (modus-ponens tm-708 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93716.        (((((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))) or J))), M:tm-708, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93717
in-theory        93717
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-665 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93717.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-665, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93718
in-theory        93718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-622 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-93718.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-622, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93719
in-theory        93719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93719.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93720
in-theory        93720
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-605 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93720.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-605, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93721
in-theory        93721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-595 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-93721.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-595, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93722
in-theory        93722
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-550 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-93722.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-550, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93723
in-theory        93723
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-540 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93723.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-540, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93724
in-theory        93724
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-530 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93724.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-530, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93725
in-theory        93725
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-520 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-93725.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-520, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93726
in-theory        93726
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-510 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-93726.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-510, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93727
in-theory        93727
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-500 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-93727.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-500, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93728
in-theory        93728
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-490 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-93728.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-490, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93729
in-theory        93729
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-480 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-93729.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-480, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93730
in-theory        93730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-469 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-93730.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-469, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93731
in-theory        93731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-93731.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93732
in-theory        93732
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-453 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93732.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-453, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93733
in-theory        93733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-443 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-93733.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-443, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93734
in-theory        93734
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-409 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93734.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-409, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93735
in-theory        93735
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-400 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93735.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-400, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93736
in-theory        93736
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-391 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-93736.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-391, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93737
in-theory        93737
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-382 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-93737.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-382, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93738
in-theory        93738
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-373 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-93738.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-373, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93739
in-theory        93739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-364 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-93739.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-364, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93740
in-theory        93740
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-354 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-93740.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-354, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93741
in-theory        93741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-93741.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93742
in-theory        93742
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))) or H)))
theorem-size     33
proof            (modus-ponens tm-338 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-93742.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-338, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93743
in-theory        93743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     55
proof            (modus-ponens tm-327 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-93743.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-327, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93744
in-theory        93744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-326 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-93744.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-326, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93745
in-theory        93745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-325 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-93745.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-325, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93746
in-theory        93746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     61
proof            (modus-ponens tm-324 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-93746.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-324, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93747
in-theory        93747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-323 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-93747.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-323, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93748
in-theory        93748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-93748.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93749
in-theory        93749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93749.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93750
in-theory        93750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-93750.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93751
in-theory        93751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-93751.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93752
in-theory        93752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-311 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-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-93752.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-311, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93753
in-theory        93753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-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-93753.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)), M:tm-310, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93754
in-theory        93754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-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-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-93754.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G))), M:tm-309, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93755
in-theory        93755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     39
proof            (modus-ponens tm-308 tm-996 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-93755.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-308, m:tm-996, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93756
in-theory        93756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (A -> (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-307 tm-996 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-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-93756.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-996, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93757
in-theory        93757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-305 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-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-93757.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-305, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93758
in-theory        93758
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-303 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93758.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-303, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93759
in-theory        93759
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-270 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-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-93759.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-270, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93760
in-theory        93760
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-239 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
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-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-93760.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-239, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93761
in-theory        93761
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))) or J)))
theorem-size     41
proof            (modus-ponens tm-210 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-93761.        ((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))) or J))), M:tm-210, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93762
in-theory        93762
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-183 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-93762.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-183, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93763
in-theory        93763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-157 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-93763.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-157, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93764
in-theory        93764
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))) or I)))
theorem-size     39
proof            (modus-ponens tm-147 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-93764.        ((((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))) or I))), M:tm-147, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93765
in-theory        93765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-134 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-93765.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-134, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93766
in-theory        93766
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))) or I)))
theorem-size     39
proof            (modus-ponens tm-125 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-93766.        (((((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))) or I))), M:tm-125, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93767
in-theory        93767
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-113 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
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-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-93767.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-113, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93768
in-theory        93768
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))) or I)))
theorem-size     43
proof            (modus-ponens tm-105 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
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-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-93768.        ((((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))) or I))), M:tm-105, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93769
in-theory        93769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-95 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
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-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-93769.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-95, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93770
in-theory        93770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-83 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-93770.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-83, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93771
in-theory        93771
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     29
proof            (modus-ponens tm-76 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-6 tm-8)
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-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-93771.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-76, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93772
in-theory        93772
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))) or H)))
theorem-size     35
proof            (modus-ponens tm-69 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-6 tm-8)
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-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-93772.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-69, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93773
in-theory        93773
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-54 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93773.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-54, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93774
in-theory        93774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-42 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-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-93774.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-42, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93775
in-theory        93775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-32 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-93775.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-32, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93776
in-theory        93776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-23 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93776.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-23, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93777
in-theory        93777
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-22 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 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-23.           (A -> ((B -> (C -> (B and 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-93777.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-22, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93778
in-theory        93778
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-21 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 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-23.           (A -> ((B -> (C -> (B and 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-93778.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-21, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93779
in-theory        93779
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-20 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-23.           (A -> ((B -> (C -> (B and 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-93779.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-20, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93780
in-theory        93780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-19 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-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-93780.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-19, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93781
in-theory        93781
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-7 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-6 tm-8)
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-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-93781.        (A or ((B -> (C -> (B and C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-7, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93782
in-theory        93782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-8)
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-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-93782.        (((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G), M:tm-6, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93783
in-theory        93783
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-93783.        (A -> (((B -> (C -> (B and C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A)), M:tm-5, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93784
in-theory        93784
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-1 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-6 tm-8)
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-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-93784.        (A -> ((B -> (C -> (B and C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-1, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93785
in-theory        93785
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93785.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-992, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93786
in-theory        93786
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 (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93786.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-980, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93787
in-theory        93787
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93787.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-930, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93788
in-theory        93788
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-93788.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-893, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93789
in-theory        93789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
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-48.           (((A -> (B and 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93789.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-855, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93790
in-theory        93790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93790.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-808, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93791
in-theory        93791
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93791.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-757, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93792
in-theory        93792
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))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93792.        (((((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))) or J))), M:tm-708, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93793
in-theory        93793
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93793.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-665, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93794
in-theory        93794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6 tm-8)
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-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-93794.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-622, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93795
in-theory        93795
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93795.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93796
in-theory        93796
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-93796.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-605, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93797
in-theory        93797
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-93797.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-595, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93798
in-theory        93798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-8)
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-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-93798.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-550, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93799
in-theory        93799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-93799.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-540, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93800
in-theory        93800
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-8)
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-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-93800.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-530, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93801
in-theory        93801
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-93801.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-520, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93802
in-theory        93802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-93802.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-510, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93803
in-theory        93803
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6 tm-8)
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-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-93803.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-500, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93804
in-theory        93804
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6 tm-8)
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-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-93804.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-490, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93805
in-theory        93805
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6 tm-8)
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-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-93805.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-480, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93806
in-theory        93806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-8)
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-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-93806.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-469, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93807
in-theory        93807
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-93807.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93808
in-theory        93808
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-93808.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-453, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93809
in-theory        93809
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-93809.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-443, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93810
in-theory        93810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-93810.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-409, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93811
in-theory        93811
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-93811.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-400, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93812
in-theory        93812
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-93812.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-391, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93813
in-theory        93813
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-8)
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-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-93813.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-382, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93814
in-theory        93814
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-8)
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-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-93814.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-373, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93815
in-theory        93815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-8)
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-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-93815.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-364, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93816
in-theory        93816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-93816.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-354, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93817
in-theory        93817
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-93817.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93818
in-theory        93818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8)
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-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-93818.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-338, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93819
in-theory        93819
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-93819.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-327, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93820
in-theory        93820
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-93820.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-326, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93821
in-theory        93821
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-93821.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-325, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93822
in-theory        93822
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-93822.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-324, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93823
in-theory        93823
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-93823.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-323, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93824
in-theory        93824
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-93824.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93825
in-theory        93825
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93825.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93826
in-theory        93826
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-93826.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93827
in-theory        93827
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-93827.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93828
in-theory        93828
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 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-7.            (A -> (B or 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-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-93828.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-311, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93829
in-theory        93829
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-93829.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)), M:tm-310, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93830
in-theory        93830
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-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-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-93830.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G))), M:tm-309, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93831
in-theory        93831
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-997 ((A (-> (and Am Bm) Bm)) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-93831.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-308, m:tm-997, u:((A (-> (and Am Bm) Bm)) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93832
in-theory        93832
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((A and B) -> B))
theorem-size     27
proof            (modus-ponens tm-307 tm-997 ((A (-> (and Am Bm) Bm)) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6 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-3.            ((A and B) -> A), axiom
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-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-93832.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((A and B) -> B)), M:tm-307, m:tm-997, u:((A (-> (and Am Bm) Bm)) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93833
in-theory        93833
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (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-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-93833.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-305, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93834
in-theory        93834
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-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-93834.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-303, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93835
in-theory        93835
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-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-93835.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-270, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93836
in-theory        93836
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6 tm-8)
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-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-93836.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-239, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93837
in-theory        93837
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-93837.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-210, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93838
in-theory        93838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-93838.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-183, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93839
in-theory        93839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-93839.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-157, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93840
in-theory        93840
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8)
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-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-93840.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-147, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93841
in-theory        93841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6 tm-8)
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-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-93841.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-134, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93842
in-theory        93842
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6 tm-8)
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-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-93842.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-125, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93843
in-theory        93843
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6 tm-8)
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-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-93843.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-113, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93844
in-theory        93844
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))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-93844.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-105, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93845
in-theory        93845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6 tm-8)
proof-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-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-93845.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-95, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93846
in-theory        93846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-93846.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-83, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93847
in-theory        93847
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-4 tm-6 tm-8)
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-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-93847.        (((not (not A)) -> A) and (((B and C) -> C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-76, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93848
in-theory        93848
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))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-4 tm-6 tm-8)
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-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-93848.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-69, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93849
in-theory        93849
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93849.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-54, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93850
in-theory        93850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-93850.        ((A -> (B or A)) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-42, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93851
in-theory        93851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-93851.        ((A -> (A or B)) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-32, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93852
in-theory        93852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-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-93852.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-23, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93853
in-theory        93853
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-93853.        (((A and B) -> B) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-22, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93854
in-theory        93854
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-93854.        (((A and B) -> A) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-21, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93855
in-theory        93855
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-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-93855.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-20, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93856
in-theory        93856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-93856.        ((A -> (B -> A)) and (((C and D) -> D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-19, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93857
in-theory        93857
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-7 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-4 tm-6 tm-8)
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-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-93857.        (A or (((B and C) -> C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-7, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93858
in-theory        93858
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-4 tm-8)
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-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-93858.        ((((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G), M:tm-6, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93859
in-theory        93859
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 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-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-93859.        (A -> ((((B and C) -> C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A)), M:tm-5, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93860
in-theory        93860
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-1 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-4 tm-6 tm-8)
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-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-93860.        (A -> (((B and C) -> C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-1, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93861
in-theory        93861
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93861.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-992, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93862
in-theory        93862
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 (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93862.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-980, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93863
in-theory        93863
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93863.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-930, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93864
in-theory        93864
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-93864.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-893, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93865
in-theory        93865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
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-48.           (((A -> (B and 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93865.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-855, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93866
in-theory        93866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93866.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-808, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93867
in-theory        93867
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93867.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-757, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93868
in-theory        93868
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))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-93868.        (((((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))) or J))), M:tm-708, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93869
in-theory        93869
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93869.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-665, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93870
in-theory        93870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6 tm-8)
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-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-93870.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-622, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93871
in-theory        93871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93871.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93872
in-theory        93872
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-93872.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-605, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93873
in-theory        93873
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-93873.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-595, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93874
in-theory        93874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-8)
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-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-93874.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-550, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93875
in-theory        93875
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-93875.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-540, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93876
in-theory        93876
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-8)
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-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-93876.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-530, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93877
in-theory        93877
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-93877.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-520, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93878
in-theory        93878
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6 tm-8)
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-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-93878.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-510, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93879
in-theory        93879
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-93879.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-500, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93880
in-theory        93880
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6 tm-8)
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-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-93880.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-490, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93881
in-theory        93881
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6 tm-8)
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-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-93881.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-480, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93882
in-theory        93882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-8)
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-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-93882.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-469, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93883
in-theory        93883
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-93883.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93884
in-theory        93884
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-93884.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-453, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93885
in-theory        93885
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-93885.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-443, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93886
in-theory        93886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-93886.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-409, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93887
in-theory        93887
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-93887.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-400, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93888
in-theory        93888
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-8)
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-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-93888.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-391, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93889
in-theory        93889
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-93889.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-382, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93890
in-theory        93890
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-8)
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-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-93890.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-373, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93891
in-theory        93891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-8)
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-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-93891.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-364, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93892
in-theory        93892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-93892.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-354, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93893
in-theory        93893
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-93893.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93894
in-theory        93894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
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-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-93894.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-338, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93895
in-theory        93895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-93895.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-327, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93896
in-theory        93896
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-93896.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-326, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93897
in-theory        93897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-93897.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-325, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93898
in-theory        93898
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-93898.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-324, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93899
in-theory        93899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-93899.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-323, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93900
in-theory        93900
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-93900.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93901
in-theory        93901
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93901.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93902
in-theory        93902
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-93902.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93903
in-theory        93903
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-93903.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93904
in-theory        93904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 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-7.            (A -> (B or 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-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-93904.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-311, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93905
in-theory        93905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-93905.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)), M:tm-310, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93906
in-theory        93906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 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-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-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-93906.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G))), M:tm-309, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93907
in-theory        93907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-998 ((A (-> (and Am Bm) Am)) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 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-4.            ((A and B) -> B), axiom
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-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-93907.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-308, m:tm-998, u:((A (-> (and Am Bm) Am)) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93908
in-theory        93908
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((A and B) -> A))
theorem-size     27
proof            (modus-ponens tm-307 tm-998 ((A (-> (and Am Bm) Am)) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
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-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-93908.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((A and B) -> A)), M:tm-307, m:tm-998, u:((A (-> (and Am Bm) Am)) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-93909
in-theory        93909
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-1.            (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-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-93909.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-305, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93910
in-theory        93910
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
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-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-93910.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-303, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93911
in-theory        93911
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6 tm-8)
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-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-93911.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-270, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93912
in-theory        93912
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))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
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-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-93912.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-239, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93913
in-theory        93913
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-93913.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-210, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93914
in-theory        93914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-93914.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-183, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93915
in-theory        93915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6 tm-8)
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-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-93915.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-157, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93916
in-theory        93916
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6 tm-8)
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-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-93916.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-147, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93917
in-theory        93917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-93917.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-134, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93918
in-theory        93918
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
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-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-93918.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-125, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93919
in-theory        93919
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6 tm-8)
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-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-93919.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-113, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93920
in-theory        93920
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))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-93920.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-105, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93921
in-theory        93921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6 tm-8)
proof-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-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-93921.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-95, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93922
in-theory        93922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-93922.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-83, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93923
in-theory        93923
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-3 tm-6 tm-8)
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-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-93923.        (((not (not A)) -> A) and (((B and C) -> B) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-76, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93924
in-theory        93924
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))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-3 tm-6 tm-8)
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-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-93924.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-69, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93925
in-theory        93925
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93925.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-54, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93926
in-theory        93926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-93926.        ((A -> (B or A)) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-42, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93927
in-theory        93927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) 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-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-93927.        ((A -> (A or B)) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-32, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93928
in-theory        93928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
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-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-93928.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-23, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93929
in-theory        93929
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-93929.        (((A and B) -> B) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-22, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93930
in-theory        93930
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-93930.        (((A and B) -> A) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-21, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93931
in-theory        93931
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-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-93931.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-20, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93932
in-theory        93932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-93932.        ((A -> (B -> A)) and (((C and D) -> C) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-19, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93933
in-theory        93933
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-7 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-3 tm-6 tm-8)
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-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-93933.        (A or (((B and C) -> B) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-7, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93934
in-theory        93934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-3 tm-8)
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-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-93934.        ((((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G), M:tm-6, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93935
in-theory        93935
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 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-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-93935.        (A -> ((((B and C) -> B) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A)), M:tm-5, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93936
in-theory        93936
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-1 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-3 tm-6 tm-8)
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-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-93936.        (A -> (((B and C) -> B) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-1, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-93937
in-theory        93937
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-992 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-93937.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-992, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93938
in-theory        93938
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 (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     57
proof            (modus-ponens tm-980 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-93938.        (((((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 (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-980, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93939
in-theory        93939
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-930 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-93939.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-930, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93940
in-theory        93940
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-893 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
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-93940.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-893, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93941
in-theory        93941
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 (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     47
proof            (modus-ponens tm-855 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-48.           (((A -> (B and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-93941.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-855, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93942
in-theory        93942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-808 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-93942.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-808, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93943
in-theory        93943
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))) or J)))
theorem-size     41
proof            (modus-ponens tm-757 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-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-93943.        (((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))) or J))), M:tm-757, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93944
in-theory        93944
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))) or K)))
theorem-size     55
proof            (modus-ponens tm-708 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-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-93944.        (((((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))) or K))), M:tm-708, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93945
in-theory        93945
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))) or J)))
theorem-size     43
proof            (modus-ponens tm-665 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-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-93945.        ((((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))) or J))), M:tm-665, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93946
in-theory        93946
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-622 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6 tm-8)
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-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-93946.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-622, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93947
in-theory        93947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I or H)))
theorem-size     35
proof            (modus-ponens tm-609 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-93947.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I or H))), M:tm-609, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93948
in-theory        93948
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-605 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-93948.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-605, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93949
in-theory        93949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-595 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-93949.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-595, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93950
in-theory        93950
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-550 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
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-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-93950.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-550, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93951
in-theory        93951
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-540 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-93951.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-540, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93952
in-theory        93952
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-530 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
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-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-93952.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-530, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93953
in-theory        93953
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-520 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-93953.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-520, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93954
in-theory        93954
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-510 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6 tm-8)
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-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-93954.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-510, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93955
in-theory        93955
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-500 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6 tm-8)
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-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-93955.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-500, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93956
in-theory        93956
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))) or K)))
theorem-size     45
proof            (modus-ponens tm-490 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-93956.        ((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))) or K))), M:tm-490, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93957
in-theory        93957
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-480 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6 tm-8)
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-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-93957.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-480, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93958
in-theory        93958
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-469 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
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-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-93958.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-469, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93959
in-theory        93959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (H or I)))
theorem-size     35
proof            (modus-ponens tm-456 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-93959.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (H or I))), M:tm-456, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93960
in-theory        93960
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-453 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-93960.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-453, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93961
in-theory        93961
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-443 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-93961.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-443, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93962
in-theory        93962
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-409 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-93962.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-409, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93963
in-theory        93963
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-400 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-93963.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-400, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93964
in-theory        93964
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-391 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
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-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-93964.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-391, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93965
in-theory        93965
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-382 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
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-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-93965.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-382, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93966
in-theory        93966
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))) or K)))
theorem-size     45
proof            (modus-ponens tm-373 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-93966.        ((((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))) or K))), M:tm-373, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93967
in-theory        93967
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-364 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
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-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-93967.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-364, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93968
in-theory        93968
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-354 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
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-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-93968.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-354, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93969
in-theory        93969
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I -> (H and I))))
theorem-size     37
proof            (modus-ponens tm-341 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-93969.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I -> (H and I)))), M:tm-341, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93970
in-theory        93970
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))) or I)))
theorem-size     39
proof            (modus-ponens tm-338 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-93970.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-338, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93971
in-theory        93971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     67
proof            (modus-ponens tm-327 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-93971.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-327, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93972
in-theory        93972
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-326 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-93972.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-326, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93973
in-theory        93973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-325 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-93973.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-325, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93974
in-theory        93974
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     73
proof            (modus-ponens tm-324 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-93974.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-324, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93975
in-theory        93975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-323 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-93975.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-323, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93976
in-theory        93976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H and I) -> I))
theorem-size     35
proof            (modus-ponens tm-322 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-93976.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H and I) -> I)), M:tm-322, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93977
in-theory        93977
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H and I) -> H))
theorem-size     35
proof            (modus-ponens tm-320 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-93977.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H and I) -> H)), M:tm-320, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93978
in-theory        93978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     43
proof            (modus-ponens tm-318 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-93978.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93979
in-theory        93979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-93979.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I -> H))), M:tm-315, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93980
in-theory        93980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     61
proof            (modus-ponens tm-311 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-93980.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-311, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93981
in-theory        93981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-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-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-93981.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) or H)), M:tm-310, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93982
in-theory        93982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-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-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-93982.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and H))), M:tm-309, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93983
in-theory        93983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     45
proof            (modus-ponens tm-308 tm-999 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-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-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-93983.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-308, m:tm-999, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))
================================================================
tm-name          tm-93984
in-theory        93984
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-999 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
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-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-93984.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-999, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))
================================================================
tm-name          tm-93985
in-theory        93985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     61
proof            (modus-ponens tm-305 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-93985.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-305, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93986
in-theory        93986
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))) or J)))
theorem-size     41
proof            (modus-ponens tm-303 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
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-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-93986.        ((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))) or J))), M:tm-303, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93987
in-theory        93987
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-270 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6 tm-8)
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-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-93987.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-270, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93988
in-theory        93988
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-239 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6 tm-8)
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-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-93988.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-239, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93989
in-theory        93989
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))) or K)))
theorem-size     47
proof            (modus-ponens tm-210 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-93989.        ((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))) or K))), M:tm-210, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93990
in-theory        93990
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-183 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
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-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-93990.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-183, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93991
in-theory        93991
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-157 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6 tm-8)
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-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-93991.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-157, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93992
in-theory        93992
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))) or J)))
theorem-size     45
proof            (modus-ponens tm-147 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8)
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-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-93992.        ((((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))) or J))), M:tm-147, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93993
in-theory        93993
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-134 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6 tm-8)
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-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-93993.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-134, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93994
in-theory        93994
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))) or J)))
theorem-size     45
proof            (modus-ponens tm-125 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
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-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-93994.        (((((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))) or J))), M:tm-125, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93995
in-theory        93995
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))) or K)))
theorem-size     45
proof            (modus-ponens tm-113 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-93995.        ((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))) or K))), M:tm-113, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93996
in-theory        93996
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))) or J)))
theorem-size     49
proof            (modus-ponens tm-105 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
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-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-93996.        ((((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))) or J))), M:tm-105, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93997
in-theory        93997
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-95 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-93997.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-95, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93998
in-theory        93998
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-83 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
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-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-93998.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-83, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-93999
in-theory        93999
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))) or H)))
theorem-size     35
proof            (modus-ponens tm-76 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-6 tm-8)
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-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-93999.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-76, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94000
in-theory        94000
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))) or I)))
theorem-size     41
proof            (modus-ponens tm-69 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-6 tm-8)
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-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-94000.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-69, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94001
in-theory        94001
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))) or J)))
theorem-size     43
proof            (modus-ponens tm-54 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-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-94001.        (((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))) or J))), M:tm-54, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94002
in-theory        94002
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-42 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94002.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-42, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94003
in-theory        94003
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-32 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-94003.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-32, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94004
in-theory        94004
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-23 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
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-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-94004.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-23, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94005
in-theory        94005
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-22 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94005.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-22, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94006
in-theory        94006
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-21 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94006.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-21, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94007
in-theory        94007
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))) or J)))
theorem-size     43
proof            (modus-ponens tm-20 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94007.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-20, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94008
in-theory        94008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-19 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94008.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-19, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94009
in-theory        94009
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-7 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-6 tm-8)
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-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-94009.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-7, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94010
in-theory        94010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) or H)
theorem-size     31
proof            (modus-ponens tm-6 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-6 tm-5 tm-2 tm-8)
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-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-94010.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) or H), M:tm-6, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94011
in-theory        94011
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6 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-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-94011.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)) and A)), M:tm-5, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94012
in-theory        94012
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-1 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-6 tm-8)
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-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-94012.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-1, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-94013
in-theory        94013
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-94013.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-992, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94014
in-theory        94014
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 (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-94014.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-980, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94015
in-theory        94015
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-94015.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-930, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94016
in-theory        94016
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-94016.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-893, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94017
in-theory        94017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-94017.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-855, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94018
in-theory        94018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-94018.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-808, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94019
in-theory        94019
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-94019.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-757, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94020
in-theory        94020
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))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) 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-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-94020.        (((((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))) or J))), M:tm-708, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94021
in-theory        94021
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-94021.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-665, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94022
in-theory        94022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-94022.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-622, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94023
in-theory        94023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-94023.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94024
in-theory        94024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-94024.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-605, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94025
in-theory        94025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-94025.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H or G)) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-595, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94026
in-theory        94026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8)
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-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-94026.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-550, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94027
in-theory        94027
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-94027.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-540, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94028
in-theory        94028
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8)
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-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-94028.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-530, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94029
in-theory        94029
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-94029.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-520, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94030
in-theory        94030
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6 tm-8)
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-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-94030.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-510, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94031
in-theory        94031
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6 tm-8)
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-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-94031.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-500, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94032
in-theory        94032
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6 tm-8)
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-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-94032.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-490, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94033
in-theory        94033
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-94033.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-480, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94034
in-theory        94034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-94034.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-469, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94035
in-theory        94035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-94035.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94036
in-theory        94036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-94036.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-453, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94037
in-theory        94037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-94037.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (G or H)) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-443, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94038
in-theory        94038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-94038.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-409, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94039
in-theory        94039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-94039.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-400, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94040
in-theory        94040
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8)
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-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-94040.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-391, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94041
in-theory        94041
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
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-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-94041.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-382, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94042
in-theory        94042
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
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-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-94042.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-373, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94043
in-theory        94043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-94043.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-364, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94044
in-theory        94044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-94044.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-354, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94045
in-theory        94045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-94045.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94046
in-theory        94046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
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-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-94046.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-338, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94047
in-theory        94047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-94047.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-327, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94048
in-theory        94048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-94048.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> H) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-326, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94049
in-theory        94049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-94049.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G and H) -> G) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-325, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94050
in-theory        94050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-94050.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-324, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94051
in-theory        94051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-94051.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-323, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94052
in-theory        94052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-94052.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94053
in-theory        94053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-94053.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94054
in-theory        94054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-94054.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94055
in-theory        94055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-94055.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94056
in-theory        94056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 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-7.            (A -> (B or 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-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-94056.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G or ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-311, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94057
in-theory        94057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-94057.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)), M:tm-310, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94058
in-theory        94058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-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-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-94058.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and G))), M:tm-309, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94059
in-theory        94059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-1000 ((A (-> Am (-> Bm Am))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
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-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-94059.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-308, m:tm-1000, u:((A (-> Am (-> Bm Am))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-94060
in-theory        94060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (A -> (B -> A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-1000 ((A (-> Am (-> Bm Am))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 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-3.            ((A and B) -> A), axiom
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-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-94060.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (A -> (B -> A))), M:tm-307, m:tm-1000, u:((A (-> Am (-> Bm Am))) (B (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))
================================================================
tm-name          tm-94061
in-theory        94061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-94061.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and (G -> ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))), M:tm-305, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94062
in-theory        94062
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))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-94062.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-303, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94063
in-theory        94063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-8)
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-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-94063.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-270, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94064
in-theory        94064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-8)
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-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-94064.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-239, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94065
in-theory        94065
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))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-94065.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-210, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94066
in-theory        94066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-94066.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-183, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94067
in-theory        94067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-94067.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-157, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94068
in-theory        94068
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6 tm-8)
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-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-94068.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-147, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94069
in-theory        94069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-94069.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-134, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94070
in-theory        94070
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6 tm-8)
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-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-94070.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-125, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94071
in-theory        94071
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))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
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-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-94071.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-113, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94072
in-theory        94072
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))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-94072.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-105, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94073
in-theory        94073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
proof-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-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-94073.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-95, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94074
in-theory        94074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-94074.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-83, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94075
in-theory        94075
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6 tm-8)
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-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-94075.        (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-76, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94076
in-theory        94076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6 tm-8)
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-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-94076.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-69, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94077
in-theory        94077
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-94077.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-54, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94078
in-theory        94078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94078.        ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-42, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94079
in-theory        94079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm 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-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-94079.        ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-32, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94080
in-theory        94080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-94080.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-23, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94081
in-theory        94081
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94081.        (((A and B) -> B) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-22, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94082
in-theory        94082
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94082.        (((A and B) -> A) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-21, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94083
in-theory        94083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-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-94083.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-20, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94084
in-theory        94084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
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-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-94084.        ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-19, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94085
in-theory        94085
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-7 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-1 tm-6 tm-8)
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-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-94085.        (A or ((B -> (C -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-7, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94086
in-theory        94086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-1 tm-8)
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-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-94086.        (((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) or G), M:tm-6, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94087
in-theory        94087
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 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-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-94087.        (A -> (((B -> (C -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and A)), M:tm-5, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94088
in-theory        94088
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-1 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-6 tm-8)
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-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-94088.        (A -> ((B -> (C -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-1, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-94089
in-theory        94089
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-992 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-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-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-94089.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-992, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94090
in-theory        94090
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     45
proof            (modus-ponens tm-980 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
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-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-94090.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-980, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94091
in-theory        94091
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-930 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-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-94091.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-930, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94092
in-theory        94092
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-893 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), 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-94092.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-893, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94093
in-theory        94093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     35
proof            (modus-ponens tm-855 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
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-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-94093.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-855, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94094
in-theory        94094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-808 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
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-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-94094.        (((A -> B) -> (((C and A) or A) -> B)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-808, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94095
in-theory        94095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-757 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-7.            (A -> (B or A)), axiom
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-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-94095.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-757, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94096
in-theory        94096
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))) or I)))
theorem-size     43
proof            (modus-ponens tm-708 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-94096.        (((((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))) or I))), M:tm-708, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94097
in-theory        94097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-665 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
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-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-94097.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-665, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94098
in-theory        94098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-622 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94098.        ((A -> (B -> (C or B))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-622, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94099
in-theory        94099
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94099.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94100
in-theory        94100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-605 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94100.        ((A -> ((B -> (C or B)) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-605, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94101
in-theory        94101
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G or F)) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-595 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-94101.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G or F)) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-595, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94102
in-theory        94102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-550 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94102.        (((A -> (B or A)) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-550, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94103
in-theory        94103
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-540 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94103.        ((A or (B -> (C or B))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-540, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94104
in-theory        94104
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-530 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94104.        ((A or (B -> (B or C))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-530, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94105
in-theory        94105
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-520 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94105.        ((A or (B -> (C -> (B and C)))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-520, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94106
in-theory        94106
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-510 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94106.        ((A or ((B and C) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-510, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94107
in-theory        94107
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-500 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94107.        ((A or ((B and C) -> B)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-500, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94108
in-theory        94108
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-490 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94108.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-490, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94109
in-theory        94109
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-480 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94109.        ((A or (B -> (C -> B))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-480, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94110
in-theory        94110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-469 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94110.        ((A -> (B -> (B or C))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-469, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94111
in-theory        94111
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94111.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94112
in-theory        94112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-453 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94112.        ((A -> ((B -> (B or C)) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-453, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94113
in-theory        94113
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (F or G)) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-443 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-94113.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (F or G)) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-443, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94114
in-theory        94114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-409 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94114.        (((A -> (A or B)) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-409, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94115
in-theory        94115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-400 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94115.        (((A -> (B -> (A and B))) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-400, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94116
in-theory        94116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-391 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94116.        ((((A and B) -> B) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-391, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94117
in-theory        94117
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-382 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94117.        ((((A and B) -> A) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-382, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94118
in-theory        94118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-373 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94118.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-373, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94119
in-theory        94119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-364 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94119.        (((A -> (B -> A)) or C) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-364, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94120
in-theory        94120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-354 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 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-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-94120.        ((A -> (B -> (C -> (B and C)))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-354, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94121
in-theory        94121
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-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-94121.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94122
in-theory        94122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-338 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 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-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-94122.        (((A -> B) -> (A -> (A and B))) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-338, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94123
in-theory        94123
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> (F and G))) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     43
proof            (modus-ponens tm-327 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-94123.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> (F and G))) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-327, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94124
in-theory        94124
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and G) -> G) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-326 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-94124.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and G) -> G) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-326, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94125
in-theory        94125
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and G) -> F) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-325 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-94125.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and G) -> F) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-325, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94126
in-theory        94126
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     49
proof            (modus-ponens tm-324 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-94126.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-324, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94127
in-theory        94127
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> F)) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-323 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-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-94127.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> F)) and (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-323, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94128
in-theory        94128
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-94128.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94129
in-theory        94129
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-94129.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94130
in-theory        94130
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-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-94130.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94131
in-theory        94131
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-94131.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94132
in-theory        94132
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F or (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-311 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or 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-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-94132.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F or (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-311, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94133
in-theory        94133
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 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-6.            (A -> (A or 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-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-94133.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) or F)), M:tm-310, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94134
in-theory        94134
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 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-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-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-94134.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and F))), M:tm-309, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94135
in-theory        94135
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-305 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 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-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-94135.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-305, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94136
in-theory        94136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-303 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-94136.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-303, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94137
in-theory        94137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-270 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-7 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-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-94137.        ((A -> (((B and C) -> C) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-270, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94138
in-theory        94138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-239 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-7 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-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-94138.        ((A -> (((B and C) -> B) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-239, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94139
in-theory        94139
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-210 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 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-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-94139.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-210, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94140
in-theory        94140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-183 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 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-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-94140.        ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-183, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94141
in-theory        94141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-157 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-94141.        ((A -> ((B and C) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-157, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94142
in-theory        94142
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))) or H)))
theorem-size     33
proof            (modus-ponens tm-147 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 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-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-94142.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-147, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94143
in-theory        94143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-134 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-94143.        ((A -> ((B and C) -> B)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-134, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94144
in-theory        94144
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))) or H)))
theorem-size     33
proof            (modus-ponens tm-125 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 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-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-94144.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-125, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94145
in-theory        94145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-113 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 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-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-94145.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-113, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94146
in-theory        94146
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))) or H)))
theorem-size     37
proof            (modus-ponens tm-105 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 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-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-94146.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-105, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94147
in-theory        94147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-95 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 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-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-94147.        (((A -> B) -> (A -> A)) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-95, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94148
in-theory        94148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-83 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-94148.        ((A -> (B -> (C -> B))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-83, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94149
in-theory        94149
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     23
proof            (modus-ponens tm-76 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-7 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-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-94149.        (((not (not A)) -> A) and (B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-76, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94150
in-theory        94150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     29
proof            (modus-ponens tm-69 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-7 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-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-94150.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-69, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94151
in-theory        94151
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-54 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
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-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-94151.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-54, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94152
in-theory        94152
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-42 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94152.        ((A -> (B or A)) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-42, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94153
in-theory        94153
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-32 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-94153.        ((A -> (A or B)) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-32, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94154
in-theory        94154
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-23 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-7 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-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-94154.        ((A -> (B -> (A and B))) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-23, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94155
in-theory        94155
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-22 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-7 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-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-94155.        (((A and B) -> B) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-22, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94156
in-theory        94156
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-21 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-7 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-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-94156.        (((A and B) -> A) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-21, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94157
in-theory        94157
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-20 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 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-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-94157.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-20, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94158
in-theory        94158
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-19 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 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-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-94158.        ((A -> (B -> A)) and (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-19, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94159
in-theory        94159
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     19
proof            (modus-ponens tm-7 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-7 tm-6 tm-8)
proof-size       79
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-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-94159.        (A or (B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-7, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94160
in-theory        94160
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-6 tm-7 tm-8)
proof-size       79
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-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-94160.        ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) or F), M:tm-6, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94161
in-theory        94161
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-94161.        (A -> ((B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and A)), M:tm-5, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94162
in-theory        94162
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     19
proof            (modus-ponens tm-1 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-1 tm-7 tm-6 tm-8)
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-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-94162.        (A -> (B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-1, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-94163
in-theory        94163
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-992 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-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-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-94163.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I)), M:tm-992, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94164
in-theory        94164
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I))
theorem-size     45
proof            (modus-ponens tm-980 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-94164.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I)), M:tm-980, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94165
in-theory        94165
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-966 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> (-> B C) (-> (or D B) C)) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-94165.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-966, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> (-> B C) (-> (or D B) C)) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94166
in-theory        94166
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-962 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> (-> B C) (-> (or D B) C)) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> (-> B C) (-> (or D B) C)))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       233
proof-steps      13
----------------------------------------------------------------
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-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-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-94166.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> C) -> ((A or B) -> C)))), M:tm-962, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> (-> B C) (-> (or D B) C)) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> (-> B C) (-> (or D B) C))))))
================================================================
tm-name          tm-94167
in-theory        94167
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-930 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-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-94167.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-930, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94168
in-theory        94168
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-917 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (or B C) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       153
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-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-94168.        ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-917, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (or B C) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94169
in-theory        94169
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-914 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (or B C) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (or B C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-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-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-94169.        ((A or (B or A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (B or A))), M:tm-914, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (or B C) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (or B C)))))
================================================================
tm-name          tm-94170
in-theory        94170
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-893 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-94170.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-893, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94171
in-theory        94171
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-879 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (or B C) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       153
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-94171.        ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-879, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (or B C) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94172
in-theory        94172
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-876 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (or B C) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (or B C))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-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-94172.        ((A or (A or B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B))), M:tm-876, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (or B C) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (or B C)))))
================================================================
tm-name          tm-94173
in-theory        94173
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-874 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-94173.        ((A -> (B or A)) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G)), M:tm-874, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94174
in-theory        94174
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-872 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-94174.        ((A -> (A or B)) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G)), M:tm-872, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94175
in-theory        94175
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G))
theorem-size     25
proof            (modus-ponens tm-870 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-94175.        ((A -> (B -> (A and B))) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G)), M:tm-870, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94176
in-theory        94176
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-869 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-94176.        (((A and B) -> B) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G)), M:tm-869, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94177
in-theory        94177
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-868 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-94177.        (((A and B) -> A) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G)), M:tm-868, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94178
in-theory        94178
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-867 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-94178.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-867, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94179
in-theory        94179
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-866 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-94179.        ((A -> (B -> A)) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G)), M:tm-866, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94180
in-theory        94180
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) or F))
theorem-size     19
proof            (modus-ponens tm-861 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-7)
proof-size       121
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-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-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-94180.        (A or ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) or F)), M:tm-861, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94181
in-theory        94181
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) or F)
theorem-size     19
proof            (modus-ponens tm-860 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6)
proof-size       121
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-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-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-94181.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) or F), M:tm-860, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94182
in-theory        94182
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) or F) and A))
theorem-size     21
proof            (modus-ponens tm-859 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       127
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-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-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-94182.        (A -> (((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) or F) and A)), M:tm-859, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94183
in-theory        94183
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) or F))
theorem-size     19
proof            (modus-ponens tm-858 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       121
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-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-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-94183.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) or F)), M:tm-858, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))
================================================================
tm-name          tm-94184
in-theory        94184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     35
proof            (modus-ponens tm-855 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-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-94184.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-855, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94185
in-theory        94185
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     23
proof            (modus-ponens tm-841 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> B (and C B)) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 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-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-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-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-94185.        ((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-841, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> B (and C B)) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94186
in-theory        94186
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-837 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> B (and C B)) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> B (and C B)))))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-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-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-94186.        ((A or (B -> (A and B))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (B -> (A and B)))), M:tm-837, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> B (and C B)) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> B (and C B))))))
================================================================
tm-name          tm-94187
in-theory        94187
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B))
theorem-size     23
proof            (modus-ponens tm-836 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-4 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-48.           (((A -> (B and 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-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-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-94187.        (((A and B) or B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B)), M:tm-836, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94188
in-theory        94188
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and A))
theorem-size     23
proof            (modus-ponens tm-835 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-3 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-48.           (((A -> (B and 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-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-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-94188.        (((A and B) or A) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and A)), M:tm-835, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94189
in-theory        94189
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-834 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> (-> B C) (-> B D)) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       223
proof-steps      13
----------------------------------------------------------------
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-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-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-94189.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> (A -> C)))), M:tm-834, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> (-> B C) (-> B D)) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-94190
in-theory        94190
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-833 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> B C) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> B C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-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-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-94190.        ((A or (B -> A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (B -> A))), M:tm-833, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> B C) (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) (-> B C)))))
================================================================
tm-name          tm-94191
in-theory        94191
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-831 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-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-94191.        ((A -> (B or A)) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C))), M:tm-831, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94192
in-theory        94192
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-829 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-94192.        ((A -> (A or B)) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C))), M:tm-829, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94193
in-theory        94193
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))
theorem-size     21
proof            (modus-ponens tm-827 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-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-94193.        (A -> (A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))), M:tm-827, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94194
in-theory        94194
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C)))
theorem-size     27
proof            (modus-ponens tm-826 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-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-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-94194.        ((A -> (B -> (A and B))) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C))), M:tm-826, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94195
in-theory        94195
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-825 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-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-94195.        (((A and B) -> B) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C))), M:tm-825, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94196
in-theory        94196
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-824 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-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-94196.        (((A and B) -> A) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C))), M:tm-824, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94197
in-theory        94197
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-823 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
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-48.           (((A -> (B and 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-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-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-94197.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-823, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94198
in-theory        94198
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-822 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-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-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-94198.        ((A -> (B -> A)) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C))), M:tm-822, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94199
in-theory        94199
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-816 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-9 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-48.           (((A -> (B and 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-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-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-94199.        ((A -> (not ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))) -> (not A)), M:tm-816, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94200
in-theory        94200
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and E) -> F) -> ((E or ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and E)) -> F))
theorem-size     41
proof            (modus-ponens tm-815 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-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-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-94200.        ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and E) -> F) -> ((E or ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and E)) -> F)), M:tm-815, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94201
in-theory        94201
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B)))
theorem-size     21
proof            (modus-ponens tm-814 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
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-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-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-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-94201.        (A or (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B))), M:tm-814, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94202
in-theory        94202
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) or F)
theorem-size     21
proof            (modus-ponens tm-813 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-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-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-94202.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) or F), M:tm-813, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94203
in-theory        94203
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B)) and A))
theorem-size     23
proof            (modus-ponens tm-812 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-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-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-94203.        (A -> ((B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B)) and A)), M:tm-812, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94204
in-theory        94204
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B)))
theorem-size     21
proof            (modus-ponens tm-811 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-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-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-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-94204.        (A -> (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B))), M:tm-811, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (and (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B))))
================================================================
tm-name          tm-94205
in-theory        94205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     29
proof            (modus-ponens tm-808 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-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-94205.        (((A -> B) -> (((C and A) or A) -> B)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-808, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94206
in-theory        94206
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-795 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-4 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-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-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-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-94206.        (((A and B) or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-795, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94207
in-theory        94207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     29
proof            (modus-ponens tm-757 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94207.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-757, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94208
in-theory        94208
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-744 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-3 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-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-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-94208.        (((A and B) or A) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-744, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94209
in-theory        94209
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) or I))
theorem-size     43
proof            (modus-ponens tm-708 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94209.        (((((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) or I)), M:tm-708, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94210
in-theory        94210
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-694 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> (-> B C) (-> B D)) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       193
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-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-94210.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-694, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> (-> B C) (-> B D)) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94211
in-theory        94211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-665 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94211.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-665, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94212
in-theory        94212
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-651 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> B C) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       153
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-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-94212.        ((A or (B -> A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-651, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (-> B C) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94213
in-theory        94213
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-649 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 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-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or 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-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-94213.        ((A -> (B or A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-649, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94214
in-theory        94214
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-647 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or 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-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-94214.        ((A -> (A or B)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-647, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94215
in-theory        94215
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))
theorem-size     19
proof            (modus-ponens tm-645 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 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-5.            (A -> (B -> (A and B))), axiom
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-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-94215.        (A -> (A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))), M:tm-645, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94216
in-theory        94216
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-644 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       153
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-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-94216.        ((A -> (B -> (A and B))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-644, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94217
in-theory        94217
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-643 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4 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-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> 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-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-94217.        (((A and B) -> B) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-643, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94218
in-theory        94218
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-642 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> 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-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-94218.        (((A and B) -> A) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-642, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94219
in-theory        94219
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-641 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6)
proof-size       177
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-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-94219.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-641, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94220
in-theory        94220
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-640 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 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-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-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-94220.        ((A -> (B -> A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-640, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94221
in-theory        94221
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F)) -> F)
theorem-size     21
proof            (modus-ponens tm-638 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (and B (-> (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) C)) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4 tm-6)
proof-size       157
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-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-94221.        ((A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F)) -> F), M:tm-638, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (and B (-> (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) C)) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94222
in-theory        94222
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) and F) -> E)
theorem-size     21
proof            (modus-ponens tm-636 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (and (-> (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B) C) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3 tm-6)
proof-size       157
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-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-94222.        ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) and F) -> E), M:tm-636, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> (and (-> (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) B) C) (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94223
in-theory        94223
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-631 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-9 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-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-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-94223.        ((A -> (not (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))) -> (not A)), M:tm-631, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94224
in-theory        94224
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) -> ((F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)) -> E))
theorem-size     37
proof            (modus-ponens tm-630 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 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-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-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-94224.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) -> ((F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)) -> E)), M:tm-630, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94225
in-theory        94225
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     19
proof            (modus-ponens tm-629 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-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-94225.        (A or (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-629, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94226
in-theory        94226
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) or F)
theorem-size     19
proof            (modus-ponens tm-628 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-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-94226.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) or F), M:tm-628, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94227
in-theory        94227
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and A))
theorem-size     21
proof            (modus-ponens tm-627 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       127
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-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-94227.        (A -> ((B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and A)), M:tm-627, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94228
in-theory        94228
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     19
proof            (modus-ponens tm-625 tm-1002 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-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-94228.        (A -> (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-625, m:tm-1002, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) (Em (-> B (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
================================================================
tm-name          tm-94229
in-theory        94229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-622 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94229.        ((A -> (B -> (C or B))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-622, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94230
in-theory        94230
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94230.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (G or F))), M:tm-609, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94231
in-theory        94231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-605 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94231.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-605, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94232
in-theory        94232
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (G or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-595 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-94232.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (G or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))), M:tm-595, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94233
in-theory        94233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-550 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94233.        (((A -> (B or A)) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-550, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94234
in-theory        94234
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-540 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94234.        ((A or (B -> (C or B))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-540, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94235
in-theory        94235
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-530 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94235.        ((A or (B -> (B or C))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-530, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94236
in-theory        94236
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-520 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94236.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-520, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94237
in-theory        94237
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-510 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94237.        ((A or ((B and C) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-510, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94238
in-theory        94238
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-500 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94238.        ((A or ((B and C) -> B)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-500, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94239
in-theory        94239
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-490 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94239.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I)), M:tm-490, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94240
in-theory        94240
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-480 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94240.        ((A or (B -> (C -> B))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-480, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94241
in-theory        94241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-469 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94241.        ((A -> (B -> (B or C))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-469, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94242
in-theory        94242
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94242.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (F or G))), M:tm-456, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94243
in-theory        94243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-453 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94243.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-453, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94244
in-theory        94244
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (F or G)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-443 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-94244.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (F or G)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))), M:tm-443, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94245
in-theory        94245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-409 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94245.        (((A -> (A or B)) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-409, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94246
in-theory        94246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-400 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94246.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-400, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94247
in-theory        94247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-391 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94247.        ((((A and B) -> B) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-391, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94248
in-theory        94248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-382 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94248.        ((((A and B) -> A) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-382, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94249
in-theory        94249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-373 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94249.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I)), M:tm-373, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94250
in-theory        94250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-364 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94250.        (((A -> (B -> A)) or C) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-364, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94251
in-theory        94251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-354 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94251.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-354, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94252
in-theory        94252
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94252.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94253
in-theory        94253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G))
theorem-size     27
proof            (modus-ponens tm-338 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94253.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G)), M:tm-338, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94254
in-theory        94254
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (G -> (F and G))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)))
theorem-size     43
proof            (modus-ponens tm-327 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-94254.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (G -> (F and G))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))), M:tm-327, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94255
in-theory        94255
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (((F and G) -> G) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-326 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-94255.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (((F and G) -> G) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))), M:tm-326, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94256
in-theory        94256
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (((F and G) -> F) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-325 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-94256.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (((F and G) -> F) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))), M:tm-325, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94257
in-theory        94257
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)))
theorem-size     49
proof            (modus-ponens tm-324 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-94257.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))), M:tm-324, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94258
in-theory        94258
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (G -> F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-323 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-94258.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (G -> F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))), M:tm-323, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94259
in-theory        94259
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94259.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F and G) -> G)), M:tm-322, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94260
in-theory        94260
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94260.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F and G) -> F)), M:tm-320, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94261
in-theory        94261
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94261.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94262
in-theory        94262
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94262.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (G -> F))), M:tm-315, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94263
in-theory        94263
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F or ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)))
theorem-size     37
proof            (modus-ponens tm-311 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 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-7.            (A -> (B or 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-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-94263.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F or ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))), M:tm-311, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94264
in-theory        94264
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-94264.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) or F)), M:tm-310, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94265
in-theory        94265
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
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-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-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-94265.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and F))), M:tm-309, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94266
in-theory        94266
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)))
theorem-size     37
proof            (modus-ponens tm-305 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-94266.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))), M:tm-305, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94267
in-theory        94267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     29
proof            (modus-ponens tm-303 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94267.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-303, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94268
in-theory        94268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-270 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94268.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-270, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94269
in-theory        94269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-239 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94269.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-239, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94270
in-theory        94270
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) or I))
theorem-size     35
proof            (modus-ponens tm-210 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94270.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I)), M:tm-210, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94271
in-theory        94271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-183 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94271.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-183, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94272
in-theory        94272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-157 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94272.        ((A -> ((B and C) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-157, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94273
in-theory        94273
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) or H))
theorem-size     33
proof            (modus-ponens tm-147 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94273.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-147, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94274
in-theory        94274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-134 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94274.        ((A -> ((B and C) -> B)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-134, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94275
in-theory        94275
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) or H))
theorem-size     33
proof            (modus-ponens tm-125 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94275.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-125, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94276
in-theory        94276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-113 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94276.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I)), M:tm-113, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94277
in-theory        94277
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) or H))
theorem-size     37
proof            (modus-ponens tm-105 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94277.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-105, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94278
in-theory        94278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G))
theorem-size     25
proof            (modus-ponens tm-95 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94278.        (((A -> B) -> (A -> A)) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G)), M:tm-95, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94279
in-theory        94279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-83 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94279.        ((A -> (B -> (C -> B))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-83, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94280
in-theory        94280
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) or F))
theorem-size     23
proof            (modus-ponens tm-76 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94280.        (((not (not A)) -> A) and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) or F)), M:tm-76, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94281
in-theory        94281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G))
theorem-size     29
proof            (modus-ponens tm-69 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94281.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) or G)), M:tm-69, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94282
in-theory        94282
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-54 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-94282.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) or H)), M:tm-54, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-94283
in-theory        94283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       101
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-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-94283.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-1003, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-94284
in-theory        94284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
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-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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-94284.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-1003, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-94285
in-theory        94285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((not (not E)) -> E))
theorem-size     21
proof            (modus-ponens tm-1003 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       85
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-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-10.           ((not (not A)) -> A), axiom
tm-94285.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((not (not E)) -> E)), M:tm-1003, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-94286
in-theory        94286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-94286.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> F)))), M:tm-1003, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-94287
in-theory        94287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-1003 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94287.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> E))), M:tm-1003, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-94288
in-theory        94288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-94288.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-1003, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-94289
in-theory        94289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-94289.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-1003, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-94290
in-theory        94290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-94290.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-1003, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-94291
in-theory        94291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-1003 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-94291.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F and G) -> F))), M:tm-1003, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-94292
in-theory        94292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-94292.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-1003, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-94293
in-theory        94293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-1003 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-94293.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F and G) -> G))), M:tm-1003, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-94294
in-theory        94294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> F)) and E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-94294.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> F)) and E))), M:tm-1003, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-94295
in-theory        94295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-94295.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-1003, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-94296
in-theory        94296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and G) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-94296.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and G) -> F) and E))), M:tm-1003, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-94297
in-theory        94297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and G) -> G) and E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-94297.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and G) -> G) and E))), M:tm-1003, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-94298
in-theory        94298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-94298.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (F and G))) and E))), M:tm-1003, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-94299
in-theory        94299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-94299.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (E and F)))), M:tm-1003, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-94300
in-theory        94300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-94300.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (F and G))))), M:tm-1003, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-94301
in-theory        94301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-1003 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
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-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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-94301.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) or G)), M:tm-1003, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-94302
in-theory        94302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-1003 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-94302.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-1003, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-94303
in-theory        94303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) or G))
theorem-size     23
proof            (modus-ponens tm-1003 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-94303.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) or G)), M:tm-1003, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-94304
in-theory        94304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) or G))
theorem-size     23
proof            (modus-ponens tm-1003 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-94304.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) or G)), M:tm-1003, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-94305
in-theory        94305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) or G))
theorem-size     25
proof            (modus-ponens tm-1003 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) 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-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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-94305.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) or G)), M:tm-1003, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-94306
in-theory        94306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) or G))
theorem-size     23
proof            (modus-ponens tm-1003 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
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-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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-94306.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) or G)), M:tm-1003, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-94307
in-theory        94307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (F or G)) and E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) 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-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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-94307.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (F or G)) and E))), M:tm-1003, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-94308
in-theory        94308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-94308.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (F or G)))), M:tm-1003, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-94309
in-theory        94309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-94309.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> F)))), M:tm-1003, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-94310
in-theory        94310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-94310.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-1003, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-94311
in-theory        94311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-1003 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-94311.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F and G) -> F))), M:tm-1003, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-94312
in-theory        94312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-1003 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-94312.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F and G) -> G))), M:tm-1003, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-94313
in-theory        94313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-94313.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (F and G))))), M:tm-1003, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-94314
in-theory        94314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-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-94314.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (F or G)))), M:tm-1003, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-94315
in-theory        94315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-94315.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G or F)))), M:tm-1003, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-94316
in-theory        94316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) or G))
theorem-size     23
proof            (modus-ponens tm-1003 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-94316.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) or G)), M:tm-1003, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-94317
in-theory        94317
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G or F)) and E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-94317.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G or F)) and E))), M:tm-1003, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-94318
in-theory        94318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-94318.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G or F)))), M:tm-1003, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-94319
in-theory        94319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-94319.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-1003, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-94320
in-theory        94320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       151
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-94320.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-1003, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-94321
in-theory        94321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-94321.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (((E and G) or E) -> F))), M:tm-1003, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-94322
in-theory        94322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-94322.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (((G and E) or E) -> F))), M:tm-1003, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-94323
in-theory        94323
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-1003 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       129
proof-steps      9
----------------------------------------------------------------
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-94323.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-1003, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-94324
in-theory        94324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-94324.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-1003, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-94325
in-theory        94325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-1003 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       119
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-94325.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-1003, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-94326
in-theory        94326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       155
proof-steps      9
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-94326.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-1003, 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-94327
in-theory        94327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-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-94327.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-1003, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-94328
in-theory        94328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-1003 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) 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-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-94328.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-1003, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-94329
in-theory        94329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-94329.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))), M:tm-1003, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-94330
in-theory        94330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
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-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-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-94330.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G)))), M:tm-1003, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-94331
in-theory        94331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-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-94331.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-1003, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-94332
in-theory        94332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94332.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> E))) -> (not E))), M:tm-1003, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-94333
in-theory        94333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
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-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-94333.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G))))), M:tm-1003, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-94334
in-theory        94334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> (not E)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94334.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> (not E)) -> (not (E and F)))), M:tm-1003, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-94335
in-theory        94335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> (not F)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94335.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> (not F)) -> (not (E and F)))), M:tm-1003, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-94336
in-theory        94336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (E and F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
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-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-94336.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (E and F)))) -> (not E))), M:tm-1003, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-94337
in-theory        94337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (E or F))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
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-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-94337.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (E or F))) -> (not E))), M:tm-1003, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-94338
in-theory        94338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F or E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94338.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F or E))) -> (not E))), M:tm-1003, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-94339
in-theory        94339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
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-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-94339.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F)))), M:tm-1003, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-94340
in-theory        94340
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
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-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-94340.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F)))), M:tm-1003, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-94341
in-theory        94341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       145
proof-steps      9
----------------------------------------------------------------
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-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-94341.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G))), M:tm-1003, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-94342
in-theory        94342
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94342.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-1003, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-94343
in-theory        94343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G))
theorem-size     29
proof            (modus-ponens tm-1003 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
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-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-94343.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G)), M:tm-1003, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-94344
in-theory        94344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-94344.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E))), M:tm-1003, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-94345
in-theory        94345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94345.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E)))), M:tm-1003, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-94346
in-theory        94346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94346.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-1003, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-94347
in-theory        94347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((not (not E)) -> (not E)) -> (not (not (not E)))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94347.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((not (not E)) -> (not E)) -> (not (not (not E))))), M:tm-1003, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-94348
in-theory        94348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (((not (not E)) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 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-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-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-94348.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (((not (not E)) or E) -> F))), M:tm-1003, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-94349
in-theory        94349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-1003 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94349.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((not (not F)) -> F))), M:tm-1003, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-94350
in-theory        94350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((not (not E)) -> E) or F))
theorem-size     23
proof            (modus-ponens tm-1003 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
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-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-94350.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((not (not E)) -> E) or F)), M:tm-1003, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-94351
in-theory        94351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((not (not F)) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       105
proof-steps      9
----------------------------------------------------------------
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-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-94351.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((not (not F)) -> F) and E))), M:tm-1003, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-94352
in-theory        94352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94352.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F))), M:tm-1003, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-94353
in-theory        94353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-1003 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94353.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((not (not F)) -> F))), M:tm-1003, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-94354
in-theory        94354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (G -> F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94354.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (G -> F)))) -> (not E))), M:tm-1003, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-94355
in-theory        94355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-1003 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       139
proof-steps      11
----------------------------------------------------------------
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-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-94355.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G))), M:tm-1003, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-94356
in-theory        94356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94356.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (H -> G))))), M:tm-1003, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-94357
in-theory        94357
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
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-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-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-94357.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (G -> F))) or H)), M:tm-1003, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-94358
in-theory        94358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-94358.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (H -> G))) and E))), M:tm-1003, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-94359
in-theory        94359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-94359.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (G -> F)))), M:tm-1003, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-94360
in-theory        94360
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm 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-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-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-94360.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (H -> G))))), M:tm-1003, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-94361
in-theory        94361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> E))
theorem-size     19
proof            (modus-ponens tm-1003 tm-86 ((A (-> Am Am))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94361.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> E)), M:tm-1003, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-94362
in-theory        94362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> G)) -> (E -> (F -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94362.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> G)) -> (E -> (F -> G)))), M:tm-1003, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-94363
in-theory        94363
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> (E and F)))
theorem-size     23
proof            (modus-ponens tm-1003 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94363.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> (E and F))), M:tm-1003, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-94364
in-theory        94364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> F)))
theorem-size     23
proof            (modus-ponens tm-1003 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94364.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> F))), M:tm-1003, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-94365
in-theory        94365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((not (not E)) -> (not (not E))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94365.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((not (not E)) -> (not (not E)))), M:tm-1003, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-94366
in-theory        94366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not (E -> E))) -> (not (E -> F))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
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-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-94366.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not (E -> E))) -> (not (E -> F)))), M:tm-1003, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-94367
in-theory        94367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-1003 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       143
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94367.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F))), M:tm-1003, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-94368
in-theory        94368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94368.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> (F -> F)))), M:tm-1003, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-94369
in-theory        94369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (E -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-1003 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94369.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (E -> E)) or G)), M:tm-1003, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-94370
in-theory        94370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> (F -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-94370.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> (F -> F)) and E))), M:tm-1003, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-94371
in-theory        94371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> E) -> ((E -> F) -> E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94371.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> E) -> ((E -> F) -> E))), M:tm-1003, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-94372
in-theory        94372
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94372.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> (F -> F)))), M:tm-1003, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-94373
in-theory        94373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-94373.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> E) -> G)) -> (E -> G))), M:tm-1003, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-94374
in-theory        94374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E -> F)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-94374.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E -> F)) -> (E -> F))), M:tm-1003, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-94375
in-theory        94375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94375.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F)))), M:tm-1003, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-94376
in-theory        94376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-9 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
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-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-94376.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F))))), M:tm-1003, 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-94377
in-theory        94377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-94377.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H))), M:tm-1003, 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-94378
in-theory        94378
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
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-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-94378.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-1003, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-94379
in-theory        94379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H))
theorem-size     37
proof            (modus-ponens tm-1003 tm-104 ((A (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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-94379.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H)), M:tm-1003, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-94380
in-theory        94380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E)))
theorem-size     39
proof            (modus-ponens tm-1003 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-94380.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E))), M:tm-1003, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-94381
in-theory        94381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-94381.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G)))), M:tm-1003, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-94382
in-theory        94382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
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-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-94382.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-1003, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-94383
in-theory        94383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-1003 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-94383.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H))), M:tm-1003, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-94384
in-theory        94384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9 tm-1 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
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-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-94384.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E))), M:tm-1003, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-94385
in-theory        94385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       187
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-94385.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H))), M:tm-1003, 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-94386
in-theory        94386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-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-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-94386.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-1003, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-94387
in-theory        94387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-1003 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-94387.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-1003, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-94388
in-theory        94388
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-94388.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-1003, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-94389
in-theory        94389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
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-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-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-94389.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H))))), M:tm-1003, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-94390
in-theory        94390
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-94390.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-1003, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-94391
in-theory        94391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) and E) -> F))
theorem-size     23
proof            (modus-ponens tm-1003 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-94391.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) and E) -> F)), M:tm-1003, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-94392
in-theory        94392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-1003 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-94392.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> E)) -> G) and H) -> G)), M:tm-1003, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-94393
in-theory        94393
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H))
theorem-size     35
proof            (modus-ponens tm-1003 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-94393.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H)), M:tm-1003, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-94394
in-theory        94394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-94394.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F))), M:tm-1003, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-94395
in-theory        94395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94395.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E))), M:tm-1003, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-94396
in-theory        94396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-9 tm-2 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
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-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-94396.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E)))), M:tm-1003, 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-94397
in-theory        94397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       175
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-94397.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H))), M:tm-1003, 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-94398
in-theory        94398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-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-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-94398.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-1003, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-94399
in-theory        94399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H))
theorem-size     33
proof            (modus-ponens tm-1003 tm-124 ((A (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       147
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-94399.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H)), M:tm-1003, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-94400
in-theory        94400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-94400.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E))), M:tm-1003, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-94401
in-theory        94401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-94401.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F))), M:tm-1003, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-94402
in-theory        94402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-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-94402.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-1003, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-94403
in-theory        94403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and F) -> E) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-1003 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-94403.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and F) -> E) -> G) and H) -> G)), M:tm-1003, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-94404
in-theory        94404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> (E -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-94404.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> (E -> G)) -> ((E and F) -> G))), M:tm-1003, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-94405
in-theory        94405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F and G) -> F))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94405.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F and G) -> F))) -> (not E))), M:tm-1003, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-94406
in-theory        94406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-1003 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       139
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-94406.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G))), M:tm-1003, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-94407
in-theory        94407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94407.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G and H) -> G)))), M:tm-1003, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-94408
in-theory        94408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-94408.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F and G) -> F)) or H)), M:tm-1003, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-94409
in-theory        94409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-94409.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G and H) -> G)) and E))), M:tm-1003, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-94410
in-theory        94410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F and G)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94410.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F and G)) -> (E -> F))), M:tm-1003, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-94411
in-theory        94411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) 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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-94411.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G and H) -> G)))), M:tm-1003, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-94412
in-theory        94412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and (E -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-1003 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-94412.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and (E -> F)) -> F)), M:tm-1003, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-94413
in-theory        94413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and ((F -> (G -> F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-94413.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and ((F -> (G -> F)) -> H)) -> H)), M:tm-1003, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-94414
in-theory        94414
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I))
theorem-size     35
proof            (modus-ponens tm-1003 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-94414.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I)), M:tm-1003, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-94415
in-theory        94415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and (((F and G) -> F) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-94415.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and (((F and G) -> F) -> H)) -> H)), M:tm-1003, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-94416
in-theory        94416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-94416.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G))), M:tm-1003, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-94417
in-theory        94417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94417.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F))), M:tm-1003, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-94418
in-theory        94418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-9 tm-2 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
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-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-94418.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F)))), M:tm-1003, 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-94419
in-theory        94419
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       175
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-94419.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H))), M:tm-1003, 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-94420
in-theory        94420
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-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-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-94420.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-1003, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-94421
in-theory        94421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H))
theorem-size     33
proof            (modus-ponens tm-1003 tm-146 ((A (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       147
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-94421.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H)), M:tm-1003, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-94422
in-theory        94422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-94422.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E))), M:tm-1003, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-94423
in-theory        94423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-94423.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G))), M:tm-1003, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-94424
in-theory        94424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-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-94424.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-1003, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-94425
in-theory        94425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and (((F and G) -> G) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-94425.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and (((F and G) -> G) -> H)) -> H)), M:tm-1003, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-94426
in-theory        94426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and F) -> F) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-1003 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-94426.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and F) -> F) -> G) and H) -> G)), M:tm-1003, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-94427
in-theory        94427
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> (F -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-94427.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> (F -> G)) -> ((E and F) -> G))), M:tm-1003, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-94428
in-theory        94428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F and G) -> G))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94428.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F and G) -> G))) -> (not E))), M:tm-1003, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-94429
in-theory        94429
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-1003 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       139
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-94429.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G))), M:tm-1003, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-94430
in-theory        94430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94430.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G and H) -> H)))), M:tm-1003, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-94431
in-theory        94431
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-94431.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F and G) -> G)) or H)), M:tm-1003, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-94432
in-theory        94432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-94432.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G and H) -> H)) and E))), M:tm-1003, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-94433
in-theory        94433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F and G)) -> (E -> G)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94433.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F and G)) -> (E -> G))), M:tm-1003, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-94434
in-theory        94434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-94434.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G and H) -> H)))), M:tm-1003, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-94435
in-theory        94435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
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-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-1.            (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-94435.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> G)))), M:tm-1003, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-94436
in-theory        94436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94436.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-94437
in-theory        94437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94437.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G and H) -> G))), M:tm-1003, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-94438
in-theory        94438
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94438.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G and H) -> H))), M:tm-1003, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-94439
in-theory        94439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-1.            (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-94439.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (G and H))))), M:tm-1003, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-94440
in-theory        94440
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
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-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-1.            (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-94440.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (G or H)))), M:tm-1003, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-94441
in-theory        94441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94441.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H or G)))), M:tm-1003, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-94442
in-theory        94442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 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-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-1.            (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-94442.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-1003, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-94443
in-theory        94443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94443.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-1003, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-94444
in-theory        94444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94444.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((not (not G)) -> G))), M:tm-1003, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-94445
in-theory        94445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-1.            (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-94445.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I -> H))))), M:tm-1003, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94446
in-theory        94446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94446.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (G -> G)))), M:tm-1003, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-94447
in-theory        94447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94447.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-1003, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-94448
in-theory        94448
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94448.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94449
in-theory        94449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94449.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-1003, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-94450
in-theory        94450
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94450.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H and I) -> H)))), M:tm-1003, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94451
in-theory        94451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94451.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-1003, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-94452
in-theory        94452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94452.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H and I) -> I)))), M:tm-1003, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94453
in-theory        94453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-1.            (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-94453.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-1003, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-94454
in-theory        94454
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94454.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E))), M:tm-1003, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-94455
in-theory        94455
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       151
proof-steps      11
----------------------------------------------------------------
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-1.            (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-94455.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H))), M:tm-1003, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-94456
in-theory        94456
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94456.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (H -> G)) and F)))), M:tm-1003, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-94457
in-theory        94457
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (G -> F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
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-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-1.            (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-94457.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (G -> F)) and E)) or H)), M:tm-1003, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-94458
in-theory        94458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (H -> G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-94458.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (H -> G)) and F)) and E))), M:tm-1003, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-94459
in-theory        94459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
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-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-1.            (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-94459.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (H -> G)) and F)))), M:tm-1003, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-94460
in-theory        94460
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94460.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H)))), M:tm-1003, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-94461
in-theory        94461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94461.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-1003, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-94462
in-theory        94462
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94462.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H))), M:tm-1003, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-94463
in-theory        94463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94463.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I))), M:tm-1003, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-94464
in-theory        94464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94464.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I))))), M:tm-1003, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-94465
in-theory        94465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94465.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I)))), M:tm-1003, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-94466
in-theory        94466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94466.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H)))), M:tm-1003, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-94467
in-theory        94467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94467.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-1003, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-94468
in-theory        94468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94468.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-1003, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-94469
in-theory        94469
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94469.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H))), M:tm-1003, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-94470
in-theory        94470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94470.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I))))), M:tm-1003, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-94471
in-theory        94471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94471.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H)))), M:tm-1003, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-94472
in-theory        94472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       223
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94472.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-1003, 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-94473
in-theory        94473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94473.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-1003, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-94474
in-theory        94474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94474.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-1003, 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-94475
in-theory        94475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94475.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I)))), M:tm-1003, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-94476
in-theory        94476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94476.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-1003, 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-94477
in-theory        94477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94477.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J)))), M:tm-1003, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-94478
in-theory        94478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94478.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-1003, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-94479
in-theory        94479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94479.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-1003, 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-94480
in-theory        94480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94480.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-1003, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-94481
in-theory        94481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
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-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-94481.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E))), M:tm-1003, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-94482
in-theory        94482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       199
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94482.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94483
in-theory        94483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-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-94483.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-1003, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-94484
in-theory        94484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I))
theorem-size     35
proof            (modus-ponens tm-1003 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94484.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I)), M:tm-1003, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-94485
in-theory        94485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-94485.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E))), M:tm-1003, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-94486
in-theory        94486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
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-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-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-94486.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-1003, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-94487
in-theory        94487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94487.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> G)))), M:tm-1003, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-94488
in-theory        94488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-94488.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-94489
in-theory        94489
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
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-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-3.            ((A and B) -> 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-94489.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G and H) -> G))), M:tm-1003, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-94490
in-theory        94490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> 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-94490.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G and H) -> H))), M:tm-1003, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-94491
in-theory        94491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-94491.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (G and H))))), M:tm-1003, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-94492
in-theory        94492
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm 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-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-3.            ((A and B) -> 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-94492.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (G or H)))), M:tm-1003, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-94493
in-theory        94493
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94493.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H or G)))), M:tm-1003, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-94494
in-theory        94494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 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-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-3.            ((A and B) -> 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-94494.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-1003, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-94495
in-theory        94495
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> 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-94495.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-1003, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-94496
in-theory        94496
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> 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-94496.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((not (not G)) -> G))), M:tm-1003, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-94497
in-theory        94497
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94497.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I -> H))))), M:tm-1003, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94498
in-theory        94498
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-94498.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (G -> G)))), M:tm-1003, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-94499
in-theory        94499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-94499.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-1003, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-94500
in-theory        94500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94500.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94501
in-theory        94501
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-94501.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-1003, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-94502
in-theory        94502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94502.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H and I) -> H)))), M:tm-1003, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94503
in-theory        94503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-94503.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-1003, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-94504
in-theory        94504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94504.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H and I) -> I)))), M:tm-1003, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94505
in-theory        94505
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94505.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G)))), M:tm-1003, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-94506
in-theory        94506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-94506.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-1003, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-94507
in-theory        94507
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-94507.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (((H and I) -> H) and G)))), M:tm-1003, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-94508
in-theory        94508
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94508.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-1003, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-94509
in-theory        94509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94509.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G)))), M:tm-1003, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-94510
in-theory        94510
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (((F and G) -> F) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94510.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (((F and G) -> F) and E))) -> (not E))), M:tm-1003, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-94511
in-theory        94511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       151
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> 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-94511.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H))), M:tm-1003, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-94512
in-theory        94512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94512.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (((G and H) -> G) and F)))), M:tm-1003, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-94513
in-theory        94513
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (((F and G) -> F) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) 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-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-3.            ((A and B) -> 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-94513.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (((F and G) -> F) and E)) or H)), M:tm-1003, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-94514
in-theory        94514
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (((G and H) -> G) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-94514.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (((G and H) -> G) and F)) and E))), M:tm-1003, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-94515
in-theory        94515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94515.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (((G and H) -> G) and F)))), M:tm-1003, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-94516
in-theory        94516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94516.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> G)))), M:tm-1003, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-94517
in-theory        94517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-94517.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-94518
in-theory        94518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> 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-94518.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G and H) -> G))), M:tm-1003, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-94519
in-theory        94519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) 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-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-4.            ((A and B) -> 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-94519.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G and H) -> H))), M:tm-1003, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-94520
in-theory        94520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-94520.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (G and H))))), M:tm-1003, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-94521
in-theory        94521
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or 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-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-4.            ((A and B) -> 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-94521.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (G or H)))), M:tm-1003, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-94522
in-theory        94522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94522.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H or G)))), M:tm-1003, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-94523
in-theory        94523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-94523.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-1003, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-94524
in-theory        94524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> 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-94524.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-1003, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-94525
in-theory        94525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> 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-94525.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((not (not G)) -> G))), M:tm-1003, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-94526
in-theory        94526
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94526.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I -> H))))), M:tm-1003, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94527
in-theory        94527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-94527.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (G -> G)))), M:tm-1003, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-94528
in-theory        94528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-94528.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-1003, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-94529
in-theory        94529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94529.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94530
in-theory        94530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-94530.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-1003, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-94531
in-theory        94531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94531.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H and I) -> H)))), M:tm-1003, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94532
in-theory        94532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-94532.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-1003, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-94533
in-theory        94533
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94533.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H and I) -> I)))), M:tm-1003, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94534
in-theory        94534
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94534.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G)))), M:tm-1003, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-94535
in-theory        94535
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-94535.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-1003, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-94536
in-theory        94536
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> 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-94536.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (((H and I) -> H) and G)))), M:tm-1003, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-94537
in-theory        94537
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-94537.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (((H and I) -> I) and G)))), M:tm-1003, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-94538
in-theory        94538
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> 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-94538.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (((H and I) -> I) and G)))), M:tm-1003, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-94539
in-theory        94539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94539.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-1003, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-94540
in-theory        94540
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94540.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G)))), M:tm-1003, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-94541
in-theory        94541
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (((F and G) -> G) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94541.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (((F and G) -> G) and E))) -> (not E))), M:tm-1003, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-94542
in-theory        94542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       151
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> 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-94542.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H))), M:tm-1003, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-94543
in-theory        94543
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94543.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (((G and H) -> H) and F)))), M:tm-1003, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-94544
in-theory        94544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (((F and G) -> G) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) 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-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-4.            ((A and B) -> 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-94544.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (((F and G) -> G) and E)) or H)), M:tm-1003, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-94545
in-theory        94545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (((G and H) -> H) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-94545.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (((G and H) -> H) and F)) and E))), M:tm-1003, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-94546
in-theory        94546
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94546.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (((G and H) -> H) and F)))), M:tm-1003, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-94547
in-theory        94547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-94547.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> G)))), M:tm-1003, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-94548
in-theory        94548
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-94548.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-94549
in-theory        94549
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
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-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-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-94549.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G and H) -> G))), M:tm-1003, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-94550
in-theory        94550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) 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-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-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-94550.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G and H) -> H))), M:tm-1003, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-94551
in-theory        94551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
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-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-94551.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H))))), M:tm-1003, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-94552
in-theory        94552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or 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-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-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-94552.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (G or H)))), M:tm-1003, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-94553
in-theory        94553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-94553.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H or G)))), M:tm-1003, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-94554
in-theory        94554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       155
proof-steps      11
----------------------------------------------------------------
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-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-94554.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-1003, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-94555
in-theory        94555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
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-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-94555.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-1003, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-94556
in-theory        94556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-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-94556.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((not (not G)) -> G))), M:tm-1003, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-94557
in-theory        94557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-94557.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H))))), M:tm-1003, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94558
in-theory        94558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-94558.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G)))), M:tm-1003, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-94559
in-theory        94559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-94559.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-1003, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-94560
in-theory        94560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
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-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-23.           (A -> ((B -> (C -> (B 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-94560.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94561
in-theory        94561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-94561.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-1003, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-94562
in-theory        94562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-23.           (A -> ((B -> (C -> (B 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-94562.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H)))), M:tm-1003, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94563
in-theory        94563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-94563.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-1003, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-94564
in-theory        94564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-23.           (A -> ((B -> (C -> (B 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-94564.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I)))), M:tm-1003, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94565
in-theory        94565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-94565.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-1003, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-94566
in-theory        94566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-94566.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-1003, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-94567
in-theory        94567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-94567.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G)))), M:tm-1003, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-94568
in-theory        94568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-94568.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G)))), M:tm-1003, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-94569
in-theory        94569
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
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-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-94569.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-1003, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-94570
in-theory        94570
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-94570.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-1003, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-94571
in-theory        94571
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-94571.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-1003, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-94572
in-theory        94572
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94572.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-1003, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-94573
in-theory        94573
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-1.            (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-94573.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-1003, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-94574
in-theory        94574
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-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-94574.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E))), M:tm-1003, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-94575
in-theory        94575
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       163
proof-steps      11
----------------------------------------------------------------
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-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-94575.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H))), M:tm-1003, 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-94576
in-theory        94576
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-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-94576.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (H -> (G and H))) and F)))), M:tm-1003, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-94577
in-theory        94577
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (G -> (F and G))) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-1003 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) 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-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-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-94577.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (G -> (F and G))) and E)) or H)), M:tm-1003, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-94578
in-theory        94578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-94578.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E))), M:tm-1003, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-94579
in-theory        94579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
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-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-94579.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (H -> (G and H))) and F)))), M:tm-1003, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-94580
in-theory        94580
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> E))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-94580.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> E)))), M:tm-1003, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-94581
in-theory        94581
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-94581.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G))))), M:tm-1003, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-94582
in-theory        94582
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> ((E and F) and E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-94582.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> ((E and F) and E))), M:tm-1003, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-94583
in-theory        94583
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> ((E and F) and F)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-94583.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> ((E and F) and F))), M:tm-1003, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-94584
in-theory        94584
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-94584.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (E and F))))), M:tm-1003, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-94585
in-theory        94585
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (E or F))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-310 ((A (-> Am (and Am (or Am Bm))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-94585.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (E or F)))), M:tm-1003, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-94586
in-theory        94586
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F or E))))
theorem-size     23
proof            (modus-ponens tm-1003 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-94586.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F or E)))), M:tm-1003, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-94587
in-theory        94587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-94587.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-94588
in-theory        94588
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-94588.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E))))), M:tm-1003, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-94589
in-theory        94589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((not (not E)) -> ((not (not E)) and E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-94589.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((not (not E)) -> ((not (not E)) and E))), M:tm-1003, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-94590
in-theory        94590
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-94590.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (G -> F))))), M:tm-1003, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-94591
in-theory        94591
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and (E -> E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-94591.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and (E -> E)))), M:tm-1003, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-94592
in-theory        94592
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-94592.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G))))), M:tm-1003, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-94593
in-theory        94593
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-94593.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-1003, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-94594
in-theory        94594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-94594.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F)))), M:tm-1003, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-94595
in-theory        94595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-94595.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F and G) -> F)))), M:tm-1003, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-94596
in-theory        94596
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-94596.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G)))), M:tm-1003, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-94597
in-theory        94597
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-94597.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F and G) -> G)))), M:tm-1003, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-94598
in-theory        94598
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-94598.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (G -> F)) and E)))), M:tm-1003, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-94599
in-theory        94599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-94599.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-1003, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-94600
in-theory        94600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-94600.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (((F and G) -> F) and E)))), M:tm-1003, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-94601
in-theory        94601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-94601.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (((F and G) -> G) and E)))), M:tm-1003, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-94602
in-theory        94602
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-94602.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (G -> (F and G))) and E)))), M:tm-1003, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-94603
in-theory        94603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-94603.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and (E -> (E and F))))), M:tm-1003, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-94604
in-theory        94604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-94604.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H))))), M:tm-1003, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-94605
in-theory        94605
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-94605.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H))))), M:tm-1003, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-94606
in-theory        94606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-94606.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H))))), M:tm-1003, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-94607
in-theory        94607
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94607.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-1003, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-94608
in-theory        94608
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94608.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H))))), M:tm-1003, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-94609
in-theory        94609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
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-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-94609.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F)))), M:tm-1003, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-94610
in-theory        94610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-1003 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       155
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-94610.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G))), M:tm-1003, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-94611
in-theory        94611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94611.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> (F -> (F and G))))), M:tm-1003, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-94612
in-theory        94612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (E -> (E and F))) or G))
theorem-size     27
proof            (modus-ponens tm-1003 tm-337 ((A (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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-94612.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (E -> (E and F))) or G)), M:tm-1003, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-94613
in-theory        94613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> (F -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-94613.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> (F -> (F and G))) and E))), M:tm-1003, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-94614
in-theory        94614
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> E) -> ((E -> F) -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-94614.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> E) -> ((E -> F) -> (E and F)))), M:tm-1003, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-94615
in-theory        94615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94615.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> (F -> (F and G))))), M:tm-1003, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-94616
in-theory        94616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-94616.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (G -> (F and G)))))), M:tm-1003, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-94617
in-theory        94617
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-94617.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I)))))), M:tm-1003, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94618
in-theory        94618
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94618.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I -> (H and I)))))), M:tm-1003, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94619
in-theory        94619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94619.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I -> (H and I)))))), M:tm-1003, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94620
in-theory        94620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94620.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-1003, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-94621
in-theory        94621
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-1.            (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-94621.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I)))))), M:tm-1003, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94622
in-theory        94622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and ((F -> (G -> (F and G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-1003 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-94622.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and ((F -> (G -> (F and G))) -> H)) -> H)), M:tm-1003, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-94623
in-theory        94623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> (E and F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-1003 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-94623.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> (E and F))) -> G) and H) -> G)), M:tm-1003, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-94624
in-theory        94624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-94624.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G))), M:tm-1003, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-94625
in-theory        94625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (G -> (F and G))))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94625.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (G -> (F and G))))) -> (not E))), M:tm-1003, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-94626
in-theory        94626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       151
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> 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-94626.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G))), M:tm-1003, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-94627
in-theory        94627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94627.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (H -> (G and H)))))), M:tm-1003, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-94628
in-theory        94628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
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-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-1.            (A -> (B -> 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-94628.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (G -> (F and G)))) or H)), M:tm-1003, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-94629
in-theory        94629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-94629.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (H -> (G and H)))) and E))), M:tm-1003, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-94630
in-theory        94630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94630.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (G -> (F and G))))), M:tm-1003, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-94631
in-theory        94631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
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-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-1.            (A -> (B -> 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-94631.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (H -> (G and H)))))), M:tm-1003, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-94632
in-theory        94632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-94632.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I))), M:tm-1003, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-94633
in-theory        94633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94633.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (H -> G)) or I))), M:tm-1003, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-94634
in-theory        94634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94634.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (H -> G)) or I))), M:tm-1003, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-94635
in-theory        94635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94635.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J))), M:tm-1003, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-94636
in-theory        94636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-1.            (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-94636.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> G)) or I))), M:tm-1003, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-94637
in-theory        94637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94637.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (G -> F)) or H))), M:tm-1003, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-94638
in-theory        94638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
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-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-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-94638.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> E)) or G) or H)), M:tm-1003, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-94639
in-theory        94639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-94639.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> F)) or H) and E))), M:tm-1003, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-94640
in-theory        94640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
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-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-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-94640.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> F)) or H))), M:tm-1003, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-94641
in-theory        94641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-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-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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-94641.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-1003, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-94642
in-theory        94642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-94642.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-1003, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-94643
in-theory        94643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-94643.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-1003, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-94644
in-theory        94644
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94644.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-1003, 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-94645
in-theory        94645
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94645.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-1003, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-94646
in-theory        94646
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94646.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-1003, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-94647
in-theory        94647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-1003 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-94647.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I)), M:tm-1003, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-94648
in-theory        94648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-94648.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E))), M:tm-1003, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-94649
in-theory        94649
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94649.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-1003, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-94650
in-theory        94650
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-94650.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I))), M:tm-1003, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-94651
in-theory        94651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> 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-94651.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G and H) -> G) or I))), M:tm-1003, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-94652
in-theory        94652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 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-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-3.            ((A and B) -> 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-94652.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G and H) -> G) or I))), M:tm-1003, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-94653
in-theory        94653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94653.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J))), M:tm-1003, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-94654
in-theory        94654
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94654.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G and H) -> G) or I))), M:tm-1003, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-94655
in-theory        94655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94655.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F and G) -> F) or H))), M:tm-1003, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-94656
in-theory        94656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) -> E) or G) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 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-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-3.            ((A and 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-94656.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) -> E) or G) or H)), M:tm-1003, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-94657
in-theory        94657
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F and G) -> F) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-94657.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F and G) -> F) or H) and E))), M:tm-1003, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-94658
in-theory        94658
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
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-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-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-94658.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and G) -> F) or H))), M:tm-1003, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-94659
in-theory        94659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-94659.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I))), M:tm-1003, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-94660
in-theory        94660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-94660.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G and H) -> H) or I))), M:tm-1003, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-94661
in-theory        94661
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> 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-94661.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G and H) -> H) or I))), M:tm-1003, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-94662
in-theory        94662
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94662.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J))), M:tm-1003, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-94663
in-theory        94663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (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-94663.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G and H) -> H) or I))), M:tm-1003, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-94664
in-theory        94664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94664.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F and G) -> G) or H))), M:tm-1003, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-94665
in-theory        94665
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) -> F) or G) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and 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-94665.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) -> F) or G) or H)), M:tm-1003, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-94666
in-theory        94666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F and G) -> G) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-94666.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F and G) -> G) or H) and E))), M:tm-1003, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-94667
in-theory        94667
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
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-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-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-94667.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F and G) -> G) or H))), M:tm-1003, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-94668
in-theory        94668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-94668.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I))), M:tm-1003, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-94669
in-theory        94669
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-94669.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I))), M:tm-1003, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-94670
in-theory        94670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-94670.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I))), M:tm-1003, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-94671
in-theory        94671
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94671.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-1003, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-94672
in-theory        94672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-1.            (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-94672.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I))), M:tm-1003, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-94673
in-theory        94673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-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-94673.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (G -> (F and G))) or H))), M:tm-1003, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-94674
in-theory        94674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> (E and F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
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-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-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-94674.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> (E and F))) or G) or H)), M:tm-1003, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-94675
in-theory        94675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> (F and G))) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-94675.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G -> (F and G))) or H) and E))), M:tm-1003, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-94676
in-theory        94676
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
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-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-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-94676.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (F and G))) or H))), M:tm-1003, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-94677
in-theory        94677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-94677.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I))), M:tm-1003, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-94678
in-theory        94678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-94678.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (G or H)) or I))), M:tm-1003, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-94679
in-theory        94679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 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-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-3.            ((A and B) -> 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-94679.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (G or H)) or I))), M:tm-1003, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-94680
in-theory        94680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94680.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J))), M:tm-1003, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-94681
in-theory        94681
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-1.            (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-94681.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (G or H)) or I))), M:tm-1003, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-94682
in-theory        94682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-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-94682.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (F or G)) or H))), M:tm-1003, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-94683
in-theory        94683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (E or F)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
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-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-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-94683.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (E or F)) or G) or H)), M:tm-1003, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-94684
in-theory        94684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (F or G)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-94684.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (F or G)) or H) and E))), M:tm-1003, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-94685
in-theory        94685
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
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-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-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-94685.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (F or G)) or H))), M:tm-1003, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-94686
in-theory        94686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
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-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-32.           (A -> ((B -> (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-94686.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> G)))), M:tm-1003, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-94687
in-theory        94687
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-94687.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-94688
in-theory        94688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
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-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-32.           (A -> ((B -> (B 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-94688.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G and H) -> G))), M:tm-1003, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-94689
in-theory        94689
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) 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-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-32.           (A -> ((B -> (B 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-94689.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G and H) -> H))), M:tm-1003, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-94690
in-theory        94690
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-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-94690.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (G and H))))), M:tm-1003, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-94691
in-theory        94691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
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-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-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-94691.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (G or H)))), M:tm-1003, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-94692
in-theory        94692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-94692.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H or G)))), M:tm-1003, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-94693
in-theory        94693
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 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       147
proof-steps      11
----------------------------------------------------------------
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-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-94693.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-1003, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-94694
in-theory        94694
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-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-94694.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-1003, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-94695
in-theory        94695
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-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-94695.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((not (not G)) -> G))), M:tm-1003, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-94696
in-theory        94696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-94696.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I -> H))))), M:tm-1003, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94697
in-theory        94697
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-32.           (A -> ((B -> (B or C)) and 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-94697.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (G -> G)))), M:tm-1003, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-94698
in-theory        94698
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-94698.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-1003, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-94699
in-theory        94699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-32.           (A -> ((B -> (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-94699.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94700
in-theory        94700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-32.           (A -> ((B -> (B or C)) and 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-94700.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-1003, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-94701
in-theory        94701
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-32.           (A -> ((B -> (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-94701.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H and I) -> H)))), M:tm-1003, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94702
in-theory        94702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-32.           (A -> ((B -> (B or C)) and 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-94702.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-1003, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-94703
in-theory        94703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-32.           (A -> ((B -> (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-94703.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H and I) -> I)))), M:tm-1003, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94704
in-theory        94704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-94704.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G)))), M:tm-1003, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-94705
in-theory        94705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-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-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-32.           (A -> ((B -> (B or C)) and 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-94705.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-1003, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-94706
in-theory        94706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-94706.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G)))), M:tm-1003, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-94707
in-theory        94707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-94707.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G)))), M:tm-1003, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-94708
in-theory        94708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-94708.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-1003, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-94709
in-theory        94709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 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-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-32.           (A -> ((B -> (B or C)) and 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-94709.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H))))), M:tm-1003, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-94710
in-theory        94710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-94710.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I)))))), M:tm-1003, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94711
in-theory        94711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-94711.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> G)) or I))), M:tm-1003, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-94712
in-theory        94712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 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-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-32.           (A -> ((B -> (B or C)) and 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-94712.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-1003, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-94713
in-theory        94713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 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-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-32.           (A -> ((B -> (B 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-94713.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G and H) -> G) or I))), M:tm-1003, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-94714
in-theory        94714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-94714.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G and H) -> H) or I))), M:tm-1003, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-94715
in-theory        94715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-94715.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I))), M:tm-1003, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-94716
in-theory        94716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-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-94716.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (G or H)) or I))), M:tm-1003, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-94717
in-theory        94717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-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-94717.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G)))), M:tm-1003, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-94718
in-theory        94718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-94718.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (F or G)) and E)))), M:tm-1003, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-94719
in-theory        94719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-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-94719.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G)))), M:tm-1003, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-94720
in-theory        94720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-94720.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G)))), M:tm-1003, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-94721
in-theory        94721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-94721.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G)))), M:tm-1003, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-94722
in-theory        94722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94722.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-1003, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-94723
in-theory        94723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-1.            (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-94723.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G)))), M:tm-1003, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-94724
in-theory        94724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (F or G)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-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-94724.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (F or G)) and E))) -> (not E))), M:tm-1003, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-94725
in-theory        94725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       151
proof-steps      11
----------------------------------------------------------------
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-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-94725.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H))), M:tm-1003, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-94726
in-theory        94726
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-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-94726.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (G or H)) and F)))), M:tm-1003, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-94727
in-theory        94727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (F or G)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
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-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-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-94727.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (F or G)) and E)) or H)), M:tm-1003, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-94728
in-theory        94728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (G or H)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-94728.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (G or H)) and F)) and E))), M:tm-1003, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-94729
in-theory        94729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
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-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-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-94729.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (G or H)) and F)))), M:tm-1003, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-94730
in-theory        94730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-94730.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (H or I))))), M:tm-1003, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94731
in-theory        94731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-94731.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (F or G))))), M:tm-1003, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-94732
in-theory        94732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-94732.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I))))), M:tm-1003, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94733
in-theory        94733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94733.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (H or I))))), M:tm-1003, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94734
in-theory        94734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94734.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (H or I))))), M:tm-1003, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94735
in-theory        94735
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94735.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J))))), M:tm-1003, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-94736
in-theory        94736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-1.            (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-94736.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (H or I))))), M:tm-1003, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94737
in-theory        94737
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and ((F -> (F or G)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-94737.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and ((F -> (F or G)) -> H)) -> H)), M:tm-1003, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-94738
in-theory        94738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (E or F)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-1003 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-94738.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (E or F)) -> G) and H) -> G)), M:tm-1003, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-94739
in-theory        94739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((E or F) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-94739.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((E or F) -> G)) -> (E -> G))), M:tm-1003, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-94740
in-theory        94740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (F or G)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94740.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (F or G)))) -> (not E))), M:tm-1003, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-94741
in-theory        94741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-1003 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       139
proof-steps      11
----------------------------------------------------------------
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-1.            (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-94741.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G))), M:tm-1003, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-94742
in-theory        94742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94742.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (G or H))))), M:tm-1003, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-94743
in-theory        94743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
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-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-1.            (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-94743.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (F or G))) or H)), M:tm-1003, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-94744
in-theory        94744
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-1.            (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-94744.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (G or H))) and E))), M:tm-1003, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-94745
in-theory        94745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94745.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (F or G)))), M:tm-1003, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-94746
in-theory        94746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
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-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-1.            (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-94746.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (G or H))))), M:tm-1003, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-94747
in-theory        94747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-32.           (A -> ((B -> (B 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-94747.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I -> H))))), M:tm-1003, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94748
in-theory        94748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-23.           (A -> ((B -> (C -> (B and 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-94748.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H))))), M:tm-1003, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94749
in-theory        94749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94749.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or (H -> (I -> H))))), M:tm-1003, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94750
in-theory        94750
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94750.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or (H -> (I -> H))))), M:tm-1003, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94751
in-theory        94751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94751.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I))))), M:tm-1003, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-94752
in-theory        94752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94752.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I -> H))))), M:tm-1003, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94753
in-theory        94753
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-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-94753.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or (G -> (H -> G))))), M:tm-1003, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-94754
in-theory        94754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-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-94754.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (G -> F))) or H)), M:tm-1003, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-94755
in-theory        94755
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-94755.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or (G -> (H -> G))) and E))), M:tm-1003, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-94756
in-theory        94756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm 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-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-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-94756.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or (G -> (H -> G))))), M:tm-1003, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-94757
in-theory        94757
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-32.           (A -> ((B -> (B 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-94757.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94758
in-theory        94758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-23.           (A -> ((B -> (C -> (B and 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-94758.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94759
in-theory        94759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94759.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94760
in-theory        94760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94760.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94761
in-theory        94761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94761.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-1003, 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-94762
in-theory        94762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94762.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94763
in-theory        94763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-94763.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-1003, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-94764
in-theory        94764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-1003 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-94764.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-1003, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-94765
in-theory        94765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-94765.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-1003, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-94766
in-theory        94766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 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-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-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-94766.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-1003, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-94767
in-theory        94767
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-32.           (A -> ((B -> (B 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-94767.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or ((H and I) -> H)))), M:tm-1003, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94768
in-theory        94768
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-23.           (A -> ((B -> (C -> (B and 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-94768.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H)))), M:tm-1003, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94769
in-theory        94769
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94769.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or ((H and I) -> H)))), M:tm-1003, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94770
in-theory        94770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94770.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or ((H and I) -> H)))), M:tm-1003, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94771
in-theory        94771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94771.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I)))), M:tm-1003, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-94772
in-theory        94772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94772.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or ((H and I) -> H)))), M:tm-1003, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94773
in-theory        94773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-94773.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or ((G and H) -> G)))), M:tm-1003, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-94774
in-theory        94774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-94774.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F and G) -> F)) or H)), M:tm-1003, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-94775
in-theory        94775
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-94775.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or ((G and H) -> G)) and E))), M:tm-1003, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-94776
in-theory        94776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94776.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or ((G and H) -> G)))), M:tm-1003, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-94777
in-theory        94777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-32.           (A -> ((B -> (B 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-94777.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or ((H and I) -> I)))), M:tm-1003, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94778
in-theory        94778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-23.           (A -> ((B -> (C -> (B and 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-94778.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I)))), M:tm-1003, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94779
in-theory        94779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94779.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or ((H and I) -> I)))), M:tm-1003, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94780
in-theory        94780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94780.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or ((H and I) -> I)))), M:tm-1003, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94781
in-theory        94781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94781.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J)))), M:tm-1003, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-94782
in-theory        94782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94782.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or ((H and I) -> I)))), M:tm-1003, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94783
in-theory        94783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-94783.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or ((G and H) -> H)))), M:tm-1003, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-94784
in-theory        94784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-94784.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F and G) -> G)) or H)), M:tm-1003, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-94785
in-theory        94785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-94785.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or ((G and H) -> H)) and E))), M:tm-1003, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-94786
in-theory        94786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94786.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or ((G and H) -> H)))), M:tm-1003, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-94787
in-theory        94787
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-94787.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I -> (H and I)))))), M:tm-1003, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94788
in-theory        94788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-94788.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I)))))), M:tm-1003, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94789
in-theory        94789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94789.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or (H -> (I -> (H and I)))))), M:tm-1003, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94790
in-theory        94790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94790.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or (H -> (I -> (H and I)))))), M:tm-1003, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94791
in-theory        94791
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94791.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-1003, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-94792
in-theory        94792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94792.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I)))))), M:tm-1003, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94793
in-theory        94793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), 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-94793.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or (G -> (H -> (G and H)))))), M:tm-1003, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-94794
in-theory        94794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), 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-94794.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (G -> (F and G)))) or H)), M:tm-1003, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-94795
in-theory        94795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-94795.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or (G -> (H -> (G and H)))) and E))), M:tm-1003, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-94796
in-theory        94796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94796.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or (G -> (H -> (G and H)))))), M:tm-1003, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-94797
in-theory        94797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-94797.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or (H -> (H or I))))), M:tm-1003, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94798
in-theory        94798
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-94798.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (H or I))))), M:tm-1003, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94799
in-theory        94799
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94799.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or (H -> (H or I))))), M:tm-1003, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94800
in-theory        94800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94800.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or (H -> (H or I))))), M:tm-1003, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94801
in-theory        94801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94801.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J))))), M:tm-1003, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-94802
in-theory        94802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94802.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (H or I))))), M:tm-1003, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94803
in-theory        94803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-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-94803.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or (G -> (G or H))))), M:tm-1003, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-94804
in-theory        94804
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-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-94804.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (F or G))) or H)), M:tm-1003, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-94805
in-theory        94805
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-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-94805.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or (G -> (G or H))) and E))), M:tm-1003, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-94806
in-theory        94806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
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-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-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-94806.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or (G -> (G or H))))), M:tm-1003, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-94807
in-theory        94807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-94807.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I or H))))), M:tm-1003, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94808
in-theory        94808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-94808.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I or H))))), M:tm-1003, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94809
in-theory        94809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94809.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or (H -> (I or H))))), M:tm-1003, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94810
in-theory        94810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94810.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or (H -> (I or H))))), M:tm-1003, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94811
in-theory        94811
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94811.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I))))), M:tm-1003, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-94812
in-theory        94812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94812.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I or H))))), M:tm-1003, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94813
in-theory        94813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B 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-94813.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or (G -> (H or G))))), M:tm-1003, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-94814
in-theory        94814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B 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-94814.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (G or F))) or H)), M:tm-1003, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-94815
in-theory        94815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-94815.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or (G -> (H or G))) and E))), M:tm-1003, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-94816
in-theory        94816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm 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-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-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-94816.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or (G -> (H or G))))), M:tm-1003, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-94817
in-theory        94817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-94817.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> (H or G)) or I))), M:tm-1003, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-94818
in-theory        94818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-94818.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I))), M:tm-1003, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-94819
in-theory        94819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94819.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> (H or G)) or I))), M:tm-1003, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-94820
in-theory        94820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94820.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> (H or G)) or I))), M:tm-1003, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-94821
in-theory        94821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94821.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J))), M:tm-1003, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-94822
in-theory        94822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94822.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> (H or G)) or I))), M:tm-1003, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-94823
in-theory        94823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B 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-94823.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> (G or F)) or H))), M:tm-1003, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-94824
in-theory        94824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F or E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B 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-94824.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F or E)) or G) or H)), M:tm-1003, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-94825
in-theory        94825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G or F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-94825.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G or F)) or H) and E))), M:tm-1003, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-94826
in-theory        94826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
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-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-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-94826.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G or F)) or H))), M:tm-1003, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-94827
in-theory        94827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94827.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> G)))), M:tm-1003, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-94828
in-theory        94828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94828.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-94829
in-theory        94829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94829.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G and H) -> G))), M:tm-1003, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-94830
in-theory        94830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94830.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G and H) -> H))), M:tm-1003, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-94831
in-theory        94831
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-94831.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (G and H))))), M:tm-1003, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-94832
in-theory        94832
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-94832.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (G or H)))), M:tm-1003, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-94833
in-theory        94833
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-94833.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H or G)))), M:tm-1003, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-94834
in-theory        94834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-94834.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-1003, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-94835
in-theory        94835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94835.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-1003, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-94836
in-theory        94836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94836.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((not (not G)) -> G))), M:tm-1003, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-94837
in-theory        94837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94837.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I -> H))))), M:tm-1003, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94838
in-theory        94838
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94838.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (G -> G)))), M:tm-1003, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-94839
in-theory        94839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94839.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-1003, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-94840
in-theory        94840
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94840.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94841
in-theory        94841
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94841.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-1003, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-94842
in-theory        94842
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94842.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H and I) -> H)))), M:tm-1003, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94843
in-theory        94843
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94843.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-1003, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-94844
in-theory        94844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94844.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H and I) -> I)))), M:tm-1003, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94845
in-theory        94845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94845.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-1003, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-94846
in-theory        94846
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94846.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-1003, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-94847
in-theory        94847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94847.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G)))), M:tm-1003, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-94848
in-theory        94848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94848.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G)))), M:tm-1003, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-94849
in-theory        94849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-94849.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-1003, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-94850
in-theory        94850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94850.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H))))), M:tm-1003, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-94851
in-theory        94851
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94851.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I)))))), M:tm-1003, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94852
in-theory        94852
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94852.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> G)) or I))), M:tm-1003, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-94853
in-theory        94853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94853.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-1003, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-94854
in-theory        94854
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94854.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G and H) -> G) or I))), M:tm-1003, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-94855
in-theory        94855
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94855.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G and H) -> H) or I))), M:tm-1003, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-94856
in-theory        94856
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-94856.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I))), M:tm-1003, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-94857
in-theory        94857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-94857.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (G or H)) or I))), M:tm-1003, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-94858
in-theory        94858
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-94858.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G)))), M:tm-1003, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-94859
in-theory        94859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94859.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (H or I))))), M:tm-1003, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94860
in-theory        94860
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94860.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I -> H))))), M:tm-1003, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-94861
in-theory        94861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94861.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-1003, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-94862
in-theory        94862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94862.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or ((H and I) -> H)))), M:tm-1003, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-94863
in-theory        94863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or 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-94863.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or ((H and I) -> I)))), M:tm-1003, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-94864
in-theory        94864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-94864.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I -> (H and I)))))), M:tm-1003, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-94865
in-theory        94865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-94865.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or (H -> (H or I))))), M:tm-1003, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-94866
in-theory        94866
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-94866.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I or H))))), M:tm-1003, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94867
in-theory        94867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-94867.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> (H or G)) or I))), M:tm-1003, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-94868
in-theory        94868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-94868.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G)))), M:tm-1003, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-94869
in-theory        94869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-94869.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G)))), M:tm-1003, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-94870
in-theory        94870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-94870.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and ((F -> (G or F)) and E)))), M:tm-1003, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-94871
in-theory        94871
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and 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-94871.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G)))), M:tm-1003, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-94872
in-theory        94872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and 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-94872.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G)))), M:tm-1003, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-94873
in-theory        94873
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and 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-94873.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G)))), M:tm-1003, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-94874
in-theory        94874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-94874.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-1003, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-94875
in-theory        94875
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94875.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G)))), M:tm-1003, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-94876
in-theory        94876
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (G or F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94876.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not ((F -> (G or F)) and E))) -> (not E))), M:tm-1003, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-94877
in-theory        94877
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       151
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-94877.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H))), M:tm-1003, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-94878
in-theory        94878
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-94878.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> ((G -> (H or G)) and F)))), M:tm-1003, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-94879
in-theory        94879
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (G or F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or 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-94879.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F -> (G or F)) and E)) or H)), M:tm-1003, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-94880
in-theory        94880
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (H or G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-94880.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> ((G -> (H or G)) and F)) and E))), M:tm-1003, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-94881
in-theory        94881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94881.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> ((G -> (H or G)) and F)))), M:tm-1003, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-94882
in-theory        94882
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94882.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I or H))))), M:tm-1003, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94883
in-theory        94883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-32.           (A -> ((B -> (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-94883.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I or H))))), M:tm-1003, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94884
in-theory        94884
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-94884.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E and (F -> (G or F))))), M:tm-1003, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-94885
in-theory        94885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-23.           (A -> ((B -> (C -> (B 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-94885.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H))))), M:tm-1003, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94886
in-theory        94886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94886.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I or H))))), M:tm-1003, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94887
in-theory        94887
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94887.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I or H))))), M:tm-1003, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94888
in-theory        94888
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94888.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I))))), M:tm-1003, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-94889
in-theory        94889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((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-94889.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I or H))))), M:tm-1003, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-94890
in-theory        94890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and ((F -> (G or F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-1003 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> 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-94890.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and ((F -> (G or F)) -> H)) -> H)), M:tm-1003, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-94891
in-theory        94891
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F or E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-1003 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and 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-94891.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F or E)) -> G) and H) -> G)), M:tm-1003, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-94892
in-theory        94892
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F or E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), 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-94892.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> ((F or E) -> G)) -> (E -> G))), M:tm-1003, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-94893
in-theory        94893
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (G or F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94893.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (not (F -> (G or F)))) -> (not E))), M:tm-1003, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-94894
in-theory        94894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-1003 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       139
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-94894.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G))), M:tm-1003, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-94895
in-theory        94895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-94895.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F -> (G -> (H or G))))), M:tm-1003, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-94896
in-theory        94896
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-1003 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-94896.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (G or F))) or H)), M:tm-1003, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-94897
in-theory        94897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-94897.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> (G -> (H or G))) and E))), M:tm-1003, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-94898
in-theory        94898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-94898.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> (E -> (G or F)))), M:tm-1003, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-94899
in-theory        94899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-1003 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm 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-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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-94899.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (G -> (H or G))))), M:tm-1003, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-94900
in-theory        94900
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), 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-94900.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (F -> E)))), M:tm-1003, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-94901
in-theory        94901
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-1003 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       153
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-94901.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F)))), M:tm-1003, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-94902
in-theory        94902
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> ((F -> E) and G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), 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-94902.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> ((F -> E) and G)))), M:tm-1003, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-94903
in-theory        94903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((F -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), 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-94903.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((F -> E) or G))), M:tm-1003, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-94904
in-theory        94904
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G or (F -> E))))
theorem-size     27
proof            (modus-ponens tm-1003 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       133
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94904.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G or (F -> E)))), M:tm-1003, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-94905
in-theory        94905
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G))))
theorem-size     31
proof            (modus-ponens tm-1003 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       149
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94905.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G)))), M:tm-1003, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-94906
in-theory        94906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F))))
theorem-size     29
proof            (modus-ponens tm-1003 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       143
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94906.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F)))), M:tm-1003, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-94907
in-theory        94907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), 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-94907.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (H -> G)))), M:tm-1003, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-94908
in-theory        94908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (F -> F)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-94908.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (F -> F))), M:tm-1003, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-94909
in-theory        94909
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-1003 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       197
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-94909.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-1003, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-94910
in-theory        94910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 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       177
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-94910.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-94911
in-theory        94911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-1003 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       173
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-94911.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-1003, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-94912
in-theory        94912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 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       145
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94912.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G and H) -> G))), M:tm-1003, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-94913
in-theory        94913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-1003 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       173
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-94913.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G))), M:tm-1003, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-94914
in-theory        94914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 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       145
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94914.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G and H) -> H))), M:tm-1003, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-94915
in-theory        94915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-1003 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94915.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E)))), M:tm-1003, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-94916
in-theory        94916
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       189
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-94916.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E)))), M:tm-1003, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-94917
in-theory        94917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-1003 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94917.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E)))), M:tm-1003, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-94918
in-theory        94918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-1003 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94918.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E)))), M:tm-1003, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-94919
in-theory        94919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-1003 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       165
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94919.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E)))), M:tm-1003, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-94920
in-theory        94920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (F -> (F and E))))
theorem-size     27
proof            (modus-ponens tm-1003 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-94920.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (F -> (F and E)))), M:tm-1003, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-94921
in-theory        94921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), 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-94921.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (H -> (G and H))))), M:tm-1003, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-94922
in-theory        94922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-1003 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94922.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E)))), M:tm-1003, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-94923
in-theory        94923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), 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-94923.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (G or H)))), M:tm-1003, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-94924
in-theory        94924
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-1003 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       157
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94924.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E)))), M:tm-1003, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-94925
in-theory        94925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 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       145
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94925.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (G -> (H or G)))), M:tm-1003, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-94926
in-theory        94926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-1003 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       167
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94926.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E))), M:tm-1003, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-94927
in-theory        94927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (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-94927.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-1003, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-94928
in-theory        94928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 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       165
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (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-94928.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-1003, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-94929
in-theory        94929
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A 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-94929.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G)))), M:tm-1003, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-94930
in-theory        94930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       173
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B 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-94930.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-1003, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-94931
in-theory        94931
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B 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-94931.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-1003, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-94932
in-theory        94932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B 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-94932.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-1003, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-94933
in-theory        94933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) 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-94933.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-1003, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-94934
in-theory        94934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-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-1.            (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-94934.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-1003, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-94935
in-theory        94935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> G) -> ((E -> F) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94935.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> G) -> ((E -> F) -> G))), M:tm-1003, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-94936
in-theory        94936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
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-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-94936.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G)))), M:tm-1003, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-94937
in-theory        94937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       169
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-94937.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H))), M:tm-1003, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-94938
in-theory        94938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-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-94938.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-1003, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-94939
in-theory        94939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-1003 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       141
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-94939.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H)), M:tm-1003, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-94940
in-theory        94940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-1003 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       147
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-94940.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E))), M:tm-1003, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-94941
in-theory        94941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
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-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-94941.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G))), M:tm-1003, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-94942
in-theory        94942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), 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-94942.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-1003, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-94943
in-theory        94943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-1003 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       177
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94943.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G))))), M:tm-1003, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-94944
in-theory        94944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       189
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94944.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G)))), M:tm-1003, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-94945
in-theory        94945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       183
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94945.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H)))), M:tm-1003, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-94946
in-theory        94946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       177
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94946.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H))), M:tm-1003, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-94947
in-theory        94947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       177
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94947.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G))))), M:tm-1003, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-94948
in-theory        94948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       197
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94948.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H)))), M:tm-1003, 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-94949
in-theory        94949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       191
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94949.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F))))), M:tm-1003, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-94950
in-theory        94950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-1003 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94950.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H)))), M:tm-1003, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-94951
in-theory        94951
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F))))
theorem-size     37
proof            (modus-ponens tm-1003 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       193
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94951.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F)))), M:tm-1003, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-94952
in-theory        94952
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94952.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-1003, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-94953
in-theory        94953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       213
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94953.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-1003, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-94954
in-theory        94954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-1003 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94954.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H))), M:tm-1003, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-94955
in-theory        94955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-1003 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94955.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I))), M:tm-1003, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-94956
in-theory        94956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94956.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G))))), M:tm-1003, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-94957
in-theory        94957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       233
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94957.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94958
in-theory        94958
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94958.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G))))), M:tm-1003, 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-94959
in-theory        94959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94959.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G))))), M:tm-1003, 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-94960
in-theory        94960
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94960.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G))))), M:tm-1003, 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-94961
in-theory        94961
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       205
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94961.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G))))), M:tm-1003, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-94962
in-theory        94962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-1003 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       189
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94962.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I))))), M:tm-1003, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-94963
in-theory        94963
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94963.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G))))), M:tm-1003, 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-94964
in-theory        94964
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-1003 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94964.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I)))), M:tm-1003, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-94965
in-theory        94965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       201
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94965.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G))))), M:tm-1003, 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-94966
in-theory        94966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-1003 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       181
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94966.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H)))), M:tm-1003, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-94967
in-theory        94967
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       203
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> 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-94967.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G)))), M:tm-1003, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-94968
in-theory        94968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       263
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94968.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94969
in-theory        94969
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       211
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> 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-94969.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E))), M:tm-1003, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-94970
in-theory        94970
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-7 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and 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-94970.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94971
in-theory        94971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       209
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and 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-94971.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94972
in-theory        94972
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-94972.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94973
in-theory        94973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       217
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), 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-94973.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94974
in-theory        94974
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-4 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and 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-94974.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94975
in-theory        94975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-3 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and 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-94975.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94976
in-theory        94976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-94976.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94977
in-theory        94977
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-1 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) 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-94977.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-1003, 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-94978
in-theory        94978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-94978.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H))), M:tm-1003, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-94979
in-theory        94979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-9 tm-2)
proof-size       211
proof-steps      11
----------------------------------------------------------------
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-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-94979.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94980
in-theory        94980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       229
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-94980.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94981
in-theory        94981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-7 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
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-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-94981.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-1003, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-94982
in-theory        94982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       185
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94982.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I)), M:tm-1003, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-94983
in-theory        94983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       191
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-94983.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E))), M:tm-1003, 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-94984
in-theory        94984
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-2)
proof-size       209
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-94984.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-94985
in-theory        94985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 tm-1 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
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-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-94985.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-1003, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-94986
in-theory        94986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> E)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 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-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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-94986.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> E))), M:tm-1003, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-94987
in-theory        94987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-1003 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       159
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-94987.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-1003, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-94988
in-theory        94988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) and G) or (E and F)) -> E))
theorem-size     27
proof            (modus-ponens tm-1003 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       131
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-94988.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) and G) or (E and F)) -> E)), M:tm-1003, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-94989
in-theory        94989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) and G) or (E and F)) -> F))
theorem-size     27
proof            (modus-ponens tm-1003 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       131
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-94989.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E and F) and G) or (E and F)) -> F)), M:tm-1003, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-94990
in-theory        94990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (E and G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 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-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-3.            ((A and B) -> A), axiom
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-94990.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (E and G)))), M:tm-1003, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-94991
in-theory        94991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (E or G)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
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-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-3.            ((A and B) -> A), axiom
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-94991.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (E or G))), M:tm-1003, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-94992
in-theory        94992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G or E)))
theorem-size     25
proof            (modus-ponens tm-1003 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       127
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-94992.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G or E))), M:tm-1003, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-94993
in-theory        94993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H))))
theorem-size     35
proof            (modus-ponens tm-1003 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       155
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-94993.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H)))), M:tm-1003, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-94994
in-theory        94994
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-1003 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       149
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-94994.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-1003, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-94995
in-theory        94995
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((not (not E)) and F) or (not (not E))) -> E))
theorem-size     27
proof            (modus-ponens tm-1003 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       131
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-94995.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((not (not E)) and F) or (not (not E))) -> E)), M:tm-1003, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-94996
in-theory        94996
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-94996.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (H -> G)))), M:tm-1003, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-94997
in-theory        94997
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (E -> E)))
theorem-size     29
proof            (modus-ponens tm-1003 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       155
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-94997.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (E -> E))), M:tm-1003, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-94998
in-theory        94998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       211
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-94998.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-1003, 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-94999
in-theory        94999
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 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       175
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-94999.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-95000
in-theory        95000
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       187
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-95000.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-1003, 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-95001
in-theory        95001
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-95001.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G and H) -> G))), M:tm-1003, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-95002
in-theory        95002
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       187
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-95002.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-1003, 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-95003
in-theory        95003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-95003.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G and H) -> H))), M:tm-1003, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-95004
in-theory        95004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (H -> G)) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-95004.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (H -> G)) and E))), M:tm-1003, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-95005
in-theory        95005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       183
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-95005.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E))), M:tm-1003, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-95006
in-theory        95006
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (((G and H) -> G) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95006.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (((G and H) -> G) and E))), M:tm-1003, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-95007
in-theory        95007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (((G and H) -> H) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95007.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (((G and H) -> H) and E))), M:tm-1003, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-95008
in-theory        95008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E)))
theorem-size     31
proof            (modus-ponens tm-1003 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       159
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95008.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E))), M:tm-1003, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-95009
in-theory        95009
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-1003 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       163
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-95009.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F)))), M:tm-1003, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-95010
in-theory        95010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-95010.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (H -> (G and H))))), M:tm-1003, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-95011
in-theory        95011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (G or H)) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95011.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (G or H)) and E))), M:tm-1003, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-95012
in-theory        95012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-95012.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (G or H)))), M:tm-1003, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-95013
in-theory        95013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (H or G)) and E)))
theorem-size     29
proof            (modus-ponens tm-1003 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       151
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95013.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> ((G -> (H or G)) and E))), M:tm-1003, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-95014
in-theory        95014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 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       143
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-95014.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or E) -> (G -> (H or G)))), M:tm-1003, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-95015
in-theory        95015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       177
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and 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-95015.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-1003, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-95016
in-theory        95016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       229
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), 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-95016.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003, 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-95017
in-theory        95017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-1003 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       167
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95017.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F))), M:tm-1003, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-95018
in-theory        95018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-95018.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G)))), M:tm-1003, 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-95019
in-theory        95019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (((F and G) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-1003 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       161
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-95019.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (((F and G) or F) -> E))), M:tm-1003, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-95020
in-theory        95020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-95020.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-1003, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-95021
in-theory        95021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 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       159
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B 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-95021.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-1003, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-95022
in-theory        95022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and 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-95022.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F)))), M:tm-1003, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-95023
in-theory        95023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       167
proof-steps      13
----------------------------------------------------------------
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-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-95023.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-1003, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-95024
in-theory        95024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> 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-95024.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-1003, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-95025
in-theory        95025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 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-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-3.            ((A and B) -> 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-95025.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-1003, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-95026
in-theory        95026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and 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-95026.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-1003, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-95027
in-theory        95027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-1.            (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-95027.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-1003, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-95028
in-theory        95028
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
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-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-95028.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F)))), M:tm-1003, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-95029
in-theory        95029
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       163
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-95029.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H))), M:tm-1003, 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-95030
in-theory        95030
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-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-95030.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> (((F and H) or F) -> G)))), M:tm-1003, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-95031
in-theory        95031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (((E and G) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-1003 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       135
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95031.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (((E and G) or E) -> F)) or H)), M:tm-1003, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-95032
in-theory        95032
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-1003 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       141
proof-steps      11
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-95032.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E))), M:tm-1003, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-95033
in-theory        95033
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-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-95033.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F))), M:tm-1003, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-95034
in-theory        95034
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-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-95034.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> (((F and H) or F) -> G)))), M:tm-1003, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-95035
in-theory        95035
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-95035.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> F))), M:tm-1003, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-95036
in-theory        95036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-1003 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       159
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-95036.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H)))), M:tm-1003, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-95037
in-theory        95037
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F and G)) or (F and G)) -> F))
theorem-size     27
proof            (modus-ponens tm-1003 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       131
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95037.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F and G)) or (F and G)) -> F)), M:tm-1003, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-95038
in-theory        95038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F and G)) or (F and G)) -> G))
theorem-size     27
proof            (modus-ponens tm-1003 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       131
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95038.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F and G)) or (F and G)) -> G)), M:tm-1003, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-95039
in-theory        95039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
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-95039.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (F and G)))), M:tm-1003, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-95040
in-theory        95040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-1003 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
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-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-4.            ((A and B) -> B), axiom
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-95040.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (F or G))), M:tm-1003, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-95041
in-theory        95041
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-1003 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       127
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95041.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G or F))), M:tm-1003, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-95042
in-theory        95042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-1003 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       155
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95042.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H)))), M:tm-1003, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-95043
in-theory        95043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-1003 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       149
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95043.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F)))), M:tm-1003, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-95044
in-theory        95044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (not (not F))) or (not (not F))) -> F))
theorem-size     27
proof            (modus-ponens tm-1003 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       131
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95044.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (not (not F))) or (not (not F))) -> F)), M:tm-1003, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-95045
in-theory        95045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 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       143
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-95045.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (H -> G)))), M:tm-1003, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-95046
in-theory        95046
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (F -> F)))
theorem-size     29
proof            (modus-ponens tm-1003 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       155
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-95046.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (F -> F))), M:tm-1003, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-95047
in-theory        95047
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       211
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-95047.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H)))), M:tm-1003, 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-95048
in-theory        95048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 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       175
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-95048.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-95049
in-theory        95049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       187
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-95049.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G))), M:tm-1003, 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-95050
in-theory        95050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 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       143
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-95050.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G and H) -> G))), M:tm-1003, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-95051
in-theory        95051
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       187
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-95051.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H))), M:tm-1003, 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-95052
in-theory        95052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 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       143
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-95052.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G and H) -> H))), M:tm-1003, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-95053
in-theory        95053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (H -> G)) and F)))
theorem-size     29
proof            (modus-ponens tm-1003 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       151
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-95053.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (H -> G)) and F))), M:tm-1003, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-95054
in-theory        95054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1003 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       183
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-95054.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))), M:tm-1003, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-95055
in-theory        95055
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (((G and H) -> G) and F)))
theorem-size     29
proof            (modus-ponens tm-1003 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       151
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95055.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (((G and H) -> G) and F))), M:tm-1003, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-95056
in-theory        95056
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (((G and H) -> H) and F)))
theorem-size     29
proof            (modus-ponens tm-1003 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       151
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95056.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (((G and H) -> H) and F))), M:tm-1003, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-95057
in-theory        95057
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F)))
theorem-size     31
proof            (modus-ponens tm-1003 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       159
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95057.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F))), M:tm-1003, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-95058
in-theory        95058
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-1003 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       163
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-95058.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G)))), M:tm-1003, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-95059
in-theory        95059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-784 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), 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-95059.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (H -> (G and H))))), M:tm-1003, m:tm-784, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-95060
in-theory        95060
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (G or H)) and F)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-785 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
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-95060.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (G or H)) and F))), M:tm-1003, m:tm-785, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-95061
in-theory        95061
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-786 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-95061.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (G or H)))), M:tm-1003, m:tm-786, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-95062
in-theory        95062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (H or G)) and F)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-787 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-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-95062.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> ((G -> (H or G)) and F))), M:tm-1003, m:tm-787, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-95063
in-theory        95063
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-788 ((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 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-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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-95063.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) or F) -> (G -> (H or G)))), M:tm-1003, m:tm-788, u:((A (-> (or (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-95064
in-theory        95064
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-789 ((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and 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-95064.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F -> G) -> H)) or ((F -> G) -> H)) -> ((G or (F -> G)) -> H))), M:tm-1003, m:tm-789, u:((A (-> (or (and Am (-> (-> Bm Cm) Dm)) (-> (-> Bm Cm) Dm)) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-95065
in-theory        95065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))
theorem-size     53
proof            (modus-ponens tm-1003 tm-790 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       229
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), 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-95065.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (((F -> G) -> (F -> H)) -> I)) or (((F -> G) -> (F -> H)) -> I)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))), M:tm-1003, m:tm-790, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-95066
in-theory        95066
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-791 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95066.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (((F and H) or F) -> G))), M:tm-1003, m:tm-791, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-95067
in-theory        95067
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-792 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95067.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (((H and F) or F) -> G))), M:tm-1003, m:tm-792, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (or (and Dm Bm) Bm) Cm))))
================================================================
tm-name          tm-95068
in-theory        95068
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-793 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95068.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (((H and E) or E) -> F))), M:tm-1003, m:tm-793, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Dm Am) Am) Bm))))
================================================================
tm-name          tm-95069
in-theory        95069
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-794 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-95069.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and (E -> F)) or (E -> F)) -> (E -> G)))), M:tm-1003, m:tm-794, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and Dm (-> Am Bm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-95070
in-theory        95070
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (((G and F) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-795 ((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-95070.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> E)) -> (((G and F) or F) -> E))), M:tm-1003, m:tm-795, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Cm Bm) Bm) Am))))
================================================================
tm-name          tm-95071
in-theory        95071
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-796 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or 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-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-95071.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-1003, m:tm-796, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-95072
in-theory        95072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-797 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 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-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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (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-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-95072.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-1003, m:tm-797, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-95073
in-theory        95073
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-798 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-95073.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> F) -> ((E -> F) and (((G and E) or E) -> F)))), M:tm-1003, m:tm-798, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
================================================================
tm-name          tm-95074
in-theory        95074
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-799 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-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-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-95074.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-1003, m:tm-799, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-95075
in-theory        95075
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-800 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-95075.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-1003, m:tm-800, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-95076
in-theory        95076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-801 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> 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-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-95076.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-1003, m:tm-801, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-95077
in-theory        95077
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-802 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-95077.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-1003, m:tm-802, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-95078
in-theory        95078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-803 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
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-1.            (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-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-95078.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-1003, m:tm-803, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Em Cm) Cm) Dm)))))
================================================================
tm-name          tm-95079
in-theory        95079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-804 ((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
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-95079.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (not (((G and E) or E) -> F))) -> (not (E -> F)))), M:tm-1003, m:tm-804, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Cm Am) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-95080
in-theory        95080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-1003 tm-805 ((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95080.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E and F) or F) -> G) -> H) -> (((F -> G) or (((E and F) or F) -> G)) -> H))), M:tm-1003, m:tm-805, u:((A (-> (-> (-> (or (and Am Bm) Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-95081
in-theory        95081
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-806 ((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
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-95081.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((F -> G) -> (((H and F) or F) -> G)))), M:tm-1003, m:tm-806, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-95082
in-theory        95082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (((G and E) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-1003 tm-807 ((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95082.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> (((G and E) or E) -> F)) or H)), M:tm-1003, m:tm-807, u:((A (or (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)) Dm)))
================================================================
tm-name          tm-95083
in-theory        95083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-808 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95083.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> (((H and F) or F) -> G)) and E))), M:tm-1003, m:tm-808, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)) Am))))
================================================================
tm-name          tm-95084
in-theory        95084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-809 ((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-95084.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((G and E) or E)) -> ((E -> F) -> F))), M:tm-1003, m:tm-809, u:((A (-> (-> (-> Am Bm) (or (and Cm Am) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-95085
in-theory        95085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-810 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
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-95085.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F -> G) -> (((H and F) or F) -> G)))), M:tm-1003, m:tm-810, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Dm Bm) Bm) Cm)))))
================================================================
tm-name          tm-95086
in-theory        95086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-811 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 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-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-48.           (((A -> (B and 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-95086.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (F -> (E and F))))), M:tm-1003, m:tm-811, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-95087
in-theory        95087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-812 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95087.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> ((F -> (E and F)) and G)))), M:tm-1003, m:tm-812, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (and (-> Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-95088
in-theory        95088
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-813 ((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
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-95088.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((F -> (E and F)) or G))), M:tm-1003, m:tm-813, u:((A (-> (or Am (-> Bm (and Am Bm))) (or (-> Bm (and Am Bm)) Cm))))
================================================================
tm-name          tm-95089
in-theory        95089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G or (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-814 ((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95089.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G or (F -> (E and F))))), M:tm-1003, m:tm-814, u:((A (-> (or Am (-> Bm (and Am Bm))) (or Cm (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-95090
in-theory        95090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-815 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95090.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((E and F) -> G) -> ((F or (E and F)) -> G)))), M:tm-1003, m:tm-815, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> (and Am Bm) Cm) (-> (or Bm (and Am Bm)) Cm)))))
================================================================
tm-name          tm-95091
in-theory        95091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-816 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95091.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((F -> (not (E and F))) -> (not F)))), M:tm-1003, m:tm-816, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Bm (not (and Am Bm))) (not Bm)))))
================================================================
tm-name          tm-95092
in-theory        95092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-817 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95092.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H -> G)))), M:tm-1003, m:tm-817, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-95093
in-theory        95093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (F -> F)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-818 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-48.           (((A -> (B and 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-95093.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (F -> F))), M:tm-1003, m:tm-818, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm Bm))))
================================================================
tm-name          tm-95094
in-theory        95094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-819 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
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-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-48.           (((A -> (B and 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-95094.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-819, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-95095
in-theory        95095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-820 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95095.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G and H) -> G))), M:tm-1003, m:tm-820, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-95096
in-theory        95096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-1003 tm-821 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95096.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G and H) -> H))), M:tm-1003, m:tm-821, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-95097
in-theory        95097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-822 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95097.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> G)) and (F -> (E and F))))), M:tm-1003, m:tm-822, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-95098
in-theory        95098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-823 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95098.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> (E and F))))), M:tm-1003, m:tm-823, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-95099
in-theory        95099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-824 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95099.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G and H) -> G) and (F -> (E and F))))), M:tm-1003, m:tm-824, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Cm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-95100
in-theory        95100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-825 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95100.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G and H) -> H) and (F -> (E and F))))), M:tm-1003, m:tm-825, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (and Cm Dm) Dm) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-95101
in-theory        95101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-826 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95101.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H -> (G and H))) and (F -> (E and F))))), M:tm-1003, m:tm-826, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-95102
in-theory        95102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (F -> (F and (E and F)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-827 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 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-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-48.           (((A -> (B and 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-95102.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (F -> (F and (E and F))))), M:tm-1003, m:tm-827, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Bm (and Bm (and Am Bm))))))
================================================================
tm-name          tm-95103
in-theory        95103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-828 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95103.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H -> (G and H))))), M:tm-1003, m:tm-828, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-95104
in-theory        95104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-829 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> 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-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-95104.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (G or H)) and (F -> (E and F))))), M:tm-1003, m:tm-829, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Cm Dm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-95105
in-theory        95105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-830 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-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-95105.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (G or H)))), M:tm-1003, m:tm-830, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-95106
in-theory        95106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-831 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95106.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> ((G -> (H or G)) and (F -> (E and F))))), M:tm-1003, m:tm-831, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> Cm (or Dm Cm)) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-95107
in-theory        95107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-832 ((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95107.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (G -> (H or G)))), M:tm-1003, m:tm-832, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-95108
in-theory        95108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G)))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-833 ((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 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-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-48.           (((A -> (B and 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-95108.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> G) -> (E and (F -> G)))) -> ((G or (F -> G)) -> (E and (F -> G))))), M:tm-1003, m:tm-833, u:((A (-> (or Am (-> (-> Bm Cm) (and Am (-> Bm Cm)))) (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
================================================================
tm-name          tm-95109
in-theory        95109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H))))))
theorem-size     59
proof            (modus-ponens tm-1003 tm-834 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95109.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (((F -> G) -> (F -> H)) -> (E and ((F -> G) -> (F -> H))))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> (E and ((F -> G) -> (F -> H)))))), M:tm-1003, m:tm-834, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) (and Am (-> (-> Bm Cm) (-> Bm Dm))))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-95110
in-theory        95110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-835 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95110.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((F and G) or F) -> (E and F)))), M:tm-1003, m:tm-835, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Bm Cm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-95111
in-theory        95111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-836 ((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95111.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G and F) or F) -> (E and F)))), M:tm-1003, m:tm-836, u:((A (-> (or Am (-> Bm (and Am Bm))) (-> (or (and Cm Bm) Bm) (and Am Bm)))))
================================================================
tm-name          tm-95112
in-theory        95112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F))))))
theorem-size     47
proof            (modus-ponens tm-1003 tm-837 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm))))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95112.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> (G and F)) -> (E and (F -> (G and F))))) -> ((G or (F -> (G and F))) -> (E and (F -> (G and F)))))), M:tm-1003, m:tm-837, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) (and Am (-> Bm (and Cm Bm))))) (-> (or Cm (-> Bm (and Cm Bm))) (and Am (-> Bm (and Cm Bm)))))))
================================================================
tm-name          tm-95113
in-theory        95113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H)))
theorem-size     43
proof            (modus-ponens tm-1003 tm-838 ((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B 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-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-95113.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F -> (G and F)) -> H)) or ((F -> (G and F)) -> H)) -> ((G or (F -> (G and F))) -> H))), M:tm-1003, m:tm-838, u:((A (-> (or (and Am (-> (-> Bm (and Cm Bm)) Dm)) (-> (-> Bm (and Cm Bm)) Dm)) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))
================================================================
tm-name          tm-95114
in-theory        95114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-1003 tm-839 ((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48.           (((A -> (B and 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-95114.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> (F and E)) -> G) and H) or ((E -> (F and E)) -> G)) -> ((F or (E -> (F and E))) -> G))), M:tm-1003, m:tm-839, u:((A (-> (or (and (-> (-> Am (and Bm Am)) Cm) Dm) (-> (-> Am (and Bm Am)) Cm)) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-95115
in-theory        95115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-840 ((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       221
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am 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-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-95115.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> ((F and E) -> G)) or ((E -> (F and E)) -> (E -> G))) -> ((F or (E -> (F and E))) -> (E -> G)))), M:tm-1003, m:tm-840, u:((A (-> (or (-> Am (-> (and Bm Am) Cm)) (-> (-> Am (and Bm Am)) (-> Am Cm))) (-> (or Bm (-> Am (and Bm Am))) (-> Am Cm)))))
================================================================
tm-name          tm-95116
in-theory        95116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-841 ((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am)))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48.           (((A -> (B and 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-95116.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> (G and F)) -> E)) -> ((G or (F -> (G and F))) -> E))), M:tm-1003, m:tm-841, u:((A (-> (or Am (-> (-> Bm (and Cm Bm)) Am)) (-> (or Cm (-> Bm (and Cm Bm))) Am))))
================================================================
tm-name          tm-95117
in-theory        95117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-842 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48.           (((A -> (B and 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-95117.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-1003, m:tm-842, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-95118
in-theory        95118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-843 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-95118.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-1003, m:tm-843, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-95119
in-theory        95119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-844 ((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-95119.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F and E)) -> G) -> (((E -> (F and E)) -> G) and ((F or (E -> (F and E))) -> G)))), M:tm-1003, m:tm-844, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (and (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
================================================================
tm-name          tm-95120
in-theory        95120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-845 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (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-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-95120.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-1003, m:tm-845, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-95121
in-theory        95121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-846 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-95121.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-1003, m:tm-846, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-95122
in-theory        95122
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-847 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48.           (((A -> (B and 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-95122.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-1003, m:tm-847, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-95123
in-theory        95123
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-1003 tm-848 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-95123.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-1003, m:tm-848, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-95124
in-theory        95124
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-849 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48.           (((A -> (B and 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-95124.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-1003, m:tm-849, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (and Dm Cm)) Em) (-> (or Dm (-> Cm (and Dm Cm))) Em)))))
================================================================
tm-name          tm-95125
in-theory        95125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-850 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48.           (((A -> (B and 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-95125.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F and E)) -> G) -> ((E -> (F and E)) -> G))), M:tm-1003, m:tm-850, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (-> Am (and Bm Am)) Cm))))
================================================================
tm-name          tm-95126
in-theory        95126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-851 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       177
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-95126.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F and E)) -> G) -> (not ((F or (E -> (F and E))) -> G))) -> (not ((E -> (F and E)) -> G)))), M:tm-1003, m:tm-851, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (not (-> (or Bm (-> Am (and Bm Am))) Cm))) (not (-> (-> Am (and Bm Am)) Cm)))))
================================================================
tm-name          tm-95127
in-theory        95127
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-1003 tm-852 ((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95127.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or (F -> (E and F))) -> G) -> H) -> ((((F -> (E and F)) -> G) or ((E or (F -> (E and F))) -> G)) -> H))), M:tm-1003, m:tm-852, u:((A (-> (-> (-> (or Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or (-> (-> Bm (and Am Bm)) Cm) (-> (or Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-95128
in-theory        95128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-853 ((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), 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-95128.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-1003, m:tm-853, u:((A (or Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-95129
in-theory        95129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-1003 tm-854 ((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95129.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)) or H)), M:tm-1003, m:tm-854, u:((A (or (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)) Dm)))
================================================================
tm-name          tm-95130
in-theory        95130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-855 ((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95130.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)) and E))), M:tm-1003, m:tm-855, u:((A (-> Am (and (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)) Am))))
================================================================
tm-name          tm-95131
in-theory        95131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G)))
theorem-size     41
proof            (modus-ponens tm-1003 tm-856 ((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm)))))
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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-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-95131.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> (F and E)) -> G) -> (F or (E -> (F and E)))) -> (((E -> (F and E)) -> G) -> G))), M:tm-1003, m:tm-856, u:((A (-> (-> (-> (-> Am (and Bm Am)) Cm) (or Bm (-> Am (and Bm Am)))) (-> (-> (-> Am (and Bm Am)) Cm) Cm))))
================================================================
tm-name          tm-95132
in-theory        95132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-857 ((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-95132.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-1003, m:tm-857, u:((A (-> Am (-> (-> (-> Bm (and Cm Bm)) Dm) (-> (or Cm (-> Bm (and Cm Bm))) Dm)))))
================================================================
tm-name          tm-95133
in-theory        95133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-858 ((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-95133.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (E or F)))), M:tm-1003, m:tm-858, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Am Bm)))))
================================================================
tm-name          tm-95134
in-theory        95134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> ((E or F) and G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-859 ((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm))))))
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-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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
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-95134.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> ((E or F) and G)))), M:tm-1003, m:tm-859, u:((A (-> (or Am (or Am Bm)) (-> Cm (and (or Am Bm) Cm)))))
================================================================
tm-name          tm-95135
in-theory        95135
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((E or F) or G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-860 ((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-49.           (((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-95135.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((E or F) or G))), M:tm-1003, m:tm-860, u:((A (-> (or Am (or Am Bm)) (or (or Am Bm) Cm))))
================================================================
tm-name          tm-95136
in-theory        95136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G or (E or F))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-861 ((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-49.           (((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-95136.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G or (E or F)))), M:tm-1003, m:tm-861, u:((A (-> (or Am (or Am Bm)) (or Cm (or Am Bm)))))
================================================================
tm-name          tm-95137
in-theory        95137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-862 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-95137.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (H -> G)))), M:tm-1003, m:tm-862, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-95138
in-theory        95138
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-863 ((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-49.           (((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-95138.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-863, u:((A (-> (or Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-95139
in-theory        95139
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-864 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-95139.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G and H) -> G))), M:tm-1003, m:tm-864, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-95140
in-theory        95140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-865 ((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-95140.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G and H) -> H))), M:tm-1003, m:tm-865, u:((A (-> (or Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-95141
in-theory        95141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-866 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-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-95141.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> G)) and (E or F)))), M:tm-1003, m:tm-866, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-95142
in-theory        95142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-867 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-49.           (((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-20.           (A -> (((B -> (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-95142.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (E or F)))), M:tm-1003, m:tm-867, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am Bm)))))
================================================================
tm-name          tm-95143
in-theory        95143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (((G and H) -> G) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-868 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-49.           (((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-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-95143.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (((G and H) -> G) and (E or F)))), M:tm-1003, m:tm-868, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Cm) (or Am Bm)))))
================================================================
tm-name          tm-95144
in-theory        95144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (((G and H) -> H) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-869 ((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-49.           (((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-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-95144.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (((G and H) -> H) and (E or F)))), M:tm-1003, m:tm-869, u:((A (-> (or Am (or Am Bm)) (and (-> (and Cm Dm) Dm) (or Am Bm)))))
================================================================
tm-name          tm-95145
in-theory        95145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-870 ((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-95145.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (H -> (G and H))) and (E or F)))), M:tm-1003, m:tm-870, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (-> Dm (and Cm Dm))) (or Am Bm)))))
================================================================
tm-name          tm-95146
in-theory        95146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-871 ((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-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-95146.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (H -> (G and H))))), M:tm-1003, m:tm-871, u:((A (-> (or Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-95147
in-theory        95147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-872 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, 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-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-95147.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (G or H)) and (E or F)))), M:tm-1003, m:tm-872, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Cm Dm)) (or Am Bm)))))
================================================================
tm-name          tm-95148
in-theory        95148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-873 ((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-95148.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (G or H)))), M:tm-1003, m:tm-873, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-95149
in-theory        95149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-874 ((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-49.           (((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-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-95149.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> ((G -> (H or G)) and (E or F)))), M:tm-1003, m:tm-874, u:((A (-> (or Am (or Am Bm)) (and (-> Cm (or Dm Cm)) (or Am Bm)))))
================================================================
tm-name          tm-95150
in-theory        95150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-875 ((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 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-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-49.           (((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-95150.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (G -> (H or G)))), M:tm-1003, m:tm-875, u:((A (-> (or Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-95151
in-theory        95151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-876 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-49.           (((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-95151.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F or G) -> (E and (F or G)))) -> ((F or (F or G)) -> (E and (F or G))))), M:tm-1003, m:tm-876, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Bm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-95152
in-theory        95152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-877 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49.           (((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-95152.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((F or (F or G)) -> H))), M:tm-1003, m:tm-877, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-95153
in-theory        95153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-878 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-49.           (((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-95153.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((E or (E or F)) -> G))), M:tm-1003, m:tm-878, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-95154
in-theory        95154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-879 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-49.           (((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-95154.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F or G) -> E)) -> ((F or (F or G)) -> E))), M:tm-1003, m:tm-879, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-95155
in-theory        95155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-880 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-49.           (((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-95155.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-1003, m:tm-880, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95156
in-theory        95156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-881 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-49.           (((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-95156.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-1003, m:tm-881, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95157
in-theory        95157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-882 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-49.           (((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-95157.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> (((E or F) -> G) and ((E or (E or F)) -> G)))), M:tm-1003, m:tm-882, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-95158
in-theory        95158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-883 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-49.           (((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-95158.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-1003, m:tm-883, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95159
in-theory        95159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-884 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-49.           (((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-95159.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-1003, m:tm-884, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95160
in-theory        95160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-885 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-49.           (((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-95160.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-1003, m:tm-885, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95161
in-theory        95161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-886 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-95161.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-1003, m:tm-886, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-95162
in-theory        95162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-887 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-49.           (((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-95162.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-1003, m:tm-887, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Cm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95163
in-theory        95163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> ((E or F) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-888 ((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-49.           (((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-95163.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> ((E or F) -> G))), M:tm-1003, m:tm-888, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-95164
in-theory        95164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-889 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-49.           (((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-95164.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> (not ((E or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-1003, m:tm-889, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Am (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-95165
in-theory        95165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-1003 tm-890 ((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
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-49.           (((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-95165.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or (E or F)) -> G) -> H) -> ((((E or F) -> G) or ((E or (E or F)) -> G)) -> H))), M:tm-1003, m:tm-890, u:((A (-> (-> (-> (or Am (or Am Bm)) Cm) Dm) (-> (or (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-95166
in-theory        95166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-891 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-49.           (((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-95166.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-1003, m:tm-891, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-95167
in-theory        95167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-1003 tm-892 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-49.           (((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-95167.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> ((E or (E or F)) -> G)) or H)), M:tm-1003, m:tm-892, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-95168
in-theory        95168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-893 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-49.           (((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-95168.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F or G) -> H) -> ((F or (F or G)) -> H)) and E))), M:tm-1003, m:tm-893, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-95169
in-theory        95169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-894 ((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-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-95169.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> (E or (E or F))) -> (((E or F) -> G) -> G))), M:tm-1003, m:tm-894, u:((A (-> (-> (-> (or Am Bm) Cm) (or Am (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-95170
in-theory        95170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-895 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), axiom
tm-49.           (((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-95170.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-1003, m:tm-895, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Bm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-95171
in-theory        95171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-896 ((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95171.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (F or E)))), M:tm-1003, m:tm-896, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Bm Am)))))
================================================================
tm-name          tm-95172
in-theory        95172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> ((F or E) and G))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-897 ((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-95172.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> ((F or E) and G)))), M:tm-1003, m:tm-897, u:((A (-> (or Am (or Bm Am)) (-> Cm (and (or Bm Am) Cm)))))
================================================================
tm-name          tm-95173
in-theory        95173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((F or E) or G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-898 ((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
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-95173.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((F or E) or G))), M:tm-1003, m:tm-898, u:((A (-> (or Am (or Bm Am)) (or (or Bm Am) Cm))))
================================================================
tm-name          tm-95174
in-theory        95174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G or (F or E))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-899 ((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95174.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G or (F or E)))), M:tm-1003, m:tm-899, u:((A (-> (or Am (or Bm Am)) (or Cm (or Bm Am)))))
================================================================
tm-name          tm-95175
in-theory        95175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-900 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95175.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (H -> G)))), M:tm-1003, m:tm-900, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-95176
in-theory        95176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-901 ((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-1 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95176.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-1003, m:tm-901, u:((A (-> (or Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-95177
in-theory        95177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-902 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95177.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G and H) -> G))), M:tm-1003, m:tm-902, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-95178
in-theory        95178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-1003 tm-903 ((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95178.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G and H) -> H))), M:tm-1003, m:tm-903, u:((A (-> (or Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-95179
in-theory        95179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-904 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-95179.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> G)) and (F or E)))), M:tm-1003, m:tm-904, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-95180
in-theory        95180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-905 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-20.           (A -> (((B -> (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-95180.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F or E)))), M:tm-1003, m:tm-905, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Bm Am)))))
================================================================
tm-name          tm-95181
in-theory        95181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (((G and H) -> G) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-906 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-95181.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (((G and H) -> G) and (F or E)))), M:tm-1003, m:tm-906, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Cm) (or Bm Am)))))
================================================================
tm-name          tm-95182
in-theory        95182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (((G and H) -> H) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-907 ((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-95182.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (((G and H) -> H) and (F or E)))), M:tm-1003, m:tm-907, u:((A (-> (or Am (or Bm Am)) (and (-> (and Cm Dm) Dm) (or Bm Am)))))
================================================================
tm-name          tm-95183
in-theory        95183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-908 ((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-95183.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (H -> (G and H))) and (F or E)))), M:tm-1003, m:tm-908, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (or Bm Am)))))
================================================================
tm-name          tm-95184
in-theory        95184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-1003 tm-909 ((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-95184.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (H -> (G and H))))), M:tm-1003, m:tm-909, u:((A (-> (or Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-95185
in-theory        95185
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-910 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (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-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-95185.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (G or H)) and (F or E)))), M:tm-1003, m:tm-910, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Cm Dm)) (or Bm Am)))))
================================================================
tm-name          tm-95186
in-theory        95186
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-911 ((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-95186.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (G or H)))), M:tm-1003, m:tm-911, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-95187
in-theory        95187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-912 ((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, 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-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-95187.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> ((G -> (H or G)) and (F or E)))), M:tm-1003, m:tm-912, u:((A (-> (or Am (or Bm Am)) (and (-> Cm (or Dm Cm)) (or Bm Am)))))
================================================================
tm-name          tm-95188
in-theory        95188
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-1003 tm-913 ((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95188.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (G -> (H or G)))), M:tm-1003, m:tm-913, u:((A (-> (or Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-95189
in-theory        95189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G)))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-914 ((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95189.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F or G) -> (E and (F or G)))) -> ((G or (F or G)) -> (E and (F or G))))), M:tm-1003, m:tm-914, u:((A (-> (or Am (-> (or Bm Cm) (and Am (or Bm Cm)))) (-> (or Cm (or Bm Cm)) (and Am (or Bm Cm))))))
================================================================
tm-name          tm-95190
in-theory        95190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-915 ((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95190.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and ((F or G) -> H)) or ((F or G) -> H)) -> ((G or (F or G)) -> H))), M:tm-1003, m:tm-915, u:((A (-> (or (and Am (-> (or Bm Cm) Dm)) (-> (or Bm Cm) Dm)) (-> (or Cm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-95191
in-theory        95191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-916 ((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95191.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E or F) -> G) and H) or ((E or F) -> G)) -> ((F or (E or F)) -> G))), M:tm-1003, m:tm-916, u:((A (-> (or (and (-> (or Am Bm) Cm) Dm) (-> (or Am Bm) Cm)) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-95192
in-theory        95192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-1003 tm-917 ((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-95192.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F or G) -> E)) -> ((G or (F or G)) -> E))), M:tm-1003, m:tm-917, u:((A (-> (or Am (-> (or Bm Cm) Am)) (-> (or Cm (or Bm Cm)) Am))))
================================================================
tm-name          tm-95193
in-theory        95193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-918 ((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-50.           (((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-95193.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-1003, m:tm-918, u:((A (and (-> Am (or Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95194
in-theory        95194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-919 ((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-95194.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-1003, m:tm-919, u:((A (and (-> Am (or Am Bm)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95195
in-theory        95195
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-920 ((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-95195.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E or F) -> G) -> (((E or F) -> G) and ((F or (E or F)) -> G)))), M:tm-1003, m:tm-920, u:((A (-> (-> (or Am Bm) Cm) (and (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
================================================================
tm-name          tm-95196
in-theory        95196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-921 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-95196.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-1003, m:tm-921, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95197
in-theory        95197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-922 ((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-95197.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-1003, m:tm-922, u:((A (and (-> (and Am Bm) Bm) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95198
in-theory        95198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-923 ((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-95198.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-1003, m:tm-923, u:((A (and (-> (and Am Bm) Am) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95199
in-theory        95199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-924 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-95199.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-1003, m:tm-924, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-95200
in-theory        95200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-925 ((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-95200.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-1003, m:tm-925, u:((A (and (-> Am (-> Bm Am)) (-> (-> (or Cm Dm) Em) (-> (or Dm (or Cm Dm)) Em)))))
================================================================
tm-name          tm-95201
in-theory        95201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-926 ((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-95201.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> (not ((F or (E or F)) -> G))) -> (not ((E or F) -> G)))), M:tm-1003, m:tm-926, u:((A (-> (-> (-> (or Am Bm) Cm) (not (-> (or Bm (or Am Bm)) Cm))) (not (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-95202
in-theory        95202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-1003 tm-927 ((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95202.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or (F or E)) -> G) -> H) -> ((((F or E) -> G) or ((E or (F or E)) -> G)) -> H))), M:tm-1003, m:tm-927, u:((A (-> (-> (-> (or Am (or Bm Am)) Cm) Dm) (-> (or (-> (or Bm Am) Cm) (-> (or Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-95203
in-theory        95203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-928 ((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95203.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-1003, m:tm-928, u:((A (or Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-95204
in-theory        95204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-1003 tm-929 ((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95204.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> ((F or (E or F)) -> G)) or H)), M:tm-1003, m:tm-929, u:((A (or (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-95205
in-theory        95205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-930 ((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-95205.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F or G) -> H) -> ((G or (F or G)) -> H)) and E))), M:tm-1003, m:tm-930, u:((A (-> Am (and (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-95206
in-theory        95206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-931 ((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-95206.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E or F) -> G) -> (F or (E or F))) -> (((E or F) -> G) -> G))), M:tm-1003, m:tm-931, u:((A (-> (-> (-> (or Am Bm) Cm) (or Bm (or Am Bm))) (-> (-> (or Am Bm) Cm) Cm))))
================================================================
tm-name          tm-95207
in-theory        95207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-1003 tm-932 ((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-95207.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-1003, m:tm-932, u:((A (-> Am (-> (-> (or Bm Cm) Dm) (-> (or Cm (or Bm Cm)) Dm)))))
================================================================
tm-name          tm-95208
in-theory        95208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-933 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95208.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-933, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95209
in-theory        95209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-934 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       195
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95209.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (E or F)) -> ((F -> G) -> G)))), M:tm-1003, m:tm-934, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (or Am Bm)) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-95210
in-theory        95210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-935 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-95210.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (((F -> G) -> ((E or F) -> G)) and H)))), M:tm-1003, m:tm-935, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-95211
in-theory        95211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H)))
theorem-size     41
proof            (modus-ponens tm-1003 tm-936 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
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-95211.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> ((E or F) -> G)) or H))), M:tm-1003, m:tm-936, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))
================================================================
tm-name          tm-95212
in-theory        95212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G)))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-937 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       183
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95212.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H or ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-937, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95213
in-theory        95213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H))))
theorem-size     49
proof            (modus-ponens tm-1003 tm-938 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95213.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((E or F) -> G) -> H) -> (((F -> G) or ((E or F) -> G)) -> H)))), M:tm-1003, m:tm-938, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (or Am Bm) Cm) Dm) (-> (or (-> Bm Cm) (-> (or Am Bm) Cm)) Dm)))))
================================================================
tm-name          tm-95214
in-theory        95214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G)))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-939 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       197
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95214.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((F -> G) -> (not ((E or F) -> G))) -> (not (F -> G))))), M:tm-1003, m:tm-939, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Bm Cm) (not (-> (or Am Bm) Cm))) (not (-> Bm Cm))))))
================================================================
tm-name          tm-95215
in-theory        95215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-940 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95215.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> H)))), M:tm-1003, m:tm-940, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95216
in-theory        95216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-941 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95216.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> (F -> G)))), M:tm-1003, m:tm-941, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (-> Bm Cm)))))
================================================================
tm-name          tm-95217
in-theory        95217
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-942 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95217.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-1003, m:tm-942, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95218
in-theory        95218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-943 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95218.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> H))), M:tm-1003, m:tm-943, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95219
in-theory        95219
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-944 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95219.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H and I) -> I))), M:tm-1003, m:tm-944, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95220
in-theory        95220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-945 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-95220.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-945, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95221
in-theory        95221
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-1003 tm-946 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-20.           (A -> (((B -> (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-95221.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-946, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95222
in-theory        95222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-947 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-95222.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> H) and ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-947, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Dm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95223
in-theory        95223
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-948 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-95223.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and I) -> I) and ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-948, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (and Dm Em) Em) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95224
in-theory        95224
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     47
proof            (modus-ponens tm-1003 tm-949 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-95224.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I -> (H and I))) and ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-949, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95225
in-theory        95225
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G)))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-950 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-95225.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((F -> G) -> ((F -> G) and ((E or F) -> G))))), M:tm-1003, m:tm-950, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Bm Cm) (and (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95226
in-theory        95226
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-951 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-95226.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I -> (H and I))))), M:tm-1003, m:tm-951, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95227
in-theory        95227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-952 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (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-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-95227.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (H or I)) and ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-952, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Dm Em)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95228
in-theory        95228
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-953 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-95228.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (H or I)))), M:tm-1003, m:tm-953, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95229
in-theory        95229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-954 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       207
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-95229.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((H -> (I or H)) and ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-954, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> Dm (or Em Dm)) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-95230
in-theory        95230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-955 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95230.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (H -> (I or H)))), M:tm-1003, m:tm-955, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95231
in-theory        95231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-956 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95231.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((G or (F -> G)) -> ((E or F) -> G)))), M:tm-1003, m:tm-956, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or Cm (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-95232
in-theory        95232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H)))))
theorem-size     63
proof            (modus-ponens tm-1003 tm-957 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       273
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95232.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or (((F -> G) -> (F -> H)) -> ((E or (F -> G)) -> (F -> H)))) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> ((E or (F -> G)) -> (F -> H))))), M:tm-1003, m:tm-957, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> (or Am (-> Bm Cm)) (-> Bm Dm)))) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or Am (-> Bm Cm)) (-> Bm Dm))))))
================================================================
tm-name          tm-95233
in-theory        95233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-958 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95233.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> ((((F -> G) and H) or (F -> G)) -> ((E or F) -> G)))), M:tm-1003, m:tm-958, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and (-> Bm Cm) Dm) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-95234
in-theory        95234
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-959 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95234.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H and (F -> G)) or (F -> G)) -> ((E or F) -> G)))), M:tm-1003, m:tm-959, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (or (and Dm (-> Bm Cm)) (-> Bm Cm)) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-95235
in-theory        95235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F)))))
theorem-size     49
proof            (modus-ponens tm-1003 tm-960 ((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-95235.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> (G and F)) -> ((E or F) -> (G and F)))) -> ((G or (F -> (G and F))) -> ((E or F) -> (G and F))))), M:tm-1003, m:tm-960, u:((A (-> (or (-> Am Bm) (-> (-> Bm (and Cm Bm)) (-> (or Am Bm) (and Cm Bm)))) (-> (or Cm (-> Bm (and Cm Bm))) (-> (or Am Bm) (and Cm Bm))))))
================================================================
tm-name          tm-95236
in-theory        95236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G)))))
theorem-size     69
proof            (modus-ponens tm-1003 tm-961 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       287
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95236.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) or (((F -> G) -> ((H or F) -> G)) -> ((E or (F -> G)) -> ((H or F) -> G)))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> ((E or (F -> G)) -> ((H or F) -> G))))), M:tm-1003, m:tm-961, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm)))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (-> (or Am (-> Bm Cm)) (-> (or Dm Bm) Cm))))))
================================================================
tm-name          tm-95237
in-theory        95237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G))))))
theorem-size     65
proof            (modus-ponens tm-1003 tm-962 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-95237.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (((F -> G) -> ((H or F) -> G)) -> (E and ((F -> G) -> ((H or F) -> G))))) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> (E and ((F -> G) -> ((H or F) -> G)))))), M:tm-1003, m:tm-962, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm))))) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) (and Am (-> (-> Bm Cm) (-> (or Dm Bm) Cm)))))))
================================================================
tm-name          tm-95238
in-theory        95238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))
theorem-size     57
proof            (modus-ponens tm-1003 tm-963 ((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-95238.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and (((F -> G) -> ((H or F) -> G)) -> I)) or (((F -> G) -> ((H or F) -> G)) -> I)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))), M:tm-1003, m:tm-963, u:((A (-> (or (and Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))
================================================================
tm-name          tm-95239
in-theory        95239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     57
proof            (modus-ponens tm-1003 tm-964 ((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> 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 tm-3)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
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-95239.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((((E -> F) -> ((G or E) -> F)) -> H) and I) or (((E -> F) -> ((G or E) -> F)) -> H)) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-1003, m:tm-964, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Em) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-95240
in-theory        95240
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H))))
theorem-size     63
proof            (modus-ponens tm-1003 tm-965 ((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       273
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-95240.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> (((G or E) -> F) -> H)) or (((E -> F) -> ((G or E) -> F)) -> ((E -> F) -> H))) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> ((E -> F) -> H)))), M:tm-1003, m:tm-965, u:((A (-> (or (-> (-> Am Bm) (-> (-> (or Cm Am) Bm) Dm)) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> (-> Am Bm) Dm))) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-95241
in-theory        95241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E)))
theorem-size     45
proof            (modus-ponens tm-1003 tm-966 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-95241.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (((F -> G) -> ((H or F) -> G)) -> E)) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> E))), M:tm-1003, m:tm-966, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Am)) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Am))))
================================================================
tm-name          tm-95242
in-theory        95242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-1003 tm-967 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or 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-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-95242.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-1003, m:tm-967, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-95243
in-theory        95243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-1003 tm-968 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-95243.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-1003, m:tm-968, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-95244
in-theory        95244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     55
proof            (modus-ponens tm-1003 tm-969 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> 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 tm-2)
proof-size       235
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (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-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-95244.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> ((((E -> F) -> ((G or E) -> F)) -> H) and (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-1003, m:tm-969, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (and (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
================================================================
tm-name          tm-95245
in-theory        95245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-1003 tm-970 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> 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-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-95245.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-1003, m:tm-970, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-95246
in-theory        95246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-1003 tm-971 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-95246.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-1003, m:tm-971, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-95247
in-theory        95247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-1003 tm-972 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am 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-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-95247.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-1003, m:tm-972, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-95248
in-theory        95248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-1003 tm-973 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       247
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> 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-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-95248.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-1003, m:tm-973, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-95249
in-theory        95249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-1003 tm-974 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> 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-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-95249.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-1003, m:tm-974, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> (or Em Cm) Dm)) Fm) (-> (or (-> Em Cm) (-> (-> Cm Dm) (-> (or Em Cm) Dm))) Fm)))))
================================================================
tm-name          tm-95250
in-theory        95250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H)))
theorem-size     39
proof            (modus-ponens tm-1003 tm-975 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-95250.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((E -> F) -> ((G or E) -> F)) -> H))), M:tm-1003, m:tm-975, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))
================================================================
tm-name          tm-95251
in-theory        95251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H))))
theorem-size     57
proof            (modus-ponens tm-1003 tm-976 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       221
proof-steps      11
----------------------------------------------------------------
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), 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-95251.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (not (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) -> (not (((E -> F) -> ((G or E) -> F)) -> H)))), M:tm-1003, m:tm-976, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (not (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))) (not (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)))))
================================================================
tm-name          tm-95252
in-theory        95252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I)))
theorem-size     63
proof            (modus-ponens tm-1003 tm-977 ((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       235
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95252.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H) -> I) -> (((((F -> G) -> ((E or F) -> G)) -> H) or (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> H)) -> I))), M:tm-1003, m:tm-977, u:((A (-> (-> (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em) (-> (or (-> (-> (-> Bm Cm) (-> (or Am Bm) Cm)) Dm) (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)) Em))))
================================================================
tm-name          tm-95253
in-theory        95253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-978 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       191
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), 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-95253.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-1003, m:tm-978, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-95254
in-theory        95254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) or I))
theorem-size     45
proof            (modus-ponens tm-1003 tm-979 ((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95254.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)) or I)), M:tm-1003, m:tm-979, u:((A (or (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)) Em)))
================================================================
tm-name          tm-95255
in-theory        95255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E)))
theorem-size     47
proof            (modus-ponens tm-1003 tm-980 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-95255.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)) and E))), M:tm-1003, m:tm-980, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)) Am))))
================================================================
tm-name          tm-95256
in-theory        95256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> ((G or E) -> F)) -> H) -> ((G -> E) or ((E -> F) -> ((G or E) -> F)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H)))
theorem-size     55
proof            (modus-ponens tm-1003 tm-981 ((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       219
proof-steps      11
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> 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-95256.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((((E -> F) -> ((G or E) -> F)) -> H) -> ((G -> E) or ((E -> F) -> ((G or E) -> F)))) -> ((((E -> F) -> ((G or E) -> F)) -> H) -> H))), M:tm-1003, m:tm-981, u:((A (-> (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) Dm))))
================================================================
tm-name          tm-95257
in-theory        95257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-982 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       191
proof-steps      11
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-95257.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-1003, m:tm-982, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> (or Dm Bm) Cm)) Em) (-> (or (-> Dm Bm) (-> (-> Bm Cm) (-> (or Dm Bm) Cm))) Em)))))
================================================================
tm-name          tm-95258
in-theory        95258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-983 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-95258.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-1003, m:tm-983, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-95259
in-theory        95259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-984 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or 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-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-95259.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-1003, m:tm-984, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-95260
in-theory        95260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-985 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and 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-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-95260.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-1003, m:tm-985, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-95261
in-theory        95261
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-986 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) 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-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-95261.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-1003, m:tm-986, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-95262
in-theory        95262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-987 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-95262.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-1003, m:tm-987, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-95263
in-theory        95263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-988 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-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-95263.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-1003, m:tm-988, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-95264
in-theory        95264
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-989 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-95264.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-1003, m:tm-989, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
================================================================
tm-name          tm-95265
in-theory        95265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-990 ((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-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-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-95265.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-1003, m:tm-990, u:((A (or Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-95266
in-theory        95266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-1003 tm-991 ((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-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-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-95266.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))) or I)), M:tm-1003, m:tm-991, u:((A (or (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) Em)))
================================================================
tm-name          tm-95267
in-theory        95267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-992 ((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-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-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-95267.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))) and E))), M:tm-1003, m:tm-992, u:((A (-> Am (and (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))) Am))))
================================================================
tm-name          tm-95268
in-theory        95268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     33
proof            (modus-ponens tm-1003 tm-993 ((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-1.            (A -> (B -> A)), axiom
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-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-95268.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-1003, m:tm-993, u:((A (-> Am (or Bm (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
================================================================
tm-name          tm-95269
in-theory        95269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-994 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
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-95269.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-1003, m:tm-994, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-95270
in-theory        95270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-995 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
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-95270.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-1003, m:tm-995, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-95271
in-theory        95271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-1003 tm-996 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
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-95271.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-1003, m:tm-996, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-95272
in-theory        95272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-997 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-95272.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-1003, m:tm-997, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-95273
in-theory        95273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-998 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-95273.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-1003, m:tm-998, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-95274
in-theory        95274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-1003 tm-999 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am 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-95274.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-1003, m:tm-999, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-95275
in-theory        95275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1000 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-95275.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-1003, m:tm-1000, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) Fm))))
================================================================
tm-name          tm-95276
in-theory        95276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-1001 ((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
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-95276.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-1003, m:tm-1001, u:((A (or Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95277
in-theory        95277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-1003 tm-1002 ((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
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-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-95277.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) or I)), M:tm-1003, m:tm-1002, u:((A (or (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm) Em)))
================================================================
tm-name          tm-95278
in-theory        95278
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-95278.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E))), M:tm-1003, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95279
in-theory        95279
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-992 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
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-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-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-95279.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E))), M:tm-992, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95280
in-theory        95280
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) -> ((G -> H) -> ((F or G) -> H))) or I) and E)))
theorem-size     47
proof            (modus-ponens tm-980 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-95280.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E))), M:tm-980, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95281
in-theory        95281
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     59
proof            (modus-ponens tm-977 tm-1003 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       231
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-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-5.            (A -> (B -> (A and B))), axiom
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-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-95281.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-977, m:tm-1003, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D))))
================================================================
tm-name          tm-95282
in-theory        95282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> ((C or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-975 tm-1003 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-5.            (A -> (B -> (A and B))), axiom
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-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-95282.        (((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> ((C or A) -> B)))), M:tm-975, m:tm-1003, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-95283
in-theory        95283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> ((C or A) -> B)))))
theorem-size     75
proof            (modus-ponens tm-969 tm-1003 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-95283.        ((((A -> B) -> ((C or A) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> ((C or A) -> B)))) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> ((C or A) -> B))))), M:tm-969, m:tm-1003, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-95284
in-theory        95284
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-930 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-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-95284.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-930, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95285
in-theory        95285
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-927 tm-1003 ((Am (-> (or A (or B A)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or A (or B A)) C)))))
axioms-used      (tm-8 tm-7 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-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-5.            (A -> (B -> (A and B))), axiom
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-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-95285.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B or (A or B)) -> C))), M:tm-927, m:tm-1003, u:((Am (-> (or A (or B A)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or A (or B A)) C))))
================================================================
tm-name          tm-95286
in-theory        95286
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B))) and ((B or (A or B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-920 tm-1003 ((Am (or A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-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-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-95286.        (((A or B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B))) and ((B or (A or B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B)))), M:tm-920, m:tm-1003, u:((Am (or A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (or A B))))
================================================================
tm-name          tm-95287
in-theory        95287
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-893 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-95287.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-893, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95288
in-theory        95288
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A or (A or B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-890 tm-1003 ((Am (-> (or A (or A B)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or A (or A B)) C)))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-5.            (A -> (B -> (A and 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-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-95288.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A or (A or B)) -> C))), M:tm-890, m:tm-1003, u:((Am (-> (or A (or A B)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or A (or A B)) C))))
================================================================
tm-name          tm-95289
in-theory        95289
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-888 tm-1003 ((Am (or A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (or A B)))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-5.            (A -> (B -> (A and 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-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-95289.        ((A or B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B))), M:tm-888, m:tm-1003, u:((Am (or A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (or A B))))
================================================================
tm-name          tm-95290
in-theory        95290
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B))) and ((A or (A or B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-1003 ((Am (or A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (or A B)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-95290.        (((A or B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B))) and ((A or (A or B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A or B)))), M:tm-882, m:tm-1003, u:((Am (or A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (or A B))))
================================================================
tm-name          tm-95291
in-theory        95291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     37
proof            (modus-ponens tm-855 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-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-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-95291.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-855, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95292
in-theory        95292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B or (A -> (B and A))) -> C)))
theorem-size     43
proof            (modus-ponens tm-852 tm-1003 ((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-48.           (((A -> (B and 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-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-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-95292.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B or (A -> (B and A))) -> C))), M:tm-852, m:tm-1003, u:((Am (-> (or A (-> B (and A B))) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or A (-> B (and A B))) C))))
================================================================
tm-name          tm-95293
in-theory        95293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> (B and A))))
theorem-size     27
proof            (modus-ponens tm-850 tm-1003 ((Am (-> A (and B A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (and B A))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 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-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-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-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-95293.        ((A -> (B and A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> (B and A)))), M:tm-850, m:tm-1003, u:((Am (-> A (and B A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (and B A)))))
================================================================
tm-name          tm-95294
in-theory        95294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> (B and A)))))
theorem-size     57
proof            (modus-ponens tm-844 tm-1003 ((Am (-> A (and B A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (and B A))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-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-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-95294.        (((A -> (B and A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> (B and A)))) and ((B or (A -> (B and A))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> (B and A))))), M:tm-844, m:tm-1003, u:((Am (-> A (and B A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (and B A)))))
================================================================
tm-name          tm-95295
in-theory        95295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     31
proof            (modus-ponens tm-808 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-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-95295.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-808, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95296
in-theory        95296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((C and A) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-805 tm-1003 ((Am (-> (or (and A B) B) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or (and A B) B) C)))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
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-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-5.            (A -> (B -> (A and B))), axiom
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-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-95296.        (((A -> B) or (((C and A) or A) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((C and A) or A) -> B))), M:tm-805, m:tm-1003, u:((Am (-> (or (and A B) B) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or (and A B) B) C))))
================================================================
tm-name          tm-95297
in-theory        95297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((F and A) or A) -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))
theorem-size     43
proof            (modus-ponens tm-798 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-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-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-95297.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((F and A) or A) -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))), M:tm-798, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95298
in-theory        95298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     31
proof            (modus-ponens tm-757 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-95298.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-757, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95299
in-theory        95299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((A and C) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-754 tm-1003 ((Am (-> (or (and A B) A) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
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-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-95299.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((A and C) or A) -> B))), M:tm-754, m:tm-1003, u:((Am (-> (or (and A B) A) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-95300
in-theory        95300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((A and F) or A) -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))
theorem-size     43
proof            (modus-ponens tm-747 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95300.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((A and F) or A) -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))), M:tm-747, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95301
in-theory        95301
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))) or I) and E)))
theorem-size     45
proof            (modus-ponens tm-708 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95301.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E))), M:tm-708, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95302
in-theory        95302
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))) or H) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-705 tm-1003 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95302.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-1003, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-95303
in-theory        95303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-703 tm-1003 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95303.        (((A -> B) -> (A -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-1003, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-95304
in-theory        95304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-697 tm-1003 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95304.        ((((A -> B) -> (A -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-1003, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-95305
in-theory        95305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-665 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-95305.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-665, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95306
in-theory        95306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B or (A -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-662 tm-1003 ((Am (-> (or A (-> B A)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((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-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-95306.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-1003, u:((Am (-> (or A (-> B A)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-95307
in-theory        95307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> B)))
theorem-size     23
proof            (modus-ponens tm-660 tm-1003 ((Am (-> A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95307.        ((A -> B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> B))), M:tm-660, m:tm-1003, u:((Am (-> A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A B))))
================================================================
tm-name          tm-95308
in-theory        95308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> B))) and ((B or (A -> B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> B))))
theorem-size     49
proof            (modus-ponens tm-654 tm-1003 ((Am (-> A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95308.        (((A -> B) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> B))) and ((B or (A -> B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> B)))), M:tm-654, m:tm-1003, u:((Am (-> A B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A B))))
================================================================
tm-name          tm-95309
in-theory        95309
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and A)))
theorem-size     21
proof            (modus-ponens tm-623 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-95309.        (A -> (B or ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and A))), M:tm-623, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95310
in-theory        95310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-622 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
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-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-95310.        ((A -> (B -> (C or B))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-622, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95311
in-theory        95311
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (B -> (C or B))))
theorem-size     29
proof            (modus-ponens tm-619 tm-1003 ((Am (-> A (or B A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
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-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-95311.        ((A or (B -> (C or B))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (B -> (C or B)))), M:tm-619, m:tm-1003, u:((Am (-> A (or B A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (or B A)))))
================================================================
tm-name          tm-95312
in-theory        95312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-95312.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (G or F))), M:tm-609, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95313
in-theory        95313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-605 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-95313.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-605, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95314
in-theory        95314
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> (C or B)) and A)))
theorem-size     33
proof            (modus-ponens tm-602 tm-1003 ((Am (and (-> A (or B A)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
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-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-95314.        ((A or ((B -> (C or B)) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> (C or B)) and A))), M:tm-602, m:tm-1003, u:((Am (and (-> A (or B A)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-95315
in-theory        95315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (G or F)) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-595 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-95315.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (G or F)) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-595, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95316
in-theory        95316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-550 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-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-95316.        (((A -> (B or A)) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-550, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95317
in-theory        95317
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-540 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-95317.        ((A or (B -> (C or B))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-540, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95318
in-theory        95318
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-530 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-95318.        ((A or (B -> (B or C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-530, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95319
in-theory        95319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-520 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-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-95319.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-520, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95320
in-theory        95320
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-510 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
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-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-95320.        ((A or ((B and C) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-510, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95321
in-theory        95321
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-500 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
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-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-95321.        ((A or ((B and C) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-500, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95322
in-theory        95322
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-490 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
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-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-95322.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E))), M:tm-490, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95323
in-theory        95323
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-480 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
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-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-95323.        ((A or (B -> (C -> B))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-480, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95324
in-theory        95324
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A) or F))
theorem-size     21
proof            (modus-ponens tm-470 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 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-5.            (A -> (B -> (A and 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-95324.        (A -> (((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A) or F)), M:tm-470, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95325
in-theory        95325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-469 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-95325.        ((A -> (B -> (B or C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-469, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95326
in-theory        95326
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (B -> (B or C))))
theorem-size     29
proof            (modus-ponens tm-466 tm-1003 ((Am (-> A (or A B))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
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-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-95326.        ((A or (B -> (B or C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (B -> (B or C)))), M:tm-466, m:tm-1003, u:((Am (-> A (or A B))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (or A B)))))
================================================================
tm-name          tm-95327
in-theory        95327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
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-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-95327.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (F or G))), M:tm-456, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95328
in-theory        95328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-453 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-95328.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-453, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95329
in-theory        95329
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> (B or C)) and A)))
theorem-size     33
proof            (modus-ponens tm-450 tm-1003 ((Am (and (-> A (or A B)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-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-95329.        ((A or ((B -> (B or C)) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> (B or C)) and A))), M:tm-450, m:tm-1003, u:((Am (and (-> A (or A B)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-95330
in-theory        95330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (F or G)) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-443 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
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-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-95330.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (F or G)) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-443, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95331
in-theory        95331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-409 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-95331.        (((A -> (A or B)) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-409, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95332
in-theory        95332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-400 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-95332.        (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-400, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95333
in-theory        95333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-391 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-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-95333.        ((((A and B) -> B) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-391, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95334
in-theory        95334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-382 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-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-95334.        ((((A and B) -> A) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-382, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95335
in-theory        95335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-373 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-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-95335.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E))), M:tm-373, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95336
in-theory        95336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-364 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-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-95336.        (((A -> (B -> A)) or C) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-364, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95337
in-theory        95337
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and A) and B)))
theorem-size     23
proof            (modus-ponens tm-355 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6 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-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-95337.        (A -> (B -> (((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and A) and B))), M:tm-355, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95338
in-theory        95338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-354 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-95338.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-354, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95339
in-theory        95339
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (B -> (C -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-351 tm-1003 ((Am (-> A (-> B (and A B)))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
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-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-95339.        ((A or (B -> (C -> (B and C)))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (B -> (C -> (B and C))))), M:tm-351, m:tm-1003, u:((Am (-> A (-> B (and A B)))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-95340
in-theory        95340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-95340.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95341
in-theory        95341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C)))
theorem-size     29
proof            (modus-ponens tm-338 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
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-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-95341.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C))), M:tm-338, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95342
in-theory        95342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-335 tm-1003 ((Am (-> A (and A B))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95342.        (((A -> B) or (A -> (A and B))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> (A and B)))), M:tm-335, m:tm-1003, u:((Am (-> A (and A B))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (and A B)))))
================================================================
tm-name          tm-95343
in-theory        95343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (A -> (A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     41
proof            (modus-ponens tm-328 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 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-328.          ((A -> 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-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-95343.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (A -> (A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-328, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95344
in-theory        95344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (G -> (F and G))) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     47
proof            (modus-ponens tm-327 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-95344.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (G -> (F and G))) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-327, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95345
in-theory        95345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((F and G) -> G) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-326 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-95345.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((F and G) -> G) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-326, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95346
in-theory        95346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((F and G) -> F) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-325 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-95346.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((F and G) -> F) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-325, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95347
in-theory        95347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     53
proof            (modus-ponens tm-324 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-95347.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-324, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95348
in-theory        95348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (G -> F)) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-323 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-95348.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (G -> F)) and (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-323, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95349
in-theory        95349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-95349.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F and G) -> G)), M:tm-322, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95350
in-theory        95350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-95350.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F and G) -> F)), M:tm-320, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95351
in-theory        95351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-95351.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95352
in-theory        95352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-95352.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (A -> A)), M:tm-316, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95353
in-theory        95353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-95353.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (G -> F))), M:tm-315, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95354
in-theory        95354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((A -> (not ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-95354.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((A -> (not ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))) -> (not A))), M:tm-313, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95355
in-theory        95355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A) -> F) -> ((A or ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) -> F)))
theorem-size     61
proof            (modus-ponens tm-312 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95355.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A) -> F) -> ((A or ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) -> F))), M:tm-312, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95356
in-theory        95356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F or (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     41
proof            (modus-ponens tm-311 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-95356.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F or (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-311, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95357
in-theory        95357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
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-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-95357.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) or F)), M:tm-310, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95358
in-theory        95358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-6 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-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-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-95358.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and F))), M:tm-309, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95359
in-theory        95359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))))
theorem-size     41
proof            (modus-ponens tm-305 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
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-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-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-95359.        ((A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)) and (F -> (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)))), M:tm-305, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95360
in-theory        95360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     31
proof            (modus-ponens tm-303 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
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-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-95360.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-303, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95361
in-theory        95361
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> (C -> (B and C))) and A)))
theorem-size     37
proof            (modus-ponens tm-300 tm-1003 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
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-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-95361.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-1003, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-95362
in-theory        95362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-270 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
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-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-95362.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-270, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95363
in-theory        95363
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((B and C) -> C) and A)))
theorem-size     33
proof            (modus-ponens tm-267 tm-1003 ((Am (and (-> (and A B) B) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
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-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-95363.        ((A or (((B and C) -> C) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((B and C) -> C) and A))), M:tm-267, m:tm-1003, u:((Am (and (-> (and A B) B) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-95364
in-theory        95364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-239 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
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-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-95364.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-239, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95365
in-theory        95365
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((B and C) -> B) and A)))
theorem-size     33
proof            (modus-ponens tm-236 tm-1003 ((Am (and (-> (and A B) A) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
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-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-95365.        ((A or (((B and C) -> B) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((B and C) -> B) and A))), M:tm-236, m:tm-1003, u:((Am (and (-> (and A B) A) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-95366
in-theory        95366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E)))
theorem-size     37
proof            (modus-ponens tm-210 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-95366.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E))), M:tm-210, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95367
in-theory        95367
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     49
proof            (modus-ponens tm-207 tm-1003 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95367.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-1003, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-95368
in-theory        95368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-183 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-95368.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-183, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95369
in-theory        95369
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> (C -> B)) and A)))
theorem-size     33
proof            (modus-ponens tm-180 tm-1003 ((Am (and (-> A (-> B A)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-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-95369.        ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-1003, u:((Am (and (-> A (-> B A)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-95370
in-theory        95370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-157 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
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-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-95370.        ((A -> ((B and C) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-157, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95371
in-theory        95371
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B and C) -> C)))
theorem-size     29
proof            (modus-ponens tm-154 tm-1003 ((Am (-> (and A B) B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
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-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-95371.        ((A or ((B and C) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B and C) -> C))), M:tm-154, m:tm-1003, u:((Am (-> (and A B) B)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (and A B) B))))
================================================================
tm-name          tm-95372
in-theory        95372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     35
proof            (modus-ponens tm-147 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-95372.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-147, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95373
in-theory        95373
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A and (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-144 tm-1003 ((Am (-> (and A (-> B C)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95373.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-1003, u:((Am (-> (and A (-> B C)) C)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-95374
in-theory        95374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-134 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
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-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-95374.        ((A -> ((B and C) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-134, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95375
in-theory        95375
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-131 tm-1003 ((Am (-> (and A B) A)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
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-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-95375.        ((A or ((B and C) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((B and C) -> B))), M:tm-131, m:tm-1003, u:((Am (-> (and A B) A)) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (and A B) A))))
================================================================
tm-name          tm-95376
in-theory        95376
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     35
proof            (modus-ponens tm-125 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-95376.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-125, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95377
in-theory        95377
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((A -> B) and C) -> B)))
theorem-size     39
proof            (modus-ponens tm-122 tm-1003 ((Am (-> (and (-> A B) C) B)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95377.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (((A -> B) and C) -> B))), M:tm-122, m:tm-1003, u:((Am (-> (and (-> A B) C) B)) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-95378
in-theory        95378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-113 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 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-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-95378.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I) and E))), M:tm-113, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95379
in-theory        95379
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-110 tm-1003 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95379.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-1003, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-95380
in-theory        95380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     39
proof            (modus-ponens tm-105 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-6 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-95380.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-105, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95381
in-theory        95381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-102 tm-1003 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95381.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-1003, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-95382
in-theory        95382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C)))
theorem-size     27
proof            (modus-ponens tm-95 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 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-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-95382.        (((A -> B) -> (A -> A)) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C))), M:tm-95, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95383
in-theory        95383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> A)))
theorem-size     27
proof            (modus-ponens tm-92 tm-1003 ((Am (-> A A)) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95383.        (((A -> B) or (A -> A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and (A -> A))), M:tm-92, m:tm-1003, u:((Am (-> A A)) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A A))))
================================================================
tm-name          tm-95384
in-theory        95384
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and A)))
theorem-size     21
proof            (modus-ponens tm-84 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
axioms-used      (tm-2 tm-1 tm-5 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-95384.        (A -> (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and A))), M:tm-84, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95385
in-theory        95385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-83 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-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-95385.        ((A -> (B -> (C -> B))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-83, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95386
in-theory        95386
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (B -> (C -> B))))
theorem-size     29
proof            (modus-ponens tm-80 tm-1003 ((Am (-> A (-> B A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
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-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-95386.        ((A or (B -> (C -> B))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and (B -> (C -> B)))), M:tm-80, m:tm-1003, u:((Am (-> A (-> B A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> A (-> B A)))))
================================================================
tm-name          tm-95387
in-theory        95387
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B)))
theorem-size     25
proof            (modus-ponens tm-76 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-10 tm-6 tm-8)
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-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-95387.        (((not (not A)) -> A) and (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and B))), M:tm-76, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95388
in-theory        95388
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))
theorem-size     23
proof            (modus-ponens tm-73 tm-1003 ((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
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-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-95388.        (((not (not A)) or A) -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)), M:tm-73, m:tm-1003, u:((A Am) (B (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))
================================================================
tm-name          tm-95389
in-theory        95389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C)))
theorem-size     31
proof            (modus-ponens tm-69 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-9 tm-6 tm-8)
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-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-95389.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G) and C))), M:tm-69, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95390
in-theory        95390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and ((A -> (not B)) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-66 tm-1003 ((Am (-> (-> A (not B)) (not A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6)
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-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-95390.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-1003, u:((Am (-> (-> A (not B)) (not A))) (C (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-95391
in-theory        95391
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-54 tm-1003 ((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
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-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-95391.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H) and D))), M:tm-54, m:tm-1003, u:((A (-> Am (and (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) Am))))
================================================================
tm-name          tm-95392
in-theory        95392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-1003 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-6 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-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-1.            (A -> (B -> A)), axiom
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-95392.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-1003, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95393
in-theory        95393
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-992 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-1.            (A -> (B -> A)), axiom
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-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-95393.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-992, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95394
in-theory        95394
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) -> E)
theorem-size     31
proof            (modus-ponens tm-981 tm-1004 ((Am (-> (-> (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) B) (-> (or (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)) D)) (C (-> Bm Cm)) (A (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (Em (-> (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) B) (-> (or (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
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-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-95394.        ((((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E) -> E), M:tm-981, m:tm-1004, u:((Am (-> (-> (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) B) (-> (or (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)) D)) (C (-> Bm Cm)) (A (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (Em (-> (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) B) (-> (or (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B))))
================================================================
tm-name          tm-95395
in-theory        95395
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) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     45
proof            (modus-ponens tm-980 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
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-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-95395.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-980, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95396
in-theory        95396
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     43
proof            (modus-ponens tm-977 tm-1004 ((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       211
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-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-1.            (A -> (B -> A)), axiom
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-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-95396.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-977, m:tm-1004, u:((Am (-> (or (-> A B) (-> (-> B C) (-> (or A B) C))) D)) (E (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95397
in-theory        95397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-975 tm-1004 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-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-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-95397.        (((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-975, m:tm-1004, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95398
in-theory        95398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     55
proof            (modus-ponens tm-969 tm-1004 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-1.            (A -> (B -> A)), axiom
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-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-95398.        ((((A -> B) -> ((C or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-969, m:tm-1004, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95399
in-theory        95399
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> E)
theorem-size     19
proof            (modus-ponens tm-931 tm-1004 ((Am (-> (or A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) C)) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (Em (or A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
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-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-95399.        (((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> E), M:tm-931, m:tm-1004, u:((Am (-> (or A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) C)) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (Em (or A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-95400
in-theory        95400
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-930 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
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-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-95400.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-930, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95401
in-theory        95401
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-927 tm-1004 ((Am (-> (or A (or B A)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
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-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-1.            (A -> (B -> A)), axiom
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-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-95401.        ((((A or B) -> C) or ((B or (A or B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-927, m:tm-1004, u:((Am (-> (or A (or B A)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95402
in-theory        95402
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((B or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     41
proof            (modus-ponens tm-920 tm-1004 ((Am (or A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-1.            (A -> (B -> A)), axiom
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-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-95402.        (((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((B or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-920, m:tm-1004, u:((Am (or A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95403
in-theory        95403
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) -> E)
theorem-size     19
proof            (modus-ponens tm-894 tm-1004 ((Am (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (Em (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B))))
axioms-used      (tm-2 tm-8 tm-6 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-95403.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) -> E), M:tm-894, m:tm-1004, u:((Am (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (Em (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)))
================================================================
tm-name          tm-95404
in-theory        95404
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-893 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-95404.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-893, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95405
in-theory        95405
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-890 tm-1004 ((Am (-> (or A (or A B)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-6 tm-1)
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-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-1.            (A -> (B -> A)), 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-95405.        ((((A or B) -> C) or ((A or (A or B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-890, m:tm-1004, u:((Am (-> (or A (or A B)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95406
in-theory        95406
times-derived    1
----------------------------------------------------------------
theorem          ((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     19
proof            (modus-ponens tm-888 tm-1004 ((Am (or A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-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-95406.        ((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-888, m:tm-1004, u:((Am (or A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95407
in-theory        95407
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     41
proof            (modus-ponens tm-882 tm-1004 ((Am (or A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-1.            (A -> (B -> A)), 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-95407.        (((A or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-882, m:tm-1004, u:((Am (or A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95408
in-theory        95408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) -> E) -> E)
theorem-size     21
proof            (modus-ponens tm-856 tm-1004 ((Am (-> (-> A (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) A)) C)) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (Em (-> A (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) A)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1 tm-6)
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-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-1.            (A -> (B -> A)), axiom
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-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-95408.        (((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) -> E) -> E), M:tm-856, m:tm-1004, u:((Am (-> (-> A (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) A)) C)) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (Em (-> A (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) A))))
================================================================
tm-name          tm-95409
in-theory        95409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     35
proof            (modus-ponens tm-855 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 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-48.           (((A -> (B and 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-1.            (A -> (B -> A)), axiom
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-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-95409.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-855, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95410
in-theory        95410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     33
proof            (modus-ponens tm-852 tm-1004 ((Am (-> (or A (-> B (and A B))) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-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-1.            (A -> (B -> A)), axiom
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-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-95410.        ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-852, m:tm-1004, u:((Am (-> (or A (-> B (and A B))) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95411
in-theory        95411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-850 tm-1004 ((Am (-> A (and B A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
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-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-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-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-95411.        ((A -> (B and A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-850, m:tm-1004, u:((Am (-> A (and B A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95412
in-theory        95412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((B or (A -> (B and A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     45
proof            (modus-ponens tm-844 tm-1004 ((Am (-> A (and B A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 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-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-1.            (A -> (B -> A)), axiom
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-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-95412.        (((A -> (B and A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((B or (A -> (B and A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-844, m:tm-1004, u:((Am (-> A (and B A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95413
in-theory        95413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-808 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
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-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-95413.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-808, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95414
in-theory        95414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-805 tm-1004 ((Am (-> (or (and A B) B) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
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-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-1.            (A -> (B -> A)), axiom
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-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-95414.        (((A -> B) or (((C and A) or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-805, m:tm-1004, u:((Am (-> (or (and A B) B) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95415
in-theory        95415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and A) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))
theorem-size     39
proof            (modus-ponens tm-798 tm-1004 ((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-1.            (A -> (B -> A)), axiom
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-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-95415.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and A) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))), M:tm-798, m:tm-1004, u:((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95416
in-theory        95416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-757 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-95416.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-757, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95417
in-theory        95417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-754 tm-1004 ((Am (-> (or (and A B) A) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
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-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-95417.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-754, m:tm-1004, u:((Am (-> (or (and A B) A) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95418
in-theory        95418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((A and F) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))
theorem-size     39
proof            (modus-ponens tm-747 tm-1004 ((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95418.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((A and F) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))), M:tm-747, m:tm-1004, u:((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95419
in-theory        95419
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) -> D) -> D)
theorem-size     21
proof            (modus-ponens tm-709 tm-1004 ((Am (-> (-> (-> (-> Bm Cm) (-> Cm Dm)) (-> (-> Bm Cm) (-> (or Bm Cm) Dm))) D)) (A (-> Bm Cm)) (B (-> Cm Dm)) (C (-> (or Bm Cm) Dm)) (Em (-> (-> (-> Bm Cm) (-> Cm Dm)) (-> (-> Bm Cm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       175
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-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-95419.        (((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) -> D) -> D), M:tm-709, m:tm-1004, u:((Am (-> (-> (-> (-> Bm Cm) (-> Cm Dm)) (-> (-> Bm Cm) (-> (or Bm Cm) Dm))) D)) (A (-> Bm Cm)) (B (-> Cm Dm)) (C (-> (or Bm Cm) Dm)) (Em (-> (-> (-> Bm Cm) (-> Cm Dm)) (-> (-> Bm Cm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-95420
in-theory        95420
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))) or I)))
theorem-size     43
proof            (modus-ponens tm-708 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95420.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-708, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95421
in-theory        95421
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))) or H))
theorem-size     41
proof            (modus-ponens tm-705 tm-1004 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95421.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-705, m:tm-1004, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95422
in-theory        95422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-703 tm-1004 ((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95422.        (((A -> B) -> (A -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-703, m:tm-1004, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95423
in-theory        95423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     53
proof            (modus-ponens tm-697 tm-1004 ((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95423.        ((((A -> B) -> (A -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-697, m:tm-1004, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95424
in-theory        95424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> E)
theorem-size     19
proof            (modus-ponens tm-666 tm-1004 ((Am (-> (-> A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) C)) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (Em (-> A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95424.        (((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E) -> E), M:tm-666, m:tm-1004, u:((Am (-> (-> A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) C)) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))) (Em (-> A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-95425
in-theory        95425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-665 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95425.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-665, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95426
in-theory        95426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-662 tm-1004 ((Am (-> (or A (-> B A)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-1 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-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((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-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-95426.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-662, m:tm-1004, u:((Am (-> (or A (-> B A)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95427
in-theory        95427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     19
proof            (modus-ponens tm-660 tm-1004 ((Am (-> A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95427.        ((A -> B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-660, m:tm-1004, u:((Am (-> A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95428
in-theory        95428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((B or (A -> B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     41
proof            (modus-ponens tm-654 tm-1004 ((Am (-> A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95428.        (((A -> B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)) and ((B or (A -> B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-654, m:tm-1004, u:((Am (-> A B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95429
in-theory        95429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-622 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95429.        ((A -> (B -> (C or B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-622, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95430
in-theory        95430
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-619 tm-1004 ((Am (-> A (or B A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
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-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-95430.        ((A or (B -> (C or B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-619, m:tm-1004, u:((Am (-> A (or B A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95431
in-theory        95431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95431.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95432
in-theory        95432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-605 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 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-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-95432.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-605, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95433
in-theory        95433
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-602 tm-1004 ((Am (and (-> A (or B A)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 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-7.            (A -> (B or 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-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-95433.        ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-602, m:tm-1004, u:((Am (and (-> A (or B A)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95434
in-theory        95434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G or F)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-595 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-95434.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G or F)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-595, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95435
in-theory        95435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-550 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95435.        (((A -> (B or A)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-550, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95436
in-theory        95436
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-540 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-95436.        ((A or (B -> (C or B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-540, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95437
in-theory        95437
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-530 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95437.        ((A or (B -> (B or C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-530, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95438
in-theory        95438
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-520 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 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-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-95438.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-520, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95439
in-theory        95439
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-510 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-95439.        ((A or ((B and C) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-510, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95440
in-theory        95440
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-500 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-95440.        ((A or ((B and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-500, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95441
in-theory        95441
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-490 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 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-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-95441.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-490, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95442
in-theory        95442
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-480 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95442.        ((A or (B -> (C -> B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-480, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95443
in-theory        95443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-469 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95443.        ((A -> (B -> (B or C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-469, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95444
in-theory        95444
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-466 tm-1004 ((Am (-> A (or A B))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
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-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-95444.        ((A or (B -> (B or C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-466, m:tm-1004, u:((Am (-> A (or A B))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95445
in-theory        95445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95445.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95446
in-theory        95446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-453 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95446.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-453, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95447
in-theory        95447
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-450 tm-1004 ((Am (and (-> A (or A B)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-6 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-6.            (A -> (A or 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-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-95447.        ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-450, m:tm-1004, u:((Am (and (-> A (or A B)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95448
in-theory        95448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (F or G)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-443 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-95448.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (F or G)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-443, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95449
in-theory        95449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-409 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95449.        (((A -> (A or B)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-409, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95450
in-theory        95450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-400 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95450.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-400, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95451
in-theory        95451
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-391 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95451.        ((((A and B) -> B) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-391, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95452
in-theory        95452
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-382 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95452.        ((((A and B) -> A) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-382, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95453
in-theory        95453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-373 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95453.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-373, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95454
in-theory        95454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-364 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95454.        (((A -> (B -> A)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-364, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95455
in-theory        95455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-354 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95455.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-354, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95456
in-theory        95456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-351 tm-1004 ((Am (-> A (-> B (and A B)))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
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-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-95456.        ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-351, m:tm-1004, u:((Am (-> A (-> B (and A B)))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95457
in-theory        95457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95457.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95458
in-theory        95458
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and E))
theorem-size     35
proof            (modus-ponens tm-339 tm-1004 ((Am (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B)) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 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-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-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-95458.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and E)), M:tm-339, m:tm-1004, u:((Am (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B)) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95459
in-theory        95459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-338 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 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-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-95459.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-338, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95460
in-theory        95460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     25
proof            (modus-ponens tm-335 tm-1004 ((Am (-> A (and A B))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95460.        (((A -> B) or (A -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-335, m:tm-1004, u:((Am (-> A (and A B))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95461
in-theory        95461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (A -> (A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-328 tm-1004 ((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
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-328.          ((A -> 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-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-95461.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (A -> (A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-328, m:tm-1004, u:((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95462
in-theory        95462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> (F and G))) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     43
proof            (modus-ponens tm-327 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-95462.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> (F and G))) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-327, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95463
in-theory        95463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and G) -> G) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-326 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-95463.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and G) -> G) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-326, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95464
in-theory        95464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and G) -> F) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-325 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-95464.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F and G) -> F) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-325, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95465
in-theory        95465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     49
proof            (modus-ponens tm-324 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-95465.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-324, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95466
in-theory        95466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> F)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-323 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-95466.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> F)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-323, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95467
in-theory        95467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95467.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95468
in-theory        95468
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F)) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F)) -> F))
theorem-size     57
proof            (modus-ponens tm-321 tm-1004 ((Am (and A (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) C))) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-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-95468.        (((A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F)) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F)) -> F)), M:tm-321, m:tm-1004, u:((Am (and A (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) C))) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95469
in-theory        95469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95469.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95470
in-theory        95470
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) and F) -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)) and ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) and F) -> E))
theorem-size     57
proof            (modus-ponens tm-319 tm-1004 ((Am (and (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B) C)) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-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-95470.        (((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) and F) -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)) and ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) and F) -> E)), M:tm-319, m:tm-1004, u:((Am (and (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B) C)) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95471
in-theory        95471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95471.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95472
in-theory        95472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-1004 ((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-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-95472.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (A -> A)), M:tm-316, m:tm-1004, u:((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95473
in-theory        95473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95473.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95474
in-theory        95474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((A -> (not (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-1004 ((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-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-95474.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((A -> (not (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))) -> (not A))), M:tm-313, m:tm-1004, u:((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95475
in-theory        95475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F) -> ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) -> F)))
theorem-size     55
proof            (modus-ponens tm-312 tm-1004 ((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95475.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F) -> ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) -> F))), M:tm-312, m:tm-1004, u:((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95476
in-theory        95476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F or (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-311 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 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-7.            (A -> (B or 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-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-95476.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F or (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-311, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95477
in-theory        95477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-95477.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) or F)), M:tm-310, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95478
in-theory        95478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 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-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-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-95478.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and F))), M:tm-309, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95479
in-theory        95479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-305 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-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-95479.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)) and (F -> (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)))), M:tm-305, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95480
in-theory        95480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-303 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-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-95480.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-303, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95481
in-theory        95481
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-300 tm-1004 ((Am (and (-> A (-> B (and A B))) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
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-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-95481.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-300, m:tm-1004, u:((Am (and (-> A (-> B (and A B))) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95482
in-theory        95482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-270 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-1 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-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-95482.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-270, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95483
in-theory        95483
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-267 tm-1004 ((Am (and (-> (and A B) B) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 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-4.            ((A and B) -> 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-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-95483.        ((A or (((B and C) -> C) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-267, m:tm-1004, u:((Am (and (-> (and A B) B) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95484
in-theory        95484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-239 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-1 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-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-95484.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-239, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95485
in-theory        95485
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-236 tm-1004 ((Am (and (-> (and A B) A) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 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-3.            ((A and B) -> 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-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-95485.        ((A or (((B and C) -> B) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-236, m:tm-1004, u:((Am (and (-> (and A B) A) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95486
in-theory        95486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-210 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 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-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-95486.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-210, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95487
in-theory        95487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     33
proof            (modus-ponens tm-207 tm-1004 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95487.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-207, m:tm-1004, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95488
in-theory        95488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-183 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95488.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-183, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95489
in-theory        95489
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-180 tm-1004 ((Am (and (-> A (-> B A)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-1 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-1.            (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-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-95489.        ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-180, m:tm-1004, u:((Am (and (-> A (-> B A)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95490
in-theory        95490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-157 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95490.        ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-157, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95491
in-theory        95491
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-154 tm-1004 ((Am (-> (and A B) B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-4 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-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-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-95491.        ((A or ((B and C) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-154, m:tm-1004, u:((Am (-> (and A B) B)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95492
in-theory        95492
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-147 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 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-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-95492.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-147, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95493
in-theory        95493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-144 tm-1004 ((Am (-> (and A (-> B C)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95493.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-144, m:tm-1004, u:((Am (-> (and A (-> B C)) C)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95494
in-theory        95494
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F)) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))
theorem-size     35
proof            (modus-ponens tm-142 tm-1004 ((Am (and A (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) C))) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-4 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-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-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-95494.        ((A and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) -> F)) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)), M:tm-142, m:tm-1004, u:((Am (and A (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) C))) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95495
in-theory        95495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-134 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95495.        ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-134, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95496
in-theory        95496
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-131 tm-1004 ((Am (-> (and A B) A)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-3 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-3.            ((A 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-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-95496.        ((A or ((B and C) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-131, m:tm-1004, u:((Am (-> (and A B) A)) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95497
in-theory        95497
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-125 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 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-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-95497.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-125, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95498
in-theory        95498
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-122 tm-1004 ((Am (-> (and (-> A B) C) B)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95498.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-122, m:tm-1004, u:((Am (-> (and (-> A B) C) B)) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95499
in-theory        95499
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) and F) -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))
theorem-size     35
proof            (modus-ponens tm-120 tm-1004 ((Am (and (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B) C)) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-3 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-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-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-95499.        ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) and F) -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)), M:tm-120, m:tm-1004, u:((Am (and (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B) C)) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95500
in-theory        95500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-113 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95500.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-113, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95501
in-theory        95501
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-110 tm-1004 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95501.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-110, m:tm-1004, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95502
in-theory        95502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     37
proof            (modus-ponens tm-105 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 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-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-95502.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-105, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95503
in-theory        95503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     35
proof            (modus-ponens tm-102 tm-1004 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95503.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-102, m:tm-1004, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95504
in-theory        95504
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))
theorem-size     33
proof            (modus-ponens tm-96 tm-1004 ((Am (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B)) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-6 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-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-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-95504.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E) -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)), M:tm-96, m:tm-1004, u:((Am (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B)) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95505
in-theory        95505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-95 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95505.        (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-95, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95506
in-theory        95506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     23
proof            (modus-ponens tm-92 tm-1004 ((Am (-> A A)) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) 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-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-95506.        (((A -> B) or (A -> A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-92, m:tm-1004, u:((Am (-> A A)) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95507
in-theory        95507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-83 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm 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-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-95507.        ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-83, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95508
in-theory        95508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-80 tm-1004 ((Am (-> A (-> B A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
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-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-95508.        ((A or (B -> (C -> B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-80, m:tm-1004, u:((Am (-> A (-> B A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95509
in-theory        95509
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E))) -> E)
theorem-size     21
proof            (modus-ponens tm-77 tm-1004 ((Am (not (not (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B)))) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-2 tm-10 tm-1 tm-6 tm-8)
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-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-95509.        ((not (not ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) -> E))) -> E), M:tm-77, m:tm-1004, u:((Am (not (not (-> (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em) B)))) (A (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95510
in-theory        95510
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)))
theorem-size     23
proof            (modus-ponens tm-76 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-1 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-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-95510.        (((not (not A)) -> A) and (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))), M:tm-76, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95511
in-theory        95511
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))
theorem-size     21
proof            (modus-ponens tm-73 tm-1004 ((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
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-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-95511.        (((not (not A)) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)), M:tm-73, m:tm-1004, u:((A Am) (B (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95512
in-theory        95512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))
theorem-size     29
proof            (modus-ponens tm-69 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-1 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-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-95512.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))), M:tm-69, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95513
in-theory        95513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     27
proof            (modus-ponens tm-66 tm-1004 ((Am (-> (-> A (not B)) (not A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
axioms-used      (tm-8 tm-9 tm-1 tm-6)
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-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-95513.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-66, m:tm-1004, u:((Am (-> (-> A (not B)) (not A))) (C (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))
================================================================
tm-name          tm-95514
in-theory        95514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-54 tm-1004 ((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
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-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-95514.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-54, m:tm-1004, u:((A (-> Am (or (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Em))))
================================================================
tm-name          tm-95515
in-theory        95515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-95515.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H)))), M:tm-1003, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95516
in-theory        95516
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-992 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-95516.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H)))), M:tm-992, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95517
in-theory        95517
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H))))
theorem-size     47
proof            (modus-ponens tm-980 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-95517.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H)))), M:tm-980, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95518
in-theory        95518
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95518.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-930, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95519
in-theory        95519
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95519.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-893, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95520
in-theory        95520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-855 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-95520.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-855, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95521
in-theory        95521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-95521.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-808, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95522
in-theory        95522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-95522.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-757, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95523
in-theory        95523
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))) and (H -> (I -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-95523.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H)))), M:tm-708, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95524
in-theory        95524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95524.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-665, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95525
in-theory        95525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95525.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-622, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95526
in-theory        95526
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-609 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95526.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F -> (G or F))), M:tm-609, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95527
in-theory        95527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95527.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-605, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95528
in-theory        95528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-95528.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-595, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95529
in-theory        95529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-95529.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-550, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95530
in-theory        95530
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-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-95530.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-540, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95531
in-theory        95531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-95531.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-530, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95532
in-theory        95532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95532.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-520, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95533
in-theory        95533
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-95533.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-510, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95534
in-theory        95534
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-95534.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-500, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95535
in-theory        95535
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95535.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H)))), M:tm-490, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95536
in-theory        95536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95536.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-480, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95537
in-theory        95537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95537.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-469, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95538
in-theory        95538
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-456 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95538.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F -> (F or G))), M:tm-456, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95539
in-theory        95539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95539.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-453, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95540
in-theory        95540
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-95540.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-443, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95541
in-theory        95541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-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-95541.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-409, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95542
in-theory        95542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95542.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-400, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95543
in-theory        95543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-95543.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-391, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95544
in-theory        95544
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-95544.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-382, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95545
in-theory        95545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95545.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H)))), M:tm-373, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95546
in-theory        95546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95546.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-364, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95547
in-theory        95547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-95547.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-354, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95548
in-theory        95548
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-341 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-95548.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95549
in-theory        95549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-95549.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F)))), M:tm-338, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95550
in-theory        95550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-95550.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-327, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95551
in-theory        95551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-95551.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-326, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95552
in-theory        95552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-95552.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-325, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95553
in-theory        95553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-95553.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-324, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95554
in-theory        95554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95554.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-323, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95555
in-theory        95555
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-322 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95555.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F and G) -> G)), M:tm-322, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95556
in-theory        95556
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-320 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95556.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F and G) -> F)), M:tm-320, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95557
in-theory        95557
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-318 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-95557.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95558
in-theory        95558
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-315 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95558.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F -> (G -> F))), M:tm-315, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95559
in-theory        95559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-95559.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-311, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95560
in-theory        95560
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))) and (D -> (E -> D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-95560.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) or F)), M:tm-310, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95561
in-theory        95561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> 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-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-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-95561.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and F))), M:tm-309, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95562
in-theory        95562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-308 tm-1005 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-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-95562.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (D -> (E -> D))), M:tm-308, m:tm-1005, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-95563
in-theory        95563
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-307 tm-1005 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-95563.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1005, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-95564
in-theory        95564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95564.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))))), M:tm-305, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95565
in-theory        95565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95565.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-303, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95566
in-theory        95566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95566.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-270, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95567
in-theory        95567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95567.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-239, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95568
in-theory        95568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-95568.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H)))), M:tm-210, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95569
in-theory        95569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-95569.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-183, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95570
in-theory        95570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95570.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-157, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95571
in-theory        95571
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-95571.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-147, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95572
in-theory        95572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95572.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-134, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95573
in-theory        95573
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-95573.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-125, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95574
in-theory        95574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95574.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> H)))), M:tm-113, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95575
in-theory        95575
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95575.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-105, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95576
in-theory        95576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95576.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F)))), M:tm-95, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95577
in-theory        95577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95577.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-83, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95578
in-theory        95578
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95578.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E)))), M:tm-76, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95579
in-theory        95579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95579.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F)))), M:tm-69, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95580
in-theory        95580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-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-95580.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-54, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95581
in-theory        95581
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-42 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95581.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F)))), M:tm-42, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95582
in-theory        95582
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-32 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95582.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F)))), M:tm-32, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95583
in-theory        95583
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-23 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95583.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F)))), M:tm-23, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95584
in-theory        95584
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-22 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95584.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F)))), M:tm-22, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95585
in-theory        95585
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-21 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95585.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F)))), M:tm-21, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95586
in-theory        95586
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-20 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95586.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> G)))), M:tm-20, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95587
in-theory        95587
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-19 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95587.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> F)))), M:tm-19, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95588
in-theory        95588
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-1)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95588.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E)))), M:tm-7, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95589
in-theory        95589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-1)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95589.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))) or F), M:tm-6, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95590
in-theory        95590
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-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-95590.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E))) and A)), M:tm-5, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95591
in-theory        95591
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-1005 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95591.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E)))), M:tm-1, m:tm-1005, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-95592
in-theory        95592
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-95592.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-1003, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95593
in-theory        95593
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-992 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-95593.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-992, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95594
in-theory        95594
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     55
proof            (modus-ponens tm-980 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-95594.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-980, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95595
in-theory        95595
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> 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-930 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95595.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-930, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95596
in-theory        95596
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> 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-893 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95596.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-893, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95597
in-theory        95597
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-855 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-95597.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-855, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95598
in-theory        95598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-808 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-95598.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-808, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95599
in-theory        95599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-95599.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-757, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95600
in-theory        95600
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))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95600.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-708, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95601
in-theory        95601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> 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-665 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-95601.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-665, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95602
in-theory        95602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95602.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-622, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95603
in-theory        95603
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-609 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95603.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H or G))), M:tm-609, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95604
in-theory        95604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-95604.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-605, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95605
in-theory        95605
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)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95605.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-595, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95606
in-theory        95606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95606.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-550, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95607
in-theory        95607
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95607.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-540, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95608
in-theory        95608
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95608.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-530, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95609
in-theory        95609
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-95609.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-520, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95610
in-theory        95610
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95610.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-510, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95611
in-theory        95611
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95611.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-500, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95612
in-theory        95612
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95612.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-490, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95613
in-theory        95613
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95613.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-480, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95614
in-theory        95614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95614.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-469, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95615
in-theory        95615
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-456 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95615.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (G or H))), M:tm-456, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95616
in-theory        95616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-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-95616.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-453, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95617
in-theory        95617
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)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95617.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-443, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95618
in-theory        95618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95618.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-409, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95619
in-theory        95619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-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-95619.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-400, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95620
in-theory        95620
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95620.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-391, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95621
in-theory        95621
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95621.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-382, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95622
in-theory        95622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95622.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-373, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95623
in-theory        95623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95623.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-364, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95624
in-theory        95624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-95624.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-354, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95625
in-theory        95625
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-341 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95625.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95626
in-theory        95626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95626.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-338, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95627
in-theory        95627
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))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95627.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-327, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95628
in-theory        95628
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) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95628.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-326, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95629
in-theory        95629
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) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95629.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-325, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95630
in-theory        95630
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))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95630.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-324, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95631
in-theory        95631
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 (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95631.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-323, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95632
in-theory        95632
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-322 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95632.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> H)), M:tm-322, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95633
in-theory        95633
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-320 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95633.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> G)), M:tm-320, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95634
in-theory        95634
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-318 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95634.        ((((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-318, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95635
in-theory        95635
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-315 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95635.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> G))), M:tm-315, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95636
in-theory        95636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95636.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-311, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95637
in-theory        95637
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))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95637.        ((((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))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-310, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95638
in-theory        95638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95638.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and G))), M:tm-309, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95639
in-theory        95639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1006 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95639.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-308, m:tm-1006, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-95640
in-theory        95640
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-307 tm-1006 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95640.        ((((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-307, m:tm-1006, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-95641
in-theory        95641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95641.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-305, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95642
in-theory        95642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-303.          (A -> ((B -> ((C -> (D -> (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-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-95642.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-303, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95643
in-theory        95643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95643.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-270, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95644
in-theory        95644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95644.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-239, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95645
in-theory        95645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95645.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-210, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95646
in-theory        95646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-183.          (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-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-95646.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-183, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95647
in-theory        95647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95647.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-157, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95648
in-theory        95648
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95648.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-147, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95649
in-theory        95649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95649.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-134, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95650
in-theory        95650
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95650.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-125, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95651
in-theory        95651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95651.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-113, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95652
in-theory        95652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95652.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-105, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95653
in-theory        95653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95653.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-95, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95654
in-theory        95654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95654.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-83, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95655
in-theory        95655
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95655.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-76, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95656
in-theory        95656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95656.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-69, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95657
in-theory        95657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> 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-54 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-95657.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-54, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95658
in-theory        95658
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-42 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95658.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-42, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95659
in-theory        95659
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-32 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95659.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-32, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95660
in-theory        95660
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-23 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95660.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-23, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95661
in-theory        95661
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-22 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95661.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-22, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95662
in-theory        95662
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-21 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95662.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-21, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95663
in-theory        95663
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-20 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95663.        (((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-20, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95664
in-theory        95664
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-19 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95664.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-19, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95665
in-theory        95665
times-derived    1
----------------------------------------------------------------
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-7 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-7 tm-5 tm-8 tm-2)
proof-size       111
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-54.           (A -> (((B -> C) -> ((C -> 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-95665.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-7, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95666
in-theory        95666
times-derived    1
----------------------------------------------------------------
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-6 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-6 tm-5 tm-8 tm-2)
proof-size       111
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-54.           (A -> (((B -> C) -> ((C -> 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-95666.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G), M:tm-6, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95667
in-theory        95667
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
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-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-95667.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and A)), M:tm-5, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95668
in-theory        95668
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-1 tm-1006 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       111
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-54.           (A -> (((B -> C) -> ((C -> 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-95668.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-1, m:tm-1006, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-95669
in-theory        95669
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-95669.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H))), M:tm-1003, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95670
in-theory        95670
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-992 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-95670.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H))), M:tm-992, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95671
in-theory        95671
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H)))
theorem-size     47
proof            (modus-ponens tm-980 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-95671.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H))), M:tm-980, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95672
in-theory        95672
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-930 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95672.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-930, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95673
in-theory        95673
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-893 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95673.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-893, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95674
in-theory        95674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-855 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-95674.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-855, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95675
in-theory        95675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-808 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-95675.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-808, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95676
in-theory        95676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-757 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95676.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-757, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95677
in-theory        95677
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))) and ((H and I) -> H)))
theorem-size     45
proof            (modus-ponens tm-708 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-95677.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H))), M:tm-708, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95678
in-theory        95678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-665 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95678.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-665, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95679
in-theory        95679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-622 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95679.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-622, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95680
in-theory        95680
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-609 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95680.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F -> (G or F))), M:tm-609, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95681
in-theory        95681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-605 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95681.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-605, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95682
in-theory        95682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-595 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95682.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-595, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95683
in-theory        95683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-550 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95683.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-550, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95684
in-theory        95684
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-540 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95684.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-540, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95685
in-theory        95685
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-530 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95685.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-530, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95686
in-theory        95686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-520 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95686.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-520, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95687
in-theory        95687
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-510 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95687.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-510, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95688
in-theory        95688
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-500 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95688.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-500, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95689
in-theory        95689
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-490 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95689.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H))), M:tm-490, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95690
in-theory        95690
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-480 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95690.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-480, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95691
in-theory        95691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-469 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95691.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-469, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95692
in-theory        95692
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-456 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95692.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F -> (F or G))), M:tm-456, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95693
in-theory        95693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-453 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95693.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-453, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95694
in-theory        95694
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-443 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95694.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-443, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95695
in-theory        95695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-409 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95695.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-409, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95696
in-theory        95696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-400 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95696.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-400, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95697
in-theory        95697
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-391 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95697.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-391, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95698
in-theory        95698
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-382 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95698.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-382, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95699
in-theory        95699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-373 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95699.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H))), M:tm-373, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95700
in-theory        95700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-364 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95700.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-364, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95701
in-theory        95701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-354 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95701.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-354, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95702
in-theory        95702
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-341 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95702.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95703
in-theory        95703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-338 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95703.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F))), M:tm-338, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95704
in-theory        95704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     47
proof            (modus-ponens tm-327 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95704.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-327, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95705
in-theory        95705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-326 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95705.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-326, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95706
in-theory        95706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-325 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95706.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-325, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95707
in-theory        95707
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))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     53
proof            (modus-ponens tm-324 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95707.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-324, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95708
in-theory        95708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-323 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95708.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-323, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95709
in-theory        95709
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-322 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95709.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F and G) -> G)), M:tm-322, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95710
in-theory        95710
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-320 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95710.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F and G) -> F)), M:tm-320, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95711
in-theory        95711
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-318 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95711.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95712
in-theory        95712
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-315 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95712.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F -> (G -> F))), M:tm-315, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95713
in-theory        95713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-311 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95713.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-311, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95714
in-theory        95714
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))) and ((D and E) -> D)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95714.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) or F)), M:tm-310, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95715
in-theory        95715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95715.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and F))), M:tm-309, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95716
in-theory        95716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-308 tm-1007 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-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-95716.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((D and E) -> D)), M:tm-308, m:tm-1007, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-95717
in-theory        95717
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-307 tm-1007 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-95717.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1007, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-95718
in-theory        95718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-305 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95718.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)))), M:tm-305, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95719
in-theory        95719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-303 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95719.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-303, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95720
in-theory        95720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-270 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95720.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-270, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95721
in-theory        95721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-239 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95721.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-239, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95722
in-theory        95722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H)))
theorem-size     37
proof            (modus-ponens tm-210 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95722.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H))), M:tm-210, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95723
in-theory        95723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-183 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95723.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-183, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95724
in-theory        95724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-157 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95724.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-157, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95725
in-theory        95725
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     35
proof            (modus-ponens tm-147 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95725.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-147, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95726
in-theory        95726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-134 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95726.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-134, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95727
in-theory        95727
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     35
proof            (modus-ponens tm-125 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95727.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-125, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95728
in-theory        95728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-113 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95728.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> H))), M:tm-113, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95729
in-theory        95729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-105 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95729.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-105, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95730
in-theory        95730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-95 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95730.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F))), M:tm-95, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95731
in-theory        95731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-83 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95731.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-83, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95732
in-theory        95732
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-76 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95732.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> E))), M:tm-76, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95733
in-theory        95733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-69 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95733.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F))), M:tm-69, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95734
in-theory        95734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-54 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-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-95734.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-54, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95735
in-theory        95735
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-42 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95735.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F))), M:tm-42, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95736
in-theory        95736
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-32 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95736.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F))), M:tm-32, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95737
in-theory        95737
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-23 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95737.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F))), M:tm-23, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95738
in-theory        95738
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-22 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95738.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F))), M:tm-22, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95739
in-theory        95739
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-21 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95739.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F))), M:tm-21, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95740
in-theory        95740
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-20 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95740.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> G))), M:tm-20, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95741
in-theory        95741
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-19 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95741.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> F))), M:tm-19, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95742
in-theory        95742
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-7 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-7 tm-5 tm-8 tm-3)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95742.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> E))), M:tm-7, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95743
in-theory        95743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-6 tm-5 tm-8 tm-3)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95743.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)) or F), M:tm-6, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95744
in-theory        95744
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> E)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-95744.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> E)) and A)), M:tm-5, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95745
in-theory        95745
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-1 tm-1007 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-1 tm-5 tm-8 tm-3)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95745.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> E))), M:tm-1, m:tm-1007, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-95746
in-theory        95746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-95746.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I))), M:tm-1003, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95747
in-theory        95747
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-992 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-95747.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I))), M:tm-992, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95748
in-theory        95748
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I)))
theorem-size     47
proof            (modus-ponens tm-980 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-95748.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I))), M:tm-980, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95749
in-theory        95749
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-930 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95749.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-930, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95750
in-theory        95750
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-893 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95750.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-893, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95751
in-theory        95751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-855 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-95751.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-855, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95752
in-theory        95752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-808 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95752.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-808, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95753
in-theory        95753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-757 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95753.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-757, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95754
in-theory        95754
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))) and ((H and I) -> I)))
theorem-size     45
proof            (modus-ponens tm-708 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-95754.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I))), M:tm-708, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95755
in-theory        95755
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-665 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95755.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-665, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95756
in-theory        95756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-622 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95756.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-622, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95757
in-theory        95757
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-609 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95757.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F -> (G or F))), M:tm-609, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95758
in-theory        95758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-605 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95758.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-605, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95759
in-theory        95759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-595 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95759.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-595, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95760
in-theory        95760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-550 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95760.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-550, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95761
in-theory        95761
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-540 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95761.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-540, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95762
in-theory        95762
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-530 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95762.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-530, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95763
in-theory        95763
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-520 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95763.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-520, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95764
in-theory        95764
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-510 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95764.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-510, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95765
in-theory        95765
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-500 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95765.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-500, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95766
in-theory        95766
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-490 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95766.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I))), M:tm-490, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95767
in-theory        95767
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-480 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95767.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-480, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95768
in-theory        95768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-469 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95768.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-469, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95769
in-theory        95769
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-456 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95769.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F -> (F or G))), M:tm-456, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95770
in-theory        95770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-453 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95770.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-453, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95771
in-theory        95771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-443 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95771.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-443, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95772
in-theory        95772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-409 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95772.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-409, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95773
in-theory        95773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-400 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95773.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-400, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95774
in-theory        95774
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-391 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95774.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-391, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95775
in-theory        95775
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-382 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95775.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-382, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95776
in-theory        95776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-373 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95776.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I))), M:tm-373, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95777
in-theory        95777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-364 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95777.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-364, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95778
in-theory        95778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-354 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95778.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-354, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95779
in-theory        95779
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-341 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95779.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95780
in-theory        95780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-338 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95780.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G))), M:tm-338, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95781
in-theory        95781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     47
proof            (modus-ponens tm-327 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95781.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-327, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95782
in-theory        95782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-326 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-95782.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-326, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95783
in-theory        95783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-325 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95783.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-325, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95784
in-theory        95784
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))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     53
proof            (modus-ponens tm-324 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95784.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-324, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95785
in-theory        95785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-323 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95785.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-323, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95786
in-theory        95786
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-322 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95786.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F and G) -> G)), M:tm-322, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95787
in-theory        95787
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-320 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95787.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F and G) -> F)), M:tm-320, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95788
in-theory        95788
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-318 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95788.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95789
in-theory        95789
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-315 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95789.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F -> (G -> F))), M:tm-315, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95790
in-theory        95790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     41
proof            (modus-ponens tm-311 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95790.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-311, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95791
in-theory        95791
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))) and ((D and E) -> E)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95791.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) or F)), M:tm-310, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95792
in-theory        95792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95792.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and F))), M:tm-309, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95793
in-theory        95793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-308 tm-1008 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95793.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((D and E) -> E)), M:tm-308, m:tm-1008, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-95794
in-theory        95794
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-307 tm-1008 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-95794.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1008, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-95795
in-theory        95795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))))
theorem-size     41
proof            (modus-ponens tm-305 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95795.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)))), M:tm-305, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95796
in-theory        95796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-303 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95796.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-303, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95797
in-theory        95797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-270 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95797.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-270, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95798
in-theory        95798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-239 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95798.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-239, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95799
in-theory        95799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I)))
theorem-size     37
proof            (modus-ponens tm-210 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95799.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I))), M:tm-210, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95800
in-theory        95800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-183 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95800.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-183, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95801
in-theory        95801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-157 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95801.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-157, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95802
in-theory        95802
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     35
proof            (modus-ponens tm-147 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95802.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-147, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95803
in-theory        95803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-134 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95803.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-134, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95804
in-theory        95804
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     35
proof            (modus-ponens tm-125 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95804.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-125, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95805
in-theory        95805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-113 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95805.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H and I) -> I))), M:tm-113, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95806
in-theory        95806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-105 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95806.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-105, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95807
in-theory        95807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-95 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95807.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G))), M:tm-95, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95808
in-theory        95808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-83 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95808.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-83, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95809
in-theory        95809
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-76 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95809.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> F))), M:tm-76, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95810
in-theory        95810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-69 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95810.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G))), M:tm-69, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95811
in-theory        95811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-54 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-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-95811.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-54, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95812
in-theory        95812
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-42 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95812.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G))), M:tm-42, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95813
in-theory        95813
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-32 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95813.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G))), M:tm-32, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95814
in-theory        95814
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-23 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95814.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G))), M:tm-23, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95815
in-theory        95815
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-22 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95815.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G))), M:tm-22, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95816
in-theory        95816
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-21 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95816.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G))), M:tm-21, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95817
in-theory        95817
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-20 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95817.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G and H) -> H))), M:tm-20, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95818
in-theory        95818
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-19 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-95818.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F and G) -> G))), M:tm-19, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95819
in-theory        95819
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-7 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-7 tm-5 tm-8 tm-4)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95819.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> F))), M:tm-7, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95820
in-theory        95820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-6 tm-5 tm-8 tm-4)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95820.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)) or F), M:tm-6, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95821
in-theory        95821
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> F)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
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-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-95821.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> F)) and A)), M:tm-5, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95822
in-theory        95822
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-1 tm-1008 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-1 tm-5 tm-8 tm-4)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95822.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> F))), M:tm-1, m:tm-1008, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-95823
in-theory        95823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-95823.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I))))), M:tm-1003, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95824
in-theory        95824
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-95824.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I))))), M:tm-992, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95825
in-theory        95825
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-95825.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I))))), M:tm-980, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95826
in-theory        95826
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95826.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-930, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95827
in-theory        95827
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95827.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-893, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95828
in-theory        95828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-95828.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-855, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95829
in-theory        95829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-95829.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-808, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95830
in-theory        95830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-95830.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-757, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95831
in-theory        95831
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))) and (H -> (I -> (H and I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-95831.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I))))), M:tm-708, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95832
in-theory        95832
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-95832.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-665, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95833
in-theory        95833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95833.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-622, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95834
in-theory        95834
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-609 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-95834.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F -> (G or F))), M:tm-609, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95835
in-theory        95835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95835.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-605, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95836
in-theory        95836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-95836.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-595, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95837
in-theory        95837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95837.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-550, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95838
in-theory        95838
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95838.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-540, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95839
in-theory        95839
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95839.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-530, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95840
in-theory        95840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95840.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-520, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95841
in-theory        95841
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95841.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-510, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95842
in-theory        95842
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95842.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-500, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95843
in-theory        95843
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95843.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I))))), M:tm-490, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95844
in-theory        95844
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95844.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-480, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95845
in-theory        95845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95845.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-469, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95846
in-theory        95846
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-456 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-95846.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F -> (F or G))), M:tm-456, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95847
in-theory        95847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95847.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-453, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95848
in-theory        95848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-95848.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-443, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95849
in-theory        95849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95849.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-409, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95850
in-theory        95850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95850.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-400, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95851
in-theory        95851
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95851.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-391, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95852
in-theory        95852
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95852.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-382, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95853
in-theory        95853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95853.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I))))), M:tm-373, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95854
in-theory        95854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95854.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-364, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95855
in-theory        95855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-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-95855.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-354, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95856
in-theory        95856
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-341 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-95856.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95857
in-theory        95857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-95857.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G))))), M:tm-338, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95858
in-theory        95858
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-95858.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-327, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95859
in-theory        95859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-95859.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-326, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95860
in-theory        95860
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-95860.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-325, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95861
in-theory        95861
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))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-95861.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-324, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95862
in-theory        95862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-95862.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-323, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95863
in-theory        95863
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-322 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-95863.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F and G) -> G)), M:tm-322, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95864
in-theory        95864
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-320 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-95864.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F and G) -> F)), M:tm-320, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95865
in-theory        95865
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-318 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-95865.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95866
in-theory        95866
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-315 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-95866.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F -> (G -> F))), M:tm-315, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95867
in-theory        95867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-95867.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-311, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95868
in-theory        95868
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))) and (D -> (E -> (D and E)))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-95868.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) or F)), M:tm-310, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95869
in-theory        95869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-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-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-95869.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and F))), M:tm-309, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95870
in-theory        95870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-1009 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95870.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (D -> (E -> (D and E)))), M:tm-308, m:tm-1009, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-95871
in-theory        95871
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-307 tm-1009 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-95871.        ((((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-307, m:tm-1009, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-95872
in-theory        95872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-95872.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))))), M:tm-305, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95873
in-theory        95873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95873.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-303, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95874
in-theory        95874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95874.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-270, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95875
in-theory        95875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95875.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-239, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95876
in-theory        95876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-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-95876.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I))))), M:tm-210, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95877
in-theory        95877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-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-95877.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-183, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95878
in-theory        95878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95878.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-157, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95879
in-theory        95879
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-95879.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-147, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95880
in-theory        95880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95880.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-134, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95881
in-theory        95881
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-95881.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-125, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95882
in-theory        95882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95882.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (H and I))))), M:tm-113, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95883
in-theory        95883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-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-95883.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-105, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95884
in-theory        95884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95884.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G))))), M:tm-95, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95885
in-theory        95885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95885.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-83, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95886
in-theory        95886
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95886.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (E and F))))), M:tm-76, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95887
in-theory        95887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95887.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G))))), M:tm-69, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95888
in-theory        95888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8)
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-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-95888.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-54, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95889
in-theory        95889
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-42 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95889.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G))))), M:tm-42, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95890
in-theory        95890
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-32 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95890.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G))))), M:tm-32, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95891
in-theory        95891
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-23 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95891.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G))))), M:tm-23, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95892
in-theory        95892
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-22 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95892.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G))))), M:tm-22, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95893
in-theory        95893
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-21 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95893.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G))))), M:tm-21, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95894
in-theory        95894
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-20 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95894.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (G and H))))), M:tm-20, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95895
in-theory        95895
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-19 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95895.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (F and G))))), M:tm-19, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95896
in-theory        95896
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       93
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-54.           (A -> (((B -> C) -> ((C -> 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-95896.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (E and F))))), M:tm-7, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95897
in-theory        95897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       93
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-54.           (A -> (((B -> C) -> ((C -> 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-95897.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))) or F), M:tm-6, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95898
in-theory        95898
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (E and F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8)
proof-size       97
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-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-95898.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (E and F)))) and A)), M:tm-5, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95899
in-theory        95899
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-1 tm-1009 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       93
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-54.           (A -> (((B -> C) -> ((C -> 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-95899.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (E and F))))), M:tm-1, m:tm-1009, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-95900
in-theory        95900
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95900.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I)))), M:tm-1003, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95901
in-theory        95901
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-992 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-95901.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I)))), M:tm-992, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95902
in-theory        95902
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I))))
theorem-size     47
proof            (modus-ponens tm-980 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-95902.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I)))), M:tm-980, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95903
in-theory        95903
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-930 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95903.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-930, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95904
in-theory        95904
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-893 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95904.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-893, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95905
in-theory        95905
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-855 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-95905.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-855, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95906
in-theory        95906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-808 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-95906.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-808, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95907
in-theory        95907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-95907.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-757, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95908
in-theory        95908
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))) and (H -> (H or I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-95908.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I)))), M:tm-708, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95909
in-theory        95909
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-95909.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-665, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95910
in-theory        95910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95910.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-622, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95911
in-theory        95911
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-609 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-95911.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F -> (G or F))), M:tm-609, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95912
in-theory        95912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95912.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-605, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95913
in-theory        95913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95913.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-595, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95914
in-theory        95914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95914.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-550, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95915
in-theory        95915
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95915.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-540, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95916
in-theory        95916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95916.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-530, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95917
in-theory        95917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95917.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-520, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95918
in-theory        95918
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95918.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-510, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95919
in-theory        95919
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95919.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-500, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95920
in-theory        95920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95920.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I)))), M:tm-490, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95921
in-theory        95921
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95921.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-480, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95922
in-theory        95922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95922.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-469, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95923
in-theory        95923
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-456 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95923.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F -> (F or G))), M:tm-456, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95924
in-theory        95924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95924.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-453, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95925
in-theory        95925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-95925.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-443, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95926
in-theory        95926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95926.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-409, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95927
in-theory        95927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95927.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-400, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95928
in-theory        95928
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95928.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-391, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95929
in-theory        95929
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95929.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-382, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95930
in-theory        95930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95930.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I)))), M:tm-373, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95931
in-theory        95931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95931.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-364, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95932
in-theory        95932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95932.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-354, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95933
in-theory        95933
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-341 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-95933.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95934
in-theory        95934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95934.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G)))), M:tm-338, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95935
in-theory        95935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95935.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-327, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95936
in-theory        95936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95936.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-326, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95937
in-theory        95937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95937.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-325, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95938
in-theory        95938
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))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95938.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-324, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95939
in-theory        95939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95939.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-323, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95940
in-theory        95940
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-322 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-95940.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F and G) -> G)), M:tm-322, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95941
in-theory        95941
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-320 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-95941.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F and G) -> F)), M:tm-320, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95942
in-theory        95942
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-318 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-95942.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95943
in-theory        95943
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-315 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-95943.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F -> (G -> F))), M:tm-315, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95944
in-theory        95944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-95944.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-311, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95945
in-theory        95945
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))) and (D -> (D or E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95945.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) or F)), M:tm-310, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95946
in-theory        95946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95946.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and F))), M:tm-309, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95947
in-theory        95947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-308 tm-1010 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95947.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (D -> (D or E))), M:tm-308, m:tm-1010, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-95948
in-theory        95948
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-307 tm-1010 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-95948.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1010, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-95949
in-theory        95949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-95949.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))))), M:tm-305, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95950
in-theory        95950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95950.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-303, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95951
in-theory        95951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95951.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-270, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95952
in-theory        95952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95952.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-239, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95953
in-theory        95953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95953.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I)))), M:tm-210, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95954
in-theory        95954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95954.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-183, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95955
in-theory        95955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95955.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-157, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95956
in-theory        95956
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95956.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-147, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95957
in-theory        95957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95957.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-134, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95958
in-theory        95958
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95958.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-125, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95959
in-theory        95959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95959.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (H or I)))), M:tm-113, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95960
in-theory        95960
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95960.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-105, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95961
in-theory        95961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95961.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G)))), M:tm-95, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95962
in-theory        95962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95962.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-83, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95963
in-theory        95963
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95963.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (E or F)))), M:tm-76, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95964
in-theory        95964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95964.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G)))), M:tm-69, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95965
in-theory        95965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-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-95965.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-54, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95966
in-theory        95966
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-42 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95966.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G)))), M:tm-42, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95967
in-theory        95967
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-32 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95967.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G)))), M:tm-32, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95968
in-theory        95968
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-23 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95968.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G)))), M:tm-23, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95969
in-theory        95969
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-22 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95969.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G)))), M:tm-22, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95970
in-theory        95970
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-21 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95970.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G)))), M:tm-21, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95971
in-theory        95971
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-20 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95971.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (G or H)))), M:tm-20, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95972
in-theory        95972
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-19 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95972.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (F or G)))), M:tm-19, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95973
in-theory        95973
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-7 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95973.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (E or F)))), M:tm-7, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95974
in-theory        95974
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95974.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))) or F), M:tm-6, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95975
in-theory        95975
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (E or F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-6)
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-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-95975.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (E or F))) and A)), M:tm-5, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95976
in-theory        95976
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-1 tm-1010 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-95976.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (E or F)))), M:tm-1, m:tm-1010, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-95977
in-theory        95977
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-1003 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-95977.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H)))), M:tm-1003, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95978
in-theory        95978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-992 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95978.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H)))), M:tm-992, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95979
in-theory        95979
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H))))
theorem-size     47
proof            (modus-ponens tm-980 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-95979.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H)))), M:tm-980, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95980
in-theory        95980
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-930 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95980.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-930, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95981
in-theory        95981
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-893 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-95981.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-893, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95982
in-theory        95982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-855 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-95982.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-855, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95983
in-theory        95983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-808 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-95983.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-808, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95984
in-theory        95984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-95984.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-757, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95985
in-theory        95985
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))) and (H -> (I or H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-95985.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H)))), M:tm-708, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95986
in-theory        95986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-95986.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-665, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95987
in-theory        95987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95987.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-622, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95988
in-theory        95988
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-609 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95988.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F -> (G or F))), M:tm-609, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95989
in-theory        95989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-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-95989.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-605, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95990
in-theory        95990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95990.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-595, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95991
in-theory        95991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95991.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-550, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95992
in-theory        95992
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95992.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-540, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95993
in-theory        95993
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95993.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-530, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95994
in-theory        95994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-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-95994.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-520, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95995
in-theory        95995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95995.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-510, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95996
in-theory        95996
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95996.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-500, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95997
in-theory        95997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95997.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H)))), M:tm-490, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95998
in-theory        95998
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-95998.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-480, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-95999
in-theory        95999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-95999.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-469, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96000
in-theory        96000
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-456 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-96000.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F -> (F or G))), M:tm-456, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96001
in-theory        96001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96001.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-453, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96002
in-theory        96002
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96002.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-443, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96003
in-theory        96003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96003.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-409, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96004
in-theory        96004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96004.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-400, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96005
in-theory        96005
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96005.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-391, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96006
in-theory        96006
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96006.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-382, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96007
in-theory        96007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96007.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H)))), M:tm-373, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96008
in-theory        96008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96008.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-364, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96009
in-theory        96009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96009.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-354, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96010
in-theory        96010
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-341 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-96010.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96011
in-theory        96011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96011.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F)))), M:tm-338, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96012
in-theory        96012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96012.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-327, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96013
in-theory        96013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96013.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-326, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96014
in-theory        96014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96014.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-325, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96015
in-theory        96015
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))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96015.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-324, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96016
in-theory        96016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96016.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-323, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96017
in-theory        96017
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-322 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-96017.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F and G) -> G)), M:tm-322, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96018
in-theory        96018
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-320 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-96018.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F and G) -> F)), M:tm-320, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96019
in-theory        96019
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-318 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-96019.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96020
in-theory        96020
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-315 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-96020.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F -> (G -> F))), M:tm-315, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96021
in-theory        96021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96021.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-311, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96022
in-theory        96022
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))) and (D -> (E or D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-96022.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) or F)), M:tm-310, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96023
in-theory        96023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96023.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and F))), M:tm-309, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96024
in-theory        96024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-308 tm-1011 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96024.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (D -> (E or D))), M:tm-308, m:tm-1011, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-96025
in-theory        96025
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-307 tm-1011 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-96025.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1011, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-96026
in-theory        96026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-96026.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))))), M:tm-305, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96027
in-theory        96027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96027.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-303, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96028
in-theory        96028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96028.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-270, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96029
in-theory        96029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96029.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-239, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96030
in-theory        96030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96030.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H)))), M:tm-210, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96031
in-theory        96031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96031.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-183, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96032
in-theory        96032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96032.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-157, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96033
in-theory        96033
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96033.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-147, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96034
in-theory        96034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96034.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-134, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96035
in-theory        96035
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96035.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-125, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96036
in-theory        96036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96036.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I or H)))), M:tm-113, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96037
in-theory        96037
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96037.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-105, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96038
in-theory        96038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96038.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F)))), M:tm-95, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96039
in-theory        96039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96039.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-83, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96040
in-theory        96040
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96040.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F or E)))), M:tm-76, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96041
in-theory        96041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96041.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F)))), M:tm-69, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96042
in-theory        96042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-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-96042.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-54, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96043
in-theory        96043
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-42 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96043.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F)))), M:tm-42, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96044
in-theory        96044
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-32 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96044.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F)))), M:tm-32, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96045
in-theory        96045
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-23 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96045.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F)))), M:tm-23, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96046
in-theory        96046
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-22 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96046.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F)))), M:tm-22, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96047
in-theory        96047
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-21 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96047.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F)))), M:tm-21, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96048
in-theory        96048
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-20 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96048.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H or G)))), M:tm-20, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96049
in-theory        96049
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-19 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96049.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G or F)))), M:tm-19, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96050
in-theory        96050
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96050.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F or E)))), M:tm-7, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96051
in-theory        96051
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-96051.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))) or F), M:tm-6, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96052
in-theory        96052
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F or E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-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-96052.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F or E))) and A)), M:tm-5, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96053
in-theory        96053
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-1 tm-1011 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-96053.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F or E)))), M:tm-1, m:tm-1011, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-96054
in-theory        96054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       179
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96054.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-1003, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96055
in-theory        96055
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     43
proof            (modus-ponens tm-992 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       179
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96055.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-992, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96056
in-theory        96056
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     55
proof            (modus-ponens tm-980 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96056.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-980, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96057
in-theory        96057
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     41
proof            (modus-ponens tm-930 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96057.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-930, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96058
in-theory        96058
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     41
proof            (modus-ponens tm-893 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96058.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-893, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96059
in-theory        96059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     45
proof            (modus-ponens tm-855 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96059.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-855, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96060
in-theory        96060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     39
proof            (modus-ponens tm-808 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96060.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-808, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96061
in-theory        96061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-96061.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-757, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96062
in-theory        96062
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))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96062.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-708, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96063
in-theory        96063
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-96063.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-665, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96064
in-theory        96064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-96064.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-622, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96065
in-theory        96065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96065.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H or G))), M:tm-609, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96066
in-theory        96066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96066.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-605, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96067
in-theory        96067
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96067.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-595, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96068
in-theory        96068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-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-96068.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-550, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96069
in-theory        96069
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96069.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-540, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96070
in-theory        96070
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-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-96070.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-530, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96071
in-theory        96071
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96071.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-520, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96072
in-theory        96072
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-96072.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-510, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96073
in-theory        96073
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-96073.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-500, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96074
in-theory        96074
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96074.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-490, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96075
in-theory        96075
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-96075.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-480, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96076
in-theory        96076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-96076.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-469, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96077
in-theory        96077
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96077.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (G or H))), M:tm-456, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96078
in-theory        96078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96078.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-453, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96079
in-theory        96079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96079.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-443, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96080
in-theory        96080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96080.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-409, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96081
in-theory        96081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96081.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-400, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96082
in-theory        96082
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-96082.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-391, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96083
in-theory        96083
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-96083.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-382, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96084
in-theory        96084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96084.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-373, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96085
in-theory        96085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-96085.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-364, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96086
in-theory        96086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96086.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-354, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96087
in-theory        96087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96087.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96088
in-theory        96088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96088.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-338, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96089
in-theory        96089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96089.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-327, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96090
in-theory        96090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96090.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-326, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96091
in-theory        96091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96091.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-325, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96092
in-theory        96092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96092.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-324, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96093
in-theory        96093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96093.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-323, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96094
in-theory        96094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96094.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G and H) -> H)), M:tm-322, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96095
in-theory        96095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96095.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G and H) -> G)), M:tm-320, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96096
in-theory        96096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96096.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96097
in-theory        96097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96097.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H -> G))), M:tm-315, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96098
in-theory        96098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96098.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-311, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96099
in-theory        96099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96099.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-310, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96100
in-theory        96100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96100.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and G))), M:tm-309, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96101
in-theory        96101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1012 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96101.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-308, m:tm-1012, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))
================================================================
tm-name          tm-96102
in-theory        96102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-307 tm-1012 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96102.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1012, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))
================================================================
tm-name          tm-96103
in-theory        96103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96103.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-305, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96104
in-theory        96104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96104.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-303, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96105
in-theory        96105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96105.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-270, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96106
in-theory        96106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96106.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-239, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96107
in-theory        96107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96107.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-210, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96108
in-theory        96108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96108.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-183, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96109
in-theory        96109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-96109.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-157, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96110
in-theory        96110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96110.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-147, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96111
in-theory        96111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-96111.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-134, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96112
in-theory        96112
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96112.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-125, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96113
in-theory        96113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96113.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-113, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96114
in-theory        96114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96114.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-105, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96115
in-theory        96115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96115.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-95, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96116
in-theory        96116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96116.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-83, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96117
in-theory        96117
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-10 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96117.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-76, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96118
in-theory        96118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-9 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96118.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-69, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96119
in-theory        96119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8)
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-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-96119.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-54, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96120
in-theory        96120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96120.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-42, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96121
in-theory        96121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96121.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-32, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96122
in-theory        96122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96122.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-23, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96123
in-theory        96123
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96123.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-22, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96124
in-theory        96124
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96124.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-21, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96125
in-theory        96125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96125.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-20, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96126
in-theory        96126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96126.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-19, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96127
in-theory        96127
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       111
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-54.           (A -> (((B -> C) -> ((C -> 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-96127.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-7, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96128
in-theory        96128
times-derived    1
----------------------------------------------------------------
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-6 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       111
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-54.           (A -> (((B -> C) -> ((C -> 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-96128.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G), M:tm-6, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96129
in-theory        96129
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8)
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-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-96129.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and A)), M:tm-5, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96130
in-theory        96130
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-1012 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       111
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-54.           (A -> (((B -> C) -> ((C -> 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-96130.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-1, m:tm-1012, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-96131
in-theory        96131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96131.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-1003, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96132
in-theory        96132
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     41
proof            (modus-ponens tm-992 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96132.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-992, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96133
in-theory        96133
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     53
proof            (modus-ponens tm-980 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-9)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96133.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-980, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96134
in-theory        96134
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     39
proof            (modus-ponens tm-930 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96134.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-930, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96135
in-theory        96135
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     39
proof            (modus-ponens tm-893 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96135.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-893, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96136
in-theory        96136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     43
proof            (modus-ponens tm-855 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96136.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-855, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96137
in-theory        96137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     37
proof            (modus-ponens tm-808 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96137.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-808, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96138
in-theory        96138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-96138.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-757, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96139
in-theory        96139
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))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96139.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-708, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96140
in-theory        96140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-96140.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-665, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96141
in-theory        96141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96141.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-622, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96142
in-theory        96142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G or F)))
theorem-size     31
proof            (modus-ponens tm-609 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-96142.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G or F))), M:tm-609, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96143
in-theory        96143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96143.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-605, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96144
in-theory        96144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96144.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-595, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96145
in-theory        96145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96145.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-550, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96146
in-theory        96146
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96146.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-540, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96147
in-theory        96147
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96147.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-530, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96148
in-theory        96148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96148.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-520, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96149
in-theory        96149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96149.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-510, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96150
in-theory        96150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96150.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-500, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96151
in-theory        96151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96151.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-490, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96152
in-theory        96152
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96152.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-480, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96153
in-theory        96153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96153.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-469, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96154
in-theory        96154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (F or G)))
theorem-size     31
proof            (modus-ponens tm-456 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-96154.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (F or G))), M:tm-456, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96155
in-theory        96155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96155.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-453, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96156
in-theory        96156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96156.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-443, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96157
in-theory        96157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96157.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-409, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96158
in-theory        96158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96158.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-400, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96159
in-theory        96159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96159.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-391, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96160
in-theory        96160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96160.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-382, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96161
in-theory        96161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96161.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-373, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96162
in-theory        96162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96162.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-364, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96163
in-theory        96163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96163.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-354, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96164
in-theory        96164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G -> (F and G))))
theorem-size     33
proof            (modus-ponens tm-341 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96164.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96165
in-theory        96165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96165.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-338, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96166
in-theory        96166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96166.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-327, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96167
in-theory        96167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96167.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-326, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96168
in-theory        96168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96168.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-325, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96169
in-theory        96169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96169.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-324, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96170
in-theory        96170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96170.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-323, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96171
in-theory        96171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F and G) -> G))
theorem-size     31
proof            (modus-ponens tm-322 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-96171.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F and G) -> G)), M:tm-322, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96172
in-theory        96172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F and G) -> F))
theorem-size     31
proof            (modus-ponens tm-320 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-96172.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F and G) -> F)), M:tm-320, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96173
in-theory        96173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96173.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96174
in-theory        96174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G -> F)))
theorem-size     31
proof            (modus-ponens tm-315 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-96174.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G -> F))), M:tm-315, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96175
in-theory        96175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96175.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-311, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96176
in-theory        96176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) or F))
theorem-size     53
proof            (modus-ponens tm-310 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96176.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) or F)), M:tm-310, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96177
in-theory        96177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and F)))
theorem-size     55
proof            (modus-ponens tm-309 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96177.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and F))), M:tm-309, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96178
in-theory        96178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1013 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96178.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-308, m:tm-1013, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))
================================================================
tm-name          tm-96179
in-theory        96179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-307 tm-1013 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-96179.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1013, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))
================================================================
tm-name          tm-96180
in-theory        96180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96180.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-305, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96181
in-theory        96181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96181.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-303, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96182
in-theory        96182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96182.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-270, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96183
in-theory        96183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96183.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-239, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96184
in-theory        96184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96184.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-210, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96185
in-theory        96185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96185.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-183, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96186
in-theory        96186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96186.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-157, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96187
in-theory        96187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96187.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-147, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96188
in-theory        96188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96188.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-134, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96189
in-theory        96189
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96189.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-125, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96190
in-theory        96190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96190.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-113, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96191
in-theory        96191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96191.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-105, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96192
in-theory        96192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-96192.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-95, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96193
in-theory        96193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96193.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-83, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96194
in-theory        96194
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96194.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-76, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96195
in-theory        96195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-9 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96195.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-69, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96196
in-theory        96196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 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-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-96196.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-54, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96197
in-theory        96197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96197.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-42, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96198
in-theory        96198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96198.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-32, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96199
in-theory        96199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96199.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-23, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96200
in-theory        96200
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96200.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-22, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96201
in-theory        96201
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96201.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-21, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96202
in-theory        96202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96202.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-20, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96203
in-theory        96203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96203.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-19, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96204
in-theory        96204
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-7 tm-5 tm-8 tm-9)
proof-size       105
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-54.           (A -> (((B -> C) -> ((C -> 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-96204.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-7, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96205
in-theory        96205
times-derived    1
----------------------------------------------------------------
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-6 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-6 tm-5 tm-8 tm-9)
proof-size       105
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-54.           (A -> (((B -> C) -> ((C -> 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-96205.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) or F), M:tm-6, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96206
in-theory        96206
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       109
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-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-96206.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))) and A)), M:tm-5, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96207
in-theory        96207
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-1013 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-1 tm-5 tm-8 tm-9)
proof-size       105
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-54.           (A -> (((B -> C) -> ((C -> 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-96207.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-1, m:tm-1013, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-96208
in-theory        96208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-1003 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96208.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H))), M:tm-1003, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96209
in-theory        96209
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-992 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       155
proof-steps      11
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96209.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H))), M:tm-992, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96210
in-theory        96210
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H)))
theorem-size     47
proof            (modus-ponens tm-980 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-10)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96210.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H))), M:tm-980, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96211
in-theory        96211
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-930 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96211.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-930, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96212
in-theory        96212
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-893 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96212.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-893, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96213
in-theory        96213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     37
proof            (modus-ponens tm-855 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-10)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96213.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-855, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96214
in-theory        96214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-808 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96214.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-808, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96215
in-theory        96215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-757 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-96215.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-757, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96216
in-theory        96216
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))) and ((not (not H)) -> H)))
theorem-size     45
proof            (modus-ponens tm-708 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96216.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H))), M:tm-708, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96217
in-theory        96217
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-665 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-96217.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-665, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96218
in-theory        96218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-622 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96218.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-622, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96219
in-theory        96219
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96219.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96220
in-theory        96220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-605 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96220.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-605, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96221
in-theory        96221
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (F or E)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-595 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96221.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (F or E)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)))), M:tm-595, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96222
in-theory        96222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-550 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96222.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-550, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96223
in-theory        96223
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-540 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96223.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-540, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96224
in-theory        96224
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-530 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96224.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-530, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96225
in-theory        96225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-520 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96225.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-520, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96226
in-theory        96226
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-510 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96226.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-510, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96227
in-theory        96227
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-500 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96227.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-500, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96228
in-theory        96228
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-490 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96228.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H))), M:tm-490, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96229
in-theory        96229
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-480 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96229.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-480, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96230
in-theory        96230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-469 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96230.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-469, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96231
in-theory        96231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96231.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96232
in-theory        96232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-453 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96232.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-453, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96233
in-theory        96233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (E or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-443 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96233.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (E or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)))), M:tm-443, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96234
in-theory        96234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-409 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96234.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-409, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96235
in-theory        96235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-400 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96235.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-400, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96236
in-theory        96236
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-391 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96236.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-391, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96237
in-theory        96237
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-382 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96237.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-382, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96238
in-theory        96238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-373 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96238.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H))), M:tm-373, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96239
in-theory        96239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-364 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96239.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-364, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96240
in-theory        96240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-354 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96240.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-354, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96241
in-theory        96241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96241.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96242
in-theory        96242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-338 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96242.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F))), M:tm-338, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96243
in-theory        96243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (F -> (E and F))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))))
theorem-size     47
proof            (modus-ponens tm-327 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96243.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (F -> (E and F))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)))), M:tm-327, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96244
in-theory        96244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (((E and F) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-326 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96244.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (((E and F) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)))), M:tm-326, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96245
in-theory        96245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (((E and F) -> E) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-325 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96245.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (((E and F) -> E) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)))), M:tm-325, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96246
in-theory        96246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))))
theorem-size     53
proof            (modus-ponens tm-324 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96246.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)))), M:tm-324, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96247
in-theory        96247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (F -> E)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-323 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96247.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (F -> E)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)))), M:tm-323, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96248
in-theory        96248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96248.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96249
in-theory        96249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96249.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96250
in-theory        96250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96250.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96251
in-theory        96251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96251.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96252
in-theory        96252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))))
theorem-size     41
proof            (modus-ponens tm-311 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96252.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)))), M:tm-311, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96253
in-theory        96253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96253.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) or E)), M:tm-310, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96254
in-theory        96254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96254.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and E))), M:tm-309, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96255
in-theory        96255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((not (not D)) -> D))
theorem-size     25
proof            (modus-ponens tm-308 tm-1014 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (not (not Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96255.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((not (not D)) -> D)), M:tm-308, m:tm-1014, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (not (not Dm)) Dm)))
================================================================
tm-name          tm-96256
in-theory        96256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-307 tm-1014 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (not (not Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96256.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1014, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (not (not Dm)) Dm)))
================================================================
tm-name          tm-96257
in-theory        96257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))))
theorem-size     41
proof            (modus-ponens tm-305 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96257.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) and (E -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)))), M:tm-305, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96258
in-theory        96258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-303 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96258.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-303, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96259
in-theory        96259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-270 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96259.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-270, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96260
in-theory        96260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-239 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96260.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-239, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96261
in-theory        96261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H)))
theorem-size     37
proof            (modus-ponens tm-210 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96261.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H))), M:tm-210, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96262
in-theory        96262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-183 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96262.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-183, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96263
in-theory        96263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-157 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96263.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-157, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96264
in-theory        96264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-147 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96264.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-147, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96265
in-theory        96265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-134 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96265.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-134, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96266
in-theory        96266
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-125 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96266.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-125, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96267
in-theory        96267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-113 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96267.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((not (not H)) -> H))), M:tm-113, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96268
in-theory        96268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-105 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96268.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-105, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96269
in-theory        96269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-95 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-96269.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F))), M:tm-95, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96270
in-theory        96270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-83 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96270.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-83, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96271
in-theory        96271
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((not (not E)) -> E)))
theorem-size     25
proof            (modus-ponens tm-76 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96271.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((not (not E)) -> E))), M:tm-76, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96272
in-theory        96272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-69 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96272.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F))), M:tm-69, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96273
in-theory        96273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-54 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 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-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-96273.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-54, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96274
in-theory        96274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-42 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96274.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F))), M:tm-42, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96275
in-theory        96275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-32 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96275.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F))), M:tm-32, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96276
in-theory        96276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-23 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96276.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F))), M:tm-23, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96277
in-theory        96277
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-22 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96277.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F))), M:tm-22, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96278
in-theory        96278
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-21 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96278.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F))), M:tm-21, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96279
in-theory        96279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-20 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96279.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((not (not G)) -> G))), M:tm-20, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96280
in-theory        96280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-19 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96280.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((not (not F)) -> F))), M:tm-19, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96281
in-theory        96281
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-7 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-7 tm-5 tm-8 tm-10)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-96281.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((not (not E)) -> E))), M:tm-7, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96282
in-theory        96282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-6 tm-5 tm-8 tm-10)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-96282.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)) or E), M:tm-6, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96283
in-theory        96283
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((not (not E)) -> E)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
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-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-96283.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((not (not E)) -> E)) and A)), M:tm-5, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96284
in-theory        96284
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-1 tm-1014 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-1 tm-5 tm-8 tm-10)
proof-size       87
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-54.           (A -> (((B -> C) -> ((C -> 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-96284.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((not (not E)) -> E))), M:tm-1, m:tm-1014, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-96285
in-theory        96285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96285.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I))))), M:tm-1003, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96286
in-theory        96286
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96286.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I))))), M:tm-992, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96287
in-theory        96287
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96287.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I))))), M:tm-980, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96288
in-theory        96288
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96288.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-930, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96289
in-theory        96289
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96289.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-893, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96290
in-theory        96290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96290.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-855, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96291
in-theory        96291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96291.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-808, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96292
in-theory        96292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-96292.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-757, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96293
in-theory        96293
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))) and (H -> (I -> (J -> I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96293.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I))))), M:tm-708, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96294
in-theory        96294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-96294.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-665, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96295
in-theory        96295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96295.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-622, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96296
in-theory        96296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-96296.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (H or G))), M:tm-609, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96297
in-theory        96297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96297.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-605, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96298
in-theory        96298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-96298.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))))), M:tm-595, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96299
in-theory        96299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96299.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-550, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96300
in-theory        96300
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96300.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-540, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96301
in-theory        96301
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96301.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-530, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96302
in-theory        96302
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96302.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-520, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96303
in-theory        96303
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96303.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-510, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96304
in-theory        96304
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96304.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-500, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96305
in-theory        96305
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96305.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I))))), M:tm-490, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96306
in-theory        96306
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96306.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-480, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96307
in-theory        96307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96307.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-469, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96308
in-theory        96308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-96308.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (G or H))), M:tm-456, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96309
in-theory        96309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96309.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-453, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96310
in-theory        96310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-96310.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))))), M:tm-443, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96311
in-theory        96311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96311.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-409, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96312
in-theory        96312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96312.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-400, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96313
in-theory        96313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96313.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-391, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96314
in-theory        96314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96314.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-382, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96315
in-theory        96315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96315.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I))))), M:tm-373, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96316
in-theory        96316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96316.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-364, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96317
in-theory        96317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96317.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-354, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96318
in-theory        96318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-96318.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96319
in-theory        96319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-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-96319.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G))))), M:tm-338, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96320
in-theory        96320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-96320.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))))), M:tm-327, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96321
in-theory        96321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-96321.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))))), M:tm-326, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96322
in-theory        96322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-96322.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))))), M:tm-325, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96323
in-theory        96323
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-96323.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))))), M:tm-324, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96324
in-theory        96324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-96324.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))))), M:tm-323, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96325
in-theory        96325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-96325.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G and H) -> H)), M:tm-322, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96326
in-theory        96326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-96326.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G and H) -> G)), M:tm-320, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96327
in-theory        96327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-96327.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96328
in-theory        96328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-96328.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (H -> G))), M:tm-315, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96329
in-theory        96329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-96329.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))))), M:tm-311, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96330
in-theory        96330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-96330.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) or G)), M:tm-310, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96331
in-theory        96331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-96331.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and G))), M:tm-309, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96332
in-theory        96332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (D -> (E -> (F -> E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-1015 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (-> Fm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96332.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (D -> (E -> (F -> E)))), M:tm-308, m:tm-1015, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (-> Fm Em)))))
================================================================
tm-name          tm-96333
in-theory        96333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1015 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (-> Fm Em))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-96333.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1015, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (-> Fm Em)))))
================================================================
tm-name          tm-96334
in-theory        96334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96334.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))))), M:tm-305, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96335
in-theory        96335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96335.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-303, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96336
in-theory        96336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96336.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-270, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96337
in-theory        96337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96337.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-239, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96338
in-theory        96338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96338.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I))))), M:tm-210, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96339
in-theory        96339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96339.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-183, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96340
in-theory        96340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96340.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-157, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96341
in-theory        96341
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96341.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-147, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96342
in-theory        96342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96342.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-134, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96343
in-theory        96343
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96343.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-125, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96344
in-theory        96344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96344.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> I))))), M:tm-113, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96345
in-theory        96345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96345.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-105, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96346
in-theory        96346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96346.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G))))), M:tm-95, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96347
in-theory        96347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96347.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-83, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96348
in-theory        96348
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96348.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> F))))), M:tm-76, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96349
in-theory        96349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96349.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G))))), M:tm-69, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96350
in-theory        96350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 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-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-96350.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-54, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96351
in-theory        96351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-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-96351.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G))))), M:tm-42, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96352
in-theory        96352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-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-96352.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G))))), M:tm-32, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96353
in-theory        96353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96353.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G))))), M:tm-23, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96354
in-theory        96354
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-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-96354.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G))))), M:tm-22, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96355
in-theory        96355
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-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-96355.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G))))), M:tm-21, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96356
in-theory        96356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96356.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> H))))), M:tm-20, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96357
in-theory        96357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96357.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> G))))), M:tm-19, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96358
in-theory        96358
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-7 tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-96358.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> F))))), M:tm-7, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96359
in-theory        96359
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-6 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-6 tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-96359.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))) or G), M:tm-6, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96360
in-theory        96360
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
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-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-96360.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> F)))) and A)), M:tm-5, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96361
in-theory        96361
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1015 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-96361.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> F))))), M:tm-1, m:tm-1015, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-96362
in-theory        96362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-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-54.           (A -> (((B -> C) -> ((C -> 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-96362.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H)))), M:tm-1003, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96363
in-theory        96363
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-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-54.           (A -> (((B -> C) -> ((C -> 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-96363.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H)))), M:tm-992, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96364
in-theory        96364
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96364.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H)))), M:tm-980, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96365
in-theory        96365
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96365.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-930, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96366
in-theory        96366
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96366.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-893, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96367
in-theory        96367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96367.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-855, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96368
in-theory        96368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96368.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-808, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96369
in-theory        96369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96369.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-757, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96370
in-theory        96370
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))) and ((H -> I) -> (H -> H))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96370.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H)))), M:tm-708, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96371
in-theory        96371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96371.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-665, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96372
in-theory        96372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96372.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-622, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96373
in-theory        96373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-96373.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (G or F))), M:tm-609, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96374
in-theory        96374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96374.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-605, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96375
in-theory        96375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96375.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))))), M:tm-595, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96376
in-theory        96376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96376.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-550, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96377
in-theory        96377
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96377.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-540, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96378
in-theory        96378
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96378.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-530, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96379
in-theory        96379
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96379.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-520, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96380
in-theory        96380
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96380.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-510, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96381
in-theory        96381
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96381.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-500, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96382
in-theory        96382
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96382.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H)))), M:tm-490, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96383
in-theory        96383
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96383.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-480, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96384
in-theory        96384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96384.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-469, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96385
in-theory        96385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-96385.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (F or G))), M:tm-456, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96386
in-theory        96386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96386.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-453, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96387
in-theory        96387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96387.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))))), M:tm-443, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96388
in-theory        96388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96388.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-409, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96389
in-theory        96389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96389.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-400, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96390
in-theory        96390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96390.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-391, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96391
in-theory        96391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96391.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-382, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96392
in-theory        96392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96392.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H)))), M:tm-373, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96393
in-theory        96393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96393.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-364, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96394
in-theory        96394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-96394.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-354, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96395
in-theory        96395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-96395.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96396
in-theory        96396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96396.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F)))), M:tm-338, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96397
in-theory        96397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96397.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))))), M:tm-327, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96398
in-theory        96398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96398.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))))), M:tm-326, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96399
in-theory        96399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96399.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))))), M:tm-325, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96400
in-theory        96400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96400.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))))), M:tm-324, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96401
in-theory        96401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96401.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))))), M:tm-323, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96402
in-theory        96402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-96402.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F and G) -> G)), M:tm-322, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96403
in-theory        96403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-96403.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F and G) -> F)), M:tm-320, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96404
in-theory        96404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-96404.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96405
in-theory        96405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-96405.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (G -> F))), M:tm-315, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96406
in-theory        96406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96406.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))))), M:tm-311, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96407
in-theory        96407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96407.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) or F)), M:tm-310, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96408
in-theory        96408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96408.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and F))), M:tm-309, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96409
in-theory        96409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((D -> E) -> (D -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-1016 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> Dm Dm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96409.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((D -> E) -> (D -> D))), M:tm-308, m:tm-1016, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> Dm Dm))))
================================================================
tm-name          tm-96410
in-theory        96410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1016 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> Dm Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-1.            (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-96410.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1016, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> Dm Dm))))
================================================================
tm-name          tm-96411
in-theory        96411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96411.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))))), M:tm-305, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96412
in-theory        96412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96412.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-303, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96413
in-theory        96413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96413.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-270, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96414
in-theory        96414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96414.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-239, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96415
in-theory        96415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (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-96415.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H)))), M:tm-210, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96416
in-theory        96416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-96416.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-183, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96417
in-theory        96417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96417.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-157, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96418
in-theory        96418
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96418.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-147, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96419
in-theory        96419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96419.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-134, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96420
in-theory        96420
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96420.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-125, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96421
in-theory        96421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96421.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> H)))), M:tm-113, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96422
in-theory        96422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96422.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-105, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96423
in-theory        96423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96423.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F)))), M:tm-95, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96424
in-theory        96424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96424.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-83, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96425
in-theory        96425
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> E))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96425.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> E)))), M:tm-76, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96426
in-theory        96426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96426.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F)))), M:tm-69, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96427
in-theory        96427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-1.            (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-96427.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-54, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96428
in-theory        96428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96428.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F)))), M:tm-42, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96429
in-theory        96429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96429.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F)))), M:tm-32, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96430
in-theory        96430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96430.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F)))), M:tm-23, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96431
in-theory        96431
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96431.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F)))), M:tm-22, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96432
in-theory        96432
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96432.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F)))), M:tm-21, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96433
in-theory        96433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96433.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> G)))), M:tm-20, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96434
in-theory        96434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96434.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> F)))), M:tm-19, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96435
in-theory        96435
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-7 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96435.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> E)))), M:tm-7, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96436
in-theory        96436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-6 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96436.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))) or F), M:tm-6, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96437
in-theory        96437
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> E))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (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-96437.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> E))) and A)), M:tm-5, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96438
in-theory        96438
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1016 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), 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-96438.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> E)))), M:tm-1, m:tm-1016, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-96439
in-theory        96439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     49
proof            (modus-ponens tm-1003 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       223
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96439.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-1003, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96440
in-theory        96440
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     49
proof            (modus-ponens tm-992 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       223
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96440.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-992, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96441
in-theory        96441
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     61
proof            (modus-ponens tm-980 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96441.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-980, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96442
in-theory        96442
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-930 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96442.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-930, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96443
in-theory        96443
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-893 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96443.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-893, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96444
in-theory        96444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     51
proof            (modus-ponens tm-855 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96444.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-855, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96445
in-theory        96445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-808 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96445.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-808, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96446
in-theory        96446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-757 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96446.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-757, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96447
in-theory        96447
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))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     59
proof            (modus-ponens tm-708 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96447.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-708, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96448
in-theory        96448
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-665 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96448.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-665, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96449
in-theory        96449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-622 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96449.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-622, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96450
in-theory        96450
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-13.           (((A -> (B -> C)) -> (A -> 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-96450.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (H or G))), M:tm-609, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96451
in-theory        96451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-605 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96451.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-605, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96452
in-theory        96452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-595 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-13.           (((A -> (B -> C)) -> (A -> 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-96452.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-595, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96453
in-theory        96453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-550 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96453.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-550, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96454
in-theory        96454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-540 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96454.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-540, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96455
in-theory        96455
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-530 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96455.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-530, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96456
in-theory        96456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-520 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96456.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-520, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96457
in-theory        96457
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-510 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96457.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-510, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96458
in-theory        96458
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-500 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96458.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-500, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96459
in-theory        96459
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     49
proof            (modus-ponens tm-490 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96459.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-490, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96460
in-theory        96460
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-480 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96460.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-480, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96461
in-theory        96461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-469 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96461.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-469, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96462
in-theory        96462
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-13.           (((A -> (B -> C)) -> (A -> 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-96462.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (G or H))), M:tm-456, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96463
in-theory        96463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-453 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96463.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-453, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96464
in-theory        96464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-443 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-13.           (((A -> (B -> C)) -> (A -> 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-96464.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-443, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96465
in-theory        96465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-409 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96465.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-409, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96466
in-theory        96466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-400 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96466.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-400, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96467
in-theory        96467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-391 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96467.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-391, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96468
in-theory        96468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-382 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96468.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-382, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96469
in-theory        96469
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     49
proof            (modus-ponens tm-373 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96469.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-373, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96470
in-theory        96470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-364 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96470.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-364, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96471
in-theory        96471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-354 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96471.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-354, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96472
in-theory        96472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-13.           (((A -> (B -> C)) -> (A -> 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-96472.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96473
in-theory        96473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-338 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96473.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-338, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96474
in-theory        96474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     75
proof            (modus-ponens tm-327 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-13.           (((A -> (B -> C)) -> (A -> 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-96474.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-327, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96475
in-theory        96475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-326 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-13.           (((A -> (B -> C)) -> (A -> 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-96475.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-326, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96476
in-theory        96476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-325 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-13.           (((A -> (B -> C)) -> (A -> 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-96476.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-325, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96477
in-theory        96477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     81
proof            (modus-ponens tm-324 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-13.           (((A -> (B -> C)) -> (A -> 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-96477.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-324, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96478
in-theory        96478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-323 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-13.           (((A -> (B -> C)) -> (A -> 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-96478.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-323, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96479
in-theory        96479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-13.           (((A -> (B -> C)) -> (A -> 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-96479.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G and H) -> H)), M:tm-322, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96480
in-theory        96480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-13.           (((A -> (B -> C)) -> (A -> 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-96480.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G and H) -> G)), M:tm-320, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96481
in-theory        96481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-13.           (((A -> (B -> C)) -> (A -> 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-96481.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96482
in-theory        96482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-13.           (((A -> (B -> C)) -> (A -> 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-96482.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (H -> G))), M:tm-315, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96483
in-theory        96483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-311 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-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-13.           (((A -> (B -> C)) -> (A -> 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-96483.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-311, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96484
in-theory        96484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) or G))
theorem-size     69
proof            (modus-ponens tm-310 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-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-13.           (((A -> (B -> C)) -> (A -> 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-96484.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) or G)), M:tm-310, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96485
in-theory        96485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and G)))
theorem-size     71
proof            (modus-ponens tm-309 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm 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-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-13.           (((A -> (B -> C)) -> (A -> 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-96485.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and G))), M:tm-309, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96486
in-theory        96486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96486.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1017, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))
================================================================
tm-name          tm-96487
in-theory        96487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     47
proof            (modus-ponens tm-307 tm-1017 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-3 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-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-13.           (((A -> (B -> C)) -> (A -> 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-96487.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1017, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))
================================================================
tm-name          tm-96488
in-theory        96488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-305 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-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-13.           (((A -> (B -> C)) -> (A -> 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-96488.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-305, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96489
in-theory        96489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-303 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96489.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-303, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96490
in-theory        96490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-270 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96490.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-270, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96491
in-theory        96491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-239 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96491.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-239, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96492
in-theory        96492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     51
proof            (modus-ponens tm-210 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96492.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-210, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96493
in-theory        96493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-183 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96493.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-183, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96494
in-theory        96494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-157 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96494.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-157, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96495
in-theory        96495
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     49
proof            (modus-ponens tm-147 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96495.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-147, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96496
in-theory        96496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-134 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96496.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-134, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96497
in-theory        96497
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     49
proof            (modus-ponens tm-125 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96497.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-125, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96498
in-theory        96498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     49
proof            (modus-ponens tm-113 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96498.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-113, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96499
in-theory        96499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     53
proof            (modus-ponens tm-105 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-96499.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-105, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96500
in-theory        96500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-95 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96500.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-95, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96501
in-theory        96501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-83 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96501.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-83, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96502
in-theory        96502
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-76 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96502.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-76, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96503
in-theory        96503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     45
proof            (modus-ponens tm-69 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96503.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-69, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96504
in-theory        96504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-54 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-13.           (((A -> (B -> C)) -> (A -> 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-96504.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-54, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96505
in-theory        96505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-42 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96505.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-42, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96506
in-theory        96506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-32 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96506.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-32, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96507
in-theory        96507
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 -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-23 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96507.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-23, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96508
in-theory        96508
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-22 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96508.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-22, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96509
in-theory        96509
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-21 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96509.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-21, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96510
in-theory        96510
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 -> (H -> I)) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-20 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-13.           (((A -> (B -> C)) -> (A -> 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-96510.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-20, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96511
in-theory        96511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-19 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96511.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-19, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96512
in-theory        96512
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-7 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-7 tm-5 tm-8 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-96512.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-7, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96513
in-theory        96513
times-derived    1
----------------------------------------------------------------
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-6 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-6 tm-5 tm-8 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-96513.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) or G), M:tm-6, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96514
in-theory        96514
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
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-13.           (((A -> (B -> C)) -> (A -> 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-96514.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))) and A)), M:tm-5, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96515
in-theory        96515
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-1 tm-1017 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> 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-96515.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-1, m:tm-1017, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-96516
in-theory        96516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96516.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-1003, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96517
in-theory        96517
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-992 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96517.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-992, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96518
in-theory        96518
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     57
proof            (modus-ponens tm-980 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96518.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-980, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96519
in-theory        96519
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-930 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96519.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-930, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96520
in-theory        96520
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-893 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96520.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-893, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96521
in-theory        96521
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-855 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96521.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-855, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96522
in-theory        96522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-808 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96522.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-808, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96523
in-theory        96523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-757 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96523.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-757, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96524
in-theory        96524
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))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     55
proof            (modus-ponens tm-708 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96524.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-708, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96525
in-theory        96525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-665 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96525.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-665, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96526
in-theory        96526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-622 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96526.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-622, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96527
in-theory        96527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I or H)))
theorem-size     35
proof            (modus-ponens tm-609 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-96527.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I or H))), M:tm-609, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96528
in-theory        96528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-605 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96528.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-605, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96529
in-theory        96529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96529.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-595, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96530
in-theory        96530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-550 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96530.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-550, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96531
in-theory        96531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-540 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96531.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-540, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96532
in-theory        96532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-530 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96532.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-530, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96533
in-theory        96533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-520 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96533.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-520, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96534
in-theory        96534
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-510 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96534.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-510, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96535
in-theory        96535
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-500 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96535.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-500, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96536
in-theory        96536
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-490 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96536.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-490, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96537
in-theory        96537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-480 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96537.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-480, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96538
in-theory        96538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-469 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96538.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-469, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96539
in-theory        96539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (H or I)))
theorem-size     35
proof            (modus-ponens tm-456 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-96539.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (H or I))), M:tm-456, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96540
in-theory        96540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-453 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96540.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-453, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96541
in-theory        96541
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96541.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-443, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96542
in-theory        96542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-409 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96542.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-409, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96543
in-theory        96543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-400 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96543.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-400, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96544
in-theory        96544
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-391 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96544.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-391, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96545
in-theory        96545
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-382 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96545.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-382, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96546
in-theory        96546
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-373 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96546.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-373, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96547
in-theory        96547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-364 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96547.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-364, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96548
in-theory        96548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-354 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96548.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-354, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96549
in-theory        96549
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-96549.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96550
in-theory        96550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-338 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96550.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-338, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96551
in-theory        96551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96551.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-327, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96552
in-theory        96552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96552.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-326, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96553
in-theory        96553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96553.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-325, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96554
in-theory        96554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96554.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-324, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96555
in-theory        96555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-14.           (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-96555.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-323, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96556
in-theory        96556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> I))
theorem-size     35
proof            (modus-ponens tm-322 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-96556.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> I)), M:tm-322, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96557
in-theory        96557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> H))
theorem-size     35
proof            (modus-ponens tm-320 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-96557.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> H)), M:tm-320, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96558
in-theory        96558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-96558.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96559
in-theory        96559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-96559.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> H))), M:tm-315, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96560
in-theory        96560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96560.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-311, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96561
in-theory        96561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96561.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H)), M:tm-310, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96562
in-theory        96562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96562.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and H))), M:tm-309, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96563
in-theory        96563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1018 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
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-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96563.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-308, m:tm-1018, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))
================================================================
tm-name          tm-96564
in-theory        96564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-1018 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-1.            (A -> (B -> A)), axiom
tm-14.           (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-96564.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1018, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))
================================================================
tm-name          tm-96565
in-theory        96565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-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-14.           (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-96565.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-305, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96566
in-theory        96566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-303 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96566.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-303, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96567
in-theory        96567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-270 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96567.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-270, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96568
in-theory        96568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-239 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96568.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-239, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96569
in-theory        96569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     47
proof            (modus-ponens tm-210 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96569.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-210, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96570
in-theory        96570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-183 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96570.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-183, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96571
in-theory        96571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-157 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96571.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-157, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96572
in-theory        96572
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     45
proof            (modus-ponens tm-147 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96572.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-147, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96573
in-theory        96573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-134 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96573.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-134, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96574
in-theory        96574
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     45
proof            (modus-ponens tm-125 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96574.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-125, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96575
in-theory        96575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-113 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-96575.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-113, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96576
in-theory        96576
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-105 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96576.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-105, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96577
in-theory        96577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-95 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-96577.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-95, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96578
in-theory        96578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-83 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96578.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-83, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96579
in-theory        96579
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-76 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-96579.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-76, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96580
in-theory        96580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-69 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-96580.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-69, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96581
in-theory        96581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-54 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-96581.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-54, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96582
in-theory        96582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-42 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96582.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-42, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96583
in-theory        96583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-32 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96583.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-32, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96584
in-theory        96584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-23 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96584.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-23, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96585
in-theory        96585
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-22 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96585.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-22, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96586
in-theory        96586
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-21 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96586.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-21, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96587
in-theory        96587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-20 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96587.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-20, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96588
in-theory        96588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-19 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-14.           (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-96588.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-19, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96589
in-theory        96589
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-7 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-7 tm-5 tm-8 tm-1 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96589.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-7, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96590
in-theory        96590
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-6 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-6 tm-5 tm-8 tm-1 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96590.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H), M:tm-6, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96591
in-theory        96591
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-96591.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) and A)), M:tm-5, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96592
in-theory        96592
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-1 tm-1018 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (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-96592.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-1, m:tm-1018, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-96593
in-theory        96593
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-96593.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-1003, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96594
in-theory        96594
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     45
proof            (modus-ponens tm-992 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-96594.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-992, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96595
in-theory        96595
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     57
proof            (modus-ponens tm-980 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96595.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-980, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96596
in-theory        96596
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-930 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96596.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-930, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96597
in-theory        96597
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-893 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96597.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-893, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96598
in-theory        96598
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     47
proof            (modus-ponens tm-855 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96598.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-855, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96599
in-theory        96599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-808 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-3)
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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96599.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-808, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96600
in-theory        96600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-757 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96600.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-757, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96601
in-theory        96601
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))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     55
proof            (modus-ponens tm-708 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96601.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-708, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96602
in-theory        96602
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-665 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96602.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-665, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96603
in-theory        96603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-622 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96603.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-622, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96604
in-theory        96604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96604.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (H or G))), M:tm-609, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96605
in-theory        96605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-605 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96605.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-605, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96606
in-theory        96606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96606.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-595, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96607
in-theory        96607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-550 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96607.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-550, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96608
in-theory        96608
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-540 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96608.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-540, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96609
in-theory        96609
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-530 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96609.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-530, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96610
in-theory        96610
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-520 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96610.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-520, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96611
in-theory        96611
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-510 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96611.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-510, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96612
in-theory        96612
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-500 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-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-96612.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-500, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96613
in-theory        96613
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     45
proof            (modus-ponens tm-490 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96613.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-490, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96614
in-theory        96614
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-480 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96614.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-480, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96615
in-theory        96615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-469 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96615.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-469, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96616
in-theory        96616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96616.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (G or H))), M:tm-456, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96617
in-theory        96617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-453 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96617.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-453, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96618
in-theory        96618
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96618.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-443, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96619
in-theory        96619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-409 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96619.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-409, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96620
in-theory        96620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-400 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96620.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-400, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96621
in-theory        96621
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-391 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96621.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-391, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96622
in-theory        96622
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-382 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-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-96622.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-382, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96623
in-theory        96623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     45
proof            (modus-ponens tm-373 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96623.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-373, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96624
in-theory        96624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-364 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96624.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-364, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96625
in-theory        96625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-354 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96625.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-354, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96626
in-theory        96626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96626.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96627
in-theory        96627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     39
proof            (modus-ponens tm-338 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96627.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-338, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96628
in-theory        96628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96628.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-327, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96629
in-theory        96629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96629.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-326, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96630
in-theory        96630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-15.           ((((A -> B) 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-96630.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-325, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96631
in-theory        96631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96631.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-324, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96632
in-theory        96632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96632.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-323, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96633
in-theory        96633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96633.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96634
in-theory        96634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-96634.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96635
in-theory        96635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96635.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96636
in-theory        96636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96636.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96637
in-theory        96637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96637.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-311, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96638
in-theory        96638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) or G))
theorem-size     61
proof            (modus-ponens tm-310 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96638.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) or G)), M:tm-310, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96639
in-theory        96639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and G)))
theorem-size     63
proof            (modus-ponens tm-309 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96639.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and G))), M:tm-309, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96640
in-theory        96640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96640.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1019, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))
================================================================
tm-name          tm-96641
in-theory        96641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-1019 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-15.           ((((A -> B) 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-96641.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1019, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))
================================================================
tm-name          tm-96642
in-theory        96642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96642.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-305, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96643
in-theory        96643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-303 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96643.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-303, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96644
in-theory        96644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-270 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96644.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-270, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96645
in-theory        96645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-239 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96645.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-239, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96646
in-theory        96646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     47
proof            (modus-ponens tm-210 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96646.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-210, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96647
in-theory        96647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-183 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96647.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-183, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96648
in-theory        96648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-157 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96648.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-157, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96649
in-theory        96649
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     45
proof            (modus-ponens tm-147 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96649.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-147, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96650
in-theory        96650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-134 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96650.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-134, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96651
in-theory        96651
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     45
proof            (modus-ponens tm-125 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96651.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-125, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96652
in-theory        96652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     45
proof            (modus-ponens tm-113 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96652.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-113, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96653
in-theory        96653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     49
proof            (modus-ponens tm-105 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96653.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-105, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96654
in-theory        96654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-95 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96654.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-95, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96655
in-theory        96655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-83 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96655.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-83, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96656
in-theory        96656
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     35
proof            (modus-ponens tm-76 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96656.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-76, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96657
in-theory        96657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     41
proof            (modus-ponens tm-69 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96657.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-69, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96658
in-theory        96658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-54 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96658.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-54, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96659
in-theory        96659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-42 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96659.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-42, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96660
in-theory        96660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-32 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96660.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-32, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96661
in-theory        96661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-23 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96661.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-23, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96662
in-theory        96662
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-22 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96662.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-22, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96663
in-theory        96663
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-21 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-15.           ((((A -> B) 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-96663.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-21, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96664
in-theory        96664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-20 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96664.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-20, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96665
in-theory        96665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-19 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96665.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-19, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96666
in-theory        96666
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-7 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-7 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96666.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-7, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96667
in-theory        96667
times-derived    1
----------------------------------------------------------------
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-6 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-6 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96667.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) or G), M:tm-6, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96668
in-theory        96668
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) 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-96668.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))) and A)), M:tm-5, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96669
in-theory        96669
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-1 tm-1019 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96669.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-1, m:tm-1019, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-96670
in-theory        96670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-96670.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I)))), M:tm-1003, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96671
in-theory        96671
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-96671.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I)))), M:tm-992, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96672
in-theory        96672
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96672.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I)))), M:tm-980, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96673
in-theory        96673
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96673.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-930, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96674
in-theory        96674
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96674.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-893, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96675
in-theory        96675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96675.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-855, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96676
in-theory        96676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96676.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-808, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96677
in-theory        96677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96677.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-757, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96678
in-theory        96678
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))) and (H -> ((I and J) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96678.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I)))), M:tm-708, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96679
in-theory        96679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96679.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-665, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96680
in-theory        96680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A 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-96680.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-622, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96681
in-theory        96681
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A 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-96681.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (H or G))), M:tm-609, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96682
in-theory        96682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96682.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-605, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96683
in-theory        96683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96683.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))))), M:tm-595, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96684
in-theory        96684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96684.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-550, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96685
in-theory        96685
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96685.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-540, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96686
in-theory        96686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96686.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-530, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96687
in-theory        96687
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96687.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-520, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96688
in-theory        96688
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96688.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-510, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96689
in-theory        96689
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96689.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-500, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96690
in-theory        96690
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96690.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I)))), M:tm-490, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96691
in-theory        96691
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A 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-96691.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-480, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96692
in-theory        96692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A 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-96692.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-469, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96693
in-theory        96693
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A 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-96693.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (G or H))), M:tm-456, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96694
in-theory        96694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96694.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-453, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96695
in-theory        96695
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96695.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))))), M:tm-443, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96696
in-theory        96696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96696.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-409, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96697
in-theory        96697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96697.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-400, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96698
in-theory        96698
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96698.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-391, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96699
in-theory        96699
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96699.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-382, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96700
in-theory        96700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96700.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I)))), M:tm-373, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96701
in-theory        96701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A 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-96701.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-364, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96702
in-theory        96702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96702.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-354, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96703
in-theory        96703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A 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-96703.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96704
in-theory        96704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96704.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G)))), M:tm-338, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96705
in-theory        96705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96705.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))))), M:tm-327, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96706
in-theory        96706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96706.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))))), M:tm-326, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96707
in-theory        96707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (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-96707.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))))), M:tm-325, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96708
in-theory        96708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96708.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))))), M:tm-324, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96709
in-theory        96709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A 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-96709.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))))), M:tm-323, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96710
in-theory        96710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A 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-96710.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96711
in-theory        96711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-96711.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96712
in-theory        96712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-3.            ((A 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-96712.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96713
in-theory        96713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A 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-96713.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96714
in-theory        96714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96714.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))))), M:tm-311, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96715
in-theory        96715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96715.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) or G)), M:tm-310, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96716
in-theory        96716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
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-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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96716.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and G))), M:tm-309, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96717
in-theory        96717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (D -> ((E and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-308 tm-1020 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (and Em Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96717.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (D -> ((E and F) -> E))), M:tm-308, m:tm-1020, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (and Em Fm) Em))))
================================================================
tm-name          tm-96718
in-theory        96718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1020 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (and Em Fm) Em)))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-1.            (A -> (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-96718.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1020, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (and Em Fm) Em))))
================================================================
tm-name          tm-96719
in-theory        96719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
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-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-3.            ((A 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-96719.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))))), M:tm-305, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96720
in-theory        96720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96720.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-303, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96721
in-theory        96721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96721.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-270, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96722
in-theory        96722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96722.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-239, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96723
in-theory        96723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96723.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I)))), M:tm-210, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96724
in-theory        96724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96724.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-183, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96725
in-theory        96725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A 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-96725.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-157, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96726
in-theory        96726
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96726.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-147, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96727
in-theory        96727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96727.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-134, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96728
in-theory        96728
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96728.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-125, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96729
in-theory        96729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96729.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> I)))), M:tm-113, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96730
in-theory        96730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96730.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-105, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96731
in-theory        96731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-3.            ((A 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-96731.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G)))), M:tm-95, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96732
in-theory        96732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A 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-96732.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-83, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96733
in-theory        96733
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96733.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> F)))), M:tm-76, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96734
in-theory        96734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96734.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G)))), M:tm-69, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96735
in-theory        96735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96735.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-54, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96736
in-theory        96736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96736.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G)))), M:tm-42, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96737
in-theory        96737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96737.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G)))), M:tm-32, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96738
in-theory        96738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96738.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G)))), M:tm-23, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96739
in-theory        96739
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96739.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G)))), M:tm-22, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96740
in-theory        96740
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-1.            (A -> (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-96740.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G)))), M:tm-21, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96741
in-theory        96741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96741.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> H)))), M:tm-20, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96742
in-theory        96742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
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-19.           (A -> ((B -> (C -> B)) and 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-3.            ((A 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-96742.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> G)))), M:tm-19, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96743
in-theory        96743
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-7 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96743.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> F)))), M:tm-7, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96744
in-theory        96744
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-6 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-6 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96744.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))) or G), M:tm-6, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96745
in-theory        96745
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A 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-96745.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> F))) and A)), M:tm-5, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96746
in-theory        96746
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1020 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-1 tm-5 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-3.            ((A 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-96746.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> F)))), M:tm-1, m:tm-1020, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-96747
in-theory        96747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-96747.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-1003, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96748
in-theory        96748
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     45
proof            (modus-ponens tm-992 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-96748.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-992, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96749
in-theory        96749
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     57
proof            (modus-ponens tm-980 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96749.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-980, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96750
in-theory        96750
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     43
proof            (modus-ponens tm-930 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96750.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-930, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96751
in-theory        96751
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     43
proof            (modus-ponens tm-893 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96751.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-893, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96752
in-theory        96752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     47
proof            (modus-ponens tm-855 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96752.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-855, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96753
in-theory        96753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     41
proof            (modus-ponens tm-808 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96753.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-808, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96754
in-theory        96754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     41
proof            (modus-ponens tm-757 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96754.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-757, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96755
in-theory        96755
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))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     55
proof            (modus-ponens tm-708 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96755.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-708, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96756
in-theory        96756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     43
proof            (modus-ponens tm-665 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96756.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-665, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96757
in-theory        96757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-622 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96757.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-622, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96758
in-theory        96758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96758.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (H or G))), M:tm-609, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96759
in-theory        96759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-605 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96759.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-605, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96760
in-theory        96760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96760.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-595, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96761
in-theory        96761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-550 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96761.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-550, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96762
in-theory        96762
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-540 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96762.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-540, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96763
in-theory        96763
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-530 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96763.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-530, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96764
in-theory        96764
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-520 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96764.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-520, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96765
in-theory        96765
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-510 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-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-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-96765.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-510, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96766
in-theory        96766
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-500 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96766.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-500, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96767
in-theory        96767
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     45
proof            (modus-ponens tm-490 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96767.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-490, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96768
in-theory        96768
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-480 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96768.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-480, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96769
in-theory        96769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-469 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96769.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-469, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96770
in-theory        96770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96770.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (G or H))), M:tm-456, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96771
in-theory        96771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-453 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96771.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-453, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96772
in-theory        96772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96772.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-443, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96773
in-theory        96773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-409 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96773.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-409, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96774
in-theory        96774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-400 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96774.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-400, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96775
in-theory        96775
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-391 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-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-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-96775.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-391, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96776
in-theory        96776
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-382 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96776.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-382, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96777
in-theory        96777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     45
proof            (modus-ponens tm-373 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96777.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-373, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96778
in-theory        96778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-364 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96778.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-364, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96779
in-theory        96779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-354 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96779.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-354, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96780
in-theory        96780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96780.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96781
in-theory        96781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     39
proof            (modus-ponens tm-338 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96781.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-338, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96782
in-theory        96782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96782.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-327, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96783
in-theory        96783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-17.           (((A and (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-96783.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-326, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96784
in-theory        96784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96784.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-325, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96785
in-theory        96785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96785.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-324, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96786
in-theory        96786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96786.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-323, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96787
in-theory        96787
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-96787.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96788
in-theory        96788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96788.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96789
in-theory        96789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96789.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96790
in-theory        96790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96790.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96791
in-theory        96791
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96791.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-311, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96792
in-theory        96792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) or G))
theorem-size     61
proof            (modus-ponens tm-310 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96792.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) or G)), M:tm-310, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96793
in-theory        96793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and G)))
theorem-size     63
proof            (modus-ponens tm-309 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96793.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and G))), M:tm-309, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96794
in-theory        96794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-17.           (((A and (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-96794.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1021, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))
================================================================
tm-name          tm-96795
in-theory        96795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-1021 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96795.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1021, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))
================================================================
tm-name          tm-96796
in-theory        96796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96796.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-305, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96797
in-theory        96797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     41
proof            (modus-ponens tm-303 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96797.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-303, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96798
in-theory        96798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-270 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96798.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-270, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96799
in-theory        96799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-239 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96799.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-239, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96800
in-theory        96800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     47
proof            (modus-ponens tm-210 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96800.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-210, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96801
in-theory        96801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-183 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96801.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-183, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96802
in-theory        96802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-157 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96802.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-157, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96803
in-theory        96803
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     45
proof            (modus-ponens tm-147 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96803.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-147, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96804
in-theory        96804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-134 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96804.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-134, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96805
in-theory        96805
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     45
proof            (modus-ponens tm-125 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96805.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-125, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96806
in-theory        96806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     45
proof            (modus-ponens tm-113 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96806.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-113, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96807
in-theory        96807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     49
proof            (modus-ponens tm-105 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96807.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-105, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96808
in-theory        96808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-95 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96808.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-95, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96809
in-theory        96809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-83 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96809.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-83, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96810
in-theory        96810
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     35
proof            (modus-ponens tm-76 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96810.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-76, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96811
in-theory        96811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     41
proof            (modus-ponens tm-69 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96811.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-69, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96812
in-theory        96812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     43
proof            (modus-ponens tm-54 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96812.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-54, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96813
in-theory        96813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-42 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96813.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-42, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96814
in-theory        96814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-32 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96814.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-32, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96815
in-theory        96815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-23 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96815.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-23, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96816
in-theory        96816
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-22 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-17.           (((A and (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-96816.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-22, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96817
in-theory        96817
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-21 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96817.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-21, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96818
in-theory        96818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     43
proof            (modus-ponens tm-20 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96818.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-20, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96819
in-theory        96819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-19 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96819.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-19, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96820
in-theory        96820
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-7 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-7 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96820.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-7, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96821
in-theory        96821
times-derived    1
----------------------------------------------------------------
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-6 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-6 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96821.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) or G), M:tm-6, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96822
in-theory        96822
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (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-96822.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))) and A)), M:tm-5, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96823
in-theory        96823
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-1 tm-1021 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96823.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-1, m:tm-1021, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-96824
in-theory        96824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-96824.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J)))), M:tm-1003, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96825
in-theory        96825
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-96825.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J)))), M:tm-992, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96826
in-theory        96826
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96826.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J)))), M:tm-980, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96827
in-theory        96827
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96827.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-930, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96828
in-theory        96828
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96828.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-893, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96829
in-theory        96829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96829.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-855, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96830
in-theory        96830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-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-96830.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-808, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96831
in-theory        96831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-96831.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-757, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96832
in-theory        96832
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))) and (H -> ((I and J) -> J))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96832.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J)))), M:tm-708, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96833
in-theory        96833
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-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-96833.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-665, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96834
in-theory        96834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96834.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-622, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96835
in-theory        96835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A 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-96835.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (H or G))), M:tm-609, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96836
in-theory        96836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96836.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-605, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96837
in-theory        96837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-96837.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))))), M:tm-595, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96838
in-theory        96838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96838.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-550, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96839
in-theory        96839
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96839.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-540, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96840
in-theory        96840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96840.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-530, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96841
in-theory        96841
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96841.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-520, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96842
in-theory        96842
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96842.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-510, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96843
in-theory        96843
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96843.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-500, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96844
in-theory        96844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96844.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J)))), M:tm-490, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96845
in-theory        96845
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96845.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-480, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96846
in-theory        96846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96846.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-469, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96847
in-theory        96847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A 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-96847.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (G or H))), M:tm-456, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96848
in-theory        96848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96848.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-453, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96849
in-theory        96849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-96849.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))))), M:tm-443, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96850
in-theory        96850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96850.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-409, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96851
in-theory        96851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96851.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-400, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96852
in-theory        96852
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96852.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-391, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96853
in-theory        96853
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96853.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-382, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96854
in-theory        96854
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96854.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J)))), M:tm-373, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96855
in-theory        96855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96855.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-364, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96856
in-theory        96856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96856.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-354, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96857
in-theory        96857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A 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-96857.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96858
in-theory        96858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96858.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H)))), M:tm-338, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96859
in-theory        96859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-96859.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))))), M:tm-327, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96860
in-theory        96860
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-96860.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))))), M:tm-326, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96861
in-theory        96861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-96861.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))))), M:tm-325, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96862
in-theory        96862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96862.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))))), M:tm-324, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96863
in-theory        96863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A 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-96863.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))))), M:tm-323, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96864
in-theory        96864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-96864.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96865
in-theory        96865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A 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-96865.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96866
in-theory        96866
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A 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-96866.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96867
in-theory        96867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A 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-96867.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96868
in-theory        96868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-96868.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))))), M:tm-311, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96869
in-theory        96869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-96869.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) or G)), M:tm-310, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96870
in-theory        96870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96870.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and G))), M:tm-309, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96871
in-theory        96871
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (D -> ((E and F) -> F)))
theorem-size     29
proof            (modus-ponens tm-308 tm-1022 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (and Em Fm) Fm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96871.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (D -> ((E and F) -> F))), M:tm-308, m:tm-1022, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (and Em Fm) Fm))))
================================================================
tm-name          tm-96872
in-theory        96872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1022 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (and Em Fm) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96872.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1022, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> (and Em Fm) Fm))))
================================================================
tm-name          tm-96873
in-theory        96873
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
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-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-4.            ((A 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-96873.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))))), M:tm-305, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96874
in-theory        96874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96874.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-303, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96875
in-theory        96875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96875.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-270, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96876
in-theory        96876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96876.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-239, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96877
in-theory        96877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96877.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J)))), M:tm-210, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96878
in-theory        96878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96878.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-183, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96879
in-theory        96879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96879.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-157, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96880
in-theory        96880
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96880.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-147, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96881
in-theory        96881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96881.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-134, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96882
in-theory        96882
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96882.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-125, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96883
in-theory        96883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96883.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I and J) -> J)))), M:tm-113, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96884
in-theory        96884
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96884.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-105, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96885
in-theory        96885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A 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-96885.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H)))), M:tm-95, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96886
in-theory        96886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96886.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-83, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96887
in-theory        96887
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96887.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> G)))), M:tm-76, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96888
in-theory        96888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96888.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H)))), M:tm-69, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96889
in-theory        96889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-96889.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-54, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96890
in-theory        96890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96890.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H)))), M:tm-42, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96891
in-theory        96891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96891.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H)))), M:tm-32, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96892
in-theory        96892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96892.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H)))), M:tm-23, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96893
in-theory        96893
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-96893.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H)))), M:tm-22, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96894
in-theory        96894
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96894.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H)))), M:tm-21, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96895
in-theory        96895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96895.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H and I) -> I)))), M:tm-20, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96896
in-theory        96896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
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-19.           (A -> ((B -> (C -> B)) and 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-4.            ((A 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-96896.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G and H) -> H)))), M:tm-19, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96897
in-theory        96897
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-7 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96897.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> G)))), M:tm-7, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96898
in-theory        96898
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-6 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-6 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96898.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))) or G), M:tm-6, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96899
in-theory        96899
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> G))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A 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-96899.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> G))) and A)), M:tm-5, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96900
in-theory        96900
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1022 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-4.            ((A 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-96900.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F and G) -> G)))), M:tm-1, m:tm-1022, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-96901
in-theory        96901
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96901.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-1003, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96902
in-theory        96902
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96902.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-992, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96903
in-theory        96903
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96903.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-980, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96904
in-theory        96904
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96904.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-930, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96905
in-theory        96905
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96905.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-893, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96906
in-theory        96906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96906.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-855, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96907
in-theory        96907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96907.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-808, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96908
in-theory        96908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-96908.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-757, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96909
in-theory        96909
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))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96909.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-708, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96910
in-theory        96910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96910.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-665, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96911
in-theory        96911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96911.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-622, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96912
in-theory        96912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-96912.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H or G))), M:tm-609, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96913
in-theory        96913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96913.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-605, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96914
in-theory        96914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (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-96914.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-595, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96915
in-theory        96915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96915.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-550, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96916
in-theory        96916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96916.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-540, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96917
in-theory        96917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96917.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-530, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96918
in-theory        96918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96918.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-520, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96919
in-theory        96919
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96919.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-510, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96920
in-theory        96920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96920.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-500, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96921
in-theory        96921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96921.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-490, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96922
in-theory        96922
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96922.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-480, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96923
in-theory        96923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96923.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-469, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96924
in-theory        96924
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-96924.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (G or H))), M:tm-456, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96925
in-theory        96925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96925.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-453, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96926
in-theory        96926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (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-96926.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-443, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96927
in-theory        96927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96927.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-409, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96928
in-theory        96928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96928.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-400, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96929
in-theory        96929
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96929.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-391, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96930
in-theory        96930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96930.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-382, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96931
in-theory        96931
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96931.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-373, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96932
in-theory        96932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96932.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-364, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96933
in-theory        96933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96933.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-354, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96934
in-theory        96934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-96934.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96935
in-theory        96935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96935.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-338, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96936
in-theory        96936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (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-96936.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-327, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96937
in-theory        96937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (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-96937.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-326, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96938
in-theory        96938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (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-96938.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-325, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96939
in-theory        96939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (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-96939.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-324, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96940
in-theory        96940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-96940.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-323, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96941
in-theory        96941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-96941.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G and H) -> H)), M:tm-322, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96942
in-theory        96942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-96942.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G and H) -> G)), M:tm-320, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96943
in-theory        96943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-96943.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96944
in-theory        96944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-96944.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H -> G))), M:tm-315, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96945
in-theory        96945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (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-96945.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-311, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96946
in-theory        96946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (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-96946.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) or G)), M:tm-310, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96947
in-theory        96947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-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-1.            (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-96947.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and G))), M:tm-309, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96948
in-theory        96948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     33
proof            (modus-ponens tm-308 tm-1023 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
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-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-1.            (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-96948.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (D -> ((E -> (F -> E)) and D))), M:tm-308, m:tm-1023, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (-> Fm Em)) Dm))))
================================================================
tm-name          tm-96949
in-theory        96949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-1023 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-1.            (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-96949.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1023, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (-> Fm Em)) Dm))))
================================================================
tm-name          tm-96950
in-theory        96950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-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-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-96950.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-305, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96951
in-theory        96951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96951.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-303, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96952
in-theory        96952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96952.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-270, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96953
in-theory        96953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96953.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-239, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96954
in-theory        96954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (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-96954.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-210, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96955
in-theory        96955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96955.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-183, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96956
in-theory        96956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96956.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-157, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96957
in-theory        96957
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96957.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-147, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96958
in-theory        96958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96958.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-134, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96959
in-theory        96959
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96959.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-125, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96960
in-theory        96960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96960.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-113, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96961
in-theory        96961
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96961.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-105, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96962
in-theory        96962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96962.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-95, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96963
in-theory        96963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-96963.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-83, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96964
in-theory        96964
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96964.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-76, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96965
in-theory        96965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96965.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-69, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96966
in-theory        96966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-1.            (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-96966.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-54, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96967
in-theory        96967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96967.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-42, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96968
in-theory        96968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96968.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-32, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96969
in-theory        96969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96969.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-23, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96970
in-theory        96970
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96970.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-22, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96971
in-theory        96971
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96971.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-21, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96972
in-theory        96972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-96972.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-20, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96973
in-theory        96973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) 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-19.           (A -> ((B -> (C -> B)) and 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-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-96973.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-19, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96974
in-theory        96974
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-1.            (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-96974.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-7, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96975
in-theory        96975
times-derived    1
----------------------------------------------------------------
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-6 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-1.            (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-96975.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))) or G), M:tm-6, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96976
in-theory        96976
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> F)) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
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-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-96976.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> F)) and E))) and A)), M:tm-5, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96977
in-theory        96977
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1023 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-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-96977.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-1, m:tm-1023, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-96978
in-theory        96978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-1003 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96978.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-1003, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96979
in-theory        96979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-992 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-96979.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-992, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96980
in-theory        96980
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     59
proof            (modus-ponens tm-980 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-96980.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-980, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96981
in-theory        96981
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-930 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96981.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-930, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96982
in-theory        96982
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-893 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-96982.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-893, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96983
in-theory        96983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     49
proof            (modus-ponens tm-855 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-96983.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-855, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96984
in-theory        96984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     43
proof            (modus-ponens tm-808 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-96984.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-808, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96985
in-theory        96985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     43
proof            (modus-ponens tm-757 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96985.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-757, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96986
in-theory        96986
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))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     57
proof            (modus-ponens tm-708 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96986.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-708, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96987
in-theory        96987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-665 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-96987.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-665, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96988
in-theory        96988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-622 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-96988.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-622, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96989
in-theory        96989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96989.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (I or H))), M:tm-609, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96990
in-theory        96990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-605 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-96990.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-605, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96991
in-theory        96991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-20.           (A -> (((B -> (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-96991.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-595, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96992
in-theory        96992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-550 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-96992.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-550, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96993
in-theory        96993
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-540 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-96993.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-540, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96994
in-theory        96994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-530 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-96994.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-530, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96995
in-theory        96995
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-520 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-96995.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-520, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96996
in-theory        96996
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-510 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-96996.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-510, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96997
in-theory        96997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-500 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-96997.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-500, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96998
in-theory        96998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-490 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-96998.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-490, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-96999
in-theory        96999
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-480 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-96999.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-480, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97000
in-theory        97000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-469 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97000.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-469, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97001
in-theory        97001
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97001.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (H or I))), M:tm-456, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97002
in-theory        97002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-453 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97002.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-453, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97003
in-theory        97003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-20.           (A -> (((B -> (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-97003.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-443, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97004
in-theory        97004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-409 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-97004.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-409, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97005
in-theory        97005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-400 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97005.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-400, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97006
in-theory        97006
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-391 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-97006.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-391, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97007
in-theory        97007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-382 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97007.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-382, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97008
in-theory        97008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-373 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97008.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-373, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97009
in-theory        97009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-364 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97009.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-364, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97010
in-theory        97010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-354 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97010.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-354, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97011
in-theory        97011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97011.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97012
in-theory        97012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-338 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97012.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-338, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97013
in-theory        97013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-20.           (A -> (((B -> (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-97013.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-327, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97014
in-theory        97014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97014.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-326, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97015
in-theory        97015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97015.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-325, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97016
in-theory        97016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-97016.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-324, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97017
in-theory        97017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-20.           (A -> (((B -> (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-97017.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-323, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97018
in-theory        97018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97018.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H and I) -> I)), M:tm-322, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97019
in-theory        97019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97019.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H and I) -> H)), M:tm-320, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97020
in-theory        97020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97020.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97021
in-theory        97021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97021.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (I -> H))), M:tm-315, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97022
in-theory        97022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-20.           (A -> (((B -> (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-97022.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-311, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97023
in-theory        97023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) or H))
theorem-size     65
proof            (modus-ponens tm-310 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-20.           (A -> (((B -> (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-97023.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) or H)), M:tm-310, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97024
in-theory        97024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and H)))
theorem-size     67
proof            (modus-ponens tm-309 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 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-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-20.           (A -> (((B -> (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-97024.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and H))), M:tm-309, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97025
in-theory        97025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-20.           (A -> (((B -> (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-97025.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1024, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))
================================================================
tm-name          tm-97026
in-theory        97026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-307 tm-1024 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97026.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1024, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))
================================================================
tm-name          tm-97027
in-theory        97027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-1.            (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-20.           (A -> (((B -> (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-97027.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-305, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97028
in-theory        97028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     43
proof            (modus-ponens tm-303 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97028.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-303, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97029
in-theory        97029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-270 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-97029.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-270, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97030
in-theory        97030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-239 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97030.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-239, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97031
in-theory        97031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     49
proof            (modus-ponens tm-210 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-97031.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-210, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97032
in-theory        97032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-183 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97032.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-183, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97033
in-theory        97033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-157 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-97033.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-157, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97034
in-theory        97034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     47
proof            (modus-ponens tm-147 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97034.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-147, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97035
in-theory        97035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-134 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97035.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-134, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97036
in-theory        97036
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     47
proof            (modus-ponens tm-125 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97036.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-125, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97037
in-theory        97037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-113 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97037.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-113, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97038
in-theory        97038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     51
proof            (modus-ponens tm-105 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97038.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-105, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97039
in-theory        97039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-95 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-97039.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-95, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97040
in-theory        97040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-83 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97040.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-83, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97041
in-theory        97041
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     37
proof            (modus-ponens tm-76 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97041.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-76, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97042
in-theory        97042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     43
proof            (modus-ponens tm-69 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97042.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-69, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97043
in-theory        97043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-54 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-97043.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-54, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97044
in-theory        97044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-42 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97044.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-42, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97045
in-theory        97045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-32 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97045.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-32, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97046
in-theory        97046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-23 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97046.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-23, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97047
in-theory        97047
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-22 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-97047.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-22, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97048
in-theory        97048
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-21 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97048.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-21, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97049
in-theory        97049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-20 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-97049.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-20, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97050
in-theory        97050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-19 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97050.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-19, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97051
in-theory        97051
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-7 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-97051.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-7, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97052
in-theory        97052
times-derived    1
----------------------------------------------------------------
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-6 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-97052.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) or H), M:tm-6, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97053
in-theory        97053
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97053.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) and A)), M:tm-5, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97054
in-theory        97054
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-1 tm-1024 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (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-97054.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-1, m:tm-1024, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-97055
in-theory        97055
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97055.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-1003, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97056
in-theory        97056
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97056.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-992, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97057
in-theory        97057
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97057.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-980, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97058
in-theory        97058
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97058.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-930, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97059
in-theory        97059
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97059.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-893, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97060
in-theory        97060
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97060.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-855, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97061
in-theory        97061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97061.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-808, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97062
in-theory        97062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-97062.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-757, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97063
in-theory        97063
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))) and (H -> (((I and J) -> I) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97063.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-708, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97064
in-theory        97064
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-97064.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-665, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97065
in-theory        97065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97065.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-622, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97066
in-theory        97066
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> 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-97066.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H or G))), M:tm-609, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97067
in-theory        97067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97067.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-605, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97068
in-theory        97068
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-3.            ((A and B) -> 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-97068.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-595, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97069
in-theory        97069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97069.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-550, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97070
in-theory        97070
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97070.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-540, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97071
in-theory        97071
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97071.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-530, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97072
in-theory        97072
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97072.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-520, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97073
in-theory        97073
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97073.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-510, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97074
in-theory        97074
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97074.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-500, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97075
in-theory        97075
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97075.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-490, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97076
in-theory        97076
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97076.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-480, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97077
in-theory        97077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97077.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-469, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97078
in-theory        97078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> 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-97078.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (G or H))), M:tm-456, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97079
in-theory        97079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97079.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-453, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97080
in-theory        97080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-3.            ((A and B) -> 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-97080.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-443, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97081
in-theory        97081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97081.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-409, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97082
in-theory        97082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97082.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-400, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97083
in-theory        97083
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97083.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-391, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97084
in-theory        97084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97084.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-382, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97085
in-theory        97085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97085.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-373, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97086
in-theory        97086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97086.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-364, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97087
in-theory        97087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-3.            ((A and B) -> 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-97087.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-354, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97088
in-theory        97088
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-3.            ((A and B) -> 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-97088.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97089
in-theory        97089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-3.            ((A and B) -> 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-97089.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-338, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97090
in-theory        97090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-3.            ((A and B) -> 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-97090.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-327, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97091
in-theory        97091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-3.            ((A and B) -> 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-97091.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-326, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97092
in-theory        97092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-97092.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-325, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97093
in-theory        97093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-3.            ((A and B) -> 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-97093.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-324, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97094
in-theory        97094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-3.            ((A and B) -> 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-97094.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-323, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97095
in-theory        97095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> 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-97095.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G and H) -> H)), M:tm-322, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97096
in-theory        97096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-97096.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G and H) -> G)), M:tm-320, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97097
in-theory        97097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-3.            ((A and B) -> 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-97097.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97098
in-theory        97098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-3.            ((A and B) -> 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-97098.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H -> G))), M:tm-315, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97099
in-theory        97099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-3.            ((A and B) -> 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-97099.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-311, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97100
in-theory        97100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-3.            ((A and B) -> 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-97100.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) or G)), M:tm-310, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97101
in-theory        97101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 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-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-3.            ((A and B) -> 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-97101.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and G))), M:tm-309, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97102
in-theory        97102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1025 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (and Em Fm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-3.            ((A and B) -> 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-97102.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (D -> (((E and F) -> E) and D))), M:tm-308, m:tm-1025, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (and Em Fm) Em) Dm))))
================================================================
tm-name          tm-97103
in-theory        97103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-1025 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (and Em Fm) Em) Dm)))))
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-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-97103.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1025, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (and Em Fm) Em) Dm))))
================================================================
tm-name          tm-97104
in-theory        97104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-3.            ((A and B) -> 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-97104.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-305, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97105
in-theory        97105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97105.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-303, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97106
in-theory        97106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97106.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-270, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97107
in-theory        97107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97107.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-239, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97108
in-theory        97108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-3.            ((A and B) -> 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-97108.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-210, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97109
in-theory        97109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-3.            ((A and B) -> 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-97109.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-183, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97110
in-theory        97110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97110.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-157, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97111
in-theory        97111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-3.            ((A and B) -> 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-97111.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-147, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97112
in-theory        97112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97112.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-134, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97113
in-theory        97113
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-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-97113.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-125, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97114
in-theory        97114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97114.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-113, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97115
in-theory        97115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-3.            ((A and B) -> 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-97115.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-105, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97116
in-theory        97116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97116.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-95, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97117
in-theory        97117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97117.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-83, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97118
in-theory        97118
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> F) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97118.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> F) and E)))), M:tm-76, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97119
in-theory        97119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97119.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-69, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97120
in-theory        97120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> 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-97120.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-54, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97121
in-theory        97121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97121.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-42, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97122
in-theory        97122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97122.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-32, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97123
in-theory        97123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97123.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-23, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97124
in-theory        97124
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97124.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-22, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97125
in-theory        97125
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97125.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-21, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97126
in-theory        97126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97126.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-20, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97127
in-theory        97127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97127.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-19, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97128
in-theory        97128
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> 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-97128.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> F) and E)))), M:tm-7, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97129
in-theory        97129
times-derived    1
----------------------------------------------------------------
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-6 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> 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-97129.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))) or G), M:tm-6, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97130
in-theory        97130
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> F) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> 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-97130.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> F) and E))) and A)), M:tm-5, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97131
in-theory        97131
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1025 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and B) -> 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-97131.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> F) and E)))), M:tm-1, m:tm-1025, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-97132
in-theory        97132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97132.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-1003, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97133
in-theory        97133
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97133.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-992, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97134
in-theory        97134
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97134.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-980, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97135
in-theory        97135
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97135.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-930, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97136
in-theory        97136
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97136.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-893, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97137
in-theory        97137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97137.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-855, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97138
in-theory        97138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97138.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-808, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97139
in-theory        97139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-97139.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-757, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97140
in-theory        97140
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))) and (H -> (((I and J) -> J) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97140.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-708, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97141
in-theory        97141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-97141.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-665, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97142
in-theory        97142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97142.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-622, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97143
in-theory        97143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> 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-97143.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H or G))), M:tm-609, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97144
in-theory        97144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97144.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-605, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97145
in-theory        97145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and B) -> 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-97145.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-595, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97146
in-theory        97146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97146.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-550, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97147
in-theory        97147
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97147.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-540, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97148
in-theory        97148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97148.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-530, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97149
in-theory        97149
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97149.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-520, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97150
in-theory        97150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97150.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-510, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97151
in-theory        97151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97151.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-500, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97152
in-theory        97152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97152.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-490, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97153
in-theory        97153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97153.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-480, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97154
in-theory        97154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97154.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-469, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97155
in-theory        97155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> 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-97155.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (G or H))), M:tm-456, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97156
in-theory        97156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97156.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-453, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97157
in-theory        97157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and B) -> 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-97157.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-443, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97158
in-theory        97158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97158.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-409, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97159
in-theory        97159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97159.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-400, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97160
in-theory        97160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97160.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-391, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97161
in-theory        97161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97161.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-382, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97162
in-theory        97162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97162.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-373, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97163
in-theory        97163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97163.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-364, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97164
in-theory        97164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-4.            ((A and B) -> 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-97164.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-354, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97165
in-theory        97165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> 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-97165.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97166
in-theory        97166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-4.            ((A and B) -> 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-97166.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-338, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97167
in-theory        97167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-4.            ((A and B) -> 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-97167.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-327, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97168
in-theory        97168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-97168.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-326, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97169
in-theory        97169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-4.            ((A and B) -> 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-97169.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-325, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97170
in-theory        97170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> 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-97170.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-324, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97171
in-theory        97171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-4.            ((A and B) -> 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-97171.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-323, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97172
in-theory        97172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-97172.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G and H) -> H)), M:tm-322, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97173
in-theory        97173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> 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-97173.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G and H) -> G)), M:tm-320, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97174
in-theory        97174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) 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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-4.            ((A and B) -> 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-97174.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97175
in-theory        97175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> 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-97175.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H -> G))), M:tm-315, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97176
in-theory        97176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> 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-97176.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-311, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97177
in-theory        97177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> 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-97177.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) or G)), M:tm-310, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97178
in-theory        97178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 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-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-4.            ((A and B) -> 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-97178.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and G))), M:tm-309, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97179
in-theory        97179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1026 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-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-97179.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (D -> (((E and F) -> F) and D))), M:tm-308, m:tm-1026, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (and Em Fm) Fm) Dm))))
================================================================
tm-name          tm-97180
in-theory        97180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-1026 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-4.            ((A and B) -> 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-97180.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1026, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (and Em Fm) Fm) Dm))))
================================================================
tm-name          tm-97181
in-theory        97181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-4.            ((A and B) -> 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-97181.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-305, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97182
in-theory        97182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97182.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-303, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97183
in-theory        97183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97183.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-270, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97184
in-theory        97184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97184.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-239, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97185
in-theory        97185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-4.            ((A and B) -> 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-97185.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-210, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97186
in-theory        97186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-4.            ((A and B) -> 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-97186.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-183, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97187
in-theory        97187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97187.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-157, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97188
in-theory        97188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-97188.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-147, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97189
in-theory        97189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97189.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-134, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97190
in-theory        97190
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> 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-97190.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-125, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97191
in-theory        97191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97191.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-113, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97192
in-theory        97192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97192.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-105, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97193
in-theory        97193
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97193.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-95, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97194
in-theory        97194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97194.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-83, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97195
in-theory        97195
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> G) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97195.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> G) and E)))), M:tm-76, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97196
in-theory        97196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97196.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-69, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97197
in-theory        97197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> 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-97197.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-54, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97198
in-theory        97198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97198.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-42, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97199
in-theory        97199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97199.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-32, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97200
in-theory        97200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97200.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-23, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97201
in-theory        97201
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97201.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-22, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97202
in-theory        97202
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97202.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-21, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97203
in-theory        97203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-4.            ((A and B) -> 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-97203.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-20, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97204
in-theory        97204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97204.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-19, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97205
in-theory        97205
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> 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-97205.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> G) and E)))), M:tm-7, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97206
in-theory        97206
times-derived    1
----------------------------------------------------------------
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-6 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> 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-97206.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))) or G), M:tm-6, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97207
in-theory        97207
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> G) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> 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-97207.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> G) and E))) and A)), M:tm-5, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97208
in-theory        97208
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1026 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> 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-97208.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F and G) -> G) and E)))), M:tm-1, m:tm-1026, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-97209
in-theory        97209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97209.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-1003, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97210
in-theory        97210
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     41
proof            (modus-ponens tm-992 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97210.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-992, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97211
in-theory        97211
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     53
proof            (modus-ponens tm-980 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97211.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-980, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97212
in-theory        97212
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     39
proof            (modus-ponens tm-930 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97212.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-930, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97213
in-theory        97213
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     39
proof            (modus-ponens tm-893 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97213.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-893, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97214
in-theory        97214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     43
proof            (modus-ponens tm-855 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97214.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-855, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97215
in-theory        97215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     37
proof            (modus-ponens tm-808 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97215.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-808, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97216
in-theory        97216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     37
proof            (modus-ponens tm-757 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-97216.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-757, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97217
in-theory        97217
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))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     51
proof            (modus-ponens tm-708 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97217.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-708, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97218
in-theory        97218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     39
proof            (modus-ponens tm-665 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-97218.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-665, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97219
in-theory        97219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-622 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97219.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-622, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97220
in-theory        97220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H or G)))
theorem-size     31
proof            (modus-ponens tm-609 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-97220.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H or G))), M:tm-609, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97221
in-theory        97221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-605 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97221.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-605, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97222
in-theory        97222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-97222.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-595, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97223
in-theory        97223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-550 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97223.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-550, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97224
in-theory        97224
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-540 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97224.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-540, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97225
in-theory        97225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-530 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97225.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-530, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97226
in-theory        97226
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-520 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97226.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-520, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97227
in-theory        97227
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-510 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97227.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-510, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97228
in-theory        97228
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-500 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97228.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-500, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97229
in-theory        97229
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     41
proof            (modus-ponens tm-490 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97229.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-490, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97230
in-theory        97230
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-480 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97230.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-480, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97231
in-theory        97231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-469 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97231.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-469, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97232
in-theory        97232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (G or H)))
theorem-size     31
proof            (modus-ponens tm-456 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-97232.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (G or H))), M:tm-456, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97233
in-theory        97233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-453 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97233.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-453, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97234
in-theory        97234
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-97234.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-443, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97235
in-theory        97235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-409 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97235.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-409, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97236
in-theory        97236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-400 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97236.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-400, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97237
in-theory        97237
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-391 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97237.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-391, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97238
in-theory        97238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-382 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97238.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-382, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97239
in-theory        97239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     41
proof            (modus-ponens tm-373 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97239.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-373, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97240
in-theory        97240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-364 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97240.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-364, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97241
in-theory        97241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-354 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97241.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-354, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97242
in-theory        97242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97242.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97243
in-theory        97243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     35
proof            (modus-ponens tm-338 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97243.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-338, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97244
in-theory        97244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-97244.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-327, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97245
in-theory        97245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-97245.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-326, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97246
in-theory        97246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97246.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-325, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97247
in-theory        97247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97247.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-324, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97248
in-theory        97248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97248.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-323, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97249
in-theory        97249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G and H) -> H))
theorem-size     31
proof            (modus-ponens tm-322 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-97249.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G and H) -> H)), M:tm-322, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97250
in-theory        97250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G and H) -> G))
theorem-size     31
proof            (modus-ponens tm-320 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97250.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G and H) -> G)), M:tm-320, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97251
in-theory        97251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-97251.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97252
in-theory        97252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H -> G)))
theorem-size     31
proof            (modus-ponens tm-315 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-97252.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H -> G))), M:tm-315, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97253
in-theory        97253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-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-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-97253.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-311, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97254
in-theory        97254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) or G))
theorem-size     53
proof            (modus-ponens tm-310 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-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-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-97254.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) or G)), M:tm-310, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97255
in-theory        97255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and G)))
theorem-size     55
proof            (modus-ponens tm-309 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 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-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-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-97255.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and G))), M:tm-309, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97256
in-theory        97256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1027 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-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-97256.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-308, m:tm-1027, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))
================================================================
tm-name          tm-97257
in-theory        97257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-307 tm-1027 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
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-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-97257.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1027, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))
================================================================
tm-name          tm-97258
in-theory        97258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-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-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-97258.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-305, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97259
in-theory        97259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     37
proof            (modus-ponens tm-303 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97259.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-303, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97260
in-theory        97260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-270 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97260.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-270, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97261
in-theory        97261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-239 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97261.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-239, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97262
in-theory        97262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     43
proof            (modus-ponens tm-210 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97262.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-210, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97263
in-theory        97263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-183 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97263.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-183, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97264
in-theory        97264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-157 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97264.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-157, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97265
in-theory        97265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     41
proof            (modus-ponens tm-147 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-97265.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-147, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97266
in-theory        97266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-134 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97266.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-134, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97267
in-theory        97267
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     41
proof            (modus-ponens tm-125 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97267.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-125, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97268
in-theory        97268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     41
proof            (modus-ponens tm-113 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97268.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-113, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97269
in-theory        97269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     45
proof            (modus-ponens tm-105 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97269.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-105, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97270
in-theory        97270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-95 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-97270.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-95, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97271
in-theory        97271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-83 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97271.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-83, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97272
in-theory        97272
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     31
proof            (modus-ponens tm-76 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-10 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97272.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-76, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97273
in-theory        97273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     37
proof            (modus-ponens tm-69 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-97273.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-69, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97274
in-theory        97274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     39
proof            (modus-ponens tm-54 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-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-97274.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-54, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97275
in-theory        97275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-42 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97275.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-42, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97276
in-theory        97276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-32 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97276.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-32, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97277
in-theory        97277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-23 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97277.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-23, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97278
in-theory        97278
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-22 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97278.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-22, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97279
in-theory        97279
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-21 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97279.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-21, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97280
in-theory        97280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     39
proof            (modus-ponens tm-20 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97280.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-20, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97281
in-theory        97281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-19 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97281.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-19, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97282
in-theory        97282
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-7 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
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-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-97282.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-7, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97283
in-theory        97283
times-derived    1
----------------------------------------------------------------
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-6 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
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-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-97283.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))) or G), M:tm-6, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97284
in-theory        97284
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> (F and G))) and E))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-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-97284.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> (F and G))) and E))) and A)), M:tm-5, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97285
in-theory        97285
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-1 tm-1027 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
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-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-97285.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-1, m:tm-1027, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-97286
in-theory        97286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97286.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-1003, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97287
in-theory        97287
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97287.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-992, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97288
in-theory        97288
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97288.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-980, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97289
in-theory        97289
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97289.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-930, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97290
in-theory        97290
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97290.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-893, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97291
in-theory        97291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97291.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-855, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97292
in-theory        97292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97292.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-808, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97293
in-theory        97293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97293.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-757, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97294
in-theory        97294
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))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97294.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-708, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97295
in-theory        97295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97295.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-665, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97296
in-theory        97296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97296.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-622, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97297
in-theory        97297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-97297.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G or F))), M:tm-609, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97298
in-theory        97298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97298.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-605, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97299
in-theory        97299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-97299.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-595, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97300
in-theory        97300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97300.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-550, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97301
in-theory        97301
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97301.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-540, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97302
in-theory        97302
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97302.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-530, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97303
in-theory        97303
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97303.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-520, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97304
in-theory        97304
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97304.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-510, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97305
in-theory        97305
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97305.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-500, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97306
in-theory        97306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97306.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-490, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97307
in-theory        97307
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97307.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-480, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97308
in-theory        97308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97308.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-469, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97309
in-theory        97309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-97309.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (F or G))), M:tm-456, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97310
in-theory        97310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97310.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-453, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97311
in-theory        97311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-97311.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (F or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-443, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97312
in-theory        97312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97312.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-409, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97313
in-theory        97313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97313.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-400, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97314
in-theory        97314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97314.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-391, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97315
in-theory        97315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97315.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-382, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97316
in-theory        97316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97316.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-373, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97317
in-theory        97317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97317.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-364, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97318
in-theory        97318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97318.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-354, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97319
in-theory        97319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97319.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97320
in-theory        97320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97320.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-338, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97321
in-theory        97321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-97321.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-327, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97322
in-theory        97322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-97322.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F and G) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-326, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97323
in-theory        97323
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-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-97323.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F and G) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-325, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97324
in-theory        97324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-97324.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-324, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97325
in-theory        97325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97325.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-323, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97326
in-theory        97326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97326.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F and G) -> G)), M:tm-322, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97327
in-theory        97327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97327.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F and G) -> F)), M:tm-320, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97328
in-theory        97328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-97328.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97329
in-theory        97329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-97329.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G -> F))), M:tm-315, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97330
in-theory        97330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-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-97330.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-311, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97331
in-theory        97331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-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-97331.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) or F)), M:tm-310, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97332
in-theory        97332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 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-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-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-97332.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and F))), M:tm-309, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97333
in-theory        97333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((D -> E) -> (D -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-1028 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> Dm (and Dm Em))))))
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-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-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-97333.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((D -> E) -> (D -> (D and E)))), M:tm-308, m:tm-1028, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> Dm (and Dm Em)))))
================================================================
tm-name          tm-97334
in-theory        97334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-1028 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> Dm (and 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-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-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-97334.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1028, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> Dm (and Dm Em)))))
================================================================
tm-name          tm-97335
in-theory        97335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97335.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-305, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97336
in-theory        97336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97336.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-303, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97337
in-theory        97337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97337.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-270, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97338
in-theory        97338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97338.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-239, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97339
in-theory        97339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97339.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-210, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97340
in-theory        97340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97340.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-183, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97341
in-theory        97341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97341.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-157, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97342
in-theory        97342
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97342.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-147, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97343
in-theory        97343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97343.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-134, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97344
in-theory        97344
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97344.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-125, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97345
in-theory        97345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97345.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-113, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97346
in-theory        97346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97346.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-105, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97347
in-theory        97347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-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-97347.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-95, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97348
in-theory        97348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97348.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-83, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97349
in-theory        97349
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97349.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> (E and F))))), M:tm-76, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97350
in-theory        97350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97350.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-69, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97351
in-theory        97351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-97351.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-54, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97352
in-theory        97352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97352.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-42, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97353
in-theory        97353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97353.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-32, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97354
in-theory        97354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97354.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-23, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97355
in-theory        97355
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97355.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-22, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97356
in-theory        97356
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-97356.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-21, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97357
in-theory        97357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97357.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-20, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97358
in-theory        97358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97358.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-19, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97359
in-theory        97359
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97359.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> (E and F))))), M:tm-7, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97360
in-theory        97360
times-derived    1
----------------------------------------------------------------
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-6 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97360.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))) or F), M:tm-6, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97361
in-theory        97361
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> (E and F)))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97361.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> (E and F)))) and A)), M:tm-5, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97362
in-theory        97362
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1028 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
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-97362.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (E -> (E and F))))), M:tm-1, m:tm-1028, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-97363
in-theory        97363
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97363.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-1003, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97364
in-theory        97364
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97364.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-992, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97365
in-theory        97365
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-1)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97365.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-980, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97366
in-theory        97366
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97366.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-930, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97367
in-theory        97367
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97367.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-893, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97368
in-theory        97368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97368.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-855, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97369
in-theory        97369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97369.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-808, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97370
in-theory        97370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-97370.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-757, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97371
in-theory        97371
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))) and (H -> (I -> (J -> (I and J))))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97371.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-708, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97372
in-theory        97372
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-1)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97372.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-665, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97373
in-theory        97373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97373.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-622, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97374
in-theory        97374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-97374.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H or G))), M:tm-609, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97375
in-theory        97375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97375.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-605, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97376
in-theory        97376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> 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-97376.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-595, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97377
in-theory        97377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97377.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-550, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97378
in-theory        97378
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97378.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-540, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97379
in-theory        97379
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97379.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-530, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97380
in-theory        97380
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97380.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-520, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97381
in-theory        97381
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97381.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-510, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97382
in-theory        97382
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97382.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-500, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97383
in-theory        97383
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97383.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-490, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97384
in-theory        97384
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97384.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-480, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97385
in-theory        97385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97385.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-469, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97386
in-theory        97386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-97386.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (G or H))), M:tm-456, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97387
in-theory        97387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97387.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-453, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97388
in-theory        97388
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-1.            (A -> (B -> 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-97388.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-443, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97389
in-theory        97389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97389.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-409, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97390
in-theory        97390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97390.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-400, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97391
in-theory        97391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97391.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-391, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97392
in-theory        97392
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97392.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-382, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97393
in-theory        97393
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97393.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-373, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97394
in-theory        97394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97394.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-364, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97395
in-theory        97395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97395.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-354, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97396
in-theory        97396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-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-97396.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97397
in-theory        97397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97397.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-338, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97398
in-theory        97398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> 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-97398.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-327, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97399
in-theory        97399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-1.            (A -> (B -> 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-97399.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-326, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97400
in-theory        97400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-1.            (A -> (B -> 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-97400.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-325, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97401
in-theory        97401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-1.            (A -> (B -> 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-97401.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-324, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97402
in-theory        97402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-97402.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-323, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97403
in-theory        97403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-97403.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G and H) -> H)), M:tm-322, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97404
in-theory        97404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-97404.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G and H) -> G)), M:tm-320, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97405
in-theory        97405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-97405.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97406
in-theory        97406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-97406.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H -> G))), M:tm-315, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97407
in-theory        97407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> 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-97407.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-311, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97408
in-theory        97408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> 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-97408.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) or G)), M:tm-310, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97409
in-theory        97409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-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-1.            (A -> (B -> 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-97409.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and G))), M:tm-309, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97410
in-theory        97410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (D -> (E -> (F -> (E and F)))))
theorem-size     33
proof            (modus-ponens tm-308 tm-1029 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (-> Fm (and Em Fm)))))))
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-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-1.            (A -> (B -> 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-97410.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (D -> (E -> (F -> (E and F))))), M:tm-308, m:tm-1029, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (-> Fm (and Em Fm))))))
================================================================
tm-name          tm-97411
in-theory        97411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-1029 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (-> Fm (and Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-1.            (A -> (B -> 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-97411.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1029, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (-> Fm (and Em Fm))))))
================================================================
tm-name          tm-97412
in-theory        97412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-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-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-97412.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-305, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97413
in-theory        97413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97413.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-303, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97414
in-theory        97414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97414.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-270, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97415
in-theory        97415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97415.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-239, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97416
in-theory        97416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-1.            (A -> (B -> 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-97416.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-210, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97417
in-theory        97417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97417.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-183, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97418
in-theory        97418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97418.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-157, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97419
in-theory        97419
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97419.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-147, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97420
in-theory        97420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97420.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-134, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97421
in-theory        97421
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97421.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-125, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97422
in-theory        97422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97422.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-113, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97423
in-theory        97423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97423.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-105, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97424
in-theory        97424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97424.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-95, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97425
in-theory        97425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97425.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-83, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97426
in-theory        97426
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97426.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> (F and G)))))), M:tm-76, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97427
in-theory        97427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97427.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-69, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97428
in-theory        97428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> 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-97428.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-54, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97429
in-theory        97429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97429.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-42, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97430
in-theory        97430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97430.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-32, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97431
in-theory        97431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97431.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-23, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97432
in-theory        97432
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97432.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-22, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97433
in-theory        97433
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97433.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-21, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97434
in-theory        97434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-1.            (A -> (B -> 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-97434.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-20, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97435
in-theory        97435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or 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-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-97435.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-19, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97436
in-theory        97436
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-7 tm-5 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> 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-97436.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> (F and G)))))), M:tm-7, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97437
in-theory        97437
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-6 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-6 tm-5 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> 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-97437.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))) or G), M:tm-6, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97438
in-theory        97438
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> (F and G))))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
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-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-97438.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> (F and G))))) and A)), M:tm-5, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97439
in-theory        97439
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1029 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-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-97439.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G -> (F and G)))))), M:tm-1, m:tm-1029, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-97440
in-theory        97440
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-97440.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J))), M:tm-1003, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97441
in-theory        97441
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-97441.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J))), M:tm-992, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97442
in-theory        97442
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97442.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J))), M:tm-980, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97443
in-theory        97443
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97443.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-930, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97444
in-theory        97444
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-97444.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-893, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97445
in-theory        97445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97445.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-855, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97446
in-theory        97446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97446.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-808, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97447
in-theory        97447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-97447.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-757, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97448
in-theory        97448
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))) and ((H -> (I -> H)) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97448.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J))), M:tm-708, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97449
in-theory        97449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-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-97449.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-665, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97450
in-theory        97450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97450.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-622, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97451
in-theory        97451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), 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-97451.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (H or G))), M:tm-609, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97452
in-theory        97452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97452.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-605, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97453
in-theory        97453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97453.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)))), M:tm-595, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97454
in-theory        97454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97454.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-550, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97455
in-theory        97455
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97455.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-540, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97456
in-theory        97456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97456.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-530, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97457
in-theory        97457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97457.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-520, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97458
in-theory        97458
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97458.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-510, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97459
in-theory        97459
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97459.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-500, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97460
in-theory        97460
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97460.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J))), M:tm-490, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97461
in-theory        97461
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97461.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-480, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97462
in-theory        97462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97462.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-469, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97463
in-theory        97463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-97463.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (G or H))), M:tm-456, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97464
in-theory        97464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97464.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-453, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97465
in-theory        97465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-97465.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)))), M:tm-443, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97466
in-theory        97466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97466.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-409, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97467
in-theory        97467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97467.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-400, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97468
in-theory        97468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97468.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-391, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97469
in-theory        97469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97469.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-382, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97470
in-theory        97470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97470.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J))), M:tm-373, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97471
in-theory        97471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97471.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-364, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97472
in-theory        97472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97472.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-354, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97473
in-theory        97473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), 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-97473.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97474
in-theory        97474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97474.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H))), M:tm-338, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97475
in-theory        97475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97475.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)))), M:tm-327, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97476
in-theory        97476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97476.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)))), M:tm-326, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97477
in-theory        97477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97477.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)))), M:tm-325, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97478
in-theory        97478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97478.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)))), M:tm-324, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97479
in-theory        97479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97479.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)))), M:tm-323, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97480
in-theory        97480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), 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-97480.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G and H) -> H)), M:tm-322, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97481
in-theory        97481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), 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-97481.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G and H) -> G)), M:tm-320, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97482
in-theory        97482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97482.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97483
in-theory        97483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), 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-97483.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (H -> G))), M:tm-315, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97484
in-theory        97484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97484.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)))), M:tm-311, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97485
in-theory        97485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-97485.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) or G)), M:tm-310, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97486
in-theory        97486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97486.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and G))), M:tm-309, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97487
in-theory        97487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((D -> (E -> D)) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-1030 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (-> Em Dm)) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97487.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((D -> (E -> D)) or F)), M:tm-308, m:tm-1030, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (-> Em Dm)) Fm)))
================================================================
tm-name          tm-97488
in-theory        97488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1030 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (-> Em Dm)) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97488.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1030, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (-> Em Dm)) Fm)))
================================================================
tm-name          tm-97489
in-theory        97489
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
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-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-6.            (A -> (A or B)), 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-97489.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)))), M:tm-305, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97490
in-theory        97490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97490.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-303, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97491
in-theory        97491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97491.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-270, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97492
in-theory        97492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97492.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-239, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97493
in-theory        97493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97493.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J))), M:tm-210, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97494
in-theory        97494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97494.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-183, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97495
in-theory        97495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97495.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-157, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97496
in-theory        97496
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97496.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-147, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97497
in-theory        97497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97497.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-134, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97498
in-theory        97498
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97498.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-125, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97499
in-theory        97499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97499.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> H)) or J))), M:tm-113, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97500
in-theory        97500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97500.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-105, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97501
in-theory        97501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97501.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H))), M:tm-95, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97502
in-theory        97502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97502.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-83, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97503
in-theory        97503
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97503.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) or G))), M:tm-76, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97504
in-theory        97504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97504.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H))), M:tm-69, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97505
in-theory        97505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-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-97505.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-54, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97506
in-theory        97506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97506.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H))), M:tm-42, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97507
in-theory        97507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97507.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H))), M:tm-32, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97508
in-theory        97508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97508.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H))), M:tm-23, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97509
in-theory        97509
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97509.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H))), M:tm-22, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97510
in-theory        97510
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97510.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H))), M:tm-21, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97511
in-theory        97511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97511.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> G)) or I))), M:tm-20, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97512
in-theory        97512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97512.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> F)) or H))), M:tm-19, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97513
in-theory        97513
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-7 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97513.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) or G))), M:tm-7, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97514
in-theory        97514
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-6 tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-97514.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)) or G), M:tm-6, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97515
in-theory        97515
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-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-97515.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) or G)) and A)), M:tm-5, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97516
in-theory        97516
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-1030 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-97516.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) or G))), M:tm-1, m:tm-1030, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-97517
in-theory        97517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-1003 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97517.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-1003, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97518
in-theory        97518
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-992 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97518.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-992, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97519
in-theory        97519
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     57
proof            (modus-ponens tm-980 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-6 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97519.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-980, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97520
in-theory        97520
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-930 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97520.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-930, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97521
in-theory        97521
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-893 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97521.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-893, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97522
in-theory        97522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     47
proof            (modus-ponens tm-855 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-6 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97522.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-855, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97523
in-theory        97523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-808 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97523.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-808, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97524
in-theory        97524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-757 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 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-54.           (A -> (((B -> C) -> ((C -> 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-97524.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-757, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97525
in-theory        97525
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))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     55
proof            (modus-ponens tm-708 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97525.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-708, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97526
in-theory        97526
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-665 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97526.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-665, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97527
in-theory        97527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-622 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97527.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-622, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97528
in-theory        97528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97528.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I or H))), M:tm-609, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97529
in-theory        97529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-605 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97529.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-605, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97530
in-theory        97530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-595 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97530.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-595, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97531
in-theory        97531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-550 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97531.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-550, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97532
in-theory        97532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-540 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97532.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-540, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97533
in-theory        97533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-530 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97533.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-530, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97534
in-theory        97534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-520 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97534.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-520, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97535
in-theory        97535
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-510 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97535.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-510, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97536
in-theory        97536
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-500 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97536.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-500, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97537
in-theory        97537
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-490 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97537.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-490, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97538
in-theory        97538
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-480 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97538.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-480, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97539
in-theory        97539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-469 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97539.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-469, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97540
in-theory        97540
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-97540.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (H or I))), M:tm-456, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97541
in-theory        97541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-453 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97541.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-453, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97542
in-theory        97542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-443 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-27.           (((A -> (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-97542.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-443, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97543
in-theory        97543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-409 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97543.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-409, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97544
in-theory        97544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-400 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97544.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-400, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97545
in-theory        97545
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-391 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97545.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-391, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97546
in-theory        97546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-382 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97546.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-382, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97547
in-theory        97547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-373 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-97547.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-373, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97548
in-theory        97548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-364 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
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-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97548.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-364, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97549
in-theory        97549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-354 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97549.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-354, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97550
in-theory        97550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97550.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I -> (H and I)))), M:tm-341, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97551
in-theory        97551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-338 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97551.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-338, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97552
in-theory        97552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     67
proof            (modus-ponens tm-327 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97552.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-327, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97553
in-theory        97553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-326 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97553.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-326, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97554
in-theory        97554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-325 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97554.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-325, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97555
in-theory        97555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     73
proof            (modus-ponens tm-324 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97555.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-324, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97556
in-theory        97556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-323 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97556.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-323, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97557
in-theory        97557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97557.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H and I) -> I)), M:tm-322, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97558
in-theory        97558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97558.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H and I) -> H)), M:tm-320, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97559
in-theory        97559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (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-97559.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97560
in-theory        97560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97560.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I -> H))), M:tm-315, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97561
in-theory        97561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     61
proof            (modus-ponens tm-311 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (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-97561.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-311, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97562
in-theory        97562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
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-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-27.           (((A -> (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-97562.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) or H)), M:tm-310, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97563
in-theory        97563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97563.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and H))), M:tm-309, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97564
in-theory        97564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1031 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97564.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1031, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))
================================================================
tm-name          tm-97565
in-theory        97565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-1031 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97565.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1031, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))
================================================================
tm-name          tm-97566
in-theory        97566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     61
proof            (modus-ponens tm-305 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (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-97566.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-305, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97567
in-theory        97567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-303 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-97567.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-303, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97568
in-theory        97568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-270 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97568.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-270, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97569
in-theory        97569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-239 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97569.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-239, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97570
in-theory        97570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     47
proof            (modus-ponens tm-210 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97570.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-210, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97571
in-theory        97571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-183 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97571.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-183, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97572
in-theory        97572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-157 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97572.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-157, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97573
in-theory        97573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     45
proof            (modus-ponens tm-147 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97573.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-147, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97574
in-theory        97574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-134 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97574.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-134, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97575
in-theory        97575
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     45
proof            (modus-ponens tm-125 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97575.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-125, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97576
in-theory        97576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-113 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97576.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-113, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97577
in-theory        97577
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-105 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97577.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-105, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97578
in-theory        97578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-95 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97578.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-95, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97579
in-theory        97579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-83 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97579.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-83, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97580
in-theory        97580
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     35
proof            (modus-ponens tm-76 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-6 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-97580.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-76, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97581
in-theory        97581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-69 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-6 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-97581.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-69, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97582
in-theory        97582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-54 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-97582.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-54, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97583
in-theory        97583
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-42 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97583.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-42, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97584
in-theory        97584
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-32 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 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-32.           (A -> ((B -> (B or C)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97584.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-32, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97585
in-theory        97585
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-23 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-97585.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-23, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97586
in-theory        97586
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-22 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97586.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-22, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97587
in-theory        97587
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))) or I)))
theorem-size     35
proof            (modus-ponens tm-21 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97587.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-21, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97588
in-theory        97588
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))) or J)))
theorem-size     43
proof            (modus-ponens tm-20 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-27.           (((A -> (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-97588.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-20, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97589
in-theory        97589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-19 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6 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-54.           (A -> (((B -> C) -> ((C -> 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-97589.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-19, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97590
in-theory        97590
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-7 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-7 tm-5 tm-8 tm-6 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97590.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-7, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97591
in-theory        97591
times-derived    1
----------------------------------------------------------------
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-6 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-6 tm-5 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97591.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) or H), M:tm-6, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97592
in-theory        97592
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-6 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-54.           (A -> (((B -> C) -> ((C -> 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-97592.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)) and A)), M:tm-5, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97593
in-theory        97593
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-1 tm-1031 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-1 tm-5 tm-8 tm-6 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (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-97593.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-1, m:tm-1031, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-97594
in-theory        97594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-97594.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J))), M:tm-1003, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97595
in-theory        97595
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-97595.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J))), M:tm-992, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97596
in-theory        97596
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97596.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J))), M:tm-980, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97597
in-theory        97597
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97597.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-930, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97598
in-theory        97598
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-97598.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-893, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97599
in-theory        97599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97599.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-855, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97600
in-theory        97600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97600.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-808, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97601
in-theory        97601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-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-97601.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-757, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97602
in-theory        97602
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))) and (((H and I) -> H) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97602.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J))), M:tm-708, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97603
in-theory        97603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-97603.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-665, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97604
in-theory        97604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97604.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-622, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97605
in-theory        97605
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97605.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (H or G))), M:tm-609, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97606
in-theory        97606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97606.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-605, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97607
in-theory        97607
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97607.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)))), M:tm-595, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97608
in-theory        97608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-3.            ((A and 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-97608.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-550, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97609
in-theory        97609
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97609.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-540, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97610
in-theory        97610
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-3.            ((A and 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-97610.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-530, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97611
in-theory        97611
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97611.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-520, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97612
in-theory        97612
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97612.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-510, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97613
in-theory        97613
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97613.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-500, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97614
in-theory        97614
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97614.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J))), M:tm-490, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97615
in-theory        97615
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97615.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-480, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97616
in-theory        97616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and 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-97616.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-469, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97617
in-theory        97617
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and 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-97617.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (G or H))), M:tm-456, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97618
in-theory        97618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97618.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-453, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97619
in-theory        97619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-3.            ((A and 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-97619.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)))), M:tm-443, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97620
in-theory        97620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-3.            ((A and 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-97620.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-409, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97621
in-theory        97621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97621.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-400, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97622
in-theory        97622
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-3.            ((A and 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-97622.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-391, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97623
in-theory        97623
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97623.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-382, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97624
in-theory        97624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97624.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J))), M:tm-373, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97625
in-theory        97625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and 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-97625.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-364, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97626
in-theory        97626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97626.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-354, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97627
in-theory        97627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97627.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97628
in-theory        97628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97628.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H))), M:tm-338, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97629
in-theory        97629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97629.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)))), M:tm-327, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97630
in-theory        97630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97630.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)))), M:tm-326, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97631
in-theory        97631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97631.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)))), M:tm-325, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97632
in-theory        97632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97632.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)))), M:tm-324, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97633
in-theory        97633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97633.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)))), M:tm-323, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97634
in-theory        97634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97634.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G and H) -> H)), M:tm-322, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97635
in-theory        97635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-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-97635.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G and H) -> G)), M:tm-320, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97636
in-theory        97636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97636.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97637
in-theory        97637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97637.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (H -> G))), M:tm-315, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97638
in-theory        97638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97638.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)))), M:tm-311, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97639
in-theory        97639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-3.            ((A and 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-97639.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) or G)), M:tm-310, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97640
in-theory        97640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97640.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and G))), M:tm-309, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97641
in-theory        97641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (((D and E) -> D) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-1032 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (and Dm Em) Dm) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97641.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (((D and E) -> D) or F)), M:tm-308, m:tm-1032, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (and Dm Em) Dm) Fm)))
================================================================
tm-name          tm-97642
in-theory        97642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1032 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (and Dm Em) Dm) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97642.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1032, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (and Dm Em) Dm) Fm)))
================================================================
tm-name          tm-97643
in-theory        97643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97643.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)))), M:tm-305, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97644
in-theory        97644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97644.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-303, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97645
in-theory        97645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97645.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-270, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97646
in-theory        97646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97646.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-239, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97647
in-theory        97647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97647.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J))), M:tm-210, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97648
in-theory        97648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97648.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-183, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97649
in-theory        97649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97649.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-157, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97650
in-theory        97650
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97650.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-147, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97651
in-theory        97651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97651.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-134, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97652
in-theory        97652
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97652.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-125, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97653
in-theory        97653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97653.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> H) or J))), M:tm-113, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97654
in-theory        97654
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97654.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-105, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97655
in-theory        97655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97655.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H))), M:tm-95, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97656
in-theory        97656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97656.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-83, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97657
in-theory        97657
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97657.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) or G))), M:tm-76, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97658
in-theory        97658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97658.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H))), M:tm-69, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97659
in-theory        97659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-97659.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-54, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97660
in-theory        97660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97660.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H))), M:tm-42, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97661
in-theory        97661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-3.            ((A and 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-97661.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H))), M:tm-32, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97662
in-theory        97662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97662.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H))), M:tm-23, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97663
in-theory        97663
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97663.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H))), M:tm-22, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97664
in-theory        97664
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97664.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H))), M:tm-21, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97665
in-theory        97665
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) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97665.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> G) or I))), M:tm-20, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97666
in-theory        97666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97666.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> F) or H))), M:tm-19, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97667
in-theory        97667
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-7 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97667.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) or G))), M:tm-7, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97668
in-theory        97668
times-derived    1
----------------------------------------------------------------
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-6 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-6 tm-5 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and 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-97668.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)) or G), M:tm-6, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97669
in-theory        97669
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-3.            ((A and 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-97669.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) or G)) and A)), M:tm-5, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97670
in-theory        97670
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-1032 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97670.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) or G))), M:tm-1, m:tm-1032, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-97671
in-theory        97671
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-97671.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J))), M:tm-1003, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97672
in-theory        97672
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-97672.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J))), M:tm-992, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97673
in-theory        97673
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97673.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J))), M:tm-980, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97674
in-theory        97674
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97674.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-930, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97675
in-theory        97675
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-97675.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-893, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97676
in-theory        97676
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97676.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-855, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97677
in-theory        97677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-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-97677.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-808, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97678
in-theory        97678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-97678.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-757, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97679
in-theory        97679
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))) and (((H and I) -> I) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97679.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J))), M:tm-708, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97680
in-theory        97680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-97680.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-665, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97681
in-theory        97681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97681.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-622, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97682
in-theory        97682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97682.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (H or G))), M:tm-609, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97683
in-theory        97683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97683.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-605, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97684
in-theory        97684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97684.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)))), M:tm-595, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97685
in-theory        97685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97685.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-550, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97686
in-theory        97686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97686.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-540, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97687
in-theory        97687
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97687.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-530, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97688
in-theory        97688
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97688.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-520, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97689
in-theory        97689
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97689.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-510, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97690
in-theory        97690
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97690.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-500, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97691
in-theory        97691
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97691.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J))), M:tm-490, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97692
in-theory        97692
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97692.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-480, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97693
in-theory        97693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97693.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-469, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97694
in-theory        97694
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and 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-97694.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (G or H))), M:tm-456, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97695
in-theory        97695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97695.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-453, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97696
in-theory        97696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-4.            ((A and 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-97696.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)))), M:tm-443, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97697
in-theory        97697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97697.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-409, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97698
in-theory        97698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97698.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-400, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97699
in-theory        97699
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97699.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-391, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97700
in-theory        97700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97700.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-382, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97701
in-theory        97701
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97701.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J))), M:tm-373, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97702
in-theory        97702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97702.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-364, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97703
in-theory        97703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97703.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-354, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97704
in-theory        97704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97704.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97705
in-theory        97705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97705.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H))), M:tm-338, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97706
in-theory        97706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97706.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)))), M:tm-327, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97707
in-theory        97707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97707.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)))), M:tm-326, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97708
in-theory        97708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97708.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)))), M:tm-325, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97709
in-theory        97709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97709.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)))), M:tm-324, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97710
in-theory        97710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97710.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)))), M:tm-323, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97711
in-theory        97711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-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-97711.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G and H) -> H)), M:tm-322, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97712
in-theory        97712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97712.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G and H) -> G)), M:tm-320, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97713
in-theory        97713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97713.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97714
in-theory        97714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97714.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (H -> G))), M:tm-315, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97715
in-theory        97715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97715.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)))), M:tm-311, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97716
in-theory        97716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-4.            ((A and 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-97716.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) or G)), M:tm-310, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97717
in-theory        97717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97717.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and G))), M:tm-309, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97718
in-theory        97718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (((D and E) -> E) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-1033 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (and Dm Em) Em) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97718.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (((D and E) -> E) or F)), M:tm-308, m:tm-1033, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (and Dm Em) Em) Fm)))
================================================================
tm-name          tm-97719
in-theory        97719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1033 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (and Dm Em) Em) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97719.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1033, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (and Dm Em) Em) Fm)))
================================================================
tm-name          tm-97720
in-theory        97720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97720.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)))), M:tm-305, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97721
in-theory        97721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97721.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-303, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97722
in-theory        97722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97722.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-270, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97723
in-theory        97723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97723.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-239, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97724
in-theory        97724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97724.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J))), M:tm-210, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97725
in-theory        97725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97725.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-183, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97726
in-theory        97726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97726.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-157, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97727
in-theory        97727
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97727.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-147, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97728
in-theory        97728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97728.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-134, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97729
in-theory        97729
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97729.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-125, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97730
in-theory        97730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97730.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H and I) -> I) or J))), M:tm-113, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97731
in-theory        97731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97731.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-105, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97732
in-theory        97732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97732.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H))), M:tm-95, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97733
in-theory        97733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97733.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-83, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97734
in-theory        97734
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97734.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) or G))), M:tm-76, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97735
in-theory        97735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97735.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H))), M:tm-69, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97736
in-theory        97736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-97736.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-54, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97737
in-theory        97737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97737.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H))), M:tm-42, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97738
in-theory        97738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
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-32.           (A -> ((B -> (B or C)) and A)), 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-4.            ((A and 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-97738.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H))), M:tm-32, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97739
in-theory        97739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97739.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H))), M:tm-23, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97740
in-theory        97740
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97740.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H))), M:tm-22, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97741
in-theory        97741
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97741.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H))), M:tm-21, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97742
in-theory        97742
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) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97742.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G and H) -> H) or I))), M:tm-20, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97743
in-theory        97743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97743.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F and G) -> G) or H))), M:tm-19, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97744
in-theory        97744
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-7 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97744.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) or G))), M:tm-7, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97745
in-theory        97745
times-derived    1
----------------------------------------------------------------
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-6 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-6 tm-5 tm-8 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and 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-97745.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)) or G), M:tm-6, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97746
in-theory        97746
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-4.            ((A and 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-97746.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) or G)) and A)), M:tm-5, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97747
in-theory        97747
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-1033 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97747.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) or G))), M:tm-1, m:tm-1033, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-97748
in-theory        97748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97748.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-1003, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97749
in-theory        97749
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     39
proof            (modus-ponens tm-992 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97749.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-992, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97750
in-theory        97750
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     51
proof            (modus-ponens tm-980 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97750.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-980, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97751
in-theory        97751
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     37
proof            (modus-ponens tm-930 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97751.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-930, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97752
in-theory        97752
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     37
proof            (modus-ponens tm-893 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97752.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-893, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97753
in-theory        97753
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     41
proof            (modus-ponens tm-855 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97753.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-855, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97754
in-theory        97754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     35
proof            (modus-ponens tm-808 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97754.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-808, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97755
in-theory        97755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     35
proof            (modus-ponens tm-757 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-97755.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-757, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97756
in-theory        97756
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))) and ((H -> (I -> (H and I))) or J)))
theorem-size     49
proof            (modus-ponens tm-708 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97756.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-708, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97757
in-theory        97757
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     37
proof            (modus-ponens tm-665 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-97757.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-665, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97758
in-theory        97758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-622 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97758.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-622, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97759
in-theory        97759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), 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-97759.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97760
in-theory        97760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-605 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97760.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-605, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97761
in-theory        97761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), 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-97761.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-595, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97762
in-theory        97762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-550 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97762.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-550, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97763
in-theory        97763
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-540 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97763.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-540, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97764
in-theory        97764
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-530 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97764.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-530, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97765
in-theory        97765
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-520 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97765.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-520, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97766
in-theory        97766
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-510 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97766.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-510, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97767
in-theory        97767
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-500 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97767.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-500, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97768
in-theory        97768
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     39
proof            (modus-ponens tm-490 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97768.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-490, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97769
in-theory        97769
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-480 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97769.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-480, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97770
in-theory        97770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-469 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97770.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-469, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97771
in-theory        97771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-97771.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97772
in-theory        97772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-453 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97772.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-453, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97773
in-theory        97773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-97773.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-443, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97774
in-theory        97774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-409 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97774.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-409, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97775
in-theory        97775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-400 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97775.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-400, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97776
in-theory        97776
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-391 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97776.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-391, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97777
in-theory        97777
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-382 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97777.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-382, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97778
in-theory        97778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     39
proof            (modus-ponens tm-373 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97778.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-373, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97779
in-theory        97779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-364 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97779.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-364, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97780
in-theory        97780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-354 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97780.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-354, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97781
in-theory        97781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97781.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97782
in-theory        97782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     33
proof            (modus-ponens tm-338 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97782.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-338, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97783
in-theory        97783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97783.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-327, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97784
in-theory        97784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), 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-97784.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-326, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97785
in-theory        97785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), 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-97785.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-325, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97786
in-theory        97786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97786.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-324, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97787
in-theory        97787
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), 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-97787.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-323, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97788
in-theory        97788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), 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-97788.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97789
in-theory        97789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), 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-97789.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97790
in-theory        97790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97790.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97791
in-theory        97791
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), 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-97791.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97792
in-theory        97792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-6.            (A -> (A or B)), 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-97792.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-311, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97793
in-theory        97793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-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-97793.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) or G)), M:tm-310, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97794
in-theory        97794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97794.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and G))), M:tm-309, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97795
in-theory        97795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1034 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (-> Em (and Dm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-6.            (A -> (A or B)), 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-97795.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((D -> (E -> (D and E))) or F)), M:tm-308, m:tm-1034, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (-> Em (and Dm Em))) Fm)))
================================================================
tm-name          tm-97796
in-theory        97796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-1034 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (-> Em (and Dm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-6.            (A -> (A or B)), 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-97796.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1034, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (-> Em (and Dm Em))) Fm)))
================================================================
tm-name          tm-97797
in-theory        97797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
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-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-6.            (A -> (A or B)), 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-97797.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-305, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97798
in-theory        97798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     35
proof            (modus-ponens tm-303 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97798.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-303, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97799
in-theory        97799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-270 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97799.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-270, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97800
in-theory        97800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-239 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97800.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-239, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97801
in-theory        97801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     41
proof            (modus-ponens tm-210 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97801.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-210, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97802
in-theory        97802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-183 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97802.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-183, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97803
in-theory        97803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-157 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97803.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-157, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97804
in-theory        97804
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     39
proof            (modus-ponens tm-147 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97804.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-147, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97805
in-theory        97805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-134 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97805.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-134, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97806
in-theory        97806
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     39
proof            (modus-ponens tm-125 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97806.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-125, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97807
in-theory        97807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     39
proof            (modus-ponens tm-113 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97807.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-113, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97808
in-theory        97808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     43
proof            (modus-ponens tm-105 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97808.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-105, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97809
in-theory        97809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-95 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97809.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-95, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97810
in-theory        97810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-83 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97810.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-83, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97811
in-theory        97811
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     29
proof            (modus-ponens tm-76 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97811.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) or G))), M:tm-76, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97812
in-theory        97812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     35
proof            (modus-ponens tm-69 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97812.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-69, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97813
in-theory        97813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     37
proof            (modus-ponens tm-54 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), 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-97813.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-54, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97814
in-theory        97814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-42 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97814.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-42, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97815
in-theory        97815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-32 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97815.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-32, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97816
in-theory        97816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-23 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97816.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-23, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97817
in-theory        97817
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-22 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97817.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-22, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97818
in-theory        97818
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-21 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97818.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-21, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97819
in-theory        97819
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))) or I)))
theorem-size     37
proof            (modus-ponens tm-20 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97819.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-20, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97820
in-theory        97820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-19 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97820.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-19, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97821
in-theory        97821
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-7 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-97821.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) or G))), M:tm-7, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97822
in-theory        97822
times-derived    1
----------------------------------------------------------------
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-6 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-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-97822.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)) or G), M:tm-6, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97823
in-theory        97823
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) or G)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), 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-97823.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) or G)) and A)), M:tm-5, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97824
in-theory        97824
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-1 tm-1034 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), 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-97824.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) or G))), M:tm-1, m:tm-1034, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-97825
in-theory        97825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97825.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J))), M:tm-1003, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97826
in-theory        97826
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97826.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J))), M:tm-992, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97827
in-theory        97827
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97827.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J))), M:tm-980, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97828
in-theory        97828
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97828.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-930, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97829
in-theory        97829
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97829.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-893, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97830
in-theory        97830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97830.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-855, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97831
in-theory        97831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97831.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-808, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97832
in-theory        97832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-97832.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-757, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97833
in-theory        97833
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))) and ((H -> (H or I)) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97833.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J))), M:tm-708, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97834
in-theory        97834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-97834.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-665, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97835
in-theory        97835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97835.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-622, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97836
in-theory        97836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A 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-97836.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (H or G))), M:tm-609, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97837
in-theory        97837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97837.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-605, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97838
in-theory        97838
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97838.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)))), M:tm-595, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97839
in-theory        97839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97839.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-550, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97840
in-theory        97840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97840.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-540, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97841
in-theory        97841
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97841.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-530, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97842
in-theory        97842
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97842.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-520, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97843
in-theory        97843
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97843.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-510, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97844
in-theory        97844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97844.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-500, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97845
in-theory        97845
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97845.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J))), M:tm-490, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97846
in-theory        97846
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97846.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-480, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97847
in-theory        97847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97847.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-469, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97848
in-theory        97848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-97848.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (G or H))), M:tm-456, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97849
in-theory        97849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97849.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-453, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97850
in-theory        97850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-97850.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)))), M:tm-443, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97851
in-theory        97851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97851.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-409, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97852
in-theory        97852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97852.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-400, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97853
in-theory        97853
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97853.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-391, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97854
in-theory        97854
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97854.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-382, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97855
in-theory        97855
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97855.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J))), M:tm-373, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97856
in-theory        97856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97856.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-364, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97857
in-theory        97857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97857.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-354, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97858
in-theory        97858
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A 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-97858.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97859
in-theory        97859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97859.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H))), M:tm-338, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97860
in-theory        97860
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A 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-97860.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)))), M:tm-327, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97861
in-theory        97861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97861.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)))), M:tm-326, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97862
in-theory        97862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97862.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)))), M:tm-325, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97863
in-theory        97863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97863.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)))), M:tm-324, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97864
in-theory        97864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97864.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)))), M:tm-323, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97865
in-theory        97865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A 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-97865.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G and H) -> H)), M:tm-322, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97866
in-theory        97866
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A 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-97866.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G and H) -> G)), M:tm-320, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97867
in-theory        97867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97867.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97868
in-theory        97868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A 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-97868.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (H -> G))), M:tm-315, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97869
in-theory        97869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-6.            (A -> (A 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-97869.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)))), M:tm-311, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97870
in-theory        97870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
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-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-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-97870.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) or G)), M:tm-310, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97871
in-theory        97871
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97871.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and G))), M:tm-309, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97872
in-theory        97872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((D -> (D or E)) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-1035 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (or Dm Em)) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97872.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((D -> (D or E)) or F)), M:tm-308, m:tm-1035, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (or Dm Em)) Fm)))
================================================================
tm-name          tm-97873
in-theory        97873
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1035 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (or Dm Em)) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97873.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1035, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (or Dm Em)) Fm)))
================================================================
tm-name          tm-97874
in-theory        97874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
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-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-6.            (A -> (A 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-97874.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)))), M:tm-305, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97875
in-theory        97875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97875.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-303, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97876
in-theory        97876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97876.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-270, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97877
in-theory        97877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97877.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-239, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97878
in-theory        97878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97878.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J))), M:tm-210, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97879
in-theory        97879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97879.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-183, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97880
in-theory        97880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97880.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-157, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97881
in-theory        97881
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97881.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-147, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97882
in-theory        97882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97882.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-134, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97883
in-theory        97883
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97883.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-125, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97884
in-theory        97884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97884.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (H or I)) or J))), M:tm-113, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97885
in-theory        97885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97885.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-105, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97886
in-theory        97886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97886.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H))), M:tm-95, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97887
in-theory        97887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97887.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-83, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97888
in-theory        97888
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97888.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) or G))), M:tm-76, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97889
in-theory        97889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97889.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H))), M:tm-69, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97890
in-theory        97890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A 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-97890.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-54, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97891
in-theory        97891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97891.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H))), M:tm-42, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97892
in-theory        97892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97892.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H))), M:tm-32, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97893
in-theory        97893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97893.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H))), M:tm-23, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97894
in-theory        97894
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97894.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H))), M:tm-22, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97895
in-theory        97895
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97895.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H))), M:tm-21, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97896
in-theory        97896
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)) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97896.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (G or H)) or I))), M:tm-20, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97897
in-theory        97897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97897.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (F or G)) or H))), M:tm-19, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97898
in-theory        97898
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A 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-97898.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) or G))), M:tm-7, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97899
in-theory        97899
times-derived    1
----------------------------------------------------------------
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-6 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-97899.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)) or G), M:tm-6, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97900
in-theory        97900
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
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-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-97900.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) or G)) and A)), M:tm-5, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97901
in-theory        97901
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-1035 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A 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-97901.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) or G))), M:tm-1, m:tm-1035, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-97902
in-theory        97902
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97902.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-1003, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97903
in-theory        97903
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-97903.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-992, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97904
in-theory        97904
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97904.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-980, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97905
in-theory        97905
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97905.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-930, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97906
in-theory        97906
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97906.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-893, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97907
in-theory        97907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97907.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-855, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97908
in-theory        97908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97908.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-808, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97909
in-theory        97909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-97909.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-757, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97910
in-theory        97910
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))) and (H -> ((I -> (I or J)) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97910.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-708, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97911
in-theory        97911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-97911.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-665, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97912
in-theory        97912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97912.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-622, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97913
in-theory        97913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or 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-97913.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H or G))), M:tm-609, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97914
in-theory        97914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97914.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-605, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97915
in-theory        97915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or 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-97915.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-595, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97916
in-theory        97916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97916.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-550, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97917
in-theory        97917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97917.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-540, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97918
in-theory        97918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97918.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-530, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97919
in-theory        97919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97919.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-520, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97920
in-theory        97920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97920.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-510, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97921
in-theory        97921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97921.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-500, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97922
in-theory        97922
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97922.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-490, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97923
in-theory        97923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97923.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-480, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97924
in-theory        97924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97924.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-469, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97925
in-theory        97925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-97925.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (G or H))), M:tm-456, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97926
in-theory        97926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-97926.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-453, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97927
in-theory        97927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-97927.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-443, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97928
in-theory        97928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97928.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-409, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97929
in-theory        97929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97929.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-400, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97930
in-theory        97930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97930.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-391, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97931
in-theory        97931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97931.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-382, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97932
in-theory        97932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97932.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-373, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97933
in-theory        97933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (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-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-97933.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-364, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97934
in-theory        97934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97934.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-354, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97935
in-theory        97935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97935.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97936
in-theory        97936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97936.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-338, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97937
in-theory        97937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97937.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-327, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97938
in-theory        97938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or 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-97938.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-326, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97939
in-theory        97939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or 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-97939.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-325, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97940
in-theory        97940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97940.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-324, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97941
in-theory        97941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or 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-97941.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-323, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97942
in-theory        97942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or 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-97942.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G and H) -> H)), M:tm-322, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97943
in-theory        97943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or 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-97943.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G and H) -> G)), M:tm-320, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97944
in-theory        97944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97944.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97945
in-theory        97945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or 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-97945.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H -> G))), M:tm-315, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97946
in-theory        97946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-6.            (A -> (A or 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-97946.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-311, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97947
in-theory        97947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 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-6.            (A -> (A or 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-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-97947.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) or G)), M:tm-310, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97948
in-theory        97948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97948.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and G))), M:tm-309, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97949
in-theory        97949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1036 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (or Em Fm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-6.            (A -> (A or 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-97949.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (D -> ((E -> (E or F)) and D))), M:tm-308, m:tm-1036, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (or Em Fm)) Dm))))
================================================================
tm-name          tm-97950
in-theory        97950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-1036 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (or Em Fm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-6.            (A -> (A or 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-97950.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1036, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (or Em Fm)) Dm))))
================================================================
tm-name          tm-97951
in-theory        97951
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) 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-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-6.            (A -> (A or 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-97951.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-305, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97952
in-theory        97952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97952.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-303, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97953
in-theory        97953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97953.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-270, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97954
in-theory        97954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97954.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-239, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97955
in-theory        97955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97955.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-210, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97956
in-theory        97956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97956.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-183, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97957
in-theory        97957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97957.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-157, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97958
in-theory        97958
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97958.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-147, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97959
in-theory        97959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97959.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-134, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97960
in-theory        97960
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97960.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-125, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97961
in-theory        97961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97961.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-113, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97962
in-theory        97962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97962.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-105, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97963
in-theory        97963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97963.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-95, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97964
in-theory        97964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97964.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-83, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97965
in-theory        97965
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97965.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (F or G)) and E)))), M:tm-76, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97966
in-theory        97966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97966.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-69, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97967
in-theory        97967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or 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-97967.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-54, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97968
in-theory        97968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97968.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-42, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97969
in-theory        97969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) 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-32.           (A -> ((B -> (B or C)) and A)), 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-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-97969.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-32, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97970
in-theory        97970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97970.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-23, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97971
in-theory        97971
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97971.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-22, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97972
in-theory        97972
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97972.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-21, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97973
in-theory        97973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97973.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-20, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97974
in-theory        97974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97974.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-19, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97975
in-theory        97975
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or 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-97975.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (F or G)) and E)))), M:tm-7, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97976
in-theory        97976
times-derived    1
----------------------------------------------------------------
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-6 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-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-97976.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))) or G), M:tm-6, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97977
in-theory        97977
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (F or G)) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or 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-97977.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (F or G)) and E))) and A)), M:tm-5, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97978
in-theory        97978
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1036 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or 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-97978.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (F or G)) and E)))), M:tm-1, m:tm-1036, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-97979
in-theory        97979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-97979.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J))))), M:tm-1003, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97980
in-theory        97980
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-97980.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J))))), M:tm-992, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97981
in-theory        97981
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-97981.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J))))), M:tm-980, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97982
in-theory        97982
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-97982.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-930, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97983
in-theory        97983
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-97983.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-893, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97984
in-theory        97984
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-97984.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-855, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97985
in-theory        97985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-97985.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-808, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97986
in-theory        97986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-97986.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-757, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97987
in-theory        97987
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))) and (H -> (I -> (I or J)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-97987.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J))))), M:tm-708, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97988
in-theory        97988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-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-97988.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-665, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97989
in-theory        97989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97989.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-622, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97990
in-theory        97990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (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-97990.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (H or G))), M:tm-609, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97991
in-theory        97991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97991.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-605, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97992
in-theory        97992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97992.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))))), M:tm-595, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97993
in-theory        97993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97993.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-550, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97994
in-theory        97994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97994.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-540, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97995
in-theory        97995
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-97995.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-530, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97996
in-theory        97996
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97996.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-520, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97997
in-theory        97997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97997.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-510, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97998
in-theory        97998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97998.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-500, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-97999
in-theory        97999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-97999.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J))))), M:tm-490, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98000
in-theory        98000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98000.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-480, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98001
in-theory        98001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98001.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-469, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98002
in-theory        98002
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-98002.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (G or H))), M:tm-456, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98003
in-theory        98003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98003.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-453, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98004
in-theory        98004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98004.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))))), M:tm-443, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98005
in-theory        98005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98005.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-409, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98006
in-theory        98006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98006.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-400, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98007
in-theory        98007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98007.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-391, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98008
in-theory        98008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98008.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-382, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98009
in-theory        98009
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98009.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J))))), M:tm-373, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98010
in-theory        98010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98010.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-364, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98011
in-theory        98011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98011.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-354, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98012
in-theory        98012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (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-98012.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98013
in-theory        98013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98013.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H))))), M:tm-338, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98014
in-theory        98014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-98014.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))))), M:tm-327, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98015
in-theory        98015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98015.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))))), M:tm-326, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98016
in-theory        98016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98016.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))))), M:tm-325, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98017
in-theory        98017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98017.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))))), M:tm-324, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98018
in-theory        98018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98018.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))))), M:tm-323, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98019
in-theory        98019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (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-98019.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G and H) -> H)), M:tm-322, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98020
in-theory        98020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (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-98020.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G and H) -> G)), M:tm-320, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98021
in-theory        98021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98021.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98022
in-theory        98022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (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-98022.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (H -> G))), M:tm-315, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98023
in-theory        98023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-98023.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))))), M:tm-311, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98024
in-theory        98024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98024.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) or G)), M:tm-310, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98025
in-theory        98025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98025.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and G))), M:tm-309, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98026
in-theory        98026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (D -> (E -> (E or F))))
theorem-size     29
proof            (modus-ponens tm-308 tm-1037 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (or Em Fm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-98026.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (D -> (E -> (E or F)))), M:tm-308, m:tm-1037, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (or Em Fm)))))
================================================================
tm-name          tm-98027
in-theory        98027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1037 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (or Em Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98027.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1037, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (or Em Fm)))))
================================================================
tm-name          tm-98028
in-theory        98028
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
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-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-6.            (A -> (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-98028.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))))), M:tm-305, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98029
in-theory        98029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98029.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-303, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98030
in-theory        98030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98030.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-270, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98031
in-theory        98031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98031.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-239, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98032
in-theory        98032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98032.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J))))), M:tm-210, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98033
in-theory        98033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98033.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-183, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98034
in-theory        98034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98034.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-157, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98035
in-theory        98035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98035.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-147, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98036
in-theory        98036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98036.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-134, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98037
in-theory        98037
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98037.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-125, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98038
in-theory        98038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98038.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (I or J))))), M:tm-113, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98039
in-theory        98039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98039.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-105, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98040
in-theory        98040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98040.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H))))), M:tm-95, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98041
in-theory        98041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98041.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-83, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98042
in-theory        98042
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98042.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (F or G))))), M:tm-76, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98043
in-theory        98043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98043.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H))))), M:tm-69, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98044
in-theory        98044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-98044.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-54, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98045
in-theory        98045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98045.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H))))), M:tm-42, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98046
in-theory        98046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98046.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H))))), M:tm-32, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98047
in-theory        98047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98047.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H))))), M:tm-23, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98048
in-theory        98048
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98048.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H))))), M:tm-22, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98049
in-theory        98049
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98049.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H))))), M:tm-21, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98050
in-theory        98050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98050.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (H or I))))), M:tm-20, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98051
in-theory        98051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98051.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (G or H))))), M:tm-19, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98052
in-theory        98052
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-7 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98052.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (F or G))))), M:tm-7, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98053
in-theory        98053
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-6 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-6 tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> A)), 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-98053.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))) or G), M:tm-6, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98054
in-theory        98054
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (F or G)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (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-98054.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (F or G)))) and A)), M:tm-5, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98055
in-theory        98055
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1037 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (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-98055.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (F or G))))), M:tm-1, m:tm-1037, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98056
in-theory        98056
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-98056.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I))))), M:tm-1003, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98057
in-theory        98057
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98057.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I))))), M:tm-992, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98058
in-theory        98058
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98058.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I))))), M:tm-980, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98059
in-theory        98059
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-98059.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-930, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98060
in-theory        98060
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98060.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-893, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98061
in-theory        98061
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98061.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-855, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98062
in-theory        98062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98062.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-808, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98063
in-theory        98063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-98063.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-757, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98064
in-theory        98064
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))) and (H or (I -> (J -> I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98064.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I))))), M:tm-708, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98065
in-theory        98065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-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-98065.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-665, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98066
in-theory        98066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98066.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-622, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98067
in-theory        98067
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-98067.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (H or G))), M:tm-609, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98068
in-theory        98068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98068.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-605, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98069
in-theory        98069
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-98069.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))))), M:tm-595, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98070
in-theory        98070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98070.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-550, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98071
in-theory        98071
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98071.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-540, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98072
in-theory        98072
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98072.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-530, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98073
in-theory        98073
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98073.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-520, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98074
in-theory        98074
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98074.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-510, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98075
in-theory        98075
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98075.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-500, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98076
in-theory        98076
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98076.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I))))), M:tm-490, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98077
in-theory        98077
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98077.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-480, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98078
in-theory        98078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98078.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-469, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98079
in-theory        98079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or 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-98079.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (G or H))), M:tm-456, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98080
in-theory        98080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98080.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-453, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98081
in-theory        98081
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98081.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))))), M:tm-443, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98082
in-theory        98082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98082.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-409, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98083
in-theory        98083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98083.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-400, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98084
in-theory        98084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98084.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-391, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98085
in-theory        98085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98085.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-382, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98086
in-theory        98086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98086.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I))))), M:tm-373, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98087
in-theory        98087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98087.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-364, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98088
in-theory        98088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98088.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-354, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98089
in-theory        98089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or 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-98089.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98090
in-theory        98090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98090.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G))))), M:tm-338, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98091
in-theory        98091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98091.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))))), M:tm-327, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98092
in-theory        98092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98092.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))))), M:tm-326, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98093
in-theory        98093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98093.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))))), M:tm-325, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98094
in-theory        98094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98094.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))))), M:tm-324, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98095
in-theory        98095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98095.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))))), M:tm-323, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98096
in-theory        98096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or 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-98096.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G and H) -> H)), M:tm-322, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98097
in-theory        98097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or 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-98097.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G and H) -> G)), M:tm-320, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98098
in-theory        98098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98098.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98099
in-theory        98099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or 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-98099.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (H -> G))), M:tm-315, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98100
in-theory        98100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98100.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))))), M:tm-311, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98101
in-theory        98101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98101.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) or G)), M:tm-310, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98102
in-theory        98102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98102.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and G))), M:tm-309, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98103
in-theory        98103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (D or (E -> (F -> E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-1038 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (-> Fm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98103.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (D or (E -> (F -> E)))), M:tm-308, m:tm-1038, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (-> Fm Em)))))
================================================================
tm-name          tm-98104
in-theory        98104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1038 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (-> Fm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98104.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1038, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (-> Fm Em)))))
================================================================
tm-name          tm-98105
in-theory        98105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
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-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-7.            (A -> (B or 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-98105.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))))), M:tm-305, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98106
in-theory        98106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98106.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-303, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98107
in-theory        98107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98107.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-270, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98108
in-theory        98108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98108.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-239, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98109
in-theory        98109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98109.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I))))), M:tm-210, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98110
in-theory        98110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98110.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-183, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98111
in-theory        98111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98111.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-157, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98112
in-theory        98112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98112.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-147, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98113
in-theory        98113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98113.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-134, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98114
in-theory        98114
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98114.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-125, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98115
in-theory        98115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98115.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> I))))), M:tm-113, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98116
in-theory        98116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98116.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-105, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98117
in-theory        98117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98117.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G))))), M:tm-95, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98118
in-theory        98118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98118.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-83, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98119
in-theory        98119
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98119.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> F))))), M:tm-76, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98120
in-theory        98120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98120.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G))))), M:tm-69, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98121
in-theory        98121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-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-98121.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-54, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98122
in-theory        98122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-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-98122.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G))))), M:tm-42, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98123
in-theory        98123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98123.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G))))), M:tm-32, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98124
in-theory        98124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98124.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G))))), M:tm-23, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98125
in-theory        98125
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98125.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G))))), M:tm-22, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98126
in-theory        98126
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98126.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G))))), M:tm-21, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98127
in-theory        98127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98127.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> H))))), M:tm-20, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98128
in-theory        98128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98128.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> G))))), M:tm-19, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98129
in-theory        98129
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-7 tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-98129.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> F))))), M:tm-7, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98130
in-theory        98130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-6 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98130.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))) or G), M:tm-6, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98131
in-theory        98131
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-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-98131.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> F)))) and A)), M:tm-5, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98132
in-theory        98132
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1038 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or 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-98132.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> F))))), M:tm-1, m:tm-1038, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-98133
in-theory        98133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-98133.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-1003, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98134
in-theory        98134
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-992 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98134.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-992, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98135
in-theory        98135
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     57
proof            (modus-ponens tm-980 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98135.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-980, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98136
in-theory        98136
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-930 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98136.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-930, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98137
in-theory        98137
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-893 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98137.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-893, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98138
in-theory        98138
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-855 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98138.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-855, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98139
in-theory        98139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-808 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98139.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-808, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98140
in-theory        98140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-757 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 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-54.           (A -> (((B -> C) -> ((C -> 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-98140.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-757, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98141
in-theory        98141
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))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     55
proof            (modus-ponens tm-708 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98141.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-708, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98142
in-theory        98142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-665 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98142.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-665, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98143
in-theory        98143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-622 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98143.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-622, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98144
in-theory        98144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-98144.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I or H))), M:tm-609, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98145
in-theory        98145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-605 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98145.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-605, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98146
in-theory        98146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-35.           (A 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-98146.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-595, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98147
in-theory        98147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-550 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98147.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-550, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98148
in-theory        98148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-540 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98148.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-540, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98149
in-theory        98149
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-530 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98149.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-530, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98150
in-theory        98150
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-520 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 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-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98150.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-520, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98151
in-theory        98151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-510 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98151.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-510, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98152
in-theory        98152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-500 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98152.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-500, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98153
in-theory        98153
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-490 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-98153.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-490, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98154
in-theory        98154
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-480 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98154.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-480, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98155
in-theory        98155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-469 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98155.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-469, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98156
in-theory        98156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98156.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (H or I))), M:tm-456, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98157
in-theory        98157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-453 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98157.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-453, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98158
in-theory        98158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98158.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-443, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98159
in-theory        98159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-409 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98159.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-409, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98160
in-theory        98160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-400 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98160.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-400, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98161
in-theory        98161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-391 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98161.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-391, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98162
in-theory        98162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-382 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98162.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-382, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98163
in-theory        98163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-373 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98163.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-373, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98164
in-theory        98164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-364 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98164.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-364, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98165
in-theory        98165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-354 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98165.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-354, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98166
in-theory        98166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98166.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98167
in-theory        98167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-338 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98167.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-338, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98168
in-theory        98168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98168.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-327, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98169
in-theory        98169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98169.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-326, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98170
in-theory        98170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98170.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-325, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98171
in-theory        98171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98171.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-324, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98172
in-theory        98172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98172.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-323, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98173
in-theory        98173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98173.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> I)), M:tm-322, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98174
in-theory        98174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98174.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> H)), M:tm-320, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98175
in-theory        98175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-35.           (A 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-98175.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98176
in-theory        98176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98176.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> H))), M:tm-315, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98177
in-theory        98177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
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-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-35.           (A 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-98177.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-311, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98178
in-theory        98178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-7.            (A -> (B or A)), axiom
tm-35.           (A 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-98178.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H)), M:tm-310, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98179
in-theory        98179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98179.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and H))), M:tm-309, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98180
in-theory        98180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1039 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98180.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1039, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))
================================================================
tm-name          tm-98181
in-theory        98181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-1039 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98181.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1039, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))
================================================================
tm-name          tm-98182
in-theory        98182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-7.            (A -> (B or A)), axiom
tm-35.           (A 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-98182.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-305, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98183
in-theory        98183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-303 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-98183.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-303, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98184
in-theory        98184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-270 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98184.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-270, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98185
in-theory        98185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-239 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98185.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-239, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98186
in-theory        98186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     47
proof            (modus-ponens tm-210 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98186.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-210, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98187
in-theory        98187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-183 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98187.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-183, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98188
in-theory        98188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-157 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98188.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-157, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98189
in-theory        98189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     45
proof            (modus-ponens tm-147 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98189.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-147, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98190
in-theory        98190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-134 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98190.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-134, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98191
in-theory        98191
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     45
proof            (modus-ponens tm-125 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98191.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-125, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98192
in-theory        98192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-113 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98192.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-113, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98193
in-theory        98193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-105 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98193.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-105, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98194
in-theory        98194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-95 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98194.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-95, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98195
in-theory        98195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-83 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98195.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-83, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98196
in-theory        98196
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-76 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-98196.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-76, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98197
in-theory        98197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-69 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-98197.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-69, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98198
in-theory        98198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-54 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-98198.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-54, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98199
in-theory        98199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-42 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 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-42.           (A -> ((B -> (C or B)) and A)), 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98199.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-42, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98200
in-theory        98200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-32 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98200.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-32, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98201
in-theory        98201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-23 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
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-54.           (A -> (((B -> C) -> ((C -> 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-98201.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-23, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98202
in-theory        98202
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-22 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98202.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-22, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98203
in-theory        98203
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-21 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98203.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-21, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98204
in-theory        98204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-20 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-35.           (A 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-98204.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-20, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98205
in-theory        98205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-19 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7 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-54.           (A -> (((B -> C) -> ((C -> 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-98205.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-19, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98206
in-theory        98206
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-7 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-7 tm-5 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98206.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-7, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98207
in-theory        98207
times-derived    1
----------------------------------------------------------------
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-6 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98207.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H), M:tm-6, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98208
in-theory        98208
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-7 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-54.           (A -> (((B -> C) -> ((C -> 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-98208.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) and A)), M:tm-5, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98209
in-theory        98209
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-1 tm-1039 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A 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-98209.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-1, m:tm-1039, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-98210
in-theory        98210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-98210.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I)))), M:tm-1003, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98211
in-theory        98211
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98211.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I)))), M:tm-992, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98212
in-theory        98212
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98212.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I)))), M:tm-980, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98213
in-theory        98213
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-98213.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-930, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98214
in-theory        98214
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98214.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-893, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98215
in-theory        98215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98215.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-855, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98216
in-theory        98216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98216.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-808, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98217
in-theory        98217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-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-98217.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-757, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98218
in-theory        98218
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))) and (H or ((I and J) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98218.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I)))), M:tm-708, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98219
in-theory        98219
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-98219.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-665, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98220
in-theory        98220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and 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-98220.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-622, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98221
in-theory        98221
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and 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-98221.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (H or G))), M:tm-609, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98222
in-theory        98222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98222.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-605, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98223
in-theory        98223
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-3.            ((A and 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-98223.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))))), M:tm-595, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98224
in-theory        98224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-3.            ((A and 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-98224.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-550, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98225
in-theory        98225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-3.            ((A and 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-98225.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-540, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98226
in-theory        98226
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-3.            ((A and 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-98226.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-530, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98227
in-theory        98227
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98227.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-520, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98228
in-theory        98228
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-3.            ((A and 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-98228.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-510, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98229
in-theory        98229
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98229.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-500, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98230
in-theory        98230
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98230.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I)))), M:tm-490, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98231
in-theory        98231
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and 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-98231.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-480, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98232
in-theory        98232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98232.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-469, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98233
in-theory        98233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98233.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (G or H))), M:tm-456, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98234
in-theory        98234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98234.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-453, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98235
in-theory        98235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98235.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))))), M:tm-443, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98236
in-theory        98236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98236.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-409, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98237
in-theory        98237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98237.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-400, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98238
in-theory        98238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98238.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-391, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98239
in-theory        98239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98239.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-382, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98240
in-theory        98240
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98240.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I)))), M:tm-373, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98241
in-theory        98241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98241.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-364, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98242
in-theory        98242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98242.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-354, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98243
in-theory        98243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98243.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98244
in-theory        98244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98244.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G)))), M:tm-338, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98245
in-theory        98245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98245.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))))), M:tm-327, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98246
in-theory        98246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98246.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))))), M:tm-326, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98247
in-theory        98247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98247.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))))), M:tm-325, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98248
in-theory        98248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98248.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))))), M:tm-324, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98249
in-theory        98249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98249.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))))), M:tm-323, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98250
in-theory        98250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98250.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98251
in-theory        98251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-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-98251.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98252
in-theory        98252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98252.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98253
in-theory        98253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98253.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98254
in-theory        98254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-3.            ((A and 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-98254.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))))), M:tm-311, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98255
in-theory        98255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98255.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) or G)), M:tm-310, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98256
in-theory        98256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98256.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and G))), M:tm-309, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98257
in-theory        98257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (D or ((E and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-308 tm-1040 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (and Em Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98257.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (D or ((E and F) -> E))), M:tm-308, m:tm-1040, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (and Em Fm) Em))))
================================================================
tm-name          tm-98258
in-theory        98258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1040 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (and Em Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98258.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1040, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (and Em Fm) Em))))
================================================================
tm-name          tm-98259
in-theory        98259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98259.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))))), M:tm-305, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98260
in-theory        98260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98260.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-303, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98261
in-theory        98261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98261.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-270, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98262
in-theory        98262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98262.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-239, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98263
in-theory        98263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98263.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I)))), M:tm-210, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98264
in-theory        98264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98264.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-183, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98265
in-theory        98265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98265.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-157, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98266
in-theory        98266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98266.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-147, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98267
in-theory        98267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98267.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-134, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98268
in-theory        98268
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98268.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-125, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98269
in-theory        98269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98269.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> I)))), M:tm-113, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98270
in-theory        98270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98270.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-105, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98271
in-theory        98271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98271.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G)))), M:tm-95, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98272
in-theory        98272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98272.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-83, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98273
in-theory        98273
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98273.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> F)))), M:tm-76, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98274
in-theory        98274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98274.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G)))), M:tm-69, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98275
in-theory        98275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-98275.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-54, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98276
in-theory        98276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-3.            ((A and 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-98276.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G)))), M:tm-42, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98277
in-theory        98277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98277.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G)))), M:tm-32, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98278
in-theory        98278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98278.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G)))), M:tm-23, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98279
in-theory        98279
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98279.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G)))), M:tm-22, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98280
in-theory        98280
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98280.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G)))), M:tm-21, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98281
in-theory        98281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98281.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> H)))), M:tm-20, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98282
in-theory        98282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98282.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> G)))), M:tm-19, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98283
in-theory        98283
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-7 tm-5 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-3.            ((A and 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-98283.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> F)))), M:tm-7, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98284
in-theory        98284
times-derived    1
----------------------------------------------------------------
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-6 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-6 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98284.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))) or G), M:tm-6, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98285
in-theory        98285
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-3.            ((A and 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-98285.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> F))) and A)), M:tm-5, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98286
in-theory        98286
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1040 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98286.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> F)))), M:tm-1, m:tm-1040, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-98287
in-theory        98287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-98287.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J)))), M:tm-1003, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98288
in-theory        98288
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98288.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J)))), M:tm-992, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98289
in-theory        98289
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98289.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J)))), M:tm-980, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98290
in-theory        98290
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-98290.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-930, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98291
in-theory        98291
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98291.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-893, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98292
in-theory        98292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98292.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-855, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98293
in-theory        98293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98293.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-808, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98294
in-theory        98294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-98294.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-757, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98295
in-theory        98295
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))) and (H or ((I and J) -> J))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98295.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J)))), M:tm-708, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98296
in-theory        98296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-98296.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-665, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98297
in-theory        98297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98297.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-622, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98298
in-theory        98298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and 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-98298.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (H or G))), M:tm-609, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98299
in-theory        98299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98299.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-605, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98300
in-theory        98300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-4.            ((A and 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-98300.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))))), M:tm-595, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98301
in-theory        98301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98301.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-550, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98302
in-theory        98302
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98302.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-540, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98303
in-theory        98303
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98303.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-530, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98304
in-theory        98304
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98304.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-520, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98305
in-theory        98305
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98305.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-510, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98306
in-theory        98306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98306.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-500, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98307
in-theory        98307
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98307.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J)))), M:tm-490, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98308
in-theory        98308
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98308.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-480, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98309
in-theory        98309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98309.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-469, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98310
in-theory        98310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98310.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (G or H))), M:tm-456, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98311
in-theory        98311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98311.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-453, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98312
in-theory        98312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98312.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))))), M:tm-443, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98313
in-theory        98313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98313.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-409, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98314
in-theory        98314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98314.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-400, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98315
in-theory        98315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98315.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-391, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98316
in-theory        98316
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98316.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-382, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98317
in-theory        98317
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98317.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J)))), M:tm-373, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98318
in-theory        98318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98318.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-364, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98319
in-theory        98319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98319.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-354, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98320
in-theory        98320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98320.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98321
in-theory        98321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98321.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H)))), M:tm-338, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98322
in-theory        98322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98322.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))))), M:tm-327, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98323
in-theory        98323
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98323.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))))), M:tm-326, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98324
in-theory        98324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98324.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))))), M:tm-325, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98325
in-theory        98325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98325.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))))), M:tm-324, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98326
in-theory        98326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98326.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))))), M:tm-323, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98327
in-theory        98327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-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-98327.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98328
in-theory        98328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98328.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98329
in-theory        98329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98329.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98330
in-theory        98330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98330.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98331
in-theory        98331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-4.            ((A and 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-98331.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))))), M:tm-311, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98332
in-theory        98332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98332.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) or G)), M:tm-310, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98333
in-theory        98333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98333.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and G))), M:tm-309, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98334
in-theory        98334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (D or ((E and F) -> F)))
theorem-size     29
proof            (modus-ponens tm-308 tm-1041 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (and Em Fm) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98334.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (D or ((E and F) -> F))), M:tm-308, m:tm-1041, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (and Em Fm) Fm))))
================================================================
tm-name          tm-98335
in-theory        98335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1041 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (and Em Fm) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98335.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1041, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (and Em Fm) Fm))))
================================================================
tm-name          tm-98336
in-theory        98336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98336.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))))), M:tm-305, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98337
in-theory        98337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98337.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-303, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98338
in-theory        98338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98338.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-270, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98339
in-theory        98339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98339.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-239, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98340
in-theory        98340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98340.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J)))), M:tm-210, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98341
in-theory        98341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98341.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-183, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98342
in-theory        98342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98342.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-157, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98343
in-theory        98343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98343.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-147, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98344
in-theory        98344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98344.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-134, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98345
in-theory        98345
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98345.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-125, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98346
in-theory        98346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98346.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I and J) -> J)))), M:tm-113, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98347
in-theory        98347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98347.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-105, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98348
in-theory        98348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98348.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H)))), M:tm-95, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98349
in-theory        98349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98349.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-83, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98350
in-theory        98350
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98350.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> G)))), M:tm-76, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98351
in-theory        98351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98351.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H)))), M:tm-69, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98352
in-theory        98352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-98352.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-54, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98353
in-theory        98353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
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-42.           (A -> ((B -> (C or B)) and A)), 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-4.            ((A and 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-98353.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H)))), M:tm-42, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98354
in-theory        98354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98354.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H)))), M:tm-32, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98355
in-theory        98355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98355.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H)))), M:tm-23, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98356
in-theory        98356
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98356.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H)))), M:tm-22, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98357
in-theory        98357
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98357.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H)))), M:tm-21, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98358
in-theory        98358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98358.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H and I) -> I)))), M:tm-20, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98359
in-theory        98359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98359.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G and H) -> H)))), M:tm-19, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98360
in-theory        98360
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and 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-98360.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> G)))), M:tm-7, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98361
in-theory        98361
times-derived    1
----------------------------------------------------------------
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-6 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-6 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98361.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))) or G), M:tm-6, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98362
in-theory        98362
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> G))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-4.            ((A and 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-98362.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> G))) and A)), M:tm-5, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98363
in-theory        98363
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1041 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98363.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F and G) -> G)))), M:tm-1, m:tm-1041, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-98364
in-theory        98364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-98364.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-1003, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98365
in-theory        98365
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98365.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-992, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98366
in-theory        98366
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98366.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-980, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98367
in-theory        98367
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98367.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-930, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98368
in-theory        98368
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98368.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-893, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98369
in-theory        98369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98369.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-855, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98370
in-theory        98370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98370.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-808, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98371
in-theory        98371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-98371.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-757, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98372
in-theory        98372
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))) and (H or (I -> (J -> (I and J))))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98372.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-708, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98373
in-theory        98373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-98373.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-665, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98374
in-theory        98374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98374.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-622, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98375
in-theory        98375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-98375.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H or G))), M:tm-609, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98376
in-theory        98376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98376.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-605, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98377
in-theory        98377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-98377.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-595, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98378
in-theory        98378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98378.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-550, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98379
in-theory        98379
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98379.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-540, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98380
in-theory        98380
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98380.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-530, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98381
in-theory        98381
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98381.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-520, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98382
in-theory        98382
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98382.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-510, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98383
in-theory        98383
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98383.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-500, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98384
in-theory        98384
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98384.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-490, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98385
in-theory        98385
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98385.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-480, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98386
in-theory        98386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98386.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-469, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98387
in-theory        98387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), 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-98387.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (G or H))), M:tm-456, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98388
in-theory        98388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98388.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-453, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98389
in-theory        98389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), 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-98389.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-443, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98390
in-theory        98390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98390.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-409, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98391
in-theory        98391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98391.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-400, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98392
in-theory        98392
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98392.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-391, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98393
in-theory        98393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98393.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-382, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98394
in-theory        98394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98394.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-373, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98395
in-theory        98395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98395.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-364, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98396
in-theory        98396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98396.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-354, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98397
in-theory        98397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98397.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98398
in-theory        98398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98398.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-338, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98399
in-theory        98399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98399.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-327, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98400
in-theory        98400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), 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-98400.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-326, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98401
in-theory        98401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), 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-98401.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-325, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98402
in-theory        98402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98402.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-324, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98403
in-theory        98403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or A)), 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-98403.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-323, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98404
in-theory        98404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), 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-98404.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G and H) -> H)), M:tm-322, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98405
in-theory        98405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), 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-98405.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G and H) -> G)), M:tm-320, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98406
in-theory        98406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98406.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98407
in-theory        98407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), 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-98407.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H -> G))), M:tm-315, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98408
in-theory        98408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-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-98408.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-311, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98409
in-theory        98409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-7.            (A -> (B or A)), 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-98409.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) or G)), M:tm-310, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98410
in-theory        98410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98410.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and G))), M:tm-309, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98411
in-theory        98411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1042 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (-> Fm (and Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-7.            (A -> (B or A)), 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-98411.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (D or (E -> (F -> (E and F))))), M:tm-308, m:tm-1042, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (-> Fm (and Em Fm))))))
================================================================
tm-name          tm-98412
in-theory        98412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-1042 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (-> Fm (and Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-7.            (A -> (B or A)), 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-98412.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1042, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (-> Fm (and Em Fm))))))
================================================================
tm-name          tm-98413
in-theory        98413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
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-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-7.            (A -> (B or A)), 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-98413.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-305, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98414
in-theory        98414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98414.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-303, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98415
in-theory        98415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98415.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-270, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98416
in-theory        98416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98416.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-239, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98417
in-theory        98417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98417.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-210, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98418
in-theory        98418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98418.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-183, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98419
in-theory        98419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98419.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-157, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98420
in-theory        98420
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98420.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-147, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98421
in-theory        98421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98421.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-134, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98422
in-theory        98422
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98422.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-125, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98423
in-theory        98423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98423.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-113, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98424
in-theory        98424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98424.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-105, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98425
in-theory        98425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98425.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-95, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98426
in-theory        98426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98426.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-83, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98427
in-theory        98427
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98427.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> (F and G)))))), M:tm-76, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98428
in-theory        98428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98428.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-69, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98429
in-theory        98429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), 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-98429.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-54, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98430
in-theory        98430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98430.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-42, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98431
in-theory        98431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98431.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-32, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98432
in-theory        98432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98432.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-23, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98433
in-theory        98433
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98433.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-22, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98434
in-theory        98434
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98434.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-21, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98435
in-theory        98435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98435.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-20, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98436
in-theory        98436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98436.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-19, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98437
in-theory        98437
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-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-98437.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> (F and G)))))), M:tm-7, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98438
in-theory        98438
times-derived    1
----------------------------------------------------------------
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-6 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), 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-98438.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))) or G), M:tm-6, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98439
in-theory        98439
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> (F and G))))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), 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-98439.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> (F and G))))) and A)), M:tm-5, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98440
in-theory        98440
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1042 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), 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-98440.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G -> (F and G)))))), M:tm-1, m:tm-1042, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-98441
in-theory        98441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98441.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J))))), M:tm-1003, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98442
in-theory        98442
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98442.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J))))), M:tm-992, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98443
in-theory        98443
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98443.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J))))), M:tm-980, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98444
in-theory        98444
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-98444.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-930, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98445
in-theory        98445
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-98445.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-893, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98446
in-theory        98446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98446.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-855, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98447
in-theory        98447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98447.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-808, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98448
in-theory        98448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-98448.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-757, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98449
in-theory        98449
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))) and (H or (I -> (I or J)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98449.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J))))), M:tm-708, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98450
in-theory        98450
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-98450.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-665, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98451
in-theory        98451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98451.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-622, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98452
in-theory        98452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A 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-98452.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (H or G))), M:tm-609, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98453
in-theory        98453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98453.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-605, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98454
in-theory        98454
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98454.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))))), M:tm-595, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98455
in-theory        98455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98455.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-550, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98456
in-theory        98456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98456.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-540, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98457
in-theory        98457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98457.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-530, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98458
in-theory        98458
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98458.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-520, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98459
in-theory        98459
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98459.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-510, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98460
in-theory        98460
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98460.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-500, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98461
in-theory        98461
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98461.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J))))), M:tm-490, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98462
in-theory        98462
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98462.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-480, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98463
in-theory        98463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98463.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-469, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98464
in-theory        98464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-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-98464.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (G or H))), M:tm-456, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98465
in-theory        98465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98465.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-453, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98466
in-theory        98466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98466.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))))), M:tm-443, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98467
in-theory        98467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98467.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-409, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98468
in-theory        98468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98468.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-400, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98469
in-theory        98469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98469.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-391, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98470
in-theory        98470
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98470.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-382, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98471
in-theory        98471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98471.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J))))), M:tm-373, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98472
in-theory        98472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98472.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-364, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98473
in-theory        98473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98473.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-354, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98474
in-theory        98474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98474.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98475
in-theory        98475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98475.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H))))), M:tm-338, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98476
in-theory        98476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98476.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))))), M:tm-327, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98477
in-theory        98477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98477.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))))), M:tm-326, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98478
in-theory        98478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98478.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))))), M:tm-325, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98479
in-theory        98479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98479.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))))), M:tm-324, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98480
in-theory        98480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98480.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))))), M:tm-323, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98481
in-theory        98481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98481.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G and H) -> H)), M:tm-322, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98482
in-theory        98482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98482.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G and H) -> G)), M:tm-320, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98483
in-theory        98483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98483.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98484
in-theory        98484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98484.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (H -> G))), M:tm-315, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98485
in-theory        98485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-6.            (A -> (A 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-98485.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))))), M:tm-311, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98486
in-theory        98486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-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-98486.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) or G)), M:tm-310, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98487
in-theory        98487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98487.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and G))), M:tm-309, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98488
in-theory        98488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (D or (E -> (E or F))))
theorem-size     29
proof            (modus-ponens tm-308 tm-1043 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (or Em Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98488.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (D or (E -> (E or F)))), M:tm-308, m:tm-1043, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (or Em Fm)))))
================================================================
tm-name          tm-98489
in-theory        98489
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1043 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (or Em Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98489.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1043, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (or Em Fm)))))
================================================================
tm-name          tm-98490
in-theory        98490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98490.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))))), M:tm-305, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98491
in-theory        98491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98491.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-303, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98492
in-theory        98492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98492.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-270, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98493
in-theory        98493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98493.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-239, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98494
in-theory        98494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98494.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J))))), M:tm-210, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98495
in-theory        98495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98495.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-183, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98496
in-theory        98496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98496.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-157, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98497
in-theory        98497
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98497.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-147, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98498
in-theory        98498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98498.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-134, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98499
in-theory        98499
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98499.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-125, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98500
in-theory        98500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98500.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (I or J))))), M:tm-113, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98501
in-theory        98501
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98501.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-105, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98502
in-theory        98502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98502.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H))))), M:tm-95, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98503
in-theory        98503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98503.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-83, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98504
in-theory        98504
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98504.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (F or G))))), M:tm-76, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98505
in-theory        98505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98505.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H))))), M:tm-69, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98506
in-theory        98506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A 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-98506.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-54, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98507
in-theory        98507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98507.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H))))), M:tm-42, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98508
in-theory        98508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98508.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H))))), M:tm-32, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98509
in-theory        98509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98509.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H))))), M:tm-23, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98510
in-theory        98510
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98510.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H))))), M:tm-22, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98511
in-theory        98511
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98511.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H))))), M:tm-21, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98512
in-theory        98512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98512.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (H or I))))), M:tm-20, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98513
in-theory        98513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98513.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (G or H))))), M:tm-19, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98514
in-theory        98514
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A 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-98514.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (F or G))))), M:tm-7, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98515
in-theory        98515
times-derived    1
----------------------------------------------------------------
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-6 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-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-98515.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))) or G), M:tm-6, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98516
in-theory        98516
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (F or G)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A 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-98516.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (F or G)))) and A)), M:tm-5, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98517
in-theory        98517
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1043 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98517.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (F or G))))), M:tm-1, m:tm-1043, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-98518
in-theory        98518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-98518.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I))))), M:tm-1003, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98519
in-theory        98519
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98519.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I))))), M:tm-992, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98520
in-theory        98520
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98520.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I))))), M:tm-980, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98521
in-theory        98521
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98521.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-930, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98522
in-theory        98522
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98522.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-893, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98523
in-theory        98523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98523.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-855, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98524
in-theory        98524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98524.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-808, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98525
in-theory        98525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-98525.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-757, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98526
in-theory        98526
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))) and (H or (I -> (J or I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98526.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I))))), M:tm-708, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98527
in-theory        98527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-98527.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-665, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98528
in-theory        98528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98528.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-622, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98529
in-theory        98529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-98529.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (H or G))), M:tm-609, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98530
in-theory        98530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98530.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-605, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98531
in-theory        98531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-98531.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))))), M:tm-595, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98532
in-theory        98532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98532.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-550, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98533
in-theory        98533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98533.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-540, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98534
in-theory        98534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98534.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-530, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98535
in-theory        98535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98535.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-520, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98536
in-theory        98536
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98536.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-510, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98537
in-theory        98537
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98537.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-500, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98538
in-theory        98538
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98538.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I))))), M:tm-490, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98539
in-theory        98539
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98539.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-480, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98540
in-theory        98540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98540.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-469, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98541
in-theory        98541
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B 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-98541.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (G or H))), M:tm-456, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98542
in-theory        98542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98542.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-453, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98543
in-theory        98543
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98543.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))))), M:tm-443, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98544
in-theory        98544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98544.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-409, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98545
in-theory        98545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98545.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-400, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98546
in-theory        98546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98546.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-391, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98547
in-theory        98547
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98547.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-382, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98548
in-theory        98548
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98548.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I))))), M:tm-373, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98549
in-theory        98549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98549.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-364, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98550
in-theory        98550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98550.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-354, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98551
in-theory        98551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B 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-98551.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98552
in-theory        98552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98552.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G))))), M:tm-338, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98553
in-theory        98553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B 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-98553.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))))), M:tm-327, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98554
in-theory        98554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98554.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))))), M:tm-326, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98555
in-theory        98555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98555.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))))), M:tm-325, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98556
in-theory        98556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98556.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))))), M:tm-324, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98557
in-theory        98557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98557.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))))), M:tm-323, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98558
in-theory        98558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B 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-98558.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G and H) -> H)), M:tm-322, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98559
in-theory        98559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B 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-98559.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G and H) -> G)), M:tm-320, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98560
in-theory        98560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98560.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98561
in-theory        98561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B 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-98561.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (H -> G))), M:tm-315, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98562
in-theory        98562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
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-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-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-98562.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))))), M:tm-311, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98563
in-theory        98563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-7.            (A -> (B 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-98563.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) or G)), M:tm-310, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98564
in-theory        98564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98564.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and G))), M:tm-309, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98565
in-theory        98565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (D or (E -> (F or E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-1044 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (or Fm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98565.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (D or (E -> (F or E)))), M:tm-308, m:tm-1044, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (or Fm Em)))))
================================================================
tm-name          tm-98566
in-theory        98566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1044 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (or Fm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98566.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1044, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> Em (or Fm Em)))))
================================================================
tm-name          tm-98567
in-theory        98567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
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-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-7.            (A -> (B 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-98567.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))))), M:tm-305, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98568
in-theory        98568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98568.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-303, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98569
in-theory        98569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98569.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-270, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98570
in-theory        98570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98570.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-239, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98571
in-theory        98571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98571.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I))))), M:tm-210, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98572
in-theory        98572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98572.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-183, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98573
in-theory        98573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98573.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-157, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98574
in-theory        98574
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98574.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-147, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98575
in-theory        98575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98575.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-134, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98576
in-theory        98576
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98576.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-125, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98577
in-theory        98577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98577.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or (I -> (J or I))))), M:tm-113, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98578
in-theory        98578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98578.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-105, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98579
in-theory        98579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98579.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G))))), M:tm-95, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98580
in-theory        98580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98580.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-83, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98581
in-theory        98581
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98581.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G or F))))), M:tm-76, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98582
in-theory        98582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98582.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G))))), M:tm-69, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98583
in-theory        98583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B 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-98583.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-54, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98584
in-theory        98584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98584.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G))))), M:tm-42, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98585
in-theory        98585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98585.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G))))), M:tm-32, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98586
in-theory        98586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98586.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G))))), M:tm-23, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98587
in-theory        98587
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98587.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G))))), M:tm-22, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98588
in-theory        98588
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98588.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G))))), M:tm-21, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98589
in-theory        98589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98589.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or (H -> (I or H))))), M:tm-20, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98590
in-theory        98590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98590.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or (G -> (H or G))))), M:tm-19, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98591
in-theory        98591
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-98591.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G or F))))), M:tm-7, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98592
in-theory        98592
times-derived    1
----------------------------------------------------------------
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-6 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B 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-98592.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))) or G), M:tm-6, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98593
in-theory        98593
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G or F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
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-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-98593.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G or F)))) and A)), M:tm-5, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98594
in-theory        98594
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1044 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B 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-98594.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or (F -> (G or F))))), M:tm-1, m:tm-1044, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98595
in-theory        98595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J)))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98595.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J))), M:tm-1003, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98596
in-theory        98596
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J)))
theorem-size     37
proof            (modus-ponens tm-992 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98596.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J))), M:tm-992, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98597
in-theory        98597
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J)))
theorem-size     49
proof            (modus-ponens tm-980 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98597.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J))), M:tm-980, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98598
in-theory        98598
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     35
proof            (modus-ponens tm-930 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-98598.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-930, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98599
in-theory        98599
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     35
proof            (modus-ponens tm-893 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-98599.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-893, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98600
in-theory        98600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     39
proof            (modus-ponens tm-855 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98600.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-855, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98601
in-theory        98601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     33
proof            (modus-ponens tm-808 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98601.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-808, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98602
in-theory        98602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-98602.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-757, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98603
in-theory        98603
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))) and ((H -> (I or H)) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98603.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J))), M:tm-708, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98604
in-theory        98604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-98604.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-665, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98605
in-theory        98605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98605.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-622, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98606
in-theory        98606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-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-98606.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (H or G))), M:tm-609, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98607
in-theory        98607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98607.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-605, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98608
in-theory        98608
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98608.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)))), M:tm-595, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98609
in-theory        98609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98609.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-550, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98610
in-theory        98610
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98610.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-540, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98611
in-theory        98611
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98611.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-530, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98612
in-theory        98612
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98612.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-520, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98613
in-theory        98613
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98613.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-510, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98614
in-theory        98614
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98614.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-500, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98615
in-theory        98615
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98615.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J))), M:tm-490, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98616
in-theory        98616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98616.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-480, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98617
in-theory        98617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98617.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-469, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98618
in-theory        98618
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B 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-98618.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (G or H))), M:tm-456, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98619
in-theory        98619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98619.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-453, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98620
in-theory        98620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98620.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)))), M:tm-443, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98621
in-theory        98621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98621.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-409, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98622
in-theory        98622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98622.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-400, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98623
in-theory        98623
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98623.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-391, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98624
in-theory        98624
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98624.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-382, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98625
in-theory        98625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98625.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J))), M:tm-373, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98626
in-theory        98626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98626.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-364, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98627
in-theory        98627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98627.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-354, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98628
in-theory        98628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98628.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98629
in-theory        98629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98629.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H))), M:tm-338, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98630
in-theory        98630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98630.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)))), M:tm-327, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98631
in-theory        98631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98631.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)))), M:tm-326, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98632
in-theory        98632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98632.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)))), M:tm-325, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98633
in-theory        98633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98633.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)))), M:tm-324, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98634
in-theory        98634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98634.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)))), M:tm-323, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98635
in-theory        98635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98635.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G and H) -> H)), M:tm-322, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98636
in-theory        98636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98636.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G and H) -> G)), M:tm-320, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98637
in-theory        98637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98637.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98638
in-theory        98638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98638.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (H -> G))), M:tm-315, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98639
in-theory        98639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-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-98639.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)))), M:tm-311, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98640
in-theory        98640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-7.            (A -> (B 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-98640.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) or G)), M:tm-310, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98641
in-theory        98641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98641.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and G))), M:tm-309, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98642
in-theory        98642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((D -> (E or D)) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-1045 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (or Em Dm)) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98642.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((D -> (E or D)) or F)), M:tm-308, m:tm-1045, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (or Em Dm)) Fm)))
================================================================
tm-name          tm-98643
in-theory        98643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1045 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (or Em Dm)) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98643.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1045, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> Dm (or Em Dm)) Fm)))
================================================================
tm-name          tm-98644
in-theory        98644
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98644.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)))), M:tm-305, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98645
in-theory        98645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98645.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-303, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98646
in-theory        98646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98646.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-270, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98647
in-theory        98647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98647.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-239, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98648
in-theory        98648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98648.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J))), M:tm-210, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98649
in-theory        98649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98649.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-183, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98650
in-theory        98650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98650.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-157, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98651
in-theory        98651
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98651.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-147, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98652
in-theory        98652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98652.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-134, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98653
in-theory        98653
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98653.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-125, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98654
in-theory        98654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98654.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> (I or H)) or J))), M:tm-113, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98655
in-theory        98655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98655.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-105, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98656
in-theory        98656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98656.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H))), M:tm-95, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98657
in-theory        98657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98657.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-83, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98658
in-theory        98658
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98658.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) or G))), M:tm-76, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98659
in-theory        98659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98659.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H))), M:tm-69, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98660
in-theory        98660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B 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-98660.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-54, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98661
in-theory        98661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98661.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H))), M:tm-42, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98662
in-theory        98662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98662.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H))), M:tm-32, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98663
in-theory        98663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98663.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H))), M:tm-23, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98664
in-theory        98664
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98664.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H))), M:tm-22, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98665
in-theory        98665
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98665.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H))), M:tm-21, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98666
in-theory        98666
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)) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98666.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> (H or G)) or I))), M:tm-20, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98667
in-theory        98667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98667.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> (G or F)) or H))), M:tm-19, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98668
in-theory        98668
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-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-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-98668.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) or G))), M:tm-7, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98669
in-theory        98669
times-derived    1
----------------------------------------------------------------
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-6 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B 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-98669.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)) or G), M:tm-6, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98670
in-theory        98670
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B 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-98670.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) or G)) and A)), M:tm-5, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98671
in-theory        98671
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-1045 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-1 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98671.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) or G))), M:tm-1, m:tm-1045, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-98672
in-theory        98672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-98672.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-1003, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98673
in-theory        98673
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98673.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-992, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98674
in-theory        98674
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98674.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-980, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98675
in-theory        98675
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98675.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-930, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98676
in-theory        98676
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98676.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-893, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98677
in-theory        98677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98677.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-855, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98678
in-theory        98678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98678.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-808, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98679
in-theory        98679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-98679.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-757, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98680
in-theory        98680
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))) and (H -> ((I -> (J or I)) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98680.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-708, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98681
in-theory        98681
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-98681.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-665, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98682
in-theory        98682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98682.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-622, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98683
in-theory        98683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-98683.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H or G))), M:tm-609, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98684
in-theory        98684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98684.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-605, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98685
in-theory        98685
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-98685.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-595, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98686
in-theory        98686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98686.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-550, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98687
in-theory        98687
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98687.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-540, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98688
in-theory        98688
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98688.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-530, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98689
in-theory        98689
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98689.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-520, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98690
in-theory        98690
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98690.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-510, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98691
in-theory        98691
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98691.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-500, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98692
in-theory        98692
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98692.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-490, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98693
in-theory        98693
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98693.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-480, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98694
in-theory        98694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98694.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-469, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98695
in-theory        98695
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or 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-98695.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (G or H))), M:tm-456, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98696
in-theory        98696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98696.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-453, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98697
in-theory        98697
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or 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-98697.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-443, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98698
in-theory        98698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98698.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-409, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98699
in-theory        98699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98699.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-400, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98700
in-theory        98700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98700.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-391, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98701
in-theory        98701
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98701.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-382, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98702
in-theory        98702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98702.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-373, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98703
in-theory        98703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98703.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-364, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98704
in-theory        98704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98704.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-354, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98705
in-theory        98705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98705.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98706
in-theory        98706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98706.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-338, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98707
in-theory        98707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98707.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-327, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98708
in-theory        98708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or 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-98708.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-326, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98709
in-theory        98709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or 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-98709.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-325, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98710
in-theory        98710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98710.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-324, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98711
in-theory        98711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or 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-98711.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-323, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98712
in-theory        98712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or 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-98712.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G and H) -> H)), M:tm-322, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98713
in-theory        98713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or 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-98713.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G and H) -> G)), M:tm-320, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98714
in-theory        98714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98714.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98715
in-theory        98715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or 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-98715.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H -> G))), M:tm-315, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98716
in-theory        98716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 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-7.            (A -> (B or 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-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-98716.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-311, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98717
in-theory        98717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-7.            (A -> (B or 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-98717.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) or G)), M:tm-310, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98718
in-theory        98718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98718.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and G))), M:tm-309, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98719
in-theory        98719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1046 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (or Fm Em)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-7.            (A -> (B or 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-98719.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (D -> ((E -> (F or E)) and D))), M:tm-308, m:tm-1046, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (or Fm Em)) Dm))))
================================================================
tm-name          tm-98720
in-theory        98720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-1046 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (or Fm Em)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-7.            (A -> (B or 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-98720.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1046, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> Em (or Fm Em)) Dm))))
================================================================
tm-name          tm-98721
in-theory        98721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
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-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-7.            (A -> (B or 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-98721.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-305, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98722
in-theory        98722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98722.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-303, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98723
in-theory        98723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98723.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-270, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98724
in-theory        98724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98724.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-239, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98725
in-theory        98725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98725.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-210, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98726
in-theory        98726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98726.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-183, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98727
in-theory        98727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98727.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-157, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98728
in-theory        98728
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98728.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-147, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98729
in-theory        98729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98729.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-134, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98730
in-theory        98730
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98730.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-125, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98731
in-theory        98731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98731.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-113, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98732
in-theory        98732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98732.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-105, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98733
in-theory        98733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98733.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-95, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98734
in-theory        98734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98734.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-83, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98735
in-theory        98735
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98735.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G or F)) and E)))), M:tm-76, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98736
in-theory        98736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98736.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-69, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98737
in-theory        98737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or 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-98737.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-54, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98738
in-theory        98738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) 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-42.           (A -> ((B -> (C or B)) and A)), 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-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-98738.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-42, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98739
in-theory        98739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98739.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-32, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98740
in-theory        98740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98740.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-23, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98741
in-theory        98741
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98741.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-22, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98742
in-theory        98742
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98742.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-21, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98743
in-theory        98743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98743.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-20, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98744
in-theory        98744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98744.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-19, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98745
in-theory        98745
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-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-98745.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G or F)) and E)))), M:tm-7, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98746
in-theory        98746
times-derived    1
----------------------------------------------------------------
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-6 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or 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-98746.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))) or G), M:tm-6, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98747
in-theory        98747
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G or F)) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or 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-98747.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G or F)) and E))) and A)), M:tm-5, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98748
in-theory        98748
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1046 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or 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-98748.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((F -> (G or F)) and E)))), M:tm-1, m:tm-1046, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-98749
in-theory        98749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-1003 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-98749.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I))))), M:tm-1003, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98750
in-theory        98750
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-992 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98750.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I))))), M:tm-992, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98751
in-theory        98751
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I)))))
theorem-size     49
proof            (modus-ponens tm-980 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98751.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I))))), M:tm-980, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98752
in-theory        98752
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-930 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-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-98752.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-930, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98753
in-theory        98753
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-893 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98753.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-893, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98754
in-theory        98754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-855 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98754.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-855, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98755
in-theory        98755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-808 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98755.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-808, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98756
in-theory        98756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-98756.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-757, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98757
in-theory        98757
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))) and (H -> (I -> (J or I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98757.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I))))), M:tm-708, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98758
in-theory        98758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 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-54.           (A -> (((B -> C) -> ((C -> 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-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-98758.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-665, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98759
in-theory        98759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98759.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-622, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98760
in-theory        98760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-98760.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (H or G))), M:tm-609, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98761
in-theory        98761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98761.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-605, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98762
in-theory        98762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-1.            (A -> (B -> 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-98762.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))))), M:tm-595, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98763
in-theory        98763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98763.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-550, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98764
in-theory        98764
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98764.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-540, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98765
in-theory        98765
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98765.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-530, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98766
in-theory        98766
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98766.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-520, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98767
in-theory        98767
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98767.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-510, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98768
in-theory        98768
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98768.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-500, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98769
in-theory        98769
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98769.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I))))), M:tm-490, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98770
in-theory        98770
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98770.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-480, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98771
in-theory        98771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98771.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-469, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98772
in-theory        98772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (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-98772.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (G or H))), M:tm-456, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98773
in-theory        98773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98773.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-453, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98774
in-theory        98774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98774.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))))), M:tm-443, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98775
in-theory        98775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98775.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-409, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98776
in-theory        98776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98776.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-400, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98777
in-theory        98777
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98777.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-391, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98778
in-theory        98778
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98778.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-382, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98779
in-theory        98779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98779.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I))))), M:tm-373, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98780
in-theory        98780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98780.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-364, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98781
in-theory        98781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98781.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-354, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98782
in-theory        98782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (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-98782.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98783
in-theory        98783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98783.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G))))), M:tm-338, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98784
in-theory        98784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-98784.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))))), M:tm-327, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98785
in-theory        98785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98785.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))))), M:tm-326, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98786
in-theory        98786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98786.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))))), M:tm-325, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98787
in-theory        98787
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98787.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))))), M:tm-324, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98788
in-theory        98788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98788.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))))), M:tm-323, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98789
in-theory        98789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (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-98789.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G and H) -> H)), M:tm-322, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98790
in-theory        98790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (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-98790.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G and H) -> G)), M:tm-320, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98791
in-theory        98791
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98791.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98792
in-theory        98792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (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-98792.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (H -> G))), M:tm-315, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98793
in-theory        98793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-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-98793.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))))), M:tm-311, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98794
in-theory        98794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-98794.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) or G)), M:tm-310, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98795
in-theory        98795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98795.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and G))), M:tm-309, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98796
in-theory        98796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (D -> (E -> (F or E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-1047 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (or Fm Em))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-98796.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (D -> (E -> (F or E)))), M:tm-308, m:tm-1047, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (or Fm Em)))))
================================================================
tm-name          tm-98797
in-theory        98797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-1047 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (or Fm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98797.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1047, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (-> Em (or Fm Em)))))
================================================================
tm-name          tm-98798
in-theory        98798
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
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-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-7.            (A -> (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-98798.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))))), M:tm-305, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98799
in-theory        98799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98799.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-303, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98800
in-theory        98800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98800.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-270, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98801
in-theory        98801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98801.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-239, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98802
in-theory        98802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98802.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I))))), M:tm-210, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98803
in-theory        98803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98803.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-183, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98804
in-theory        98804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98804.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-157, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98805
in-theory        98805
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98805.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-147, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98806
in-theory        98806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98806.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-134, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98807
in-theory        98807
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98807.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-125, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98808
in-theory        98808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98808.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (I -> (J or I))))), M:tm-113, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98809
in-theory        98809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98809.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-105, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98810
in-theory        98810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98810.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G))))), M:tm-95, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98811
in-theory        98811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98811.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-83, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98812
in-theory        98812
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98812.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G or F))))), M:tm-76, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98813
in-theory        98813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98813.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G))))), M:tm-69, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98814
in-theory        98814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-98814.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-54, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98815
in-theory        98815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-1.            (A -> (B -> 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-98815.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G))))), M:tm-42, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98816
in-theory        98816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98816.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G))))), M:tm-32, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98817
in-theory        98817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98817.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G))))), M:tm-23, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98818
in-theory        98818
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98818.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G))))), M:tm-22, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98819
in-theory        98819
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98819.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G))))), M:tm-21, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98820
in-theory        98820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98820.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (H -> (I or H))))), M:tm-20, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98821
in-theory        98821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-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-98821.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (G -> (H or G))))), M:tm-19, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98822
in-theory        98822
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-7 tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-1.            (A -> (B -> 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-98822.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G or F))))), M:tm-7, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98823
in-theory        98823
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-6 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-6 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98823.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))) or G), M:tm-6, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98824
in-theory        98824
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G or F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (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-98824.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G or F)))) and A)), M:tm-5, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98825
in-theory        98825
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-1047 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (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-98825.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (G or F))))), M:tm-1, m:tm-1047, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-98826
in-theory        98826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-98826.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-1003, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98827
in-theory        98827
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-992 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-98827.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-992, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98828
in-theory        98828
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     55
proof            (modus-ponens tm-980 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98828.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-980, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98829
in-theory        98829
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-930 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98829.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-930, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98830
in-theory        98830
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-893 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98830.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-893, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98831
in-theory        98831
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-855 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98831.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-855, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98832
in-theory        98832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-808 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98832.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-808, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98833
in-theory        98833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-757 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-1.            (A -> (B -> A)), 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-98833.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-757, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98834
in-theory        98834
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))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     53
proof            (modus-ponens tm-708 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98834.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-708, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98835
in-theory        98835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-665 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-98835.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-665, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98836
in-theory        98836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-622 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-98836.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-622, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98837
in-theory        98837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98837.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H or G))), M:tm-609, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98838
in-theory        98838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-605 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98838.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-605, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98839
in-theory        98839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98839.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-595, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98840
in-theory        98840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-550 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-1.            (A -> (B -> A)), 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-98840.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-550, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98841
in-theory        98841
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-540 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98841.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-540, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98842
in-theory        98842
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-530 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-1.            (A -> (B -> A)), 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-98842.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-530, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98843
in-theory        98843
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-520 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98843.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-520, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98844
in-theory        98844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-510 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-1.            (A -> (B -> A)), 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-98844.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-510, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98845
in-theory        98845
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-500 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-1.            (A -> (B -> A)), 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-98845.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-500, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98846
in-theory        98846
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-490 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98846.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-490, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98847
in-theory        98847
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-480 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-98847.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-480, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98848
in-theory        98848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-469 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-98848.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-469, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98849
in-theory        98849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98849.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (G or H))), M:tm-456, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98850
in-theory        98850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-453 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98850.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-453, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98851
in-theory        98851
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98851.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-443, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98852
in-theory        98852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-409 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98852.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-409, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98853
in-theory        98853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-400 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98853.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-400, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98854
in-theory        98854
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-391 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-1.            (A -> (B -> A)), 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-98854.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-391, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98855
in-theory        98855
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-382 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-1.            (A -> (B -> A)), 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-98855.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-382, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98856
in-theory        98856
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-373 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98856.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-373, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98857
in-theory        98857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-364 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-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-98857.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-364, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98858
in-theory        98858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-354 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98858.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-354, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98859
in-theory        98859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98859.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98860
in-theory        98860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-338 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98860.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-338, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98861
in-theory        98861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98861.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-327, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98862
in-theory        98862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98862.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-326, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98863
in-theory        98863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98863.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-325, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98864
in-theory        98864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98864.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-324, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98865
in-theory        98865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98865.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-323, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98866
in-theory        98866
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98866.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98867
in-theory        98867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98867.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98868
in-theory        98868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98868.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98869
in-theory        98869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98869.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98870
in-theory        98870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98870.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-311, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98871
in-theory        98871
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98871.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) or G)), M:tm-310, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98872
in-theory        98872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98872.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and G))), M:tm-309, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98873
in-theory        98873
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1048 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98873.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-308, m:tm-1048, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))
================================================================
tm-name          tm-98874
in-theory        98874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-307 tm-1048 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98874.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1048, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))
================================================================
tm-name          tm-98875
in-theory        98875
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98875.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-305, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98876
in-theory        98876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-303 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98876.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-303, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98877
in-theory        98877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-270 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98877.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-270, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98878
in-theory        98878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-239 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98878.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-239, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98879
in-theory        98879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     45
proof            (modus-ponens tm-210 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98879.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-210, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98880
in-theory        98880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-183 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98880.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-183, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98881
in-theory        98881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-157 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-98881.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-157, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98882
in-theory        98882
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-147 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98882.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-147, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98883
in-theory        98883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-134 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-98883.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-134, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98884
in-theory        98884
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-125 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98884.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-125, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98885
in-theory        98885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-113 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98885.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-113, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98886
in-theory        98886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-105 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98886.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-105, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98887
in-theory        98887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-95 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98887.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-95, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98888
in-theory        98888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-83 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98888.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-83, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98889
in-theory        98889
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-76 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-10 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98889.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-76, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98890
in-theory        98890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-69 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-9 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98890.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-69, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98891
in-theory        98891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-54 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), 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-98891.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-54, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98892
in-theory        98892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-42 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98892.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-42, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98893
in-theory        98893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-32 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98893.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-32, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98894
in-theory        98894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-23 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98894.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-23, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98895
in-theory        98895
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-22 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98895.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-22, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98896
in-theory        98896
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-21 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98896.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-21, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98897
in-theory        98897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-20 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98897.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-20, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98898
in-theory        98898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-19 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-98898.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-19, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98899
in-theory        98899
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-7 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-7 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98899.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-7, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98900
in-theory        98900
times-derived    1
----------------------------------------------------------------
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-6 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-6 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98900.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) or G), M:tm-6, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98901
in-theory        98901
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), 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-98901.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))) and A)), M:tm-5, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98902
in-theory        98902
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-1 tm-1048 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
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-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-98902.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-1, m:tm-1048, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-98903
in-theory        98903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     55
proof            (modus-ponens tm-1003 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-98903.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-1003, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98904
in-theory        98904
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     55
proof            (modus-ponens tm-992 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       241
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-98904.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-992, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98905
in-theory        98905
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     67
proof            (modus-ponens tm-980 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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       285
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-98905.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-980, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98906
in-theory        98906
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     53
proof            (modus-ponens tm-930 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98906.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-930, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98907
in-theory        98907
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     53
proof            (modus-ponens tm-893 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98907.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-893, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98908
in-theory        98908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     57
proof            (modus-ponens tm-855 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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       249
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-98908.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-855, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98909
in-theory        98909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     51
proof            (modus-ponens tm-808 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98909.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-808, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98910
in-theory        98910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98910.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-757, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98911
in-theory        98911
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))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     65
proof            (modus-ponens tm-708 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-98911.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-708, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98912
in-theory        98912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98912.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-665, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98913
in-theory        98913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98913.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-622, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98914
in-theory        98914
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))) -> G))) and (H -> (I or H)))
theorem-size     45
proof            (modus-ponens tm-609 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98914.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98915
in-theory        98915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98915.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-605, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98916
in-theory        98916
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))) -> G))) and ((H -> (I or H)) and (((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     85
proof            (modus-ponens tm-595 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98916.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I or H)) and (((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-595, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98917
in-theory        98917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98917.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-550, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98918
in-theory        98918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98918.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-540, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98919
in-theory        98919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98919.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-530, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98920
in-theory        98920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98920.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-520, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98921
in-theory        98921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-4 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98921.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-510, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98922
in-theory        98922
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98922.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-500, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98923
in-theory        98923
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98923.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-490, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98924
in-theory        98924
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98924.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-480, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98925
in-theory        98925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98925.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-469, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98926
in-theory        98926
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))) -> G))) and (H -> (H or I)))
theorem-size     45
proof            (modus-ponens tm-456 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98926.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98927
in-theory        98927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98927.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-453, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98928
in-theory        98928
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))) -> G))) and ((H -> (H or I)) and (((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     85
proof            (modus-ponens tm-443 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98928.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (H or I)) and (((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-443, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98929
in-theory        98929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98929.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-409, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98930
in-theory        98930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98930.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-400, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98931
in-theory        98931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-4 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98931.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-391, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98932
in-theory        98932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98932.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-382, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98933
in-theory        98933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98933.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-373, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98934
in-theory        98934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98934.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-364, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98935
in-theory        98935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98935.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-354, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98936
in-theory        98936
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))) -> G))) and (H -> (I -> (H and I))))
theorem-size     47
proof            (modus-ponens tm-341 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98936.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98937
in-theory        98937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98937.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-338, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98938
in-theory        98938
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))) -> G))) and ((H -> (I -> (H and I))) and (((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     87
proof            (modus-ponens tm-327 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98938.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-327, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98939
in-theory        98939
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))) -> G))) and (((H and I) -> I) and (((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     85
proof            (modus-ponens tm-326 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98939.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((H and I) -> I) and (((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-326, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98940
in-theory        98940
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))) -> G))) and (((H and I) -> H) and (((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     85
proof            (modus-ponens tm-325 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98940.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((H and I) -> H) and (((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-325, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98941
in-theory        98941
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))) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((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     93
proof            (modus-ponens tm-324 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98941.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-324, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98942
in-theory        98942
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))) -> G))) and ((H -> (I -> H)) and (((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     85
proof            (modus-ponens tm-323 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98942.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I -> H)) and (((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-323, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98943
in-theory        98943
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))) -> G))) and ((H and I) -> I))
theorem-size     45
proof            (modus-ponens tm-322 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98943.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98944
in-theory        98944
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))) -> G))) and ((H and I) -> H))
theorem-size     45
proof            (modus-ponens tm-320 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98944.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98945
in-theory        98945
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))) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     53
proof            (modus-ponens tm-318 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98945.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98946
in-theory        98946
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))) -> G))) and (H -> (I -> H)))
theorem-size     45
proof            (modus-ponens tm-315 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98946.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98947
in-theory        98947
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))) -> G))) and (H or (((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     81
proof            (modus-ponens tm-311 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98947.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H or (((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-311, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98948
in-theory        98948
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))) -> G))) and ((((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     81
proof            (modus-ponens tm-310 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98948.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((((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-310, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98949
in-theory        98949
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))) -> G))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98949.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and H))), M:tm-309, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98950
in-theory        98950
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))) -> 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-1049 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98950.        ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1049, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-98951
in-theory        98951
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))) -> G))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     53
proof            (modus-ponens tm-307 tm-1049 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98951.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1049, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-98952
in-theory        98952
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))) -> G))) and (H -> (((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     81
proof            (modus-ponens tm-305 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98952.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (((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-305, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98953
in-theory        98953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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       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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98953.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-303, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98954
in-theory        98954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98954.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-270, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98955
in-theory        98955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98955.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-239, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98956
in-theory        98956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98956.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-210, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98957
in-theory        98957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98957.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-183, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98958
in-theory        98958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98958.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-157, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98959
in-theory        98959
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98959.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-147, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98960
in-theory        98960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98960.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-134, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98961
in-theory        98961
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98961.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-125, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98962
in-theory        98962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98962.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-113, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98963
in-theory        98963
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98963.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-105, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98964
in-theory        98964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98964.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-95, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98965
in-theory        98965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98965.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-83, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98966
in-theory        98966
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98966.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-76, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98967
in-theory        98967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98967.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-69, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98968
in-theory        98968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98968.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-54, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98969
in-theory        98969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98969.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-42, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98970
in-theory        98970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98970.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-32, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98971
in-theory        98971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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       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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98971.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-23, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98972
in-theory        98972
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98972.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-22, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98973
in-theory        98973
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98973.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-21, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98974
in-theory        98974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-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-98974.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-20, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98975
in-theory        98975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98975.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-19, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98976
in-theory        98976
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-2)
proof-size       173
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98976.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-7, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98977
in-theory        98977
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))) -> G))) or H)
theorem-size     41
proof            (modus-ponens tm-6 tm-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-2)
proof-size       173
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98977.        ((((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-6, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98978
in-theory        98978
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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       177
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98978.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) and A)), M:tm-5, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98979
in-theory        98979
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> 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-1049 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       173
proof-steps      9
----------------------------------------------------------------
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-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> 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-98979.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-1, m:tm-1049, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-98980
in-theory        98980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-98980.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-1003, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98981
in-theory        98981
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-992 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-98981.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-992, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98982
in-theory        98982
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     53
proof            (modus-ponens tm-980 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-3)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-98982.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-980, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98983
in-theory        98983
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-930 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98983.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-930, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98984
in-theory        98984
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-893 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-98984.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-893, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98985
in-theory        98985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-855 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-98985.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-855, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98986
in-theory        98986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-808 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-98986.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-808, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98987
in-theory        98987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-757 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-3)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-98987.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-757, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98988
in-theory        98988
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))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     51
proof            (modus-ponens tm-708 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-98988.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-708, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98989
in-theory        98989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-665 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-3.            ((A and B) -> A), axiom
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-98989.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-665, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98990
in-theory        98990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-622 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-3.            ((A and B) -> A), axiom
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-98990.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-622, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98991
in-theory        98991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H or G)))
theorem-size     31
proof            (modus-ponens tm-609 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98991.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H or G))), M:tm-609, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98992
in-theory        98992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-605 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98992.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-605, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98993
in-theory        98993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98993.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-595, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98994
in-theory        98994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-550 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-3.            ((A and B) -> A), axiom
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-98994.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-550, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98995
in-theory        98995
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-540 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98995.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-540, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98996
in-theory        98996
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-530 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-3.            ((A and B) -> A), axiom
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-98996.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-530, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98997
in-theory        98997
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-520 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-98997.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-520, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98998
in-theory        98998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-510 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-3.            ((A and B) -> A), axiom
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-98998.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-510, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-98999
in-theory        98999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-500 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-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-98999.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-500, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99000
in-theory        99000
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-490 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99000.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-490, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99001
in-theory        99001
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-480 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and B) -> A), axiom
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-99001.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-480, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99002
in-theory        99002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-469 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-3.            ((A and B) -> A), axiom
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-99002.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-469, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99003
in-theory        99003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (G or H)))
theorem-size     31
proof            (modus-ponens tm-456 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99003.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (G or H))), M:tm-456, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99004
in-theory        99004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-453 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99004.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-453, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99005
in-theory        99005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99005.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-443, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99006
in-theory        99006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-409 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99006.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-409, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99007
in-theory        99007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-400 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99007.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-400, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99008
in-theory        99008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-391 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-3.            ((A and B) -> A), axiom
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-99008.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-391, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99009
in-theory        99009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-382 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-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-99009.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-382, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99010
in-theory        99010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-373 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99010.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-373, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99011
in-theory        99011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-364 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-3.            ((A and B) -> A), axiom
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-99011.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-364, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99012
in-theory        99012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-354 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99012.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-354, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99013
in-theory        99013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99013.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99014
in-theory        99014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-338 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99014.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-338, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99015
in-theory        99015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99015.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-327, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99016
in-theory        99016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99016.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-326, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99017
in-theory        99017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99017.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-325, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99018
in-theory        99018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-99018.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-324, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99019
in-theory        99019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99019.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-323, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99020
in-theory        99020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G and H) -> H))
theorem-size     31
proof            (modus-ponens tm-322 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99020.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99021
in-theory        99021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G and H) -> G))
theorem-size     31
proof            (modus-ponens tm-320 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99021.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99022
in-theory        99022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99022.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99023
in-theory        99023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H -> G)))
theorem-size     31
proof            (modus-ponens tm-315 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99023.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99024
in-theory        99024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99024.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-311, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99025
in-theory        99025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) or G))
theorem-size     53
proof            (modus-ponens tm-310 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99025.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) or G)), M:tm-310, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99026
in-theory        99026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and G)))
theorem-size     55
proof            (modus-ponens tm-309 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99026.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and G))), M:tm-309, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99027
in-theory        99027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> 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-1050 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99027.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-308, m:tm-1050, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))
================================================================
tm-name          tm-99028
in-theory        99028
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-307 tm-1050 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99028.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1050, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))
================================================================
tm-name          tm-99029
in-theory        99029
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99029.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-305, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99030
in-theory        99030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-303 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99030.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-303, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99031
in-theory        99031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-270 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99031.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-270, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99032
in-theory        99032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-239 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99032.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-239, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99033
in-theory        99033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     43
proof            (modus-ponens tm-210 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-99033.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-210, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99034
in-theory        99034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-183 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99034.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-183, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99035
in-theory        99035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-157 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-3.            ((A and B) -> A), axiom
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-99035.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-157, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99036
in-theory        99036
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     41
proof            (modus-ponens tm-147 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99036.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-147, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99037
in-theory        99037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-134 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-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-99037.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-134, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99038
in-theory        99038
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     41
proof            (modus-ponens tm-125 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99038.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-125, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99039
in-theory        99039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-113 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99039.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-113, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99040
in-theory        99040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-105 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99040.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-105, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99041
in-theory        99041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-95 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99041.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-95, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99042
in-theory        99042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-83 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99042.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-83, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99043
in-theory        99043
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-76 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-10 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99043.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-76, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99044
in-theory        99044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-69 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-9 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99044.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-69, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99045
in-theory        99045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-54 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
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-99045.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-54, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99046
in-theory        99046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-42 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99046.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-42, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99047
in-theory        99047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-32 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99047.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-32, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99048
in-theory        99048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-23 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99048.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-23, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99049
in-theory        99049
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-22 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-4 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99049.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-22, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99050
in-theory        99050
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-21 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-3 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99050.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-21, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99051
in-theory        99051
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 I) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-20 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-54.           (A -> (((B -> C) -> ((C -> 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-99051.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-20, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99052
in-theory        99052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-19 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99052.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-19, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99053
in-theory        99053
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-7 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-7 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99053.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-7, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99054
in-theory        99054
times-derived    1
----------------------------------------------------------------
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-6 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-6 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99054.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))) or G), M:tm-6, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99055
in-theory        99055
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((E and G) or E) -> F))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
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-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-99055.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((E and G) or E) -> F))) and A)), M:tm-5, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99056
in-theory        99056
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-1 tm-1050 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-1 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99056.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-1, m:tm-1050, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-99057
in-theory        99057
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-1003 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99057.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-1003, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99058
in-theory        99058
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-992 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99058.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-992, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99059
in-theory        99059
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     53
proof            (modus-ponens tm-980 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-4)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99059.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-980, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99060
in-theory        99060
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-930 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99060.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-930, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99061
in-theory        99061
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-893 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99061.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-893, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99062
in-theory        99062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-855 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-4)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-99062.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-855, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99063
in-theory        99063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-808 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99063.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-808, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99064
in-theory        99064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-757 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
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-54.           (A -> (((B -> C) -> ((C -> 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-99064.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-757, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99065
in-theory        99065
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))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     51
proof            (modus-ponens tm-708 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) 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-54.           (A -> (((B -> C) -> ((C -> 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-99065.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-708, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99066
in-theory        99066
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-665 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-4.            ((A and B) -> B), axiom
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-99066.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-665, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99067
in-theory        99067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-622 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-99067.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-622, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99068
in-theory        99068
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H or G)))
theorem-size     31
proof            (modus-ponens tm-609 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-4.            ((A and B) -> B), axiom
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-99068.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H or G))), M:tm-609, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99069
in-theory        99069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-605 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99069.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-605, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99070
in-theory        99070
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99070.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-595, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99071
in-theory        99071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-550 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-7 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-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-4.            ((A and B) -> B), axiom
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-99071.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-550, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99072
in-theory        99072
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-540 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 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-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-4.            ((A and B) -> B), axiom
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-99072.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-540, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99073
in-theory        99073
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-530 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-6 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-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-4.            ((A and B) -> B), axiom
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-99073.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-530, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99074
in-theory        99074
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-520 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99074.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-520, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99075
in-theory        99075
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-510 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99075.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-510, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99076
in-theory        99076
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-500 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-3 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-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-4.            ((A and B) -> B), axiom
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-99076.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-500, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99077
in-theory        99077
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-490 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99077.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-490, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99078
in-theory        99078
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-480 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-1 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-99078.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-480, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99079
in-theory        99079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-469 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-99079.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-469, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99080
in-theory        99080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (G or H)))
theorem-size     31
proof            (modus-ponens tm-456 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-4.            ((A and B) -> B), axiom
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-99080.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (G or H))), M:tm-456, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99081
in-theory        99081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-453 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99081.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-453, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99082
in-theory        99082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99082.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-443, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99083
in-theory        99083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-409 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 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-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-4.            ((A and B) -> B), axiom
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-99083.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-409, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99084
in-theory        99084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-400 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99084.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-400, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99085
in-theory        99085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-391 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99085.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-391, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99086
in-theory        99086
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-382 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-3 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-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-4.            ((A and B) -> B), axiom
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-99086.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-382, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99087
in-theory        99087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-373 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99087.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-373, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99088
in-theory        99088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-364 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-1 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-4.            ((A and B) -> B), axiom
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-99088.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-364, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99089
in-theory        99089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-354 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99089.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-354, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99090
in-theory        99090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H -> (G and H))))
theorem-size     33
proof            (modus-ponens tm-341 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-4.            ((A and B) -> B), axiom
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-99090.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99091
in-theory        99091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-338 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99091.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-338, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99092
in-theory        99092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99092.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-327, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99093
in-theory        99093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-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-99093.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-326, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99094
in-theory        99094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99094.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-325, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99095
in-theory        99095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-4.            ((A and B) -> B), axiom
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-99095.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-324, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99096
in-theory        99096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99096.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-323, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99097
in-theory        99097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G and H) -> H))
theorem-size     31
proof            (modus-ponens tm-322 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-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-99097.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99098
in-theory        99098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G and H) -> G))
theorem-size     31
proof            (modus-ponens tm-320 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-99098.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99099
in-theory        99099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     39
proof            (modus-ponens tm-318 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99099.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99100
in-theory        99100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H -> G)))
theorem-size     31
proof            (modus-ponens tm-315 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-99100.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99101
in-theory        99101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-4.            ((A and B) -> B), axiom
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-99101.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-311, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99102
in-theory        99102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) or G))
theorem-size     53
proof            (modus-ponens tm-310 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-4.            ((A and B) -> B), axiom
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-99102.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) or G)), M:tm-310, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99103
in-theory        99103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and G)))
theorem-size     55
proof            (modus-ponens tm-309 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-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-4.            ((A and B) -> B), axiom
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-99103.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and G))), M:tm-309, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99104
in-theory        99104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     37
proof            (modus-ponens tm-308 tm-1051 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-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-99104.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-308, m:tm-1051, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))
================================================================
tm-name          tm-99105
in-theory        99105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-307 tm-1051 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
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-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-4.            ((A and B) -> B), axiom
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-99105.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1051, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))
================================================================
tm-name          tm-99106
in-theory        99106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-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-4.            ((A and B) -> B), axiom
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-99106.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))))), M:tm-305, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99107
in-theory        99107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-303 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99107.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-303, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99108
in-theory        99108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-270 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99108.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-270, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99109
in-theory        99109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-239 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99109.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-239, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99110
in-theory        99110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     43
proof            (modus-ponens tm-210 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99110.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-210, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99111
in-theory        99111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-183 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99111.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-183, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99112
in-theory        99112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-157 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99112.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-157, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99113
in-theory        99113
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     41
proof            (modus-ponens tm-147 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-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-99113.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-147, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99114
in-theory        99114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-134 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-4.            ((A and B) -> B), axiom
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-99114.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-134, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99115
in-theory        99115
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     41
proof            (modus-ponens tm-125 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-4.            ((A and B) -> B), axiom
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-99115.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-125, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99116
in-theory        99116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-113 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99116.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((H -> I) -> (((J and H) or H) -> I)))), M:tm-113, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99117
in-theory        99117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-105 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-4.            ((A and B) -> B), axiom
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-99117.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-105, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99118
in-theory        99118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-95 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-4.            ((A and B) -> B), axiom
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-99118.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-95, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99119
in-theory        99119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-83 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-4.            ((A and B) -> B), axiom
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-99119.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-83, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99120
in-theory        99120
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-76 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99120.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-76, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99121
in-theory        99121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-69 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99121.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-69, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99122
in-theory        99122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-54 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-99122.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-54, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99123
in-theory        99123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-42 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99123.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-42, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99124
in-theory        99124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-32 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99124.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-32, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99125
in-theory        99125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-23 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99125.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-23, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99126
in-theory        99126
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-22 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-4 tm-8)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-99126.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-22, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99127
in-theory        99127
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-21 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99127.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-21, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99128
in-theory        99128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-20 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99128.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((G -> H) -> (((I and G) or G) -> H)))), M:tm-20, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99129
in-theory        99129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-19 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99129.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((F -> G) -> (((H and F) or F) -> G)))), M:tm-19, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99130
in-theory        99130
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-7 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-7 tm-5 tm-8 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-99130.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-7, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99131
in-theory        99131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) or G)
theorem-size     27
proof            (modus-ponens tm-6 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-6 tm-5 tm-8 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-99131.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))) or G), M:tm-6, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99132
in-theory        99132
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((G and E) or E) -> F))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
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-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-99132.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((G and E) or E) -> F))) and A)), M:tm-5, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99133
in-theory        99133
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((G and E) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-1 tm-1051 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em))))))
axioms-used      (tm-1 tm-5 tm-8 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
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-4.            ((A and B) -> B), axiom
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-99133.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((E -> F) -> (((G and E) or E) -> F)))), M:tm-1, m:tm-1051, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> Dm Em) (-> (or (and Fm Dm) Dm) Em)))))
================================================================
tm-name          tm-99134
in-theory        99134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-1003 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99134.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-1003, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99135
in-theory        99135
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-992 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99135.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-992, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99136
in-theory        99136
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     59
proof            (modus-ponens tm-980 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99136.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-980, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99137
in-theory        99137
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-930 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99137.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-930, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99138
in-theory        99138
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-893 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99138.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-893, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99139
in-theory        99139
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-855 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99139.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-855, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99140
in-theory        99140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-808 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-99140.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-808, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99141
in-theory        99141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-757 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-48.           (((A -> (B and 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-99141.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-757, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99142
in-theory        99142
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))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     57
proof            (modus-ponens tm-708 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99142.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-708, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99143
in-theory        99143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-665 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-48.           (((A -> (B and 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-99143.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-665, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99144
in-theory        99144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-622 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99144.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-622, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99145
in-theory        99145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H or G)))
theorem-size     37
proof            (modus-ponens tm-609 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99145.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99146
in-theory        99146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-605 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99146.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-605, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99147
in-theory        99147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-48.           (((A -> (B and 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-99147.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-595, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99148
in-theory        99148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-550 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99148.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-550, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99149
in-theory        99149
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-540 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99149.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-540, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99150
in-theory        99150
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-530 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99150.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-530, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99151
in-theory        99151
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-520 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99151.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-520, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99152
in-theory        99152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-510 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99152.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-510, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99153
in-theory        99153
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-500 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99153.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-500, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99154
in-theory        99154
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-490 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99154.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-490, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99155
in-theory        99155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-480 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99155.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-480, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99156
in-theory        99156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-469 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99156.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-469, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99157
in-theory        99157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (G or H)))
theorem-size     37
proof            (modus-ponens tm-456 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99157.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99158
in-theory        99158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-453 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99158.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-453, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99159
in-theory        99159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-48.           (((A -> (B and 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-99159.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-443, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99160
in-theory        99160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-409 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99160.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-409, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99161
in-theory        99161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-400 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99161.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-400, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99162
in-theory        99162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-391 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99162.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-391, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99163
in-theory        99163
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-382 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99163.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-382, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99164
in-theory        99164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-373 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99164.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-373, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99165
in-theory        99165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-364 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99165.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-364, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99166
in-theory        99166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-354 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99166.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-354, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99167
in-theory        99167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H -> (G and H))))
theorem-size     39
proof            (modus-ponens tm-341 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99167.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99168
in-theory        99168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     41
proof            (modus-ponens tm-338 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99168.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-338, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99169
in-theory        99169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-48.           (((A -> (B and 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-99169.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-327, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99170
in-theory        99170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99170.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-326, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99171
in-theory        99171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99171.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-325, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99172
in-theory        99172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-48.           (((A -> (B and 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-99172.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-324, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99173
in-theory        99173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-48.           (((A -> (B and 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-99173.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-323, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99174
in-theory        99174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G and H) -> H))
theorem-size     37
proof            (modus-ponens tm-322 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99174.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99175
in-theory        99175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G and H) -> G))
theorem-size     37
proof            (modus-ponens tm-320 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99175.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99176
in-theory        99176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     45
proof            (modus-ponens tm-318 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99176.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99177
in-theory        99177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H -> G)))
theorem-size     37
proof            (modus-ponens tm-315 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99177.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99178
in-theory        99178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-48.           (((A -> (B and 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-99178.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-311, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99179
in-theory        99179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) or G))
theorem-size     65
proof            (modus-ponens tm-310 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-48.           (((A -> (B and 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-99179.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) or G)), M:tm-310, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99180
in-theory        99180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and G)))
theorem-size     67
proof            (modus-ponens tm-309 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-2 tm-5 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-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-48.           (((A -> (B and 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-99180.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and G))), M:tm-309, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99181
in-theory        99181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     49
proof            (modus-ponens tm-308 tm-1052 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-48.           (((A -> (B and 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-99181.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-308, m:tm-1052, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))
================================================================
tm-name          tm-99182
in-theory        99182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-307 tm-1052 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99182.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1052, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))
================================================================
tm-name          tm-99183
in-theory        99183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-1.            (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-48.           (((A -> (B and 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-99183.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))))), M:tm-305, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99184
in-theory        99184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     43
proof            (modus-ponens tm-303 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99184.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-303, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99185
in-theory        99185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-270 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99185.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-270, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99186
in-theory        99186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-239 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99186.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-239, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99187
in-theory        99187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-210 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99187.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-210, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99188
in-theory        99188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     41
proof            (modus-ponens tm-183 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99188.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-183, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99189
in-theory        99189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-157 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99189.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-157, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99190
in-theory        99190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-147 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99190.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-147, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99191
in-theory        99191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-134 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99191.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-134, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99192
in-theory        99192
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-125 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99192.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-125, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99193
in-theory        99193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J))))
theorem-size     47
proof            (modus-ponens tm-113 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99193.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> (I and H)) -> J) -> ((I or (H -> (I and H))) -> J)))), M:tm-113, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99194
in-theory        99194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-105 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99194.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-105, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99195
in-theory        99195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-95 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99195.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-95, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99196
in-theory        99196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     39
proof            (modus-ponens tm-83 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99196.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-83, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99197
in-theory        99197
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     37
proof            (modus-ponens tm-76 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-10 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99197.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-76, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99198
in-theory        99198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     43
proof            (modus-ponens tm-69 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99198.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-69, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99199
in-theory        99199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-54 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-99199.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-54, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99200
in-theory        99200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-42 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99200.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-42, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99201
in-theory        99201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-32 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99201.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-32, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99202
in-theory        99202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     39
proof            (modus-ponens tm-23 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99202.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-23, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99203
in-theory        99203
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-22 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99203.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-22, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99204
in-theory        99204
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-21 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99204.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-21, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99205
in-theory        99205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I))))
theorem-size     45
proof            (modus-ponens tm-20 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99205.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> (H and G)) -> I) -> ((H or (G -> (H and G))) -> I)))), M:tm-20, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99206
in-theory        99206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H))))
theorem-size     37
proof            (modus-ponens tm-19 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99206.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> (G and F)) -> H) -> ((G or (F -> (G and F))) -> H)))), M:tm-19, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99207
in-theory        99207
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-7 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-48.           (((A -> (B and 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-99207.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-7, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99208
in-theory        99208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) or G)
theorem-size     33
proof            (modus-ponens tm-6 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-48.           (((A -> (B and 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-99208.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))) or G), M:tm-6, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99209
in-theory        99209
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99209.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))) and A)), M:tm-5, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99210
in-theory        99210
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))))
theorem-size     33
proof            (modus-ponens tm-1 tm-1052 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-48.           (((A -> (B and 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-99210.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))), M:tm-1, m:tm-1052, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> Dm (and Em Dm)) Fm) (-> (or Em (-> Dm (and Em Dm))) Fm)))))
================================================================
tm-name          tm-99211
in-theory        99211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99211.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-1003, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99212
in-theory        99212
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-992 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99212.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-992, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99213
in-theory        99213
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     55
proof            (modus-ponens tm-980 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99213.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-980, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99214
in-theory        99214
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-930 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99214.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-930, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99215
in-theory        99215
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-893 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99215.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-893, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99216
in-theory        99216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-855 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-99216.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-855, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99217
in-theory        99217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-808 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-99217.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-808, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99218
in-theory        99218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-757 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99218.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-757, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99219
in-theory        99219
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))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     53
proof            (modus-ponens tm-708 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99219.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-708, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99220
in-theory        99220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-665 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99220.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-665, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99221
in-theory        99221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-622 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99221.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-622, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99222
in-theory        99222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99222.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H or G))), M:tm-609, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99223
in-theory        99223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-605 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99223.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-605, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99224
in-theory        99224
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99224.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-595, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99225
in-theory        99225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-550 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99225.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-550, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99226
in-theory        99226
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-540 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99226.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-540, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99227
in-theory        99227
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-530 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99227.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-530, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99228
in-theory        99228
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-520 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99228.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-520, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99229
in-theory        99229
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-510 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99229.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-510, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99230
in-theory        99230
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-500 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99230.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-500, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99231
in-theory        99231
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-490 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99231.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-490, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99232
in-theory        99232
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-480 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99232.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-480, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99233
in-theory        99233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-469 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-49.           (((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-99233.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-469, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99234
in-theory        99234
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99234.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (G or H))), M:tm-456, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99235
in-theory        99235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-453 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99235.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-453, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99236
in-theory        99236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-49.           (((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-99236.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-443, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99237
in-theory        99237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-409 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99237.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-409, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99238
in-theory        99238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-400 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99238.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-400, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99239
in-theory        99239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-391 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99239.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-391, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99240
in-theory        99240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-382 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99240.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-382, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99241
in-theory        99241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-373 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99241.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-373, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99242
in-theory        99242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-364 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-49.           (((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-99242.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-364, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99243
in-theory        99243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-354 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99243.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-354, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99244
in-theory        99244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H -> (G and H))))
theorem-size     35
proof            (modus-ponens tm-341 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99244.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99245
in-theory        99245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-338 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99245.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-338, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99246
in-theory        99246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99246.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-327, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99247
in-theory        99247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99247.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-326, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99248
in-theory        99248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99248.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-325, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99249
in-theory        99249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99249.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-324, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99250
in-theory        99250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99250.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-323, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99251
in-theory        99251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99251.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99252
in-theory        99252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99252.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99253
in-theory        99253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     41
proof            (modus-ponens tm-318 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99253.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99254
in-theory        99254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99254.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99255
in-theory        99255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99255.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-311, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99256
in-theory        99256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
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-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-49.           (((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-99256.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) or G)), M:tm-310, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99257
in-theory        99257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99257.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and G))), M:tm-309, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99258
in-theory        99258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-308 tm-1053 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99258.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-308, m:tm-1053, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-99259
in-theory        99259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-307 tm-1053 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99259.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1053, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-99260
in-theory        99260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
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-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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99260.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))))), M:tm-305, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99261
in-theory        99261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-303 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99261.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-303, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99262
in-theory        99262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-270 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99262.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-270, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99263
in-theory        99263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-239 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99263.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-239, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99264
in-theory        99264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     45
proof            (modus-ponens tm-210 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99264.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-210, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99265
in-theory        99265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-183 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99265.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-183, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99266
in-theory        99266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-157 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99266.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-157, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99267
in-theory        99267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-147 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99267.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-147, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99268
in-theory        99268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-134 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99268.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-134, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99269
in-theory        99269
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-125 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99269.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-125, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99270
in-theory        99270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-113 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99270.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((H or (H or I)) -> J)))), M:tm-113, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99271
in-theory        99271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-105 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99271.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-105, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99272
in-theory        99272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-95 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99272.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-95, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99273
in-theory        99273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-83 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99273.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-83, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99274
in-theory        99274
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-76 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99274.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-76, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99275
in-theory        99275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-69 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99275.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-69, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99276
in-theory        99276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-54 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99276.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-54, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99277
in-theory        99277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-42 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99277.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-42, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99278
in-theory        99278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-32 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am 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-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-99278.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-32, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99279
in-theory        99279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-23 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99279.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-23, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99280
in-theory        99280
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-22 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99280.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-22, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99281
in-theory        99281
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-21 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99281.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-21, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99282
in-theory        99282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-20 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99282.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((G or (G or H)) -> I)))), M:tm-20, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99283
in-theory        99283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-19 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-54.           (A -> (((B -> C) -> ((C -> 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-99283.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((F or (F or G)) -> H)))), M:tm-19, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99284
in-theory        99284
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-7 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99284.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-7, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99285
in-theory        99285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) or G)
theorem-size     29
proof            (modus-ponens tm-6 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
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-49.           (((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-99285.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))) or G), M:tm-6, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99286
in-theory        99286
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99286.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))) and A)), M:tm-5, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99287
in-theory        99287
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-1 tm-1053 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99287.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))), M:tm-1, m:tm-1053, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Dm (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99288
in-theory        99288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99288.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-1003, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99289
in-theory        99289
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-992 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99289.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-992, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99290
in-theory        99290
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     55
proof            (modus-ponens tm-980 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99290.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-980, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99291
in-theory        99291
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-930 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99291.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-930, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99292
in-theory        99292
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-893 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99292.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-893, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99293
in-theory        99293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-855 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-99293.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-855, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99294
in-theory        99294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-808 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-99294.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-808, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99295
in-theory        99295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-757 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99295.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-757, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99296
in-theory        99296
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))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     53
proof            (modus-ponens tm-708 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99296.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-708, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99297
in-theory        99297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-665 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99297.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-665, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99298
in-theory        99298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-622 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-50.           (((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-99298.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-622, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99299
in-theory        99299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99299.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H or G))), M:tm-609, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99300
in-theory        99300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-605 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99300.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-605, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99301
in-theory        99301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-50.           (((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-99301.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H or G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-595, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99302
in-theory        99302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-550 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99302.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-550, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99303
in-theory        99303
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-540 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99303.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-540, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99304
in-theory        99304
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-530 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99304.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-530, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99305
in-theory        99305
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-520 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99305.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-520, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99306
in-theory        99306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-510 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99306.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-510, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99307
in-theory        99307
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-500 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99307.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-500, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99308
in-theory        99308
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-490 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99308.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-490, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99309
in-theory        99309
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-480 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-50.           (((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-99309.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-480, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99310
in-theory        99310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-469 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99310.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-469, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99311
in-theory        99311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99311.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (G or H))), M:tm-456, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99312
in-theory        99312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-453 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99312.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-453, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99313
in-theory        99313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99313.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (G or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-443, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99314
in-theory        99314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-409 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99314.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-409, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99315
in-theory        99315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-400 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99315.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-400, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99316
in-theory        99316
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-391 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99316.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-391, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99317
in-theory        99317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-382 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99317.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-382, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99318
in-theory        99318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-373 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99318.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-373, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99319
in-theory        99319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-364 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99319.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-364, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99320
in-theory        99320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-354 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99320.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-354, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99321
in-theory        99321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H -> (G and H))))
theorem-size     35
proof            (modus-ponens tm-341 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99321.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99322
in-theory        99322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-338 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99322.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-338, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99323
in-theory        99323
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99323.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-327, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99324
in-theory        99324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99324.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G and H) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-326, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99325
in-theory        99325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99325.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G and H) -> G) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-325, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99326
in-theory        99326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99326.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-324, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99327
in-theory        99327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99327.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> G)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-323, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99328
in-theory        99328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99328.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99329
in-theory        99329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99329.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99330
in-theory        99330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     41
proof            (modus-ponens tm-318 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99330.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99331
in-theory        99331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99331.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99332
in-theory        99332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
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-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-50.           (((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-99332.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-311, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99333
in-theory        99333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99333.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) or G)), M:tm-310, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99334
in-theory        99334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99334.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and G))), M:tm-309, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99335
in-theory        99335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-308 tm-1054 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99335.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-308, m:tm-1054, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))
================================================================
tm-name          tm-99336
in-theory        99336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-307 tm-1054 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99336.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1054, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))
================================================================
tm-name          tm-99337
in-theory        99337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
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-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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99337.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) and (G -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))))), M:tm-305, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99338
in-theory        99338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-303 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99338.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-303, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99339
in-theory        99339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-270 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99339.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-270, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99340
in-theory        99340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-239 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99340.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-239, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99341
in-theory        99341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     45
proof            (modus-ponens tm-210 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99341.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-210, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99342
in-theory        99342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-183 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99342.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-183, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99343
in-theory        99343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-157 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99343.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-157, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99344
in-theory        99344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-147 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99344.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-147, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99345
in-theory        99345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-134 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99345.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-134, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99346
in-theory        99346
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-125 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99346.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-125, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99347
in-theory        99347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-113 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99347.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H or I) -> J) -> ((I or (H or I)) -> J)))), M:tm-113, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99348
in-theory        99348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-105 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99348.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-105, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99349
in-theory        99349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-95 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99349.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-95, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99350
in-theory        99350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-83 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99350.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-83, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99351
in-theory        99351
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-76 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99351.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-76, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99352
in-theory        99352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-69 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99352.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-69, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99353
in-theory        99353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-54 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99353.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-54, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99354
in-theory        99354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-42 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-50.           (((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-99354.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-42, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99355
in-theory        99355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-32 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99355.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-32, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99356
in-theory        99356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-23 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99356.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-23, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99357
in-theory        99357
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-22 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99357.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-22, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99358
in-theory        99358
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-21 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99358.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-21, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99359
in-theory        99359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-20 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99359.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G or H) -> I) -> ((H or (G or H)) -> I)))), M:tm-20, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99360
in-theory        99360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-19 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-54.           (A -> (((B -> C) -> ((C -> 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-99360.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F or G) -> H) -> ((G or (F or G)) -> H)))), M:tm-19, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99361
in-theory        99361
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-7 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
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-50.           (((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-99361.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-7, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99362
in-theory        99362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) or G)
theorem-size     29
proof            (modus-ponens tm-6 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99362.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))) or G), M:tm-6, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99363
in-theory        99363
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99363.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))) and A)), M:tm-5, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99364
in-theory        99364
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-1 tm-1054 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99364.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))), M:tm-1, m:tm-1054, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (or Dm Em) Fm) (-> (or Em (or Dm Em)) Fm)))))
================================================================
tm-name          tm-99365
in-theory        99365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-1003 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99365.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-1003, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99366
in-theory        99366
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-992 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99366.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-992, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99367
in-theory        99367
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     69
proof            (modus-ponens tm-980 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8)
proof-size       291
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> 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-99367.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-980, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99368
in-theory        99368
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-930 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99368.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-930, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99369
in-theory        99369
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-893 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99369.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-893, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99370
in-theory        99370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     59
proof            (modus-ponens tm-855 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-99370.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-855, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99371
in-theory        99371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     53
proof            (modus-ponens tm-808 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-99371.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-808, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99372
in-theory        99372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     53
proof            (modus-ponens tm-757 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-3)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99372.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-757, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99373
in-theory        99373
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))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     67
proof            (modus-ponens tm-708 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       285
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99373.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-708, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99374
in-theory        99374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-665 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99374.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-665, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99375
in-theory        99375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-622 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99375.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-622, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99376
in-theory        99376
times-derived    1
----------------------------------------------------------------
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))) and (H -> (I or H)))
theorem-size     47
proof            (modus-ponens tm-609 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99376.        ((((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))) and (H -> (I or H))), M:tm-609, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99377
in-theory        99377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-605 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99377.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-605, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99378
in-theory        99378
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (I or H)) and (((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     89
proof            (modus-ponens tm-595 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99378.        ((((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))) and ((H -> (I or H)) and (((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-595, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99379
in-theory        99379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-550 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99379.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-550, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99380
in-theory        99380
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-540 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99380.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-540, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99381
in-theory        99381
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-530 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99381.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-530, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99382
in-theory        99382
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-520 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99382.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-520, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99383
in-theory        99383
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-510 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99383.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-510, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99384
in-theory        99384
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-500 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99384.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-500, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99385
in-theory        99385
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-490 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99385.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-490, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99386
in-theory        99386
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-480 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99386.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-480, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99387
in-theory        99387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-469 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99387.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-469, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99388
in-theory        99388
times-derived    1
----------------------------------------------------------------
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))) and (H -> (H or I)))
theorem-size     47
proof            (modus-ponens tm-456 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99388.        ((((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))) and (H -> (H or I))), M:tm-456, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99389
in-theory        99389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-453 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99389.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-453, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99390
in-theory        99390
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (H or I)) and (((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     89
proof            (modus-ponens tm-443 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99390.        ((((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))) and ((H -> (H or I)) and (((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-443, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99391
in-theory        99391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-409 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99391.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-409, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99392
in-theory        99392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-400 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99392.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-400, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99393
in-theory        99393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-391 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99393.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-391, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99394
in-theory        99394
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-382 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99394.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-382, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99395
in-theory        99395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-373 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99395.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-373, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99396
in-theory        99396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-364 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99396.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-364, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99397
in-theory        99397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-354 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99397.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-354, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99398
in-theory        99398
times-derived    1
----------------------------------------------------------------
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))) and (H -> (I -> (H and I))))
theorem-size     49
proof            (modus-ponens tm-341 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99398.        ((((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))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99399
in-theory        99399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     51
proof            (modus-ponens tm-338 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99399.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-338, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99400
in-theory        99400
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (I -> (H and I))) and (((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     91
proof            (modus-ponens tm-327 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-8)
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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99400.        ((((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))) and ((H -> (I -> (H and I))) and (((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-327, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99401
in-theory        99401
times-derived    1
----------------------------------------------------------------
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))) and (((H and I) -> I) and (((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     89
proof            (modus-ponens tm-326 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99401.        ((((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))) and (((H and I) -> I) and (((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-326, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99402
in-theory        99402
times-derived    1
----------------------------------------------------------------
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))) and (((H and I) -> H) and (((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     89
proof            (modus-ponens tm-325 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99402.        ((((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))) and (((H and I) -> H) and (((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-325, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99403
in-theory        99403
times-derived    1
----------------------------------------------------------------
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))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((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     97
proof            (modus-ponens tm-324 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       313
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99403.        ((((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))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((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-324, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99404
in-theory        99404
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (I -> H)) and (((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     89
proof            (modus-ponens tm-323 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99404.        ((((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))) and ((H -> (I -> H)) and (((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-323, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99405
in-theory        99405
times-derived    1
----------------------------------------------------------------
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))) and ((H and I) -> I))
theorem-size     47
proof            (modus-ponens tm-322 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99405.        ((((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))) and ((H and I) -> I)), M:tm-322, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99406
in-theory        99406
times-derived    1
----------------------------------------------------------------
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))) and ((H and I) -> H))
theorem-size     47
proof            (modus-ponens tm-320 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99406.        ((((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))) and ((H and I) -> H)), M:tm-320, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99407
in-theory        99407
times-derived    1
----------------------------------------------------------------
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))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     55
proof            (modus-ponens tm-318 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99407.        ((((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))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99408
in-theory        99408
times-derived    1
----------------------------------------------------------------
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))) and (H -> (I -> H)))
theorem-size     47
proof            (modus-ponens tm-315 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99408.        ((((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))) and (H -> (I -> H))), M:tm-315, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99409
in-theory        99409
times-derived    1
----------------------------------------------------------------
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))) and (H or (((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     85
proof            (modus-ponens tm-311 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99409.        ((((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))) and (H or (((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-311, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99410
in-theory        99410
times-derived    1
----------------------------------------------------------------
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))) and ((((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))) or H))
theorem-size     85
proof            (modus-ponens tm-310 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99410.        ((((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))) and ((((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))) or H)), M:tm-310, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99411
in-theory        99411
times-derived    1
----------------------------------------------------------------
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))) and (H -> ((((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))) and H)))
theorem-size     87
proof            (modus-ponens tm-309 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-8)
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-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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99411.        ((((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))) and (H -> ((((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))) and H))), M:tm-309, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99412
in-theory        99412
times-derived    1
----------------------------------------------------------------
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))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     69
proof            (modus-ponens tm-308 tm-1055 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99412.        ((((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))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-308, m:tm-1055, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))
================================================================
tm-name          tm-99413
in-theory        99413
times-derived    1
----------------------------------------------------------------
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))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     55
proof            (modus-ponens tm-307 tm-1055 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
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-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99413.        ((((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))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1055, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))
================================================================
tm-name          tm-99414
in-theory        99414
times-derived    1
----------------------------------------------------------------
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))) and (H -> (((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     85
proof            (modus-ponens tm-305 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99414.        ((((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))) and (H -> (((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-305, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99415
in-theory        99415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     53
proof            (modus-ponens tm-303 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99415.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-303, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99416
in-theory        99416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-270 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99416.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-270, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99417
in-theory        99417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-239 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99417.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-239, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99418
in-theory        99418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     59
proof            (modus-ponens tm-210 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99418.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-210, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99419
in-theory        99419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     51
proof            (modus-ponens tm-183 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99419.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-183, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99420
in-theory        99420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-157 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99420.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-157, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99421
in-theory        99421
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     57
proof            (modus-ponens tm-147 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99421.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-147, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99422
in-theory        99422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-134 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99422.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-134, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99423
in-theory        99423
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     57
proof            (modus-ponens tm-125 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99423.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-125, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99424
in-theory        99424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K))))
theorem-size     57
proof            (modus-ponens tm-113 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99424.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((((H -> I) -> ((J or H) -> I)) -> K) -> (((J -> H) or ((H -> I) -> ((J or H) -> I))) -> K)))), M:tm-113, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99425
in-theory        99425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     61
proof            (modus-ponens tm-105 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99425.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-105, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99426
in-theory        99426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-95 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99426.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-95, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99427
in-theory        99427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     49
proof            (modus-ponens tm-83 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99427.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-83, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99428
in-theory        99428
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))))
theorem-size     47
proof            (modus-ponens tm-76 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99428.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-76, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99429
in-theory        99429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     53
proof            (modus-ponens tm-69 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99429.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-69, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99430
in-theory        99430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-54 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99430.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-54, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99431
in-theory        99431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-42 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99431.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-42, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99432
in-theory        99432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-32 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99432.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-32, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99433
in-theory        99433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     49
proof            (modus-ponens tm-23 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99433.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-23, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99434
in-theory        99434
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-22 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99434.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-22, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99435
in-theory        99435
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-21 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99435.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-21, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99436
in-theory        99436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J))))
theorem-size     55
proof            (modus-ponens tm-20 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99436.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((((G -> H) -> ((I or G) -> H)) -> J) -> (((I -> G) or ((G -> H) -> ((I or G) -> H))) -> J)))), M:tm-20, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99437
in-theory        99437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I))))
theorem-size     47
proof            (modus-ponens tm-19 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99437.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((((F -> G) -> ((H or F) -> G)) -> I) -> (((H -> F) or ((F -> G) -> ((H or F) -> G))) -> I)))), M:tm-19, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99438
in-theory        99438
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> 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-7 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       179
proof-steps      9
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99438.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-7, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99439
in-theory        99439
times-derived    1
----------------------------------------------------------------
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))) or H)
theorem-size     43
proof            (modus-ponens tm-6 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       179
proof-steps      9
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99439.        ((((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))) or H), M:tm-6, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99440
in-theory        99440
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) and A))
theorem-size     45
proof            (modus-ponens tm-5 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99440.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))) and A)), M:tm-5, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99441
in-theory        99441
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> 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-1 tm-1055 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       179
proof-steps      9
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99441.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))), M:tm-1, m:tm-1055, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> (-> (-> (-> Dm Em) (-> (or Fm Dm) Em)) Gm) (-> (or (-> Fm Dm) (-> (-> Dm Em) (-> (or Fm Dm) Em))) Gm)))))
================================================================
tm-name          tm-99442
in-theory        99442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-1003 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99442.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-1003, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99443
in-theory        99443
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-992 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, 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-99443.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-992, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99444
in-theory        99444
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     57
proof            (modus-ponens tm-980 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99444.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-980, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99445
in-theory        99445
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-930 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99445.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-930, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99446
in-theory        99446
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-893 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99446.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-893, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99447
in-theory        99447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     47
proof            (modus-ponens tm-855 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-99447.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-855, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99448
in-theory        99448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     41
proof            (modus-ponens tm-808 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-99448.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-808, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99449
in-theory        99449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     41
proof            (modus-ponens tm-757 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-99449.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-757, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99450
in-theory        99450
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))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     55
proof            (modus-ponens tm-708 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) 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-54.           (A -> (((B -> C) -> ((C -> 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-99450.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-708, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99451
in-theory        99451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-665 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-99451.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-665, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99452
in-theory        99452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-622 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99452.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-622, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99453
in-theory        99453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I or H)))
theorem-size     35
proof            (modus-ponens tm-609 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99453.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I or H))), M:tm-609, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99454
in-theory        99454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-605 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99454.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-605, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99455
in-theory        99455
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-99455.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-595, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99456
in-theory        99456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-550 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99456.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-550, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99457
in-theory        99457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-540 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99457.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-540, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99458
in-theory        99458
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-530 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99458.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-530, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99459
in-theory        99459
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-520 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99459.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-520, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99460
in-theory        99460
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-510 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99460.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-510, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99461
in-theory        99461
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-500 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99461.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-500, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99462
in-theory        99462
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-490 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99462.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-490, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99463
in-theory        99463
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-480 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99463.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-480, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99464
in-theory        99464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-469 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99464.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-469, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99465
in-theory        99465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (H or I)))
theorem-size     35
proof            (modus-ponens tm-456 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99465.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (H or I))), M:tm-456, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99466
in-theory        99466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-453 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99466.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-453, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99467
in-theory        99467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99467.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-443, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99468
in-theory        99468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-409 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99468.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-409, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99469
in-theory        99469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-400 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99469.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-400, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99470
in-theory        99470
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-391 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99470.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-391, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99471
in-theory        99471
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-382 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99471.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-382, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99472
in-theory        99472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-373 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99472.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-373, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99473
in-theory        99473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-364 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99473.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-364, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99474
in-theory        99474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-354 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99474.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-354, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99475
in-theory        99475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I -> (H and I))))
theorem-size     37
proof            (modus-ponens tm-341 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99475.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99476
in-theory        99476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     39
proof            (modus-ponens tm-338 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99476.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-338, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99477
in-theory        99477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99477.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-327, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99478
in-theory        99478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99478.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-326, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99479
in-theory        99479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99479.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-325, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99480
in-theory        99480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99480.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-324, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99481
in-theory        99481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99481.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-323, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99482
in-theory        99482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H and I) -> I))
theorem-size     35
proof            (modus-ponens tm-322 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99482.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H and I) -> I)), M:tm-322, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99483
in-theory        99483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H and I) -> H))
theorem-size     35
proof            (modus-ponens tm-320 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99483.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H and I) -> H)), M:tm-320, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99484
in-theory        99484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     43
proof            (modus-ponens tm-318 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-99484.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99485
in-theory        99485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99485.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (I -> H))), M:tm-315, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99486
in-theory        99486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
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-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-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-99486.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-311, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99487
in-theory        99487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-99487.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) or H)), M:tm-310, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99488
in-theory        99488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99488.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and H))), M:tm-309, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99489
in-theory        99489
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     45
proof            (modus-ponens tm-308 tm-1056 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99489.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-308, m:tm-1056, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))
================================================================
tm-name          tm-99490
in-theory        99490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-1056 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99490.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1056, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))
================================================================
tm-name          tm-99491
in-theory        99491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-99491.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))))), M:tm-305, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99492
in-theory        99492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     41
proof            (modus-ponens tm-303 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99492.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-303, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99493
in-theory        99493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-270 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99493.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-270, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99494
in-theory        99494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-239 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99494.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-239, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99495
in-theory        99495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     47
proof            (modus-ponens tm-210 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99495.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-210, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99496
in-theory        99496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     39
proof            (modus-ponens tm-183 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99496.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-183, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99497
in-theory        99497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-157 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99497.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-157, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99498
in-theory        99498
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     45
proof            (modus-ponens tm-147 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99498.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-147, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99499
in-theory        99499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-134 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99499.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-134, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99500
in-theory        99500
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     45
proof            (modus-ponens tm-125 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99500.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-125, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99501
in-theory        99501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K))))))
theorem-size     45
proof            (modus-ponens tm-113 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99501.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H or ((I -> J) -> ((J -> K) -> ((I or J) -> K)))))), M:tm-113, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99502
in-theory        99502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     49
proof            (modus-ponens tm-105 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99502.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-105, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99503
in-theory        99503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-95 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99503.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-95, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99504
in-theory        99504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     37
proof            (modus-ponens tm-83 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99504.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-83, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99505
in-theory        99505
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     35
proof            (modus-ponens tm-76 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99505.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-76, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99506
in-theory        99506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     41
proof            (modus-ponens tm-69 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99506.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-69, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99507
in-theory        99507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-54 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 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-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-99507.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-54, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99508
in-theory        99508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-42 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99508.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-42, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99509
in-theory        99509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-32 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-6 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99509.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-32, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99510
in-theory        99510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     37
proof            (modus-ponens tm-23 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99510.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-23, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99511
in-theory        99511
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-22 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99511.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-22, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99512
in-theory        99512
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-21 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99512.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-21, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99513
in-theory        99513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J))))))
theorem-size     43
proof            (modus-ponens tm-20 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99513.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G or ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))), M:tm-20, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99514
in-theory        99514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I))))))
theorem-size     35
proof            (modus-ponens tm-19 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99514.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F or ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))), M:tm-19, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99515
in-theory        99515
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-7 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-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-99515.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-7, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99516
in-theory        99516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) or H)
theorem-size     31
proof            (modus-ponens tm-6 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-6 tm-5 tm-8 tm-7)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-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-99516.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))) or H), M:tm-6, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99517
in-theory        99517
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-5 tm-8 tm-7)
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-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-99517.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))) and A)), M:tm-5, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99518
in-theory        99518
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))))
theorem-size     31
proof            (modus-ponens tm-1 tm-1056 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))))))))
axioms-used      (tm-1 tm-5 tm-8 tm-7)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-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-99518.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))), M:tm-1, m:tm-1056, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or Dm (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm)))))))
================================================================
tm-name          tm-99519
in-theory        99519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-1003 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, 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-99519.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-1003, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99520
in-theory        99520
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-992 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99520.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-992, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99521
in-theory        99521
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     57
proof            (modus-ponens tm-980 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99521.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-980, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99522
in-theory        99522
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-930 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99522.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-930, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99523
in-theory        99523
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-893 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99523.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-893, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99524
in-theory        99524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     47
proof            (modus-ponens tm-855 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-99524.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-855, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99525
in-theory        99525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-808 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-99525.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-808, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99526
in-theory        99526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-757 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-3 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-54.           (A -> (((B -> C) -> ((C -> 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-99526.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-757, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99527
in-theory        99527
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))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     55
proof            (modus-ponens tm-708 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) 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-54.           (A -> (((B -> C) -> ((C -> 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-99527.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-708, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99528
in-theory        99528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-665 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-99528.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-665, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99529
in-theory        99529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-622 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99529.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-622, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99530
in-theory        99530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I or H)))
theorem-size     35
proof            (modus-ponens tm-609 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99530.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I or H))), M:tm-609, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99531
in-theory        99531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-605 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99531.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-605, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99532
in-theory        99532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-595 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99532.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-595, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99533
in-theory        99533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-550 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99533.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-550, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99534
in-theory        99534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-540 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99534.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-540, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99535
in-theory        99535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-530 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99535.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-530, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99536
in-theory        99536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-520 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99536.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-520, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99537
in-theory        99537
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-510 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99537.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-510, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99538
in-theory        99538
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-500 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99538.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-500, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99539
in-theory        99539
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-490 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99539.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-490, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99540
in-theory        99540
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-480 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99540.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-480, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99541
in-theory        99541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-469 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99541.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-469, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99542
in-theory        99542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (H or I)))
theorem-size     35
proof            (modus-ponens tm-456 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99542.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (H or I))), M:tm-456, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99543
in-theory        99543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-453 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99543.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-453, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99544
in-theory        99544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-443 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-99544.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-443, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99545
in-theory        99545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-409 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99545.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-409, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99546
in-theory        99546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-400 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99546.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-400, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99547
in-theory        99547
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-391 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99547.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-391, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99548
in-theory        99548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-382 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99548.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-382, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99549
in-theory        99549
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-373 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99549.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-373, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99550
in-theory        99550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-364 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99550.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-364, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99551
in-theory        99551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-354 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99551.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-354, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99552
in-theory        99552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I -> (H and I))))
theorem-size     37
proof            (modus-ponens tm-341 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99552.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I -> (H and I)))), M:tm-341, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99553
in-theory        99553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-338 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99553.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-338, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99554
in-theory        99554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     67
proof            (modus-ponens tm-327 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99554.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-327, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99555
in-theory        99555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-326 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99555.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-326, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99556
in-theory        99556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-325 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99556.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-325, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99557
in-theory        99557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     73
proof            (modus-ponens tm-324 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99557.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-324, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99558
in-theory        99558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-323 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99558.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-323, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99559
in-theory        99559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H and I) -> I))
theorem-size     35
proof            (modus-ponens tm-322 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99559.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H and I) -> I)), M:tm-322, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99560
in-theory        99560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H and I) -> H))
theorem-size     35
proof            (modus-ponens tm-320 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99560.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H and I) -> H)), M:tm-320, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99561
in-theory        99561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     43
proof            (modus-ponens tm-318 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-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-99561.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99562
in-theory        99562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99562.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (I -> H))), M:tm-315, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99563
in-theory        99563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     61
proof            (modus-ponens tm-311 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-99563.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-311, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99564
in-theory        99564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
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-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-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-99564.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) or H)), M:tm-310, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99565
in-theory        99565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99565.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and H))), M:tm-309, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99566
in-theory        99566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     45
proof            (modus-ponens tm-308 tm-1057 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99566.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-308, m:tm-1057, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))
================================================================
tm-name          tm-99567
in-theory        99567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-1057 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99567.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1057, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))
================================================================
tm-name          tm-99568
in-theory        99568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))))
theorem-size     61
proof            (modus-ponens tm-305 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-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-99568.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)))), M:tm-305, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99569
in-theory        99569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-303 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99569.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-303, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99570
in-theory        99570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-270 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99570.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-270, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99571
in-theory        99571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-239 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99571.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-239, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99572
in-theory        99572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     47
proof            (modus-ponens tm-210 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99572.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-210, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99573
in-theory        99573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-183 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99573.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-183, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99574
in-theory        99574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-157 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99574.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-157, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99575
in-theory        99575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     45
proof            (modus-ponens tm-147 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99575.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-147, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99576
in-theory        99576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-134 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99576.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-134, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99577
in-theory        99577
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     45
proof            (modus-ponens tm-125 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99577.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-125, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99578
in-theory        99578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-113 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99578.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((H -> I) -> ((I -> J) -> ((H or I) -> J))) or K))), M:tm-113, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99579
in-theory        99579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-105 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99579.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-105, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99580
in-theory        99580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-95 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99580.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-95, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99581
in-theory        99581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-83 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99581.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-83, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99582
in-theory        99582
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     35
proof            (modus-ponens tm-76 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-10 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99582.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-76, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99583
in-theory        99583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-69 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-9 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99583.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-69, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99584
in-theory        99584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-54 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 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-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-99584.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-54, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99585
in-theory        99585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-42 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99585.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-42, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99586
in-theory        99586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-32 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-6 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
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-99586.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-32, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99587
in-theory        99587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-23 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99587.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-23, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99588
in-theory        99588
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-22 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-4 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99588.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-22, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99589
in-theory        99589
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-21 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-3 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99589.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-21, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99590
in-theory        99590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-20 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99590.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((G -> H) -> ((H -> I) -> ((G or H) -> I))) or J))), M:tm-20, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99591
in-theory        99591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-19 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-8 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99591.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (((F -> G) -> ((G -> H) -> ((F or G) -> H))) or I))), M:tm-19, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99592
in-theory        99592
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-7 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-7 tm-5 tm-8 tm-6)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-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-99592.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-7, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99593
in-theory        99593
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) or H)
theorem-size     31
proof            (modus-ponens tm-6 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-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-99593.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)) or H), M:tm-6, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99594
in-theory        99594
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-6)
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-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-99594.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)) and A)), M:tm-5, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99595
in-theory        99595
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-1 tm-1057 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm)))))
axioms-used      (tm-1 tm-5 tm-8 tm-6)
proof-size       135
proof-steps      9
----------------------------------------------------------------
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-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-99595.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))), M:tm-1, m:tm-1057, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (or (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) Gm))))
================================================================
tm-name          tm-99596
in-theory        99596
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-1003 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99596.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H)))), M:tm-1003, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99597
in-theory        99597
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-992 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99597.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H)))), M:tm-992, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99598
in-theory        99598
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H))))
theorem-size     59
proof            (modus-ponens tm-980 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99598.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H)))), M:tm-980, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99599
in-theory        99599
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-930 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99599.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-930, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99600
in-theory        99600
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-893 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99600.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-893, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99601
in-theory        99601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     49
proof            (modus-ponens tm-855 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-99601.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-855, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99602
in-theory        99602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     43
proof            (modus-ponens tm-808 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-54.           (A -> (((B -> C) -> ((C -> 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-99602.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-808, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99603
in-theory        99603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     43
proof            (modus-ponens tm-757 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-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-99603.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-757, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99604
in-theory        99604
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))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H))))
theorem-size     57
proof            (modus-ponens tm-708 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) 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-54.           (A -> (((B -> C) -> ((C -> 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-99604.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H)))), M:tm-708, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99605
in-theory        99605
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-665 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-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-99605.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-665, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99606
in-theory        99606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-622 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99606.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-622, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99607
in-theory        99607
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (I or H)))
theorem-size     37
proof            (modus-ponens tm-609 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99607.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (I or H))), M:tm-609, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99608
in-theory        99608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-605 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99608.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-605, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99609
in-theory        99609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-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-99609.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (I or H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))))), M:tm-595, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99610
in-theory        99610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-550 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99610.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-550, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99611
in-theory        99611
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-540 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99611.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-540, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99612
in-theory        99612
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-530 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99612.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-530, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99613
in-theory        99613
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-520 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99613.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-520, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99614
in-theory        99614
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-510 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99614.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-510, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99615
in-theory        99615
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-500 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99615.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-500, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99616
in-theory        99616
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-490 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99616.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H)))), M:tm-490, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99617
in-theory        99617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-480 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99617.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-480, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99618
in-theory        99618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-469 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99618.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-469, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99619
in-theory        99619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (H or I)))
theorem-size     37
proof            (modus-ponens tm-456 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99619.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (H or I))), M:tm-456, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99620
in-theory        99620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-453 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99620.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-453, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99621
in-theory        99621
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-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-99621.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (H or I)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))))), M:tm-443, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99622
in-theory        99622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-409 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99622.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-409, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99623
in-theory        99623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-400 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99623.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-400, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99624
in-theory        99624
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-391 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99624.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-391, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99625
in-theory        99625
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-382 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99625.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-382, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99626
in-theory        99626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-373 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99626.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H)))), M:tm-373, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99627
in-theory        99627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-364 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99627.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-364, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99628
in-theory        99628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-354 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99628.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-354, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99629
in-theory        99629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (I -> (H and I))))
theorem-size     39
proof            (modus-ponens tm-341 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99629.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99630
in-theory        99630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-338 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99630.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F)))), M:tm-338, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99631
in-theory        99631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-2 tm-5 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-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-99631.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (I -> (H and I))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))))), M:tm-327, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99632
in-theory        99632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-99632.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (((H and I) -> I) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))))), M:tm-326, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99633
in-theory        99633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99633.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (((H and I) -> H) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))))), M:tm-325, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99634
in-theory        99634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-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-99634.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))))), M:tm-324, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99635
in-theory        99635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) 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-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-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-99635.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (I -> H)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))))), M:tm-323, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99636
in-theory        99636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H and I) -> I))
theorem-size     37
proof            (modus-ponens tm-322 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-99636.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H and I) -> I)), M:tm-322, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99637
in-theory        99637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H and I) -> H))
theorem-size     37
proof            (modus-ponens tm-320 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99637.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H and I) -> H)), M:tm-320, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99638
in-theory        99638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     45
proof            (modus-ponens tm-318 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99638.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99639
in-theory        99639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (I -> H)))
theorem-size     37
proof            (modus-ponens tm-315 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99639.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (I -> H))), M:tm-315, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99640
in-theory        99640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-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-99640.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))))), M:tm-311, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99641
in-theory        99641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) or H))
theorem-size     65
proof            (modus-ponens tm-310 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-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-99641.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) or H)), M:tm-310, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99642
in-theory        99642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and H)))
theorem-size     67
proof            (modus-ponens tm-309 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-2 tm-5 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-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-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-99642.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and H))), M:tm-309, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99643
in-theory        99643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     49
proof            (modus-ponens tm-308 tm-1058 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B 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-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-99643.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-308, m:tm-1058, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))
================================================================
tm-name          tm-99644
in-theory        99644
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-307 tm-1058 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99644.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-307, m:tm-1058, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))
================================================================
tm-name          tm-99645
in-theory        99645
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-1.            (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-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-99645.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) and (H -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))))), M:tm-305, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99646
in-theory        99646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     43
proof            (modus-ponens tm-303 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99646.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-303, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99647
in-theory        99647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-270 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99647.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-270, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99648
in-theory        99648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-239 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99648.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-239, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99649
in-theory        99649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H))))
theorem-size     49
proof            (modus-ponens tm-210 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99649.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H)))), M:tm-210, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99650
in-theory        99650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-183 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99650.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-183, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99651
in-theory        99651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-157 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99651.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-157, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99652
in-theory        99652
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     47
proof            (modus-ponens tm-147 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) 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-54.           (A -> (((B -> C) -> ((C -> 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-99652.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-147, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99653
in-theory        99653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-134 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99653.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-134, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99654
in-theory        99654
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     47
proof            (modus-ponens tm-125 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99654.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-125, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99655
in-theory        99655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-113 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99655.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (H -> (((I -> J) -> ((J -> K) -> ((I or J) -> K))) and H)))), M:tm-113, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99656
in-theory        99656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     51
proof            (modus-ponens tm-105 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99656.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-105, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99657
in-theory        99657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-95 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99657.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F)))), M:tm-95, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99658
in-theory        99658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-83 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99658.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-83, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99659
in-theory        99659
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))))
theorem-size     37
proof            (modus-ponens tm-76 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-10 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99659.        (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))), M:tm-76, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99660
in-theory        99660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F))))
theorem-size     43
proof            (modus-ponens tm-69 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-9 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99660.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F)))), M:tm-69, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99661
in-theory        99661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-54 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-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-99661.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-54, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99662
in-theory        99662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-42 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99662.        ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F)))), M:tm-42, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99663
in-theory        99663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-32 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99663.        ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F)))), M:tm-32, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99664
in-theory        99664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-23 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99664.        ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F)))), M:tm-23, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99665
in-theory        99665
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-22 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99665.        (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F)))), M:tm-22, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99666
in-theory        99666
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-21 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99666.        (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F)))), M:tm-21, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99667
in-theory        99667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-20 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> 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-99667.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (G -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and G)))), M:tm-20, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99668
in-theory        99668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-19 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99668.        ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (F -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and F)))), M:tm-19, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99669
in-theory        99669
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-7 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-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-99669.        (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))), M:tm-7, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99670
in-theory        99670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) or H)
theorem-size     33
proof            (modus-ponens tm-6 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-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-99670.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))) or H), M:tm-6, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99671
in-theory        99671
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-99671.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))) and A)), M:tm-5, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99672
in-theory        99672
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-1 tm-1058 ((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
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-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-99672.        (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))), M:tm-1, m:tm-1058, u:((A (and (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (-> Dm (and (-> (-> Em Fm) (-> (-> Fm Gm) (-> (or Em Fm) Gm))) Dm)))))
================================================================
tm-name          tm-99673
in-theory        99673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F or D))) -> ((F or D) -> (E -> (F or D)))))
theorem-size     31
proof            (modus-ponens tm-1059 tm-81 ((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-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-99673.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F or D))) -> ((F or D) -> (E -> (F or D))))), M:tm-1059, m:tm-81, u:((Am (-> A B)) (Bm (-> B (-> Dm (or A B)))) (Cm (or A B)) (C (-> Dm (or A B))))
================================================================
tm-name          tm-99674
in-theory        99674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> ((F or D) and E))) -> ((F or D) -> (E -> ((F or D) and E)))))
theorem-size     35
proof            (modus-ponens tm-1059 tm-352 ((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
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-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-99674.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> ((F or D) and E))) -> ((F or D) -> (E -> ((F or D) and E))))), M:tm-1059, m:tm-352, u:((Am (-> A B)) (Bm (-> B (-> Dm (and (or A B) Dm)))) (Cm (or A B)) (C (-> Dm (and (or A B) Dm))))
================================================================
tm-name          tm-99675
in-theory        99675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E or D) or F)) -> ((E or D) -> ((E or D) or F))))
theorem-size     31
proof            (modus-ponens tm-1059 tm-467 ((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-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-99675.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E or D) or F)) -> ((E or D) -> ((E or D) or F)))), M:tm-1059, m:tm-467, u:((Am (-> A B)) (Bm (-> B (or (or A B) Dm))) (Cm (or A B)) (C (or (or A B) Dm)))
================================================================
tm-name          tm-99676
in-theory        99676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or (F or D))) -> ((F or D) -> (E or (F or D)))))
theorem-size     31
proof            (modus-ponens tm-1059 tm-620 ((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-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-99676.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or (F or D))) -> ((F or D) -> (E or (F or D))))), M:tm-1059, m:tm-620, u:((Am (-> A B)) (Bm (-> B (or Dm (or A B)))) (Cm (or A B)) (C (or Dm (or A B))))
================================================================
tm-name          tm-99677
in-theory        99677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-1003 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99677.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-1003, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99678
in-theory        99678
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-992 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99678.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-992, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99679
in-theory        99679
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 ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     65
proof            (modus-ponens tm-980 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       283
proof-steps      13
----------------------------------------------------------------
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-54.           (A -> (((B -> C) -> ((C -> 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-99679.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-980, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99680
in-theory        99680
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-930 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99680.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-930, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99681
in-theory        99681
times-derived    1
----------------------------------------------------------------
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)))) and ((((B -> C) -> ((A or B) -> C)) or ((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     85
proof            (modus-ponens tm-920 tm-1059 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99681.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((((B -> C) -> ((A or B) -> C)) or ((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-920, m:tm-1059, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99682
in-theory        99682
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-893 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99682.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-893, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99683
in-theory        99683
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> B) or ((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     79
proof            (modus-ponens tm-882 tm-1059 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99683.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((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-882, m:tm-1059, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99684
in-theory        99684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     55
proof            (modus-ponens tm-855 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99684.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-855, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99685
in-theory        99685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-808 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-4)
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-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99685.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-808, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99686
in-theory        99686
times-derived    1
----------------------------------------------------------------
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)))) and (((G and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((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     91
proof            (modus-ponens tm-798 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99686.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G and ((A -> B) or ((B -> C) -> ((A or B) -> C)))) or ((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-798, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99687
in-theory        99687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-757 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3)
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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-54.           (A -> (((B -> C) -> ((C -> 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-99687.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99688
in-theory        99688
times-derived    1
----------------------------------------------------------------
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)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and G) or ((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     91
proof            (modus-ponens tm-747 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-54.           (A -> (((B -> C) -> ((C -> 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-99688.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and G) or ((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-747, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99689
in-theory        99689
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     63
proof            (modus-ponens tm-708 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       277
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and 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-54.           (A -> (((B -> C) -> ((C -> 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-99689.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99690
in-theory        99690
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-665 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-54.           (A -> (((B -> C) -> ((C -> 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-99690.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99691
in-theory        99691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     39
proof            (modus-ponens tm-623 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-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-99691.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> C) -> ((A or B) -> C))))), M:tm-623, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99692
in-theory        99692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-622 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99692.        ((A -> (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99693
in-theory        99693
times-derived    1
----------------------------------------------------------------
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)))) and (G -> (H or G)))
theorem-size     43
proof            (modus-ponens tm-609 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99693.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (H or G))), M:tm-609, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99694
in-theory        99694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-605 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((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-54.           (A -> (((B -> C) -> ((C -> 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-99694.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99695
in-theory        99695
times-derived    1
----------------------------------------------------------------
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)))) and ((G -> (H or G)) and (((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     81
proof            (modus-ponens tm-595 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99695.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H or G)) and (((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-595, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99696
in-theory        99696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-550 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99696.        (((A -> (B or A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99697
in-theory        99697
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-540 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99697.        ((A or (B -> (C or B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99698
in-theory        99698
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-530 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99698.        ((A or (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99699
in-theory        99699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-520 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B 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-54.           (A -> (((B -> C) -> ((C -> 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-99699.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99700
in-theory        99700
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-510 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99700.        ((A or ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99701
in-theory        99701
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-500 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99701.        ((A or ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99702
in-theory        99702
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-490 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((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-54.           (A -> (((B -> C) -> ((C -> 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-99702.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99703
in-theory        99703
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-480 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99703.        ((A or (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99704
in-theory        99704
times-derived    1
----------------------------------------------------------------
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))) or G))
theorem-size     39
proof            (modus-ponens tm-470 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-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-99704.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))) or G)), M:tm-470, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99705
in-theory        99705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-469 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99705.        ((A -> (B -> (B or C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99706
in-theory        99706
times-derived    1
----------------------------------------------------------------
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)))) and (G -> (G or H)))
theorem-size     43
proof            (modus-ponens tm-456 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99706.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (G or H))), M:tm-456, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99707
in-theory        99707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-453 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((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-54.           (A -> (((B -> C) -> ((C -> 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-99707.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99708
in-theory        99708
times-derived    1
----------------------------------------------------------------
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)))) and ((G -> (G or H)) and (((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     81
proof            (modus-ponens tm-443 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99708.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (G or H)) and (((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-443, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99709
in-theory        99709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-409 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99709.        (((A -> (A or B)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99710
in-theory        99710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-400 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (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-54.           (A -> (((B -> C) -> ((C -> 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-99710.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99711
in-theory        99711
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-391 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99711.        ((((A and B) -> B) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99712
in-theory        99712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-382 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99712.        ((((A and B) -> A) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99713
in-theory        99713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-373 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (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-54.           (A -> (((B -> C) -> ((C -> 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-99713.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99714
in-theory        99714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-364 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99714.        (((A -> (B -> A)) or C) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99715
in-theory        99715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     41
proof            (modus-ponens tm-355 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       213
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99715.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> C) -> ((A or B) -> C))) and D))), M:tm-355, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99716
in-theory        99716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-354 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99716.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99717
in-theory        99717
times-derived    1
----------------------------------------------------------------
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)))) and (G -> (H -> (G and H))))
theorem-size     45
proof            (modus-ponens tm-341 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99717.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99718
in-theory        99718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     47
proof            (modus-ponens tm-338 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
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-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99718.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99719
in-theory        99719
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     89
proof            (modus-ponens tm-328 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       287
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99719.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99720
in-theory        99720
times-derived    1
----------------------------------------------------------------
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)))) and ((G -> (H -> (G and H))) and (((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     83
proof            (modus-ponens tm-327 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) 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-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (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-54.           (A -> (((B -> C) -> ((C -> 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-99720.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H -> (G and H))) and (((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-327, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99721
in-theory        99721
times-derived    1
----------------------------------------------------------------
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)))) and (((G and H) -> H) and (((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     81
proof            (modus-ponens tm-326 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99721.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G and H) -> H) and (((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-326, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99722
in-theory        99722
times-derived    1
----------------------------------------------------------------
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)))) and (((G and H) -> G) and (((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     81
proof            (modus-ponens tm-325 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99722.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G and H) -> G) and (((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-325, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99723
in-theory        99723
times-derived    1
----------------------------------------------------------------
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)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((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     89
proof            (modus-ponens tm-324 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (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-54.           (A -> (((B -> C) -> ((C -> 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-99723.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((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-324, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99724
in-theory        99724
times-derived    1
----------------------------------------------------------------
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)))) and ((G -> (H -> G)) and (((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     81
proof            (modus-ponens tm-323 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99724.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H -> G)) and (((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-323, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99725
in-theory        99725
times-derived    1
----------------------------------------------------------------
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)))) and ((G and H) -> H))
theorem-size     43
proof            (modus-ponens tm-322 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99725.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G and H) -> H)), M:tm-322, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99726
in-theory        99726
times-derived    1
----------------------------------------------------------------
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)))) and ((G and H) -> G))
theorem-size     43
proof            (modus-ponens tm-320 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99726.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G and H) -> G)), M:tm-320, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99727
in-theory        99727
times-derived    1
----------------------------------------------------------------
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)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     51
proof            (modus-ponens tm-318 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-54.           (A -> (((B -> C) -> ((C -> 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-99727.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99728
in-theory        99728
times-derived    1
----------------------------------------------------------------
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)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-316 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-54.           (A -> (((B -> C) -> ((C -> 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-99728.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-316, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99729
in-theory        99729
times-derived    1
----------------------------------------------------------------
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)))) and (G -> (H -> G)))
theorem-size     43
proof            (modus-ponens tm-315 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-54.           (A -> (((B -> C) -> ((C -> 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-99729.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (H -> G))), M:tm-315, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99730
in-theory        99730
times-derived    1
----------------------------------------------------------------
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)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))))
theorem-size     91
proof            (modus-ponens tm-313 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99730.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))), M:tm-313, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99731
in-theory        99731
times-derived    1
----------------------------------------------------------------
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)))) and (((((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))) -> G) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) -> G)))
theorem-size     103
proof            (modus-ponens tm-312 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((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-54.           (A -> (((B -> C) -> ((C -> 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-99731.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (((((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))) -> G) -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) -> G))), M:tm-312, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99732
in-theory        99732
times-derived    1
----------------------------------------------------------------
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)))) and (G or (((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     77
proof            (modus-ponens tm-311 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or 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-54.           (A -> (((B -> C) -> ((C -> 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-99732.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G or (((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-311, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99733
in-theory        99733
times-derived    1
----------------------------------------------------------------
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)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) or G))
theorem-size     77
proof            (modus-ponens tm-310 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or 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-54.           (A -> (((B -> C) -> ((C -> 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-99733.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) or G)), M:tm-310, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99734
in-theory        99734
times-derived    1
----------------------------------------------------------------
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)))) and (G -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and G)))
theorem-size     79
proof            (modus-ponens tm-309 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99734.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and G))), M:tm-309, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99735
in-theory        99735
times-derived    1
----------------------------------------------------------------
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)))) and (G -> (((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     77
proof            (modus-ponens tm-305 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 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-1.            (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-54.           (A -> (((B -> C) -> ((C -> 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-99735.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) and (G -> (((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-305, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99736
in-theory        99736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-303 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (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-54.           (A -> (((B -> C) -> ((C -> 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-99736.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99737
in-theory        99737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-270 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((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-54.           (A -> (((B -> C) -> ((C -> 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-99737.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99738
in-theory        99738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-239 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((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-54.           (A -> (((B -> C) -> ((C -> 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-99738.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99739
in-theory        99739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     55
proof            (modus-ponens tm-210 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
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-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99739.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99740
in-theory        99740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     47
proof            (modus-ponens tm-183 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99740.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99741
in-theory        99741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-157 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99741.        ((A -> ((B and C) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99742
in-theory        99742
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     53
proof            (modus-ponens tm-147 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-54.           (A -> (((B -> C) -> ((C -> 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-99742.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99743
in-theory        99743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-134 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99743.        ((A -> ((B and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99744
in-theory        99744
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     53
proof            (modus-ponens tm-125 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-54.           (A -> (((B -> C) -> ((C -> 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-99744.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99745
in-theory        99745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     53
proof            (modus-ponens tm-113 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99745.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((F -> G) -> ((E or F) -> G))) -> (((H -> I) -> ((I -> J) -> ((H or I) -> J))) and ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99746
in-theory        99746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     57
proof            (modus-ponens tm-105 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       259
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99746.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99747
in-theory        99747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     45
proof            (modus-ponens tm-95 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-54.           (A -> (((B -> C) -> ((C -> 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-99747.        (((A -> B) -> (A -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99748
in-theory        99748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     39
proof            (modus-ponens tm-84 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-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-99748.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> C) -> ((A or B) -> C))))), M:tm-84, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99749
in-theory        99749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     45
proof            (modus-ponens tm-83 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-54.           (A -> (((B -> C) -> ((C -> 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-99749.        ((A -> (B -> (C -> B))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99750
in-theory        99750
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-76 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99750.        (((not (not A)) -> A) and (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99751
in-theory        99751
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((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     53
proof            (modus-ponens tm-73 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99751.        (((not (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))) or ((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-73, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99752
in-theory        99752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     49
proof            (modus-ponens tm-69 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99752.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99753
in-theory        99753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-54 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
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-54.           (A -> (((B -> C) -> ((C -> 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-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-99753.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99754
in-theory        99754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> ((C or A) -> B))))
theorem-size     47
proof            (modus-ponens tm-50 tm-1059 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       205
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99754.        ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> ((C or A) -> B)))), M:tm-50, m:tm-1059, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99755
in-theory        99755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((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     41
proof            (modus-ponens tm-49 tm-1059 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       199
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99755.        (((A -> B) or ((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-49, m:tm-1059, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (C (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99756
in-theory        99756
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D))))
theorem-size     53
proof            (modus-ponens tm-47 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99756.        (((A and ((B -> C) or ((C -> D) -> ((B or C) -> D)))) or ((B -> C) or ((C -> D) -> ((B or C) -> D)))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99757
in-theory        99757
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     53
proof            (modus-ponens tm-46 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       209
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99757.        (((((A -> B) or ((B -> C) -> ((A or B) -> C))) and D) or ((A -> B) or ((B -> C) -> ((A or B) -> C)))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> C) -> ((A or B) -> C)))), M:tm-46, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99758
in-theory        99758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-42 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), 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-54.           (A -> (((B -> C) -> ((C -> 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-99758.        ((A -> (B or A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99759
in-theory        99759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-32 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), 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-54.           (A -> (((B -> C) -> ((C -> 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-99759.        ((A -> (A or B)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99760
in-theory        99760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     51
proof            (modus-ponens tm-24 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) 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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99760.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99761
in-theory        99761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     45
proof            (modus-ponens tm-23 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M: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-54.           (A -> (((B -> C) -> ((C -> 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-99761.        ((A -> (B -> (A and B))) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99762
in-theory        99762
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-22 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), 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-54.           (A -> (((B -> C) -> ((C -> 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-99762.        (((A and B) -> B) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99763
in-theory        99763
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-21 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), 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-54.           (A -> (((B -> C) -> ((C -> 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-99763.        (((A and B) -> A) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99764
in-theory        99764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     51
proof            (modus-ponens tm-20 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, 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-54.           (A -> (((B -> C) -> ((C -> 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-99764.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((E -> F) -> ((D or E) -> F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99765
in-theory        99765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     43
proof            (modus-ponens tm-19 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and 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-54.           (A -> (((B -> C) -> ((C -> 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-99765.        ((A -> (B -> A)) and (((C -> D) or ((D -> E) -> ((C or D) -> E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99766
in-theory        99766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-9 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-8 tm-5)
proof-size       191
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-99766.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (not (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))))) -> (not ((A -> B) or ((B -> C) -> ((A or B) -> C))))), M:tm-9, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99767
in-theory        99767
times-derived    1
----------------------------------------------------------------
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))) or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((F or D) -> E)))) -> G))
theorem-size     65
proof            (modus-ponens tm-8 tm-1059 ((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-5)
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-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-99767.        (((((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))) or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((F or D) -> E)))) -> G)), M:tm-8, m:tm-1059, u:((A (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (B (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-99768
in-theory        99768
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     39
proof            (modus-ponens tm-7 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       171
proof-steps      9
----------------------------------------------------------------
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-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-99768.        (A or (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99769
in-theory        99769
times-derived    1
----------------------------------------------------------------
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)))) or G)
theorem-size     39
proof            (modus-ponens tm-6 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       171
proof-steps      9
----------------------------------------------------------------
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-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-99769.        ((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))) or G), M:tm-6, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99770
in-theory        99770
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     41
proof            (modus-ponens tm-5 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, 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-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-99770.        (A -> ((((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99771
in-theory        99771
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     39
proof            (modus-ponens tm-1 tm-1059 ((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       171
proof-steps      9
----------------------------------------------------------------
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-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-99771.        (A -> (((B -> C) or ((C -> D) -> ((B or C) -> D))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-1059, u:((A (-> (or (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) (and (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-99772
in-theory        99772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99772.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E)))), M:tm-1003, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99773
in-theory        99773
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99773.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E)))), M:tm-992, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99774
in-theory        99774
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99774.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E)))), M:tm-980, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99775
in-theory        99775
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99775.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-930, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99776
in-theory        99776
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((B or A) or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))
theorem-size     51
proof            (modus-ponens tm-920 tm-1060 ((A Am) (B (or Bm Am)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99776.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((B or A) or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))), M:tm-920, m:tm-1060, u:((A Am) (B (or Bm Am)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99777
in-theory        99777
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99777.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-893, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99778
in-theory        99778
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((A or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))
theorem-size     49
proof            (modus-ponens tm-882 tm-1060 ((A Am) (B (or Bm Am)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99778.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((A or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))), M:tm-882, m:tm-1060, u:((A Am) (B (or Bm Am)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99779
in-theory        99779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99779.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-855, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99780
in-theory        99780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99780.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-808, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99781
in-theory        99781
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((F and (A or (B or A))) or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))
theorem-size     55
proof            (modus-ponens tm-798 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99781.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((F and (A or (B or A))) or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))), M:tm-798, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99782
in-theory        99782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-54.           (A -> (((B -> C) -> ((C -> 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-99782.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-757, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99783
in-theory        99783
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((((A or (B or A)) and F) or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))
theorem-size     55
proof            (modus-ponens tm-747 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-54.           (A -> (((B -> C) -> ((C -> 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-99783.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((((A or (B or A)) and F) or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))), M:tm-747, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99784
in-theory        99784
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99784.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E)))), M:tm-708, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99785
in-theory        99785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-54.           (A -> (((B -> C) -> ((C -> 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-99785.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-665, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99786
in-theory        99786
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or A))))
theorem-size     25
proof            (modus-ponens tm-623 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or 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-50.           (((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-99786.        ((A or (B or A)) -> (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or A)))), M:tm-623, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99787
in-theory        99787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99787.        ((A -> (B -> (C or B))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-622, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99788
in-theory        99788
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or 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-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99788.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (G or F))), M:tm-609, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99789
in-theory        99789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99789.        ((A -> ((B -> (C or B)) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-605, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99790
in-theory        99790
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (G or F)) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99790.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (G or F)) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-595, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99791
in-theory        99791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99791.        (((A -> (B or A)) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-550, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99792
in-theory        99792
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99792.        ((A or (B -> (C or B))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-540, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99793
in-theory        99793
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99793.        ((A or (B -> (B or C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-530, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99794
in-theory        99794
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99794.        ((A or (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-520, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99795
in-theory        99795
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99795.        ((A or ((B and C) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-510, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99796
in-theory        99796
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99796.        ((A or ((B and C) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-500, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99797
in-theory        99797
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99797.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E)))), M:tm-490, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99798
in-theory        99798
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99798.        ((A or (B -> (C -> B))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-480, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99799
in-theory        99799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)) or F))
theorem-size     25
proof            (modus-ponens tm-470 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99799.        ((A or (B or A)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)) or F)), M:tm-470, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99800
in-theory        99800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99800.        ((A -> (B -> (B or C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-469, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99801
in-theory        99801
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99801.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (F or G))), M:tm-456, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99802
in-theory        99802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99802.        ((A -> ((B -> (B or C)) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-453, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99803
in-theory        99803
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (F or G)) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99803.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (F or G)) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-443, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99804
in-theory        99804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99804.        (((A -> (A or B)) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-409, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99805
in-theory        99805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99805.        (((A -> (B -> (A and B))) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-400, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99806
in-theory        99806
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99806.        ((((A and B) -> B) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-391, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99807
in-theory        99807
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99807.        ((((A and B) -> A) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-382, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99808
in-theory        99808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99808.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E)))), M:tm-373, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99809
in-theory        99809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99809.        (((A -> (B -> A)) or C) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-364, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99810
in-theory        99810
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or A)) and C)))
theorem-size     27
proof            (modus-ponens tm-355 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-54.           (A -> (((B -> C) -> ((C -> 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-99810.        ((A or (B or A)) -> (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or A)) and C))), M:tm-355, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99811
in-theory        99811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99811.        ((A -> (B -> (C -> (B and C)))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-354, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99812
in-theory        99812
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99812.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99813
in-theory        99813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99813.        (((A -> B) -> (A -> (A and B))) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C)))), M:tm-338, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99814
in-theory        99814
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99814.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((A or (B or A)) -> ((A or (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-328, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99815
in-theory        99815
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (G -> (F and G))) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99815.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (G -> (F and G))) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-327, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99816
in-theory        99816
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((F and G) -> G) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99816.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((F and G) -> G) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-326, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99817
in-theory        99817
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((F and G) -> F) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99817.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((F and G) -> F) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-325, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99818
in-theory        99818
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99818.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-324, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99819
in-theory        99819
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (G -> F)) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99819.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (G -> F)) and ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-323, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99820
in-theory        99820
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99820.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F and G) -> G)), M:tm-322, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99821
in-theory        99821
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99821.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F and G) -> F)), M:tm-320, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99822
in-theory        99822
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-54.           (A -> (((B -> C) -> ((C -> 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-99822.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99823
in-theory        99823
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((A or (B or A)) -> (A or (B or A))))
theorem-size     35
proof            (modus-ponens tm-316 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-54.           (A -> (((B -> C) -> ((C -> 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-99823.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and ((A or (B or A)) -> (A or (B or A)))), M:tm-316, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99824
in-theory        99824
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-54.           (A -> (((B -> C) -> ((C -> 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-99824.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (G -> F))), M:tm-315, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99825
in-theory        99825
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((A or (B or A)) -> (not (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))) -> (not (A or (B or A)))))
theorem-size     55
proof            (modus-ponens tm-313 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99825.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((A or (B or A)) -> (not (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))) -> (not (A or (B or A))))), M:tm-313, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99826
in-theory        99826
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)) -> F) -> (((A or (B or A)) or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) -> F)))
theorem-size     69
proof            (modus-ponens tm-312 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99826.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)) -> F) -> (((A or (B or A)) or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) -> F))), M:tm-312, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99827
in-theory        99827
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F or ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
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-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-54.           (A -> (((B -> C) -> ((C -> 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-99827.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F or ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-311, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99828
in-theory        99828
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99828.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) or F)), M:tm-310, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99829
in-theory        99829
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99829.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and F))), M:tm-309, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99830
in-theory        99830
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99830.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) and (F -> ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))), M:tm-305, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99831
in-theory        99831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99831.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-303, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99832
in-theory        99832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99832.        ((A -> (((B and C) -> C) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-270, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99833
in-theory        99833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99833.        ((A -> (((B and C) -> B) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-239, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99834
in-theory        99834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99834.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E)))), M:tm-210, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99835
in-theory        99835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99835.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-183, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99836
in-theory        99836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99836.        ((A -> ((B and C) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-157, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99837
in-theory        99837
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-54.           (A -> (((B -> C) -> ((C -> 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-99837.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-147, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99838
in-theory        99838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99838.        ((A -> ((B and C) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-134, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99839
in-theory        99839
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-54.           (A -> (((B -> C) -> ((C -> 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-99839.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-125, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99840
in-theory        99840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99840.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F or E)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F or E)))), M:tm-113, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99841
in-theory        99841
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99841.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-105, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99842
in-theory        99842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-54.           (A -> (((B -> C) -> ((C -> 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-99842.        (((A -> B) -> (A -> A)) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C)))), M:tm-95, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99843
in-theory        99843
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or A))))
theorem-size     25
proof            (modus-ponens tm-84 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99843.        ((A or (B or A)) -> (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or A)))), M:tm-84, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99844
in-theory        99844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-54.           (A -> (((B -> C) -> ((C -> 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-99844.        ((A -> (B -> (C -> B))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-83, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99845
in-theory        99845
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C or B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99845.        (((not (not A)) -> A) and ((B or (C or B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B)))), M:tm-76, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99846
in-theory        99846
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B or A)))) or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))
theorem-size     31
proof            (modus-ponens tm-73 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-7 tm-5)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99846.        (((not (not (A or (B or A)))) or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))), M:tm-73, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99847
in-theory        99847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99847.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C)))), M:tm-69, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99848
in-theory        99848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-99848.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-54, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99849
in-theory        99849
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (B or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))
theorem-size     27
proof            (modus-ponens tm-50 tm-1060 ((A Am) (B (or Bm Am)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-5)
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-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-99849.        (((A or B) or (B or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))), M:tm-50, m:tm-1060, u:((A Am) (B (or Bm Am)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99850
in-theory        99850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-49 tm-1060 ((A Am) (B (or Bm Am)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-6 tm-7 tm-5)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99850.        ((A or (A or (B or A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))), M:tm-49, m:tm-1060, u:((A Am) (B (or Bm Am)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99851
in-theory        99851
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C or B))) or (B or (C or B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B)))
theorem-size     31
proof            (modus-ponens tm-47 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-7 tm-5)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99851.        (((A and (B or (C or B))) or (B or (C or B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B))), M:tm-47, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99852
in-theory        99852
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B or A)) and C) or (A or (B or A))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or A)))
theorem-size     31
proof            (modus-ponens tm-46 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-7 tm-5)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99852.        ((((A or (B or A)) and C) or (A or (B or A))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or A))), M:tm-46, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99853
in-theory        99853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99853.        ((A -> (B or A)) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C)))), M:tm-42, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99854
in-theory        99854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99854.        ((A -> (A or B)) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C)))), M:tm-32, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99855
in-theory        99855
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((A or (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))))
theorem-size     29
proof            (modus-ponens tm-24 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99855.        ((A or (B or A)) -> ((A or (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))), M:tm-24, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99856
in-theory        99856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99856.        ((A -> (B -> (A and B))) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C)))), M:tm-23, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99857
in-theory        99857
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99857.        (((A and B) -> B) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C)))), M:tm-22, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99858
in-theory        99858
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99858.        (((A and B) -> A) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C)))), M:tm-21, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99859
in-theory        99859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99859.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E or D)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E or D)))), M:tm-20, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99860
in-theory        99860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99860.        ((A -> (B -> A)) and ((C or (D or C)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (D or C)))), M:tm-19, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99861
in-theory        99861
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (not (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))) -> (not (A or (B or A))))
theorem-size     31
proof            (modus-ponens tm-9 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-9 tm-8 tm-7 tm-5)
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99861.        (((A or (B or A)) -> (not (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))) -> (not (A or (B or A)))), M:tm-9, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99862
in-theory        99862
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or E)) -> F) -> (((E or (D or E)) or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or E))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-1060 ((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       149
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-54.           (A -> (((B -> C) -> ((C -> 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-99862.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or E)) -> F) -> (((E or (D or E)) or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or E))) -> F)), M:tm-8, m:tm-1060, u:((A (or Am (or Bm Am))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))
================================================================
tm-name          tm-99863
in-theory        99863
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C or B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-7 tm-8 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-50.           (((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-99863.        (A or ((B or (C or B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B)))), M:tm-7, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99864
in-theory        99864
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-6 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99864.        (((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))) or F), M:tm-6, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99865
in-theory        99865
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C or B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-7)
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-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or 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-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-99865.        (A -> (((B or (C or B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B))) and A)), M:tm-5, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99866
in-theory        99866
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C or B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1060 ((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am))))))
axioms-used      (tm-1 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-99866.        (A -> ((B or (C or B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (C or B)))), M:tm-1, m:tm-1060, u:((A (-> (or Am (or Bm Am)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Bm Am)))))
================================================================
tm-name          tm-99867
in-theory        99867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-1003 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99867.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F)))), M:tm-1003, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99868
in-theory        99868
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-992 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99868.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F)))), M:tm-992, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99869
in-theory        99869
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F))))
theorem-size     51
proof            (modus-ponens tm-980 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99869.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F)))), M:tm-980, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99870
in-theory        99870
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-930 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-7 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99870.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-930, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99871
in-theory        99871
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((A or B) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))
theorem-size     51
proof            (modus-ponens tm-920 tm-1061 ((A Am) (B (or Am Bm)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99871.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((A or B) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))), M:tm-920, m:tm-1061, u:((A Am) (B (or Am Bm)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99872
in-theory        99872
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-893 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99872.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-893, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99873
in-theory        99873
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((A or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))
theorem-size     49
proof            (modus-ponens tm-882 tm-1061 ((A Am) (B (or Am Bm)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((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-54.           (A -> (((B -> C) -> ((C -> 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-99873.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((A or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))), M:tm-882, m:tm-1061, u:((A Am) (B (or Am Bm)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99874
in-theory        99874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     41
proof            (modus-ponens tm-855 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-48.           (((A -> (B and 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99874.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-855, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99875
in-theory        99875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-808 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99875.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-808, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99876
in-theory        99876
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((F and (A or (A or B))) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))
theorem-size     55
proof            (modus-ponens tm-798 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 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-4.            ((A and B) -> B), axiom
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99876.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((F and (A or (A or B))) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))), M:tm-798, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99877
in-theory        99877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-757 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B 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-54.           (A -> (((B -> C) -> ((C -> 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-99877.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-757, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99878
in-theory        99878
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((((A or (A or B)) and F) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))
theorem-size     55
proof            (modus-ponens tm-747 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 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-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-54.           (A -> (((B -> C) -> ((C -> 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-99878.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((((A or (A or B)) and F) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))), M:tm-747, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99879
in-theory        99879
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F))))
theorem-size     49
proof            (modus-ponens tm-708 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99879.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F)))), M:tm-708, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99880
in-theory        99880
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-665 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-54.           (A -> (((B -> C) -> ((C -> 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-99880.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-665, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99881
in-theory        99881
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (A or B))))
theorem-size     25
proof            (modus-ponens tm-623 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99881.        ((A or (A or B)) -> (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (A or B)))), M:tm-623, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99882
in-theory        99882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-622 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99882.        ((A -> (B -> (C or B))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-622, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99883
in-theory        99883
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99883.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (G or F))), M:tm-609, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99884
in-theory        99884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-605 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99884.        ((A -> ((B -> (C or B)) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-605, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99885
in-theory        99885
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (G or F)) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99885.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (G or F)) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-595, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99886
in-theory        99886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-550 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99886.        (((A -> (B or A)) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-550, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99887
in-theory        99887
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-540 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99887.        ((A or (B -> (C or B))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-540, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99888
in-theory        99888
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-530 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99888.        ((A or (B -> (B or C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-530, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99889
in-theory        99889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-520 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99889.        ((A or (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-520, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99890
in-theory        99890
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-510 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99890.        ((A or ((B and C) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-510, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99891
in-theory        99891
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-500 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99891.        ((A or ((B and C) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-500, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99892
in-theory        99892
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-490 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99892.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F)))), M:tm-490, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99893
in-theory        99893
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-480 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99893.        ((A or (B -> (C -> B))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-480, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99894
in-theory        99894
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)) or F))
theorem-size     25
proof            (modus-ponens tm-470 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
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-49.           (((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-99894.        ((A or (A or B)) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)) or F)), M:tm-470, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99895
in-theory        99895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-469 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99895.        ((A -> (B -> (B or C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-469, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99896
in-theory        99896
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
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-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99896.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (F or G))), M:tm-456, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99897
in-theory        99897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-453 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99897.        ((A -> ((B -> (B or C)) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-453, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99898
in-theory        99898
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (F or G)) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 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-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99898.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (F or G)) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-443, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99899
in-theory        99899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-409 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99899.        (((A -> (A or B)) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-409, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99900
in-theory        99900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-400 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99900.        (((A -> (B -> (A and B))) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-400, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99901
in-theory        99901
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-391 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99901.        ((((A and B) -> B) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-391, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99902
in-theory        99902
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-382 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99902.        ((((A and B) -> A) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-382, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99903
in-theory        99903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-373 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99903.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F)))), M:tm-373, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99904
in-theory        99904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-364 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99904.        (((A -> (B -> A)) or C) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-364, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99905
in-theory        99905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (A or B)) and C)))
theorem-size     27
proof            (modus-ponens tm-355 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 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-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((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-54.           (A -> (((B -> C) -> ((C -> 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-99905.        ((A or (A or B)) -> (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (A or B)) and C))), M:tm-355, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99906
in-theory        99906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-354 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99906.        ((A -> (B -> (C -> (B and C)))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-354, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99907
in-theory        99907
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99907.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99908
in-theory        99908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D))))
theorem-size     33
proof            (modus-ponens tm-338 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99908.        (((A -> B) -> (A -> (A and B))) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D)))), M:tm-338, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99909
in-theory        99909
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-328.          ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99909.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((A or (A or B)) -> ((A or (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-328, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99910
in-theory        99910
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (G -> (F and G))) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99910.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (G -> (F and G))) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-327, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99911
in-theory        99911
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((F and G) -> G) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99911.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((F and G) -> G) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-326, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99912
in-theory        99912
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((F and G) -> F) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A 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-54.           (A -> (((B -> C) -> ((C -> 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-99912.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((F and G) -> F) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-325, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99913
in-theory        99913
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99913.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-324, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99914
in-theory        99914
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (G -> F)) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (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-54.           (A -> (((B -> C) -> ((C -> 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-99914.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (G -> F)) and ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-323, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99915
in-theory        99915
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99915.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F and G) -> G)), M:tm-322, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99916
in-theory        99916
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99916.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F and G) -> F)), M:tm-320, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99917
in-theory        99917
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (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-54.           (A -> (((B -> C) -> ((C -> 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-99917.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99918
in-theory        99918
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((A or (A or B)) -> (A or (A or B))))
theorem-size     35
proof            (modus-ponens tm-316 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C 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-54.           (A -> (((B -> C) -> ((C -> 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-99918.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and ((A or (A or B)) -> (A or (A or B)))), M:tm-316, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99919
in-theory        99919
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-54.           (A -> (((B -> C) -> ((C -> 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-99919.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (G -> F))), M:tm-315, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99920
in-theory        99920
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((A or (A or B)) -> (not (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))) -> (not (A or (A or B)))))
theorem-size     55
proof            (modus-ponens tm-313 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 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-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99920.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((A or (A or B)) -> (not (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))) -> (not (A or (A or B))))), M:tm-313, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99921
in-theory        99921
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)) -> F) -> (((A or (A or B)) or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) -> F)))
theorem-size     69
proof            (modus-ponens tm-312 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99921.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)) -> F) -> (((A or (A or B)) or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) -> F))), M:tm-312, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99922
in-theory        99922
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F or ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99922.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F or ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-311, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99923
in-theory        99923
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
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-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-54.           (A -> (((B -> C) -> ((C -> 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-99923.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) or F)), M:tm-310, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99924
in-theory        99924
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99924.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and F))), M:tm-309, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99925
in-theory        99925
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99925.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) and (F -> ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))), M:tm-305, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99926
in-theory        99926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     35
proof            (modus-ponens tm-303 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99926.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-303, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99927
in-theory        99927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-270 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99927.        ((A -> (((B and C) -> C) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-270, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99928
in-theory        99928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-239 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99928.        ((A -> (((B and C) -> B) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-239, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99929
in-theory        99929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F))))
theorem-size     41
proof            (modus-ponens tm-210 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99929.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F)))), M:tm-210, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99930
in-theory        99930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     33
proof            (modus-ponens tm-183 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99930.        ((A -> ((B -> (C -> B)) and A)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-183, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99931
in-theory        99931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-157 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 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-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99931.        ((A -> ((B and C) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-157, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99932
in-theory        99932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     39
proof            (modus-ponens tm-147 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 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-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (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-54.           (A -> (((B -> C) -> ((C -> 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-99932.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-147, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99933
in-theory        99933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-134 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 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-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
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-54.           (A -> (((B -> C) -> ((C -> 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-99933.        ((A -> ((B and C) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-134, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99934
in-theory        99934
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     39
proof            (modus-ponens tm-125 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 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-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) 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-54.           (A -> (((B -> C) -> ((C -> 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-99934.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-125, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99935
in-theory        99935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F))))
theorem-size     39
proof            (modus-ponens tm-113 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99935.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (E or F)) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (E or F)))), M:tm-113, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99936
in-theory        99936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     43
proof            (modus-ponens tm-105 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
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-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> 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-54.           (A -> (((B -> C) -> ((C -> 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-99936.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-105, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99937
in-theory        99937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D))))
theorem-size     31
proof            (modus-ponens tm-95 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 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-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (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-54.           (A -> (((B -> C) -> ((C -> 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-99937.        (((A -> B) -> (A -> A)) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D)))), M:tm-95, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99938
in-theory        99938
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (A or B))))
theorem-size     25
proof            (modus-ponens tm-84 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99938.        ((A or (A or B)) -> (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (A or B)))), M:tm-84, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99939
in-theory        99939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     31
proof            (modus-ponens tm-83 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 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-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> 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-54.           (A -> (((B -> C) -> ((C -> 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-99939.        ((A -> (B -> (C -> B))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-83, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99940
in-theory        99940
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (B or C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C))))
theorem-size     29
proof            (modus-ponens tm-76 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99940.        (((not (not A)) -> A) and ((B or (B or C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C)))), M:tm-76, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99941
in-theory        99941
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (A or B)))) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))
theorem-size     31
proof            (modus-ponens tm-73 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-6 tm-5)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99941.        (((not (not (A or (A or B)))) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))), M:tm-73, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99942
in-theory        99942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D))))
theorem-size     35
proof            (modus-ponens tm-69 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99942.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D)))), M:tm-69, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99943
in-theory        99943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-54 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 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-54.           (A -> (((B -> C) -> ((C -> 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-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-99943.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-54, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99944
in-theory        99944
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))
theorem-size     27
proof            (modus-ponens tm-50 tm-1061 ((A Am) (B (or Am Bm)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-7 tm-6 tm-5)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99944.        (((A or B) or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))), M:tm-50, m:tm-1061, u:((A Am) (B (or Am Bm)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99945
in-theory        99945
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-49 tm-1061 ((A Am) (B (or Am Bm)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5)
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-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-99945.        ((A or (A or (A or B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))), M:tm-49, m:tm-1061, u:((A Am) (B (or Am Bm)) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99946
in-theory        99946
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (B or C))) or (B or (B or C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C)))
theorem-size     31
proof            (modus-ponens tm-47 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-6 tm-5)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99946.        (((A and (B or (B or C))) or (B or (B or C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C))), M:tm-47, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99947
in-theory        99947
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (A or B)) and C) or (A or (A or B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (A or B)))
theorem-size     31
proof            (modus-ponens tm-46 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-6 tm-5)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99947.        ((((A or (A or B)) and C) or (A or (A or B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (A or B))), M:tm-46, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99948
in-theory        99948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-42 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99948.        ((A -> (B or A)) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D)))), M:tm-42, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99949
in-theory        99949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-32 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-6 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-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-54.           (A -> (((B -> C) -> ((C -> 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-99949.        ((A -> (A or B)) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D)))), M:tm-32, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99950
in-theory        99950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))))
theorem-size     29
proof            (modus-ponens tm-24 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99950.        ((A or (A or B)) -> ((A or (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))), M:tm-24, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99951
in-theory        99951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D))))
theorem-size     31
proof            (modus-ponens tm-23 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99951.        ((A -> (B -> (A and B))) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D)))), M:tm-23, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99952
in-theory        99952
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-22 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99952.        (((A and B) -> B) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D)))), M:tm-22, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99953
in-theory        99953
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-21 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99953.        (((A and B) -> A) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D)))), M:tm-21, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99954
in-theory        99954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E))))
theorem-size     37
proof            (modus-ponens tm-20 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99954.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (D or E)) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (D or E)))), M:tm-20, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99955
in-theory        99955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D))))
theorem-size     29
proof            (modus-ponens tm-19 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99955.        ((A -> (B -> A)) and ((C or (C or D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (C or D)))), M:tm-19, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99956
in-theory        99956
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (not (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))) -> (not (A or (A or B))))
theorem-size     31
proof            (modus-ponens tm-9 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-9 tm-8 tm-6 tm-5)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99956.        (((A or (A or B)) -> (not (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))) -> (not (A or (A or B)))), M:tm-9, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99957
in-theory        99957
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or E)) -> F) -> (((D or (D or E)) or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or E))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-1061 ((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       149
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-54.           (A -> (((B -> C) -> ((C -> 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-99957.        (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or E)) -> F) -> (((D or (D or E)) or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or E))) -> F)), M:tm-8, m:tm-1061, u:((A (or Am (or Am Bm))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))
================================================================
tm-name          tm-99958
in-theory        99958
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (B or C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C))))
theorem-size     25
proof            (modus-ponens tm-7 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-7 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99958.        (A or ((B or (B or C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C)))), M:tm-7, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99959
in-theory        99959
times-derived    1
----------------------------------------------------------------
theorem          (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-6 tm-8 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-49.           (((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-99959.        (((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))) or F), M:tm-6, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99960
in-theory        99960
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (B or C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or 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-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-99960.        (A -> (((B or (B or C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C))) and A)), M:tm-5, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99961
in-theory        99961
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (B or C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C))))
theorem-size     25
proof            (modus-ponens tm-1 tm-1061 ((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm))))))
axioms-used      (tm-1 tm-8 tm-6 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-99961.        (A -> ((B or (B or C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B or C)))), M:tm-1, m:tm-1061, u:((A (-> (or Am (or Am Bm)) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (or Am Bm)))))
================================================================
tm-name          tm-99962
in-theory        99962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-1003 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-99962.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F))))), M:tm-1003, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99963
in-theory        99963
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-992 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
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-48.           (((A -> (B and 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-99963.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F))))), M:tm-992, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99964
in-theory        99964
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F)))))
theorem-size     55
proof            (modus-ponens tm-980 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8)
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-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> 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-48.           (((A -> (B and 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-99964.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F))))), M:tm-980, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99965
in-theory        99965
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-930 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-99965.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-930, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99966
in-theory        99966
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))))
theorem-size     61
proof            (modus-ponens tm-920 tm-1062 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
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-7.            (A -> (B or A)), axiom
tm-50.           (((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-48.           (((A -> (B and 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-99966.        (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and (((B -> (A and B)) or (A or (B -> (A and B)))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B))))), M:tm-920, m:tm-1062, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-99967
in-theory        99967
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-893 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-99967.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-893, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99968
in-theory        99968
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))))
theorem-size     57
proof            (modus-ponens tm-882 tm-1062 ((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
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-6.            (A -> (A or B)), axiom
tm-49.           (((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-48.           (((A -> (B and 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-99968.        (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and ((A or (A or (B -> (A and B)))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B))))), M:tm-882, m:tm-1062, u:((A Am) (B (-> Bm (and Am Bm))) (C (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-99969
in-theory        99969
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     45
proof            (modus-ponens tm-855 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8)
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-48.           (((A -> (B and 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-54.           (A -> (((B -> C) -> ((C -> 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-99969.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-855, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99970
in-theory        99970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-808 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-99970.        (((A -> B) -> (((C and A) or A) -> B)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-808, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99971
in-theory        99971
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and (((F and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))))
theorem-size     65
proof            (modus-ponens tm-798 tm-1062 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
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-48.           (((A -> (B and 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-99971.        (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and (((F and (A or (B -> (A and B)))) or (A or (B -> (A and B)))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B))))), M:tm-798, m:tm-1062, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-99972
in-theory        99972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3)
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-48.           (((A -> (B and 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-99972.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-757, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99973
in-theory        99973
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and F) or (A or (B -> (A and B)))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))))
theorem-size     65
proof            (modus-ponens tm-747 tm-1062 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
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-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((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-54.           (A -> (((B -> C) -> ((C -> 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-99973.        (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and ((((A or (B -> (A and B))) and F) or (A or (B -> (A and B)))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B))))), M:tm-747, m:tm-1062, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-99974
in-theory        99974
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
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-48.           (((A -> (B and 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-99974.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F))))), M:tm-708, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99975
in-theory        99975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 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-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((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-54.           (A -> (((B -> C) -> ((C -> 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-99975.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-665, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99976
in-theory        99976
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-623 tm-1062 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 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-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99976.        ((A or (B -> (A and B))) -> (C or (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (A and B))))), M:tm-623, m:tm-1062, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-99977
in-theory        99977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
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-48.           (((A -> (B and 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-99977.        ((A -> (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-622, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99978
in-theory        99978
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-99978.        (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and (F -> (G or F))), M:tm-609, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99979
in-theory        99979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-99979.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-605, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99980
in-theory        99980
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and ((F -> (G or F)) and ((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-99980.        (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and ((F -> (G or F)) and ((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))))), M:tm-595, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99981
in-theory        99981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
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-48.           (((A -> (B and 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-99981.        (((A -> (B or A)) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-550, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99982
in-theory        99982
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-99982.        ((A or (B -> (C or B))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-540, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99983
in-theory        99983
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
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-48.           (((A -> (B and 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-99983.        ((A or (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-530, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99984
in-theory        99984
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8)
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-48.           (((A -> (B and 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-99984.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-520, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99985
in-theory        99985
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
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-48.           (((A -> (B and 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-99985.        ((A or ((B and C) -> C)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-510, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99986
in-theory        99986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
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-48.           (((A -> (B and 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-99986.        ((A or ((B and C) -> B)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-500, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99987
in-theory        99987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
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-48.           (((A -> (B and 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-99987.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F))))), M:tm-490, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99988
in-theory        99988
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
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-48.           (((A -> (B and 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-99988.        ((A or (B -> (C -> B))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-480, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99989
in-theory        99989
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B))) or F))
theorem-size     29
proof            (modus-ponens tm-470 tm-1062 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 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-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
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-54.           (A -> (((B -> C) -> ((C -> 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-99989.        ((A or (B -> (A and B))) -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B))) or F)), M:tm-470, m:tm-1062, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-99990
in-theory        99990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
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-48.           (((A -> (B and 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-99990.        ((A -> (B -> (B or C))) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-469, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99991
in-theory        99991
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-99991.        (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and (F -> (F or G))), M:tm-456, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99992
in-theory        99992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-99992.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-453, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99993
in-theory        99993
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and ((F -> (F or G)) and ((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
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-48.           (((A -> (B and 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-99993.        (((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))) and ((F -> (F or G)) and ((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))))), M:tm-443, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99994
in-theory        99994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-99994.        (((A -> (A or B)) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-409, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99995
in-theory        99995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8)
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-48.           (((A -> (B and 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-99995.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-400, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99996
in-theory        99996
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
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-48.           (((A -> (B and 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-99996.        ((((A and B) -> B) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-391, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99997
in-theory        99997
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
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-48.           (((A -> (B and 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-99997.        ((((A and B) -> A) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-382, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99998
in-theory        99998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
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-48.           (((A -> (B and 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-99998.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (E and F))) -> (((G -> H) -> ((H -> I) -> ((G or H) -> I))) and (F -> (E and F))))), M:tm-373, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-99999
in-theory        99999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-1062 ((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
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-48.           (((A -> (B and 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-99999.        (((A -> (B -> A)) or C) and ((D or (E -> (D and E))) -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and (E -> (D and E))))), M:tm-364, m:tm-1062, u:((A (-> (or Am (-> Bm (and Am Bm))) (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-100000
in-theory        100000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (A and B))) and C)))
theorem-size     31
proof            (modus-ponens tm-355 tm-1062 ((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm))))))
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-48.           (((A -> (B and 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-100000.       ((A or (B -> (A and B))) -> (C -> ((((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (A and B))) and C))), M:tm-355, m:tm-1062, u:((A (or Am (-> Bm (and Am Bm)))) (B (and (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))) (-> Bm (and Am Bm)))))
